diff --git "a/data_all_eng_slimpj/shuffled/split2/finalzzehbl" "b/data_all_eng_slimpj/shuffled/split2/finalzzehbl" new file mode 100644--- /dev/null +++ "b/data_all_eng_slimpj/shuffled/split2/finalzzehbl" @@ -0,0 +1,5 @@ +{"text":"\\section{Proofs of main results}\n\nThis appendix contains full proofs of the main results that are substantially novel (\\cref{NysInvBnd,NysPCGThm,ConvergenceCorollary}).\nThe supplement contains proofs of results that are similar to existing work, but do not appear explicitly in the literature.\n\n\\subsection{Proof \\cref{NysInvBnd}}\n\\label{section:NysSketchSolveProof}\n\nThis result contains the analysis of the Nystr{\\\"o}m sketch-and-solve method.\nWe begin with \\cref{eq-NysInvExpErr}, which provides an error bound that compares the regularized inverse of\na psd matrix $A$ with the regularized inverse of the randomized Nystr{\\\"o}m approximation $\\hat{A}_{\\mathrm{nys}}$.\nSince $0 \\preceq \\hat{A}_{\\mathrm{nys}} \\preceq A$, we can apply~\\cref{GenInvErrBnd} to obtain a deterministic\nbound for the discrepancy:\n\\[\n\\|(\\hat{A}_{\\textrm{nys}}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\|\\leq \\frac{1}{\\mu}\\frac{\\|E\\|}{\\|E\\|+\\mu}\n\\quad\\text{where $E = A - \\hat{A}_{\\mathrm{nys}}$.}\n\\]\nThe function $f(t) = t\/(t+\\mu)$ is concave, so we can take expectations and invoke Jensen's inequality to obtain\n\\[\n\\E\\|(\\hat{A}_{\\textrm{nys}}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\|\\leq \\frac{1}{\\mu}\\frac{\\E\\|E\\|}{\\E\\|E\\|+\\mu}.\n\\]\nInserting the bound \\cref{eq-RandNysAppxErrBnd} on $\\E \\| E \\|$ from \\cref{NysExpCorr} gives\n\\[\\E\\|(\\hat{A}_{\\textrm{nys}}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\|\n \\leq \\frac{1}{\\mu} \\cdot \\frac{(3+ 4\\textup{e}^{2} \\textup{sr}_{p}(A) \/ p)\\lambda_{p}}\n {\\mu + (3+4\\textup{e}^{2}\\textup{sr}_{p}(A)\/p)\\lambda_{p} }.\\] \nTo conclude, observe that the denominator of the second fraction exceeds\n$\\mu + \\lambda_p$.\n\n\nNow, let us establish \\cref{eq-NysSSRelErr}, the error bound for Nystr{\\\"o}m sketch-and-solve.\nIntroduce the solution $\\hat{x}$ to the Nystr{\\\"o}m sketch-and-solve problem and the solution\n$x_{\\star}$ to the regularized linear system:\n\\begin{align*}\n (\\hat{A}_{\\textrm{nys}}+\\mu I)\\hat{x} = b \\quad\\text{and}\\quad\n (A+\\mu I)x_{\\star} = b.\n\\end{align*}\nWe may decompose the regularized matrix as $A+\\mu I = \\hat{A}_{\\textrm{nys}}+\\mu I+E$.\nSubtract the two equations in the last display to obtain\n\\[(\\hat{A}_{\\textrm{nys}}+\\mu I)(\\hat{x}-x_{\\star})-Ex_{\\star} = 0.\\]\nRearranging to isolate the error in the solution, we have\n\\[\\hat{x}-x_{\\star} = (\\hat{A}_{\\textrm{nys}}+\\mu I)^{-1}Ex_{\\star}.\\]\nTake the norm, apply the operator norm inequality, and use the elementary bound\n$\\| (\\hat{A}_{\\mathrm{nys}} + \\mu I)^{-1} \\| \\leq \\mu^{-1}$. We obtain\n\\[\\frac{\\|\\hat{x}-x_{\\star}\\|_{2}}{\\|x_{\\star}\\|_{2}}\\leq \\frac{\\|E\\|}{\\mu}.\\]\nFinally, take the expectation and repeat the argument used to control $\\E\\|E\\|\/\\mu$\nin the proof of \\cref{NysPCGEffDimThm}.\n\\qed\n\n\\subsubsection{Proof of \\cref{NysPCGThm}}\n\\label{section:NysPCGThmProof}\n\nLet $\\hat{A} = U \\hat{\\Lambda} U^T$ be an arbitrary rank-$\\ell$ Nystr{\\\"o}m approximation\nwhose $\\ell$th eigenvalue is $\\hat{\\lambda}_{\\ell}$.\n\\Cref{NysPCGThm} provides a deterministic bound on the condition number of\nthe regularized matrix $A_{\\mu}$ after preconditioning with\n\\[\nP = \\frac{1}{\\hat{\\lambda}_\\ell + \\mu} U (\\hat{\\Lambda} + \\mu I) U^T + (I - UU^T). \n\\]\nWe remind the reader that this argument is completely deterministic.\n\nFirst, note that the preconditioned matrix $P^{-1\/2}A_{\\mu}P^{-1\/2}$ is psd, so\n\\[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) = \\frac{\\lambda_1(P^{-1\/2}A_{\\mu}P^{-1\/2})}{\\lambda_n(P^{-1\/2}A_{\\mu}P^{-1\/2})}.\\]\nLet us begin with the upper bound on the condition number. We have the decomposition\n\\begin{equation}\n \\label{KeyDecomp}\n P^{-1\/2}A_{\\mu}P^{-1\/2} = P^{-1\/2}(\\hat{A}+\\mu I)P^{-1\/2} +P^{-1\/2}EP^{-1\/2},\n\\end{equation}\nowing to the relation $A_{\\mu} = \\hat{A} +\\mu I+E$.\nRecall that the error matrix $E$ is psd, so the matrix $P^{-1\/2}EP^{-1\/2}$ is also psd.\n\nFirst, we bound the maximum eigenvalue. Weyl's inequalities imply that\n\\[\\lambda_1(P^{-1\/2}A_{\\mu}P^{-1\/2})\\leq \\lambda_1(P^{-1\/2}(\\hat{A} +\\mu I)P^{-1\/2})+\\lambda_{1}(P^{-1\/2}EP^{-1\/2}).\\]\nA short calculation shows that $\\lambda_1(P^{-1\/2}(\\hat{A}+\\mu I)P^{-1\/2}) = \\hat{\\lambda}_{\\ell}+\\mu$.\nWhen $\\ell < n$, we have $\\lambda_{1}(P^{-1}) = 1$. Therefore,\n\\[\n\\lambda_{1}(P^{-1\/2}EP^{-1\/2}) = \\lambda_{1}(P^{-1}E) \\leq \\lambda_{1}(P^{-1})\\lambda_{1}(E) = \\lambda_{1}(E) = \\|E\\|.\n\\]\nIn summary,\n\\begin{equation}\n\\label{TopEigValBnd}\n \\lambda_1(P^{-1\/2}A_{\\mu}P^{-1\/2})\\leq \\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|.\n\\end{equation}\nFor the minimum eigenvalue, we first assume that $\\mu>0$. Apply Weyl's inequality to \\cref{KeyDecomp} to obtain\nto obtain\n\\begin{equation}\n\\label{SmallEigValBnd1}\n\\begin{aligned}\n\\lambda_{n}(P^{-1\/2}A_\\mu P^{-1\/2}) &\\geq \\lambda_{n}(P^{-1\/2}(\\hat{A}+\\mu I)P^{-1\/2})+\\lambda_{n}(P^{-1\/2}EP^{-1\/2}) \\\\\n &\\geq \\lambda_{n}(P^{-1\/2}(\\hat{A}+\\mu I)P^{-1\/2}) = \\mu.\n\\end{aligned}\n\\end{equation}\nCombining \\cref{TopEigValBnd} and \\cref{SmallEigValBnd1}, we reach\n\\[\n\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\leq \\frac{\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|}{\\mu}.\n\\]\nThis gives a bound for the maximum in case $\\mu > 0$.\n\nIf we only have $\\mu \\geq 0$, then a different argument is required for the smallest eigenvalue.\nAssume that $A$ is positive definite, in which case $\\hat{\\lambda}_{\\ell} > 0$.\nBy similarity,\n\\[\\lambda_n(P^{-1\/2}A_\\mu P^{-1\/2})\n = \\lambda_n(A_{\\mu}^{-1\/2}PA_{\\mu}^{-1\/2}))\n = \\frac{1}{\\lambda_{1}(A_{\\mu}^{-1\/2}PA_{\\mu}^{-1\/2})}.\n\\]\nIt suffices to produce an upper bound for $\\lambda_{1}(A_{\\mu}^{-1\/2}PA_{\\mu}^{-1\/2})$.\nTo that end, we expand\n\\begin{align*}\n\\lambda_{1}(A_{\\mu}^{-1\/2}PA_{\\mu}^{-1\/2})\n &= \\lambda_{1}\\bigg(A_{\\mu}^{-1\/2}\\left(\\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}(\\hat{A}+\\mu UU^{T})+(I-UU)^{T}\\right)A_{\\mu}^{-1\/2}\\bigg) \\\\\n &\\leq \\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}\\lambda_{1}\\left(A_{\\mu}^{-1\/2}(\\hat{A}+\\mu UU^{T})A_{\\mu}^{-1\/2}\\right)\\\\\n &+\\lambda_{1}\\bigg(A_{\\mu}^{-1\/2}\\left(I-UU^{T}\\right)A_{\\mu}^{-1\/2}\\bigg).\n\\end{align*}\nThe second inequality is Weyl's.\nSince $\\hat{A}\\preceq A$, we have $\\hat{A} +\\mu UU^{T} \\preceq A_{\\mu}$.\nThe last display simplifies to\n\\[\n\\lambda_{1}(A_{\\mu}^{-1\/2}PA_{\\mu}^{-1\/2}) \\leq \\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}+\\frac{1}{\\lambda_{n}+\\mu}.\n\\]\nPutting the pieces together with \\cref{TopEigValBnd}, we obtain\n\\[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\leq (\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|)\\bigg(\\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}+\\frac{1}{\\lambda_{n}+\\mu}\\bigg).\\]\nThus,\n\\[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\leq \\left(\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|\\right)\\min\\bigg\\{\\frac{1}{\\mu},~\n \\frac{\\hat{\\lambda}_{\\ell} + \\lambda_n + 2 \\mu}{(\\hat{\\lambda}_\\ell + \\mu)(\\lambda_n + \\mu)}\\bigg\\}.\n\\] \nThis formula is valid when $A$ is positive definite or when $\\mu > 0$.\n\nWe now prove the lower bound on $\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})$. Returning to \\cref{KeyDecomp} and invoking Weyl's inequalities yields\n\\[ \\lambda_1(P^{-1\/2}A_{\\mu}P^{-1\/2})\\geq \\lambda_1(P^{-1\/2}(\\hat{A}+\\mu I)P^{-1\/2})+\\lambda_{n}(P^{-1\/2}EP^{-1\/2})\\geq \\hat{\\lambda}_{\\ell}+\\mu.\\]\nFor the smallest eigenvalue we observe that\n\\[\\lambda_{n}(P^{-1\/2}A_{\\mu}P^{-1\/2}) = \\lambda_{n}(A_{\\mu}P^{-1}) \\leq \\lambda_{n}(A_{\\mu})\\lambda_{1}(P^{-1}) = \\lambda_{n}+\\mu.\\]\nCombining the last two displays, we obtain\n\\[\n\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\lambda_{n}+\\mu}\\leq \\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}).\n\\]\nCondition numbers always exceed one, so\n\\[\n\\max\\bigg\\{\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\lambda_{n}+\\mu},1\\bigg\\}\\leq \\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}).\n\\]\nThis point concludes the argument.\n\n\n\\subsubsection{Proof of \\cref{KeyLemma}}\n\\label{section:KeyLemmaProof}\n\n\\Cref{KeyLemma} establishes the central facts about the effective dimension.\nFirst, we prove \\cref{l-eff-max}.\nFix a parameter $\\gamma \\geq 1$, and set $j_{\\star} = \\max\\{1\\leq j\\leq n: \\lambda_{j}>\\gamma\\mu\\}$.\nWe can bound the effective dimension below by the following mechanism.\n\\[\nd_{\\textrm{eff}}(\\mu)\n = \\sum^{n}_{j=1}\\frac{\\lambda_{j}}{\\lambda_{j}+\\mu}\n \\geq \\sum^{j_{\\star}}_{j=1}\\frac{\\lambda_{j}}{\\lambda_{j}+\\mu}\\geq j_{\\star} \\cdot \\frac{\\lambda_{j_{\\star}}}{\\lambda_{j_{\\star}}+\\mu}.\n\\]\nWe have used the fact that $t \\mapsto t\/(1+t)$ is increasing for $t \\geq 0$,\nSolving for $j_{\\star}$, we determine that\n\\[\nj_{\\star}\\leq(1+\\mu\/\\lambda_{j_{\\star}})d_{\\textrm{eff}}(\\mu)<(1+\\gamma^{-1})d_{\\textrm{eff}}(\\mu).\n\\]\nThe last inequality depends on the definition of $j_{\\star}$. This is the required result.\n\n\\cref{l-eff-avg} follows from a short calculation:\n\\[\n\\begin{aligned}\n\\frac{1}{k}\\sum_{j>k}\\lambda_{j}\n &= \\frac{\\lambda_k+\\mu}{k}\\sum_{j>k}\\frac{\\lambda_{j}}{\\lambda_{k}+\\mu}\n \\leq \\frac{\\lambda_k+\\mu}{k}\\sum_{j>k}\\frac{\\lambda_{j}}{\\lambda_{j}+\\mu} \\\\\n &= \\frac{\\lambda_k+\\mu}{k}\\left(d_{\\textrm{eff}}(\\mu)-\\sum^{k}_{j=1}\\frac{\\lambda_{j}}{\\lambda_{j}+\\mu}\\right)\n \\leq\\frac{\\lambda_k+\\mu}{k}\\left(d_{\\textrm{eff}}(\\mu)-\\frac{k\\lambda_{k}}{\\lambda_{k}+\\mu}\\right) \\\\\n &= \\frac{\\mu \\,d_{\\textrm{eff}}(\\mu)}{k} +\\lambda_{k}\\left(\\frac{d_{\\textrm{eff}}(\\mu)}{k}-1\\right)\n \\leq \\frac{\\mu \\, d_{\\textrm{eff}}(\\mu)}{k}.\n\\end{aligned}\n\\]\nThe last inequality depends on the assumption that $k\\geq d_{\\textrm{eff}}(\\mu)$.\n\n\n\n\\subsection{Proof of \\cref{ConvergenceCorollary}}\n\\label{section:ConvergenceCorollaryPf}\n\nThis result gives a bound for the relative error $\\delta_t$ in the iterates of PCG.\nRecall the standard convergence bound for CG~\\cite[Theorem 38.5]{trefethen1997numerical}:\n\\[\n\\delta_{t}\\leq 2 \\, \\bigg(\\frac{\\sqrt{\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})}-1}{\\sqrt{\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})}+1}\\bigg)^{t}.\n\\]\nWe conditioned on the event that $\\{\\kappa(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\leq 56\\}$. On this event,\nthe relative error must satisfy\n\\[\n\\delta_{t} < 2 \\, \\left( \\frac{\\sqrt{56} - 1}{\\sqrt{56} + 1}\\right)^t\n \\leq 2 \\cdot (0.77)^{t}.\n\\]\nSolving for $t$, we see that $\\delta_t < \\epsilon$ when $t\\geq \\lceil 3.8\\log\\left( 1\/\\epsilon \\right)\\rceil$. This concludes the proof.\n\\subsection{Proof of \\cref{AdaNysRankThm}}\n\\cref{AdaNysRankThm} establishes that with high probability \\cref{alg:AdaRandNysAppx} terminates in a logarithmic number of steps, the sketch size remains $O(d_{\\textrm{eff}}(\\delta\\tau\\mu))$, and PCG with the preconditioner constructed from the output converges fast. \n\\label{section:AdaNysRankThmPf}\n\n\\begin{proof}\nWe first recall that \\cref{alg:AdaRandNysAppx} terminates when the event\n\\[\\mathcal{E} = \\{\\|E\\|\\leq \\tau\\mu\\}\\cap\\{\\hat{\\lambda}_{\\ell}\\leq \\frac{\\tau\\mu}{11}\\}\\] \nholds. Observe that conditioned on $\\mathcal{E}$, \\cref{NysPCGThm} yields\n\\[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\leq \\frac{\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|}{\\mu} \\leq 1+(1+\\frac{1}{11})\\tau = 1+\\frac{12}{11}\\tau.\\]\nStatement 3 now follows from the above display and the standard convergence theorem for CG.\n\nNow, if \\cref{alg:AdaRandNysAppx} terminates with $N\\leq \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil-1$ steps of sketch size doubling, then $\\mathcal{E}$ holds with probability $1$.\nStatement 3 then follows by our initial observation, while statements 1 and 2 hold trivially. Hence statements $1$-$3$ all hold if the algorithm terminates in $N\\leq \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil-1$ steps.\n\nThus to conclude the proof, it suffices to show that if $N \\geq \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil$, then $\\mathcal{E}$ holds with probability at least $1-\\delta$, which implies that statements $1$-$3$ hold with probability at least $1-\\delta$, as above. \n\nWe now show that $\\mathcal{E}$ holds with probability at least $1-\\delta$ when $N = \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil$. To see this note that when $N = \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil$, we have $\\ell\\geq \\tilde{\\ell}$. Consequently, we may\ninvoke \\cref{NysExpBound} with $p = \\lceil 2d_{\\textup{eff}}\\left(\\frac{\\delta\\tau\\mu}{11}\\right)\\rceil+1 $ and \\cref{KeyLemma} to show\n\\begin{align*}\n \\mathbb{E}[\\|E\\|] &\\overset{(1)}{\\leq} 3\\lambda_{p}+\\frac{2\\textrm{e}^{2}}{p}\\left(\\sum^{n}_{j=p}\\lambda_{j}\\right)\\\\\n &\\overset{(2)}{\\leq} 3\\frac{\\delta \\tau \\mu}{11}+2\\textrm{e}^{2}\\frac{d_{\\textrm{eff}}(\\delta \\tau \\mu\/11)}{p}\\frac{\\delta \\tau \\mu}{11}\\\\\n &\\overset{(3)}{\\leq} \\frac{3}{11}\\delta \\tau \\mu+\\frac{2\\textrm{e}^{2}}{2}\\frac{\\delta \\tau \\mu}{11}= \\left(\\frac{3+\\textrm{e}^{2}}{11}\\right)\\delta \\tau \\mu \\leq \\delta \\tau \\mu.\n\\end{align*}\nWhere step (1) uses \\cref{NysExpBound}, step (2) uses items 1 and 2 of \\cref{KeyLemma} with $\\gamma = 1$, and step (3) follows from $p\\geq 2d_{\\textrm{eff}}(\\delta\\tau\\mu)$.\nThus,\n\\[\\mathbb{E}[\\|E\\|] \\leq \\delta\\tau \\mu.\\]\nBy Markov's inequality,\n\\[\\mathbb{P}\\{\\|E\\|>\\tau \\mu\\}\\leq \\delta.\\]\nHence $\\{\\|E\\|\\leq \\tau \\mu\\}$ holds with probability at least $1-\\delta$. Furthermore, by \\cref{KeyLemma} we have $\\{\\hat{\\lambda}_{\\ell}\\leq \\delta \\tau \\mu\/11\\}$ with probability $1$ as $\\hat{\\lambda}_{\\ell}\\leq \\lambda_{\\ell}\\leq \\lambda_{p}$. Thus when $N = \\lceil\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)\\rceil$, $\\mathcal{E}$ holds with probability at least $1-\\delta$, this immediately implies statements 1 and 3. Statement 2 follows as\n\\[\\ell = 2^{N}\\ell_0 \\leq 2^{\\log_{2}\\left(\\tilde{\\ell}\/\\ell_{0}\\right)+1}\\ell_0 = 2\\tilde{\\ell} = 4\\lceil2d_{\\textup{eff}}\\left(\\frac{\\delta\\tau\\mu}{11}\\right)\\rceil+2,\\] \nwhere in the first inequality we used $\\lceil x\\rceil\\leq x+1$, this completes the proof. \n\\end{proof}\n\n\\subsection{Proof of \\cref{AdaRankRatProp}}\n\\cref{AdaRankRatProp} shows once $\\ell = \\Omega\\left(d_{\\textrm{eff}}(\\tau \\mu)\\right)$, then with high probability $\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})$ differs from $(\\hat{\\lambda}_{\\ell}+\\mu)$ by at most a constant.\n\\begin{proof}\n\\cref{NysPCGThm} implies that\n\\[\\left(\\kappa_2(P^{-1\/2}A_{\\mu}P^{-1\/2})-\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\mu}\\right)_{+}\\leq \\frac{\\|E\\|}{\\mu}.\\]\n Combining the previous display with Markov's inequality yields \n\\[\\mathbb{P}\\left\\{\\left(\\kappa_2(P^{-1\/2}A_{\\mu}P^{-1\/2})-\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\mu}\\right)_{+}>\\frac{\\tau}{\\delta}\\right\\} \\leq \\frac{\\delta}{\\tau}\\frac{\\mathbb{E}[\\|E\\|]}{\\mu}.\\]\nNow, our choice of $\\ell$ combined with \\cref{NysExpBound} and \\cref{KeyLemma} implies that $\\mathbb{E}[\\|E\\|]\\leq \\tau\\mu$. \nHence we have\n\\[\\mathbb{P}\\left\\{\\left(\\kappa_2(P^{-1\/2}A_{\\mu}P^{-1\/2})-\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\mu}\\right)_{+}>\\frac{\\tau}{\\delta}\\right\\} \\leq \\delta,\\]\nwhich implies the desired claim.\n\\end{proof}\n\n\\section{Applications and experiments}\n\\label{section:NumericalExperiments}\nIn this section, we study the performance of Nystr{\\\"o}m PCG on real world data from three different applications: ridge regression, kernel ridge regression, and approximate cross-validation. \nThe experiments demonstrate the effectiveness of the preconditioner and our strategies for choosing the rank $\\ell$ compared to other algorithms in the literature:\non large datasets, we find that our method outperforms competitors by a factor of 5--10 (\\Cref{t-rfregress_results} and \\Cref{t-largekrr-results}).\n\n\\subsection{Preliminaries}\n\\label{section:ExperimentalPrelims}\nWe implemented all experiments in MATLAB R2019a and MATLAB R2021a on a server with 128 Intel Xeon E7-4850 v4 2.10GHz CPU cores and 1056 GB. Except for the very large scale datasets ($n\\geq 10^{5})$, every numerical experiment in this section was repeated twenty times;\ntables report the mean over the twenty runs, and the standard deviation (in parentheses) when it is non-zero. We highlight the best-performing method in a table in bold. \n\nWe select hyperparameters of competing methods by grid search to optimize performance.\nThis procedure tends to be very charitable to the competitors, and it may not be representative of their real-world performance.\nIndeed, grid search is computationally expensive, and it cannot be used as part of a practical implementation.\nA detailed overview of the experimental setup for each application may be found in the appropriate section of \\cref{section:Experimentaldetails}, and additional numerical results in \\cref{section:AddNumerics}.\n\n\\subsection{Ridge regression}\n\\label{section:RidgeRegression}\nIn this section, we solve the ridge regression problem \\eqref{eq-RidgeRegression} described in \\cref{IntroRidgeEx} on some standard machine learning data sets (\\cref{t-ridge-datasets}) from OpenML \\cite{vanschoren2014openml} and LIBSVM \\cite{chang2011libsvm}. \nWe compare Nystr{\\\"o}m PCG to standard CG and two state-of-the-art randomized preconditioning methods, \nthe sketch-and-precondition method of Rokhlin and Tygert~(R\\&T)~\\cite{rokhlin2008fast} and the Adaptive Iterative Hessian Sketch (AdaIHS)~\\cite{lacotte2020effective}.\n\n\\subsubsection{Experimental overview}\n\n \\begin{table}[t]\n \\caption{\\label{t-ridge-datasets} \\textbf{Ridge regression datasets.}}\n\\footnotesize\n\\begin{center}\n \\begin{tabular}{|c|c|c|}\n \\hline\n \\textbf{Dataset} & $\\mathbf{n}$ & $\\mathbf{d}$ \\\\\n \\hline\n CIFAR-10 & 50,000 & 3,072 \\\\\n \\hline\n Guillermo & 20,000 & 4,297 \\\\\n \\hline \n smallNorb-rf & 24,300 & 10,000 \\\\\n \\hline\n shuttle-rf & 43,300 & 10,000 \\\\\n \\hline\n Higgs-rf & 800,000 & 10,000 \\\\\n \\hline\n \n \n YearMSD-rf & 463,715 & 15,000\\\\\n \\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\n\nWe perform two sets of experiments: computing regularization paths on CIFAR-10 and Guillermo, \nand random features regression \\cite{rahimi2007random,rahimi2008uniform} \non shuttle, smallNORB, Higgs and YearMSD with specified values of $\\mu$. The values of $\\mu$ may be found in \\cref{section:RidgeRegressionDetails}.\nWe use Euclidean norm $\\|r\\|_{2}$ of the residual as our stopping criteria, with convergence declared when $\\|r\\|_2\\leq 10^{-10}$. \nFor both sets of experiments, we use Nystr{\\\"o}m PCG with adaptive rank selection, \\cref{alg:AdaRandNysAppx} in \\cref{section:AdaRankSelection}. For complete details of the experimental methodology, see \\cref{section:RidgeRegressionDetails}. \n\nThe regularization path experiments solve \\cref{eq-RidgeRegression} over a regularization path $\\mu = 10^{j}$ where $j = 3,\\cdots,-6$. \nWe begin by solving the problem for the largest $\\mu$ (initialized at zero), and solve for progressively smaller $\\mu$ with warm starting. For each value of $\\mu$, every method is allowed at most 500 iterations to reach the desired tolerance. \n\n\\subsubsection{Computing the regularization path}\n\\label{sec:RegPath}\n\\cref{fig:EffDimPlots} shows the evolution of $d_{\\textrm{eff}}(\\mu)$ along the regularization path. CIFAR-10 and Guillermo are both small, so we compute the exact effective dimension as a point of reference. \nWe see that we reach the sketch size cap of $\\ell_{\\textrm{max}} = 0.5d$ for CIFAR-10 and $\\ell_{\\textrm{max}} = 0.4d$ for Guillermo when $\\mu$ is small enough. For CIFAR-10, \nNystr{\\\"o}m PCG chooses a rank much smaller than the effective dimension for small values of $\\mu$. Nevertheless, the method still performs well (\\cref{fig:RidgeRegPathPlots}). \n\n\\begin{figure}[t]\n \\centering\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/CIFAREffDimPlot.pdf}\n \\caption{CIFAR 10}\n \\label{fig:CifarEffDim}\n \\end{subfigure}\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/GuillermoEffDimPlot.pdf}\n \\caption{Guillermo}\n \\label{fig:GuilEffDim}\n \\end{subfigure}\n\\caption{\\label{fig:EffDimPlots} \\textbf{Ridge regression: Adaptive sketch size selection.}\nNystr{\\\"o}m PCG with adaptive rank selection (\\cref{alg:AdaRandNysAppx}) selects a preconditioner whose rank is less than or equal to the effective dimension.We report error bars for the rank selected by the adaptive algorithm, however the variation is so small that the error bars aren't visible. Hence despite being inherently random, the adaptive algorithm's behavior is practically deterministic across runs. See \\cref{sec:RegPath}.} \n\\end{figure}\n\n\\begin{figure}[t]\n \\centering\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/CIFARRegPathPlot.pdf}\n \\caption{CIFAR 10: Runtime versus $\\mu$}\n \\label{fig:CifarCumTime}\n \\end{subfigure}\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/GuillermoRegPathPlot.pdf}\n \\caption{Guillermo: Runtime versus $\\mu$}\n \\label{fig:GuilCumTime}\n \\end{subfigure}\n \\centering\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/CIFARResidPlot.pdf}\n \\caption{CIFAR 10: Residual versus $\\mu$}\n \\label{fig:CifarResid}\n \\end{subfigure}\n \\begin{subfigure}[b]{0.48\\textwidth}\n \\centering\n \\includegraphics[width=\\textwidth]{lstsquaresfigs\/GuillermoResidPlot.pdf}\n \\caption{Guillermo: Residual versus $\\mu$}\n \\label{fig:GuilResid}\n \\end{subfigure} \n\\caption{\\label{fig:RidgeRegPathPlots} \\textbf{Ridge regression: Runtime and residual.} Nystr{\\\"o}m PCG is either the fastest method, or it is competitive with the fastest method for all values of the regularization parameter $\\mu$. CG is generally the slowest method. All the methods reliably achieve the target residual along the entire regularization path, except for ordinary CG at small values of $\\mu$. See \\cref{sec:RegPath}.} \n\\end{figure}\n\n \\cref{fig:RidgeRegPathPlots} show the effectiveness of each method for computing the entire regularization path. Nystr{\\\"o}m PCG is the fastest of the methods along most of the regularization path. \n For CIFAR-10, Nystr{\\\"o}m PCG is faster than R\\&T until the very end of the regularization path, when $d_{\\textrm{eff}}(\\mu) \\approx d$. \n That is, the $O(d^{3})$ cost of forming the R\\&T preconditioner is not worthwhile unless $d_{\\textrm{eff}}(\\mu)\\approx d$.\n We expect Nystr{\\\"o}m PCG to perform better on ridge regression problems with non-vanishing regularization.\n\nAdaIHS is rather slow. It increases the sketch size parameter several times along the regularization path. Each time, AdaIHS must form a new sketch of the matrix, approximate the Hessian, and compute a Cholesky factorization. \n\n\\subsubsection{Random features regression}\n\n \\Cref{t-rfregress_results,t-rf-ErrCondEst} compare the performance of Nystr{\\\"o}m PCG, AdaIHS, and R\\&T PCG for random features regression. \\cref{t-rfregress_results} shows that Nystr{\\\"o}m PCG performs best on all datasets for all metrics.\nThe most striking feature is the difference between sketch sizes: \nAdaIHS and R\\&T require much larger sketch sizes than Nystr{\\\"o}m PCG, leading to greater computation time and higher storage costs.\n\\cref{t-rf-ErrCondEst} contains estimates for $\\|E\\|$ and the condition number of the preconditioned system,\nwhich explain the fast convergence.\n\n\\begin{table}[t]\n\\footnotesize\n\\caption{\\label{t-rfregress_results} \\textbf{Ridge regression: Nystr{\\\"o}m PCG versus AdaIHS and R\\&T PCG.} Nystr{\\\"o}m PCG outperforms AdaIHS and R\\&T PCG in iteration and runtime complexity for both datasets. Additionally, Nystr{\\\"o}m PCG requires much less storage.}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\\hline\n\\thead{Dataset} & \\thead{Method} & \\thead{Final sketch size}& \\thead{Number of \\\\ iterations} & \\thead{Total \\\\\nruntime (s)}\\\\ \\hline\n\\multirow{3}{*}{shuttle-rf} & AdaIHS & $10,000$ & $66.9\\hspace{2pt}(0.933)$ & $66.9\\hspace{2pt}(5.27)$\\\\ \\cline{2-5}\n & R\\&T PCG & $20,000$ & $60.15$ & $242.6\\hspace{2pt} (12.24) $ \\\\ \\cline{2-5}\n & Nystr{\\\"o}m PCG & $800$ & $\\mathbf{13.1\\hspace{2pt}(1.47)}$ & $\\mathbf{9.78\\hspace{2pt}(0.943)}$ \\\\ \\hline\n\\multirow{3}{*}{smallNORB-rf} & AdaIHS & $12,800$ & $38.7\\hspace{2pt}(1.42)$ & $41.0\\hspace{2pt}(2.46)$\\\\ \\cline{2-5}\n & R\\&T PCG & $20,000$ & $34.5\\hspace{2pt}(1.31)$ & $181.5\\hspace{2pt}(6.53)$ \\\\ \\cline{2-5}\n & Nystr{\\\"o}m PCG & $800$ & $\\mathbf{31.5\\hspace{2pt}(0.489)}$ & $\\mathbf{6.67\\hspace{2pt}(0.372)}$ \\\\ \\hline\n\\multirow{3}{*}{YearMSD-rf} & AdaIHS & $30,000$ & $44$ & 1,327.3\\\\ \\cline{2-5}\n & R\\&T PCG & $30,000$ & $49$ & $766.5$ \\\\ \\cline{2-5}\n & Nystr{\\\"o}m PCG & $2,000$ & $\\mathbf{22}$ & $\\mathbf{209.7}$ \\\\ \\hline\n\\multirow{3}{*}{Higgs-rf} & AdaIHS & $6,400$ & $55$ & 1,052.7\\\\ \\cline{2-5}\n & R\\&T PCG & $20,000$ & $53$ & $607.4$ \\\\ \\cline{2-5}\n & Nystr{\\\"o}m PCG & $800$ & $\\mathbf{28}$ & $\\mathbf{91.26}$ \\\\ \\hline\n\\end{tabular}\n\n\\end{center}\n\\end{table}\n\n\\begin{table}[t]\n \\begin{center}\n\\footnotesize\n \\caption{\\label{t-rf-ErrCondEst} \\textbf{Ridge regression: Quality of Nystr{\\\"o}m preconditioner.} We use Nystr{\\\"o}m PCG as outlined in \\cref{section:LargeLStrategy}. The first column gives an estimate for the error $\\|E\\|$ in the randomized Nystr{\\\"o}m approximation. The second column gives an estimate for the condition number $\\kappa_2(P^{-1\/2}A_{\\mu}P^{-1\/2})$.}\n \\begin{tabular}{|c|c|c|}\n \\hline\n \\textbf{Dataset} & \\textbf{Estimate of $\\| E\\|$} & \\thead{Estimated condition number \\\\ of preconditioned system}\\\\\n \\hline\n shuttle-rf & $\\num{7.29e-13}$ & $4.17$ $(0.161)$ \\\\\n \\hline\n smallNorb-rf & $\\num{9.90e-3}$ & $18.5$ $(0.753)$ \\\\\n \\hline\n YearMSD-rf & $\\num{2.07e-4}$ & $22.7$\\\\\n \\hline\n Higgs-rf & $\\num{2.21e-3}$ & $23.8$\\\\\n \\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{Approximate cross-validation}\nIn this subsection we use our preconditioner to compute approximate leave-one-out cross-validation (ALOOCV), which requires solving a large linear system with multiple right-hand sides.\n\n\\label{section:ALOOCV}\n\\subsubsection{Background}\nCross-validation is an important machine-learning technique\nto assess and select models and hyperparameters.\nGenerally, it requires re-fitting a model on many subsets of the data,\nso can take quite a long time.\nThe worst culprit is leave-one-out cross-validation (LOOCV), which requires running an expensive training algorithm $n$ times. \nRecent work has developed approximate leave-one-out cross-validation (ALOOCV), a faster alternative\nthat replaces model retraining by a linear system solve \\cite{giordano2019swiss,rad2020scalable,wilson2020approximate}. \nIn particular, these techniques yield accurate and computationally tractable approximations to LOOCV.\n\nTo present the approach, we consider the infinitesimal jacknife (IJ) approximation to LOOCV \\cite{giordano2019swiss,stephenson2020approximate}.\nThe IJ approximation computes\n\\begin{equation}\n \\label{eq-IJ} \n \\tilde{\\theta}_{\\textrm{IJ}}^{n\/j} = \\hat{\\theta}+\\frac{1}{n}H^{-1}(\\hat{\\theta})\\nabla_{\\theta} l(\\hat{\\theta},a_{j}),\n\\end{equation}\nwhere $H(\\hat{\\theta}) \\in \\R^{d \\times d}$ is the Hessian of the loss function at the solution $\\hat \\theta$, for each datapoint $a_j$.\nThe main computational challenge is computing the inverse Hessian vector product $H^{-1}(\\hat{\\theta})\\nabla_{\\theta} l(\\hat{\\theta},a_{j})$.\nWhen $n$ is very large, \nwe can also subsample the data and average \\cref{eq-IJ} over the subsample to estimate ALOOCV.\nSince ALOOCV solves the same problem with several right-hand sides,\nblocked PCG methods (here, Nystr{\\\"o}m blocked PCG) \nare the tool of choice\nto efficiently solve for multiple right-hand sides at once. \nTo demonstrate the idea, we perform numerical experiments on ALOOCV for logistic regression. \nThe datasets we use are all from LIBSVM \\cite{chang2011libsvm}; see \\cref{t-logistic-datasets}.\n\n\\begin{table}[t]\n\\footnotesize\n \\centering\n \\caption{\\label{t-logistic-datasets} \\textbf{ALOOCV datasets and experimental parameters.}} \n \\begin{tabular}{|c|c|c|c||c|c|}\n \\hline\n \\textbf{Dataset} & $\\mathbf{n}$ & $\\mathbf{d}$ & $\\mathbf{\\%} \\textbf{\\textrm{nz}}(\\mathbf{A})$\n & $\\boldsymbol \\mu$ & \\thead{Initial sketch size}\\\\\n \\hline\n Gisette & 6,000 & 5,000 & $99.1\\%$ & 1, 1e-4 & 850\\\\\n \\hline\n real-sim & 72,308 & 20,958 & $0.245\\%$ & 1e-4, 1e-8 & $500$ \\\\\n \\hline \n rcv1.binary & 20,242 & 47,236 & $0.157\\%$ & 1e-4, 1e-8 & $500$\\\\\n \\hline\n SVHN & 73,257 & 3,072 & $100\\%$ & 1, 1e-4 & 850\\\\\n \\hline\n \\end{tabular}\n\\end{table}\n\\subsubsection{Experimental overview}\nWe perform two sets of experiments in this section. The first set of experiments uses Gisette and SVHN to test the efficacy of Nystr{\\\"o}m sketch-and-solve. These datasets are small enough that we can factor $H(\\theta)$ using a direct method. We also compare to block CG and block PCG with the computed Nystr{\\\"o}m approximation as a preconditioner. \nTo assess the error due to an inexact solve for datapoint $a_j$, \nlet $x_\\star(a_j) = H^{-1}(\\theta)\\nabla_{\\theta} l(\\hat{\\theta},a_{j})$. \nFor any putative solution $\\hat{x}(a_j)$,\nwe compute the relative error $\\|\\hat{x}(a_j)-x_{\\star}(a_j) \\|_{2}\/\\|x_{\\star}(a_j)\\|_{2}$.\nWe average the relative error over 100 data-points $a_j$.\n\n The second set of experiments uses the larger datasets real-sim and rcv1.binary and small values of $\\mu$, the most challenging setting for ALOOCV. \n We restrict our comparison to block Nystr{\\\"o}m PCG versus the block CG algorithm, as Nystr{\\\"o}m sketch-and-solve is so inaccurate in this regime. We employ \\cref{alg:AdaRandNysAppx} to construct the preconditioner for block Nystr{\\\"o}m PCG.\n \n\\subsubsection{Nystr{\\\"o}m sketch-and-solve}\n\nAs predicted, Nystr{\\\"o}m sketch-and-solve works poorly (\\cref{t-gisette-svhn-results}).\nWhen $\\mu = 1$, the approximate solutions are modestly accurate,\nand the accuracy degrades as $\\mu$ decreases to $10^{-4}$. \nThe experimental results agree with the theoretical analysis presented in \\cref{Section:NystromSketchSolve}, which indicate that sketch-and-solve degrades as $\\mu$ decreases. In contrast, block CG and block Nystr{\\\"o}m PCG both provide high-quality solutions for each datapoint for both values of the regularization parameter. \n \n\\begin{table}[t]\n\\footnotesize\n \\caption{\\label{t-gisette-svhn-results} \\textbf{ALOOCV: Small datasets.} The error for a given value of $\\mu$ is the maximum relative error on $100$ randomly sampled datapoints, averaged over 20 trials.}\n\\begin{center}\n \\begin{tabular}{|c|c|c|c|c|}\n \\hline\n \\thead{Dataset} & $\\bm{\\mu}$ & \\thead{Nystr{\\\"o}m \\\\ sketch-and-solve \\\\ } & \\thead{Block CG } & \\thead{Block \\\\ Nystr{\\\"o}m PCG } \\\\\n \\hline\n Gisette & $1$ & $\\num{4.99e-2}$ & $\\num{2.68e-11}$ & $\\num{2.58e-12}$\\\\\n \\hline\n Gisette & $\\num{1e-4}$ & $\\num{1.22e-0}$ & $\\num{1.19e-11}$ & $\\num{6.59e-12}$ \\\\\n \\hline\n SVHN & $1$& $\\num{9.12e-5}$ & $\\num{2.80e-13}$ & $\\num{1.26e-13}$\\\\\n \\hline \n SVHN & $\\num{1e-4}$ & $\\num{3.42e-1}$ & $\\num{2.01e-10}$ & $\\num{1.41e-11}$\\\\\n \\hline\n \\end{tabular}\n\n\\end{center}\n\\end{table}\n\n\\subsection{Large scale ALOOCV experiments}\n \\cref{t-rcv1-realsim-results-part-i} summarizes results for block Nystr{\\\"o}m PCG and block CG on the larger datasets. \nWhen $\\mu = 10^{-4}$, block Nystr{\\\"o}m PCG offers little or no benefit over block CG\nbecause the data matrices are very sparse (see \\cref{t-logistic-datasets}) and the rcv1 problem is well-conditioned (see \\cref{t-rcv1-realsim-results-part-ii}).\n\nFor $\\mu = 10^{-8}$, block Nystr{\\\"o}m PCG reduces the number of iterations substantially,\nbut the speedup is negligible. \nThe data matrix $A$ is sparse, which reduces the benefit of the Nystr{\\\"o}m method.\nBlock CG also benefits from the presence of multiple right-hand sides just as block Nystr{\\\"o}m PCG.\nIndeed, O'Leary proved that the convergence of block CG depends on the ratio $(\\lambda_{s}+\\mu)\/(\\lambda_n+\\mu)$, where $s$ is is the number of right-hand sides \\cite{o1980block}. Consequently, multiple right-hand sides precondition block CG and accelerate convergence. \nWe expect bigger gains over block CG when $A$ is dense. \n\n\\begin{table}[t]\n\\footnotesize\n\\begin{center}\n\\caption{\\label{t-rcv1-realsim-results-part-i} \\textbf{ALOOCV: Large datasets}. Block Nystr{\\\"o}m PCG outperforms block CG as $\\mu$ becomes small.}\n\\begin{tabular}{|c|c|c|c|c|}\\hline\n\\thead{Dataset} & $\\bm{\\mu}$ & \\thead{Method} & \\thead{Number of \\\\ iterations} & \\thead{ \nRuntime (s)}\\\\ \\hline\n\\multirow{2}{*}{rcv1} & $\\num{1e-4}$ & Block CG & $12$ & $\\mathbf{11.06\\hspace{2pt}(0.874)}$\\\\ \\cline{2-5}\n & $\\num{1e-4}$ & Block Nystr{\\\"o}m PCG & $\\mathbf{10}$ & $11.87\\hspace{2pt}(0.767)$ \\\\ \\hline\n\\multirow{2}{*}{rcv1} & $\\num{1e-8}$ & Block CG & $52$ & $39.03\\hspace{2pt}(2.97)$\\\\ \\cline{2-5}\n & $\\num{1e-8}$ & Block Nystr{\\\"o}m PCG & $\\mathbf{15}$ & $\\mathbf{24.1\\hspace{2pt}(1.79)}$ \\\\ \\hline\n\\multirow{2}{*}{realsim} & $\\num{1e-4}$ & Block CG & $12$ & $23.04\\hspace{2pt}(2.04)$\\\\ \\cline{2-5}\n & $\\num{1e-4}$ & Block Nystr{\\\"o}m PCG & $\\mathbf{8}$ & $\\mathbf{19.05\\hspace{2pt}(1.10)}$ \\\\ \\hline\n\\multirow{2}{*}{realsim} & $\\num{1e-8}$ & Block CG & $90$ & $163.7\\hspace{2pt}(12.3)$\\\\ \\cline{2-5}\n & $\\num{1e-8}$ & Block Nystr{\\\"o}m PCG & $\\mathbf{32}$ & $\\mathbf{68.9\\hspace{2pt}(5.30)}$ \\\\ \\hline \n\\end{tabular}\n\n\n\\end{center}\n\\end{table}\n\n\\subsection{Kernel ridge regression}\nOur last application is kernel ridge regression (KRR),\na supervised learning technique that uses a kernel to \nmodel nonlinearity in the data. KRR leads to large dense linear systems that are challenging to solve. \n\\label{section:KernelRidgeRegression}\n\n\\subsubsection{Background}\nWe briefly review KRR \\cite{scholkopf2002learning}. Given a dataset of inputs $x_i \\in \\mathcal{D}$ and their corresponding outputs $b_i \\in \\R$ for $i = 1,\\dots, n$\nand a kernel function $\\mathcal{K}(x,y)$,\nKRR finds a function $f_{\\star}: \\mathcal{D} \\to \\R$ in the associated reproducing kernel Hilbert space $\\mathcal{H}$ that best predicts the outputs for the given inputs. \nThe solution $f_{\\star}\\in \\mathcal{H}$ minimizes the square error \nsubject to a complexity penalty:\n\\begin{equation}\n \\label{KRR}\n f_\\star = \\argmin_{f\\in \\Hc} \\quad \\frac{1}{2n}\\sum_{i=1}^{n}(f(x_{i})-b_{i})^{2}+\\frac{\\mu}{2}\\|f\\|^2_{\\Hc},\n\\end{equation}\nwhere $\\|\\cdot\\|_\\Hc$ denotes the norm on $\\Hc$. \nDefine the kernel matrix $K \\in \\R^{n \\times n}$ with entries $K_{ij} = \\mathcal{K}(x_i,x_j)$. \nThe representer theorem \\cite{steinwart2008support} states the solution to (\\ref{KRR}) is \n\\[\nf_\\star(x) = \\sum_{i=1}^{n}\\alpha_i \\mathcal{K}(x,x_{i}),\n\\]\nwhere $\\alpha = (\\alpha_1, \\ldots, \\alpha_n )$ solves the linear system\n\\begin{equation}\n\\label{KRRSys}\n (K+n\\mu I)\\alpha = b.\n\\end{equation}\nSolving the linear system (\\ref{KRRSys}) is the computational bottleneck of KRR. Direct factorization methods to solve \\eqref{KRRSys} are prohibitive for large $n$ as their costs grow as $n^3$; for $n > 10^{4}$ or so, iterative methods are generally preferred.\nHowever, $K$ is often extremely ill-conditioned, even with the regularization term $n\\mu I$. As a result, CG for Problem \\eqref{KRRSys} converges slowly.\n\n\\subsubsection{Experimental overview}\nWe use\nNystr{\\\"o}m PCG to solve several KRR problems derived from classification problems on real world datasets from \\cite{chang2011libsvm,vanschoren2014openml}.\nFor all experiments, we use the Gaussian kernel $\\mathcal{K}(x,y) = \\exp(-\\|x-y\\|^{2} \/ (2\\sigma^2))$. \nWe compare our method to random features PCG, proposed in \\cite{avron2017faster}. \nWe do not compare to vanilla CG as it is much slower than Nystr{\\\"o}m PCG \nand random features PCG. \n\nAll datasets either come with specified test sets, or we create one from a random $80$-$20$ split. \nThe PCG tolerance, $\\sigma$, and $\\mu$ were all chosen to achieve good performance \non the test sets (see \\cref{t-krr-ranks} below). \nBoth methods were allowed to run for a maximum of 500 iterations. \nThe statistics for each dataset and the experimental parameters are given in \n\\cref{t-KRR-datasets}. \n\nWe run two sets of experiments. For the datasets with $n<10^{5}$ we run oracle random features PCG against two versions of the Nystr{\\\"o}m PCG algorithm.\nThe first version uses the oracle best value of $\\ell$ found by grid search (from the same grid used to select $m_{\\textrm{rf}}$) to minimize the total runtime,\nand the second is the adaptive algorithm described in \\cref{section:RatioRankDoubling}. The grid for $\\ell$ and $m_{\\textrm{rf}}$ is restriced to less than $10,000$ to keep the preconditioners cheap to apply and store. \nThe adaptive algorithm for each dataset was initialized at $\\ell = 2,000$, which is smaller than $0.05n$ for all datasets.\nFor the datasets with $n\\geq 10^{5}$, we restricted both $\\ell$ and $m_{\\textrm{rf}}$ to $1,000$, which corresponds to less than $0.01n$. We then run both algorithms till they reach the desired tolerance or the maximum number of iterations are reached. \n\nWe use column sampling to construct the Nystr{\\\"o}m preconditioner for all KRR problems: on these problems, random projections take longer and yield similar performance (with somewhat lower variance).\n\n\\begin{table}[t]\n\\footnotesize\n\\begin{center}\n \\caption{\\label{t-KRR-datasets} \\textbf{Kernel ridge regression datasets and experimental parameters.}}\n \\begin{tabular}{|c|c|c|c|c|c|c|}\n \\hline\n \\textbf{Dataset} & $\\mathbf{n}$ & $\\mathbf{d}$ & $\\mathbf{n}_{\\textbf{\\textrm{classes}}}$ & $\\boldsymbol \\mu$ & $\\boldsymbol\\sigma$ & \\textbf{PCG tolerance}\\\\\n \\hline\n ijcnn1 & 49,990 & 49 & 2 & 1e-6 & 0.5 & 1e-3 \\\\\n \\hline\n MNIST & 60,000 & 784 & 10 & 1e-7 & 5 & 1e-4 \\\\\n \\hline\n Sensorless & 48,509 & 48 & 11 & 1e-8 & 0.8 & 1e-4 \\\\\n \\hline \n SensIT & 78,823 & 100 & 3 & 1e-8 & 3 & 1e-3 \\\\\n \\hline\n MiniBooNE & 104,052 & 50 & 2 & 1e-7& 5 & 1e-4 \\\\\n \\hline\n EMNIST-Balanced & 105,280 & 784 & 47 &1e-6 & 8 & 1e-3\\\\\n \\hline\n Santander & 160,000 & 200 & 2 & 1e-6 & 7 & 1e-3\\\\\n \\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsubsection{Experimental results}\n\n\\Cref{t-krr-results,t-largekrr-results,t-krr-ranks} summarize the results for the KRR experiments. \n\\Cref{t-krr-results} shows that both versions of Nystr{\\\"o}m PCG deliver better performance than random features preconditioning on all the datasets considered. Nystr{\\\"o}m PCG also uses less storage. \\Cref{t-largekrr-results} shows that Nystro{\\\"o}m PCG yields better performance than random features PCG on the larger scale datasets when both are restricted to ranks of $1,000$. \n\\cref{t-krr-ranks} shows the adaptive strategy proposed in \\cref{section:RatioRankDoubling} to select $\\ell$ works very well. \nIn contrast, it is difficult to choose $m_\\textrm{rf}$ for random features preconditioning: the authors of \\cite{avron2017faster} provide no guidance except for the polynomial kernel. \n \n\\begin{table}[t]\n\\footnotesize\n\\begin{center}\n\\caption{\\label{t-krr-results} \\textbf{Kernel ridge regression: Iteration count and runtime.} The adaptive and oracle Nystr{\\\"o}m PCG algorithms outperform oracle random features PCG in both time and iteration complexity.}\n\\begin{tabular}{|c|c|c|c|}\\hline\n\\thead{Dataset} & \\thead{Method} & \\thead{Number of \\\\ iterations} & \\thead{Total \\\\ runtime (s)}\\\\ \\hline\n\\multirow{3}{*}{icjnn1} & Oracle random features PCG & $63.8(2.66)$ & $38.3(2.33)$\\\\ \\cline{2-4}\n & Adaptive Nystr{\\\"o}m PCG & $43.7(1.77)$ & $\\mathbf{32.0(1.47)}$ \\\\\\cline{2-4}\n & Oracle Nystr{\\\"o}m PCG & $\\mathbf{31.8(0.835)}$ & $33.3(1.60)$ \\\\ \\hline\n\\multirow{3}{*}{MNIST} & Oracle random features PCG & $314.5(2.88)$ & $254.7(6.93)$\\\\ \\cline{2-4}\n & Adaptive Nystr{\\\"o}m PCG & $78.5(17.65)$ & $148.1(46.39)$ \\\\\\cline{2-4}\n & Oracle Nystr{\\\"o}m PCG & $\\mathbf{77.9(2.08)}$ & $\\mathbf{91.7(2.08)}$\\\\ \\hline\n\\multirow{3}{*}{Sensorless} & Oracle random features PCG & $55.4(2.35)$ & $39.9(3.96)$ \\\\ \\cline{2-4}\n & Adaptive Nystr{\\\"o}m PCG & $22.0(0.510)$ & $24.3(1.26)$\\\\\\cline{2-4}\n & Oracle Nystr{\\\"o}m PCG& $\\mathbf{21.7(0.571)}$ & $\\mathbf{22.7(1.63)}$ \\\\ \\hline\n\\multirow{3}{*}{SensIT} & Oracle random features PCG & $68.0(4.31)$ & $95.2(6.19)$ \\\\ \\cline{2-4}\n & Adaptive Nystr{\\\"o}m PCG & $\\mathbf{47.8(1.72)}$ & $70.1(2.43)$\\\\\\cline{2-4}\n & Oracle Nystr{\\\"o}m PCG & $48.7(3.40)$ & $\\mathbf{61.6(6.41)}$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}[t]\n\\footnotesize\n\\caption{\\label{t-largekrr-results} \\textbf{Kernel ridge regression regression: Nystr{\\\"o}m PCG fixed rank versus random features PCG fixed rank.} Nystr{\\\"o}m PCG again outperforms random features PCG in iteration and time complexity.}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\\hline\n\\thead{Dataset} & \\thead{Method} & \\thead{Number of \\\\ iterations} & \\thead{Total \\\\\nruntime (s)}\\\\ \\hline\n\\multirow{2}{*}{MiniBooNE} & Random Features PCG & $92$ & $154.2$\\\\ \\cline{2-4}\n & Nystr{\\\"o}m PCG & $\\mathbf{72}$ & $\\mathbf{137.4}$ \\\\ \\hline\n\\multirow{2}{*}{EMNIST-Balanced} & Random Features PCG & $154$ & $635.2$\\\\ \\cline{2-4}\n & Nystr{\\\"o}m PCG & $\\mathbf{32}$ & $\\mathbf{268.4}$ \\\\ \\hline \n\\multirow{2}{*}{Santander} & Random Features PCG & $160$ & $810.4$\\\\ \\cline{2-4}\n & Nystr{\\\"o}m PCG & $\\mathbf{31}$ & $\\mathbf{164.8}$ \\\\ \\hline \n\\end{tabular}\n\n\\end{center}\n\\end{table}\n\n\n\\begin{table}[ht]\n\\footnotesize\n\\begin{center}\n \\caption{\\label{t-krr-ranks} \\textbf{Kernel ridge regression: Oracle parameters and test errors.} The final ranks selected by the adaptive algorithm are almost in full agreement with the oracle ranks. Furthermore, the adaptive and oracle ranks for Nystr{\\\"o}m PCG are never larger than $m_{\\textrm{rf}}$.}\n \\begin{tabular}{|c|c|c|c|c|}\n \\hline\n \\textbf{Dataset} & \\thead{Adaptive \\\\Nystr{\\\"o}m \\\\ final rank} & \\thead{Oracle \\\\ Nystr{\\\"o}m \\\\ rank} & \\thead{Oracle} $\\mathbf{m_{\\textrm{rf}}}$ & \\thead{Test set error} \\\\\n \\hline\n ijcnn1 & $2,000$ & $3,000$ & $3,000$ & $1.25\\%$\\\\\n \\hline\n MNIST & $6,000\\hspace{2pt} (1,716)$ & $4,000$ & $9,000$ & $1.22\\%$ \\\\\n \\hline\n Sensorless & $2,000$ & $2,000$ & $5,000$ & $2.01\\%$ \\\\\n \\hline \n SensIT & $2,000$ & $2,000$ & $7,000$ & $12.83\\%$ \\\\\n \\hline\n MiniBooNE & NA & NA & NA & $7.93\\%$ \\\\\n \\hline\n EMNIST-Balanced &NA &NA &NA & $15\\%$ \\\\\n \\hline\n Santander & NA &NA &NA & $8.90\\%$\\\\\n \\hline\n \\end{tabular}\n\n\\end{center}\n\\end{table}\n\n\n\\section{Conclusion}\nWe have shown that Nystr{\\\"o}m PCG delivers a strong benefit \nover standard CG both in the theory and in practice,\nthanks to the ease of parameter selection,\non a range of interesting large-scale computational problems\nincluding ridge regression, kernel ridge regression, and ALOOCV.\nIn our experience, Nystr{\\\"o}m PCG outperforms all generic methods\nfor solving large-scale dense linear systems with spectral decay.\nIt is our hope that this paper motivates further research on randomized preconditioning for solving large scale linear systems\nand offers a useful speedup to practitioners.\n\n\\section{The Nystr{\\\"o}m approximation}\n\\label{section:NystromApproximation}\n\nLet us begin with a review of the Nystr{\\\"o}m approximation and the randomized Nystr{\\\"o}m approximation. \n\n\\subsection{Definition and basic properties}\n\nThe Nystr{\\\"o}m approximation is a natural way to construct a low-rank psd approximation of a psd matrix $A\\in \\mathbb{S}_{n}^+(\\R)$. Let $X\\in \\R^{n\\times \\ell}$ be an arbitrary test matrix. The \\textit{Nystr{\\\"o}m approximation} of $A$ with respect to the range of $X$ is defined by\n\\begin{equation}\n \\label{NysApprox}\n A\\langle X \\rangle = (AX)(X^{T}AX)^{\\dagger}(AX)^{T} \\in \\mathbb{S}_n^+(\\R).\n\\end{equation}\nThe Nystr{\\\"o}m approximation is the best psd approximation of $A$\nwhose range coincides with the range of $AX$. It has a deep relationship with the Schur complement and with Cholesky factorization~\\cite[Sec.~14]{MartTroppSurvey}.\n\nThe Nystr{\\\"o}m approximation enjoys several elementary properties that we record in the following lemma. \n\n\\begin{lemma}\n\\label{NysPropLemma}\nLet $A\\langle X\\rangle \\in \\mathbb{S}_n^+(\\R)$ be a Nystr{\\\"o}m approximation of the psd matrix $A \\in \\mathbb{S}_{n}^+(\\mathbb{R})$.\nThen \n\\begin{enumerate}\n \\item The approximation $A\\langle X\\rangle$ is psd and has rank at most $\\ell$.\n \\item The approximation $A\\langle X \\rangle$ depends only on $\\mathrm{range}(X)$.\n \\item\\label{it:nys-order} In the Loewner order, $A\\langle X\\rangle\\preceq A$.\n \\item\\label{it:nys-eigs} In particular, the eigenvalues satisfy $\\lambda_j(\\hat{A}) \\leq \\lambda_{j}(A)$ for each $1 \\leq j \\leq n$.\n\\end{enumerate}\n\\end{lemma}\nThe proof of \\cref{NysPropLemma}, \\cref{it:nys-order} is not completely obvious. It is a consequence of the fact that we may express $\\hat{A}_{\\textrm{nys}} = A^{1\/2}\\Pi A^{1\/2}$, where $\\Pi$ is an orthogonal projector.\n\n\n\\subsection{Randomized Nystr{\\\"o}m approximation}\n\\label{section:RandNysAppx}\n\\begin{algorithm}[t]\n\t\\caption{Randomized Nystr{\\\"o}m Approximation \\cite{li2017algorithm,tropp2017fixed}}\n\t\\label{alg:RandNysAppx}\n\t\\begin{algorithmic}[1]\n\t\t\\Require{Positive-semidefinite matrix $A \\in \\mathbb{S}_n^+(\\R)$, rank $\\ell$}\n\t\t\\Ensure{ Nystr{\\\"o}m approximation in factored form $\\hat{A}_{\\mathrm{nys}} = U \\hat{\\Lambda} U^T$}\n\t\t\n\t\t\\vspace{0.5pc}\n\n\t\t\\State $\\Omega = \\textrm{randn}(n, \\ell)$\n\t\t \\Comment{Gaussian test matrix}\n\t\t\\State $\\Omega = \\textrm{qr}(\\Omega,0)$\n\t\t \\Comment{Thin QR decomposition}\n\t\t\\State $Y = A\\Omega$\n\t\t \\Comment{$\\ell$ matvecs with $A$}\n\t\t\\State $\\nu = \\textrm{eps}(\\textrm{norm}(Y,\\textrm{'fro'}))$\n\t\t \\Comment{Compute shift}\n\t\t\\State $Y_{\\nu} = Y+\\nu\\Omega$\n\t\t \\Comment{Shift for stability}\n\t\t\\State $C = \\textrm{chol}(\\Omega^{T}Y_{\\nu})$\n\t\t\\State $B = Y_{\\nu}\/C$\n\t\t\\State $[U,\\Sigma,\\sim] = \\textrm{svd}(B,0)$\n\t\t \\Comment{Thin SVD}\n\t\t\\State $\\hat{\\Lambda} = \\max\\{0,\\Sigma^{2}-\\nu I\\}$ \\Comment{Remove shift, compute eigs}\n\t\\end{algorithmic}\n\\end{algorithm}\n\nHow should we choose the test matrix $X$ so that the Nystr{\\\"o}m approximation $A\\langle X\\rangle$ provides a good low-rank model for $A$? Surprisingly, we can obtain a good approximation simply by drawing the test matrix at random.\nSee~\\cite{tropp2017fixed} for theoretical justification of this claim.\n\nLet us outline the construction of the randomized Nystr{\\\"o}m approximation.\nDraw a standard normal test matrix $\\Omega \\in \\R^{n \\times \\ell}$ where $\\ell$\nis the sketch size, and compute the sketch $Y = A\\Omega$ By \\cref{NysPropLemma}, the sketch size $\\ell$ is equal to the rank of $\\hat{A}_{\\textrm{nys}}$ with probability 1,\nhence we use these terms interchangeably.\nThe Nystr{\\\"o}m approximation~\\cref{NysApprox} is constructed \ndirectly from the test matrix $\\Omega$ and the sketch $Y$:\n\\begin{equation} \\label{eqn:nys-unstable}\n \\hat{A}_{\\textrm{nys}} = A\\langle\\Omega\\rangle = Y(\\Omega^{T}Y)^{\\dagger}Y^{T}.\n\\end{equation}\nThe formula~\\cref{eqn:nys-unstable} is not numerically sound.\nWe refer the reader to~\\cref{alg:RandNysAppx}\nfor a stable and efficient implementation of the\nrandomized Nystr{\\\"o}m approximation~\\cite{li2017algorithm,tropp2017fixed}.\nConveniently, \\cref{alg:RandNysAppx} returns the truncated eigendecomposition $\\hat{A}_{\\textrm{nys}} = U\\hat{\\Lambda}U^{T}$, where $U \\in \\mathbb{R}^{n\\times \\ell}$ is an orthonormal matrix whose columns\nare eigenvectors and $\\hat{\\Lambda}\\in \\R^{\\ell\\times \\ell}$\nis a diagonal matrix listing the eigenvalues, which we often abbreviate\nas $\\hat{\\lambda}_1, \\dots, \\hat{\\lambda}_{\\ell}$.\n\nThe randomized Nystr{\\\"o}m approximation described in this section\nhas a key difference from the Nystr{\\\"o}m approximations that\nhave traditionally been used in the machine learning literature~\\cite{el2014fast,bach2013sharp,derezinski2020improved,gittens2011spectral,williams2001using}.\nIn machine learning settings, the Nystr{\\\"o}m approximation is usually constructed from a sketch $Y$ that samples random columns from the matrix (i.e., the random test matrix $\\Omega$ has 1-sparse columns). In contrast, \\cref{alg:RandNysAppx} computes a sketch $Y$ via random projection (i.e., the test matrix $\\Omega$ is standard normal). In most applications, we have strong reasons (\\cref{RandProjvsColSamp}) for preferring random projections to column sampling.\n\n\\subsubsection{Cost of randomized Nystr{\\\"o}m approximation} \n\\label{section:NystromAppxCost}\n Throughout the paper, we write $T_{\\textrm{mv}}$ for the time required to compute a matrix--vector product (matvec) with $A$. Forming the sketch $Y = A\\Omega$ with sketch size $\\ell$ requires $\\ell$ matvecs, which costs $T_{\\textrm{mv}}\\ell$. The other steps in the algorithm have arithmetic cost $O(n\\ell^{2})$. Hence, the total computational cost of \\cref{alg:RandNysAppx} is $O( T_{\\textrm{mv}}\\ell + \\ell^{2} n )$ operations. The storage cost is $O(\\ell n)$ floating-point numbers. \n\nFor \\cref{alg:RandNysAppx}, the worst-case performance occurs when $A$ is dense and unstructured. In this case, forming $Y$ costs $O(n^{2}\\ell)$ operations. However, if we have access to the columns of $A$ then we may reduce the cost of forming $Y$ to $O(n^{2}\\log \\ell)$ by using a structured test matrix $\\Omega$, such as a scrambled subsampled randomized Fourier transform (SSRFT) map or a sparse map~\\cite{MartTroppSurvey,tropp2017fixed}.\n\n\\subsubsection{A priori guarantees for the randomized Nystr{\\\"o}m approximation}\n\nIn this section, we present an a priori error bound for the randomized Nystr{\\\"o}m approximation.\nThe result improves over previous analyses~\\cite{gittens2011spectral,gittens2013revisiting,tropp2017fixed}\nby sharpening the error terms. This refinement is critical for the analysis of the preconditioner.\n\\begin{proposition}[Randomized Nystr{\\\"o}m approximation: Error] \n\\label{NysExpBound} \nConsider a psd matrix $A\\in \\mathbb{S}_{n}^+(\\R)$ with \neigenvalues $\\lambda_{1} \\geq \\cdots \\geq \\lambda_{n}$. \nChoose a sketch size $\\ell \\geq 4$, and draw a standard normal test matrix $\\Omega \\in \\R^{n\\times \\ell}$. \nThen the rank-$\\ell$ Nystr{\\\"o}m approximation $\\hat{A}_{\\textup{nys}}$ computed by \\cref{alg:RandNysAppx} satisfies\n\\begin{equation}\n\\label{eq-RandNysAppxErrBnd}\n \\mathbb{E}\\|A-\\hat{A}_{\\textup{nys}}\\| \\leq \\min_{2 \\leq p \\leq \\ell-2} \\left[ \\left(1+\\frac{2(\\ell-p)}{p-1}\\right)\\lambda_{\\ell-p+1}\n +\\frac{2\\textup{e}^{2}\\ell}{p^{2}-1}\\left(\\sum_{j>\\ell - p}\\lambda_{j}\\right) \\right].\n\\end{equation}\n\\end{proposition}\n\n\\noindent\nThe proof of \\cref{NysExpBound} may be found in \\cref{Section:NysExpBoundPf}. \n\n\\cref{NysExpBound} shows that, in expectation, the randomized Nystr{\\\"o}m approximation $\\hat{A}_{\\textrm{nys}}$ provides a good rank-$\\ell$ approximation to $A$. The first term in the bound is comparable with the spectral-norm error $\\lambda_{\\ell - p + 1}$ in the optimal rank-$(\\ell - p)$ approximation, $\\lfloor A \\rfloor_{\\ell - p}$. The second term in the bound is comparable with the trace-norm error $\\sum_{j > \\ell - p} \\lambda_j$ in the optimal rank-$(\\ell - p)$ approximation.\n\n\\Cref{NysExpBound} is better understood via the following simplification.\n\n\\begin{corollary}[Randomized Nystr{\\\"o}m approximation]\n \\label{NysExpCorr}\nInstate the assumptions of~\\cref{NysExpBound}. For $p \\geq 2$ and $\\ell = 2p - 1$, we have the bound \n\\[\\mathbb{E}\\|A-\\hat{A}_{\\textup{nys}}\\| \\leq \\left(3+\\frac{4\\textup{e}^{2}}{p}\\textup{sr}_{p}(A)\\right)\\lambda_{p}.\\]\nThe $p$-stable rank, $\\textup{sr}_{p}(A) = \\lambda_{p}^{-1}\\sum^{n}_{j = p}\\lambda_{j}$, reflects decay in the tail eigenvalues.\n\\end{corollary}\n\n\n\\cref{NysExpCorr} shows that the Nystr{\\\"o}m approximation error is on the order of $\\lambda_{p}$ when the rank parameter $\\ell = 2p - 1$. The constant depends on the $p$-stable rank $\\textrm{sr}_p(A)$, which is small when the tail eigenvalues decay quickly starting at $\\lambda_p$. This bound is critical for establishing our main results (\\cref{NysInvBnd,NysPCGEffDimThm}). \n\n\\subsubsection{Random projection versus column sampling}\n\\label{RandProjvsColSamp}\n\nMost papers in the machine learning literature~\\cite{el2014fast,bach2013sharp} construct Nystr{\\\"o}m approximations by sampling columns at random from an adaptive distribution.\nIn contrast, for most applications, we advocate using an oblivious random projection of the matrix to construct a Nystr{\\\"o}m approximation.\n\nRandom projection has several advantages over column sampling. \nFirst, column sampling may not be practical when we only have black-box matvec access to the matrix,\nwhile random projections are natural in this setting.\nSecond, it can be very expensive to obtain adaptive distributions for column sampling. Indeed, computing approximate ridge leverage scores costs just as much as solving the ridge regression problem directly using random projections \\cite[Theorem 2]{drineas2012fast}. \nThird, even with a good sampling distribution, column sampling\nproduces higher variance results than random projection,\nso it is far less reliable.\n\nOn the other hand, we have found that there are a few applications where it is more effective to compute a randomized Nystr{\\\"o}m preconditioner using column sampling in lieu of random projections. In particular, this seems to be the case for kernel ridge regression (\\cref{section:KernelRidgeRegression}). Indeed, the entries of the kernel matrix are given by an explicit formula, so we can extract full columns with ease. Sampling $\\ell$ columns may cost only $O(\\ell n)$ operations, whereas a single matvec generally costs $O(n^2)$. Furthermore, kernel matrices usually exhibit fast spectral decay, which limits the performance loss that results from using column sampling in lieu of random projection.\n\n\n\n\\section{Nystr{\\\"o}m Preconditioned Conjugate Gradients}\n\\label{section:NystromPCG}\nWe now present our main algorithm, Nystr{\\\"o}m PCG. This algorithm produces high accuracy solutions to a regularized linear system by using the Nystr{\\\"o}m approximation $\\hat{A}_{\\textrm{nys}}$ as a preconditioner. We provide a rigorous estimate for the condition number of the preconditioned system, and we prove that Nystr{\\\"o}m PCG leads to fast convergence for regularized linear systems. In contrast, we have shown that Nystr{\\\"o}m sketch-and-solve cannot be expected to yield accurate solutions.\n \n\\subsection{The preconditioner}\n\nIn this section, we introduce the optimal low-rank preconditioner,\nand we argue that the randomized Nystr{\\\"o}m preconditioner provides an approximation that is easy to compute.\n\n\\subsubsection{Motivation}\nAs a warmup, suppose we knew the eigenvalue decomposition of the best rank-$\\ell$ approximation of the matrix: $\\lfloor A \\rfloor_\\ell = V_{\\ell} \\Lambda_{\\ell} V_{\\ell}^T$.\nHow should we use this information to construct a good preconditioner for the regularized linear system~\\cref{eqn:reg-linsys-intro}?\n\nConsider the family of symmetric psd matrices that act as the identity on the orthogonal complement of $\\mathrm{range}(V_{\\ell})$. Within this class, we claim that the following matrix is the \\textit{optimal preconditioner}:\n\\begin{equation}\n\\label{eq-OptLowRankPre} \n P_\\star = \\frac{1}{\\lambda_{\\ell+1}+\\mu}V_{\\ell}(\\Lambda_{\\ell}+\\mu I)V_{\\ell}^{T}+(I-V_{\\ell}V_{\\ell}^{T}). \n\\end{equation}\nThe optimal preconditioner $P_{\\star}$ requires $O(n\\ell)$ storage, and we can solve linear systems in $P_{\\star}$ in $O(n\\ell)$ time. Whereas the regularized matrix $A_{\\mu}$ has condition number $\\kappa_2(A_{\\mu}) = (\\lambda_{1}+\\mu)\/(\\lambda_{n}+\\mu)$, the preconditioner yields\n\\begin{equation}\n\\label{eq-OptCondNumber}\n\\kappa_{2}(P_\\star^{-1\/2}A_{\\mu}P^{-1\/2}_{\\star}) = \\frac{\\lambda_{\\ell+1}+\\mu}{\\lambda_{n}+\\mu}.\n\\end{equation}\nThis is the minimum possible condition number attainable by a preconditioner from the class that we have delineated. It represents a significant improvement when $\\lambda_{\\ell + 1} \\ll \\lambda_1$.\nThe proofs of these claims are straightforward; for details, see \\cref{section:PrecondPfs}.\n\n\\subsubsection{Randomized Nystr{\\\"o}m preconditioner}\n\nIt is expensive to compute the best rank-$\\ell$ approximation $\\lfloor A \\rfloor_\\ell$ accurately. In contrast, we can compute the rank-$\\ell$ randomized Nystr{\\\"o}m approximation $\\hat{A}_{\\mathrm{nys}}$ efficiently (\\cref{alg:RandNysAppx}).\nFurthermore, we have seen that $\\hat{A}_{\\mathrm{nys}}$ approximates $A$ nearly as well as the optimal rank-$\\ell$ approximation (\\cref{NysExpCorr}).\nThese facts lead us to study the randomized Nystr{\\\"o}m preconditioner,\nproposed in~\\cite[Sec.~17]{MartTroppSurvey} without a complete justification.\n\nConsider the eigenvalue decomposition $\\hat{A}_{\\mathrm{nys}} = U \\hat{\\Lambda} U^T$, and write $\\hat{\\lambda}_{\\ell}$ for its $\\ell$th eigenvalue. The randomized Nystr{\\\"o}m preconditioner and its inverse take the form\n\\begin{equation}\n\\label{eq-NysPre}\n\\begin{aligned}\n P &= \\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}U(\\hat{\\Lambda}+\\mu I)U^{T}+(I-UU^{T}); \\\\\n P^{-1} &= (\\hat{\\lambda}_{\\ell}+\\mu)U(\\hat{\\Lambda}+\\mu I)^{-1}U^{T}+(I-UU^{T}).\n\\end{aligned}\n\\end{equation}\nLike the optimal preconditioner $P_\\star$, the randomized Nystr{\\\"o}m preconditioner \\eqref{eq-NysPre} is cheap to apply and to store.\nWe may hope that it damps the condition number of the preconditioned system $P^{-1\/2}A_{\\mu}P^{-1\/2}$ nearly as well as the optimal preconditioner $P_\\star$. We will support this intuition with a rigorous bound (\\cref{NysPCGThm}).\n\n\\subsection{Nystr{\\\"o}m PCG}\n\nWe can obviously use the randomized Nystr{\\\"o}m preconditioner within the framework of PCG.\nWe call this approach Nystr{\\\"o}m PCG, and we present a basic implementation in \\cref{alg:NysPCG}.\n\nMore precisely, \\cref{alg:NysPCG} uses left-preconditioned CG. This algorithm implicitly works with the unsymmetric matrix $P^{-1}A_{\\mu}$, rather than the symmetric matrix $P^{-1\/2}{A_\\mu}P^{-1\/2}$. The two methods yield identical sequences of iterates~\\cite{saad2003iterative}, but the former is more efficient. For ease of analysis, our theoretical results are presented in terms of the symmetrically preconditioned matrix.\n\n\\begin{algorithm}[t]\n\t\\caption{Nystr{\\\"o}m PCG} \n\t\\label{alg:NysPCG}\n\t\\begin{algorithmic}[1] \n\t\\Require{Psd matrix $A$, righthand side $b$, initial guess $x_{0}$, \n\tregularization parameter $\\mu$, sketch size $\\ell$,\n\tsolution tolerance $\\eta$}\n \\Ensure{Approximate solution $\\hat{x}$ to regularized system~\\cref{eqn:reg-linsys-intro}}\n\\vspace{0.5pc}\n \\State $[U, \\hat{\\Lambda}] =$ RandomizedNystr{\\\"o}mApproximation$(A, \\ell)$\n\t\\State $r_{0} = b-(A+ \\mu I) x_{0}$\n\t\\State $z_{0} = P^{-1}r_{0}$ \\Comment{using \\eqref{eq-NysPre}}\n\t\\State $p_{0} = z_{0}$\n\t\t\\While {$\\|r\\|_{2}>\\eta$}\n\t\t\\State $v = (A+ \\mu I) p_{0}$ \n\t\t\\State $\\alpha = (r_0^{T}z_{0}) \/ (p_{0}^{T}v_{0})$ \\Comment{compute step size} \n\t\t\\State $x = x_{0}+\\alpha p_{0}$ \\Comment{update solution}\n\t\t\\State $r = r_{0}-\\alpha v$ \\Comment{update residual}\n\t\t\\State $z = P^{-1}r$ \\Comment{find search direction via \\eqref{eq-NysPre}}\n\t\t\\State $\\beta = (r^{T}z)\/(r_{0}^{T}z_{0})$\n\t\t\\State $x_{0}\\leftarrow x$, $r_{0} \\leftarrow r$, $p_{0}\\leftarrow z+\\beta p_{0}$, $z_{0}\\leftarrow z$ \n\t\t\\EndWhile\n\t\\end{algorithmic}\n\\end{algorithm}\n\n\\subsubsection{Complexity of Nystr{\\\"o}m PCG}\n\nNystr{\\\"o}m PCG has two steps. First, we construct the randomized Nystr{\\\"o}m approximation, and then we solve the regularized linear system using PCG.\nWe have already discussed the cost of constructing the Nystr{\\\"o}m approximation (\\cref{section:NystromAppxCost}).\nThe PCG stage costs $O(T_{\\max})$ operations per iteration, and it uses a total of $O(n)$ additional storage.\n\nFor the regularized linear system~\\cref{eqn:reg-linsys-intro}, \\cref{NysPCGEffDimThm,ConvergenceCorollary} demonstrate that it is enough to choose the sketch size $\\ell = 2 \\, \\lceil 1.5 d_{\\mathrm{eff}}(\\mu) \\rceil + 1$. In this case, the overall runtime of Nystr{\\\"o}m PCG is\n$$\nO\\big(d_{\\mathrm{eff}}(\\mu)^2 n + T_{\\mathrm{mv}} ( d_{\\mathrm{eff}}(\\mu) + \\log(1\/\\epsilon) ) \\big)\n\\quad\\text{operations.}\n$$\nWhen the effective dimension $d_{\\mathrm{eff}}(\\mu)$ is modest, Nystr{\\\"o}m PCG is very efficient.\n\nIn contrast, \\cref{NysSketchSolveAnalysis} shows that the running time for Nystr{\\\"o}m sketch-and-solve has the same form---with $d_{\\mathrm{eff}}(\\epsilon \\mu)$ in place of $d_{\\mathrm{eff}}(\\mu)$. This is a massive difference. Nystr{\\\"o}m PCG can produce solutions whose residual norm is close to machine precision; this type of successful computation is impossible with Nystr{\\\"o}m sketch-and-solve.\n\n\\subsubsection{Comparison to other randomized preconditioning methods}\n\\label{sec:preconditioner-comparison}\nIn this subsection we give a more comprehensive discussion of how Nystr{\\\"o}m PCG compares to prior work on randomized preconditioning \\cite{avron2010blendenpik,lacotte2020effective,meng2014lsrn,rokhlin2008fast} based on sketch-and-precondition and related ideas. All these prior methods were developed for least squares problems. We summarize the complexity of each method for regularized least-squares problems in \\cref{t-ComplexityComparison}. \n\n\\begin{table}[h]\n \\begin{center}\n\\footnotesize\n \\caption{\\label{t-ComplexityComparison} \\textbf{Regularized least-squares: complexity of prior randomized preconditoning methods vs. Nystr{\\\"o}m PCG}. The table compares the complexity of Nystr{\\\"o}m PCG and state-of-the-art randomized preconditioning methods in the overdetermined case $n\\geq d$, \n assuming we can access $A$ only via matrix-vector products. \n The sketch-and-precondition preconditioner is constructed from a sketch $SA$, where $S\\in \\mathbb{R}^{m\\times n}$ is a $(1\\pm \\gamma)$ Gaussian subspace embedding with sketch size $\\Omega(d\/\\gamma)$ and $\\gamma \\in (0,1).$ \n The time to compute the sketch is $O(T_{\\textrm{mv}}d \/ \\gamma)$ and the iteration complexity follows from the argument in ~\\cite[Sec ~2.6]{woodruff2014sketching}. \n For AdaIHS we use a sketch constructed from a Gaussian subspace embedding with sketch size $O(d_{\\textrm{eff}}(\\mu)\/\\rho)$ where $\\rho \\in (0,0.18)$. The complexity of AdaIHS follows from ~\\cite[Theorem 5]{lacotte2020effective}. \n The complexity of Nystr{\\\"o}m PCG is derived from \\cref{NysPCGEffDimThm,ConvergenceCorollary}.}\n \\begin{tabular}{|c|c|c|}\n \\hline\n \\textbf{Method} & \\thead{Complexity} & \\thead{References}\\\\\n \\hline\n Sketch-and-precondition & $O\\left(T_\\textrm{mv}d\/\\gamma + d^{3}\/\\gamma+T_{\\textrm{mv}}\\frac{\\log\\left(2\/\\epsilon\\right)}{\\log\\left(1\/\\gamma\\right)}\\right)$ & \\cite{avron2010blendenpik,meng2014lsrn,rokhlin2008fast} \\\\\n \\hline\n AdaIHS & $\\makecell{O\\left((T_{\\textrm{mv}}d_{\\textrm{eff}}\/\\rho+dd_{\\textrm{eff}}^{2}\/\\rho^{2})\\log(d_{\\textrm{eff}}\/\\rho)+T_{\\textrm{mv}}\\frac{\\log(1\/\\epsilon)}{\\log(1\/{\\rho})}\\right)}$ & \\cite{lacotte2020effective}\\\\\n \\hline\n Nystr{\\\"o}m PCG & $O\\left(T_\\textrm{mv}d_{\\textrm{eff}}+dd_{\\textrm{eff}}^{2}+T_{\\textrm{mv}}\\log(2\/\\epsilon)\\right)$ & This work \\\\\n \\hline\n \\end{tabular}\n\\end{center}\n\\end{table}\nThe time to construct the sketch-and-precondition preconditioner is always larger than the Nystr{\\\"o}m preconditioner,\nsince $d_\\text{eff} < d$ and $\\gamma < 1$.\nIndeed, constructing the preconditioner for sketch-and-precondition costs $\\Omega(d^{3})$, \nwhich is the same as a direct method when $d = \\Omega(n)$\nand is prohibitive for high-dimensional problems. \nHence Nystr{\\\"o}m PCG is amenable to problems with large $d$ and runs much faster than sketch-and-precondition whenever $d_{\\textrm{eff}}(\\mu)\\ll d$.\nThe Nystr{\\\"o}m preconditioner also enjoys wider applicability then sketch-precondition: it applies to square-ish systems, whereas the others only work for strongly overdetermined or underdetermined problems.\nIn addition to sketch-and-precondition, Nystr{\\\"o}m PCG also enjoys better complexity than AdaIHS. AdaIHS has linear dependence in $d$, but possesses additional logarithmic factors and scales in terms of $d_{\\textrm{eff}}(\\mu)\/\\rho$ where $\\rho<0.18$, leading to a worse runtime. \n\n\nIn the context of kernel ridge regression (KRR), \nthe random features method of \\cite{avron2017faster}\nmay be viewed as a randomized preconditioning technique.\n\\cite{avron2017faster} prove convergence guarantees for the polynomial kernel with a potentially prohibitive sketch size $\\ell = O(d_{\\textrm{eff}}(\\mu)^{2})$. \nIn contrast, Nystr{\\\"o}m PCG can be used for KRR with any kernel and requires smaller sketch size $\\ell = O(d_{\\textrm{eff}}(\\mu))$ to obtain fast convergence. \n\nIn summary, Nystr{\\\"o}m PCG applies to a wider class of problems than prior randomized preconditioners and enjoys stronger theoretical guarantees for regularized problems. \nNystr{\\\"o}m PCG also outperforms other randomized preconditioners numerically (\\cref{section:NumericalExperiments}). \n\n\\subsubsection{Block Nystr{\\\"o}m PCG}\n\nWe can also use the Nystr{\\\"o}m preconditioner with the block CG algorithm~\\cite{o1980block} to solve regularized linear systems with multiple right-hand sides. For this approach, we also use an orthogonalization pre-processing proposed in~\\cite{feng1995block} that ensures numerical stability without further orthogonalization steps during the iteration.\n\n\n\n\\subsection{Analysis of Nystr{\\\"o}m PCG}\n\nWe now turn to the analysis of the randomized Nystr{\\\"o}m preconditioner $P$.\n\\cref{NysPCGEffDimThm} provides a bound for the rank $\\ell$ of the Nystr{\\\"o}m preconditioner that reduces the condition number of $A_{\\mu}$ to a constant. In this case, we deduce that Nystr{\\\"o}m PCG converges rapidly (\\cref{ConvergenceCorollary}).\n\n\\begin{theorem}[Nystr{\\\"o}m preconditioning]\n\\label{NysPCGEffDimThm}\nSuppose we construct the Nystr{\\\"o}m preconditioner $P$ in \\cref{eq-NysPre} using \\cref{alg:RandNysAppx} with sketch size $\\ell = 2\\,\\lceil 1.5\\,d_{\\textup{eff}}(\\mu)\\rceil+1$.\nUsing $P$ to precondition the regularized matrix $A_{\\mu}$ results in the condition number bound\n\\[\n\\E\\big[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\big] < 28.\n\\]\n\\end{theorem}\n\n\\noindent\nThe proof of \\cref{NysPCGEffDimThm} may be found in \\cref{Section:NysPCGEffDimThmProof}.\n\n\\cref{NysPCGEffDimThm} has several appealing features. \nMany other authors have noticed that the effective dimension controls \nsample size requirements for particular applications\nsuch as discriminant analysis \\cite{chowdhury2018randomized},\nridge regression \\cite{lacotte2020effective}, and kernel ridge regression \\cite{el2014fast,bach2013sharp}. \nIn contrast, our result holds for any regularized linear system.\n\nOur argument makes the role of the effective dimension conceptually simpler,\nand it leads to explicit, practical parameter recommendations.\nIndeed, the effective dimension $d_{\\mathrm{eff}}(\\mu)$ is essentially\nthe same as the sketch size $\\ell$ that makes the approximation error\n$\\|A - \\hat{A}_{\\mathrm{nys}}\\|$ proportional to $\\mu$. \nIn previous arguments, such as those in \\cite{el2014fast,bach2013sharp,chowdhury2018randomized},\nthe effective dimension arises because the authors reduce the analysis to approximate matrix multiplication~\\cite{cohen2015optimal}, which produces inscrutable constant factors.\n\n\\Cref{NysPCGEffDimThm} ensures that Nystr{\\\"o}m PCG converges quickly.\n\\begin{corollary}[Nystr{\\\"o}m PCG: Convergence]\n\\label{ConvergenceCorollary}\nDefine $P$ as in \\cref{NysPCGEffDimThm}, and condition on the event \n$\\big\\{\\kappa_2\\left(P^{-1\/2}A_\\mu P^{-1\/2}\\right)\\leq 56\\big\\}$.\nLet $M = P^{-1\/2}A_{\\mu}P^{-1\/2}$. If we initialize \\cref{alg:NysPCG}\nwith initial iterate $x_0 = 0$, then the relative error $\\delta_t$ in the iterate $x_t$ satisfies\n\\[\n\\delta_t = \\frac{\\|x_{t}-x_{\\star}\\|_M}{\\|x_{\\star}\\|_{M}}\n < 2\\cdot \\left(0.77 \\right)^{t}\n \\quad\\text{where $A_{\\mu} x_{\\star} = b$.}\n\\] \nIn particular, after $t = \\lceil{3.8 \\log(2\/\\epsilon)\\rceil}$ iterations,\nwe have relative error $\\delta_t<\\epsilon$.\n\\end{corollary}\n\nThe proof of \\cref{ConvergenceCorollary} is an immediate consequence of the standard convergence result for CG \\cite[Theorem 38.5, p.~299]{trefethen1997numerical}. See~\\cref{section:ConvergenceCorollaryPf}. \n\n\\subsubsection{Analyzing the condition number}\n\nThe first step in the proof of \\cref{NysPCGEffDimThm} is a deterministic\nbound on how the preconditioner \\eqref{eq-NysPre} reduces the condition number\nof the regularized matrix $A_{\\mu}$. Let us emphasize that this bound is valid\nfor any rank-$\\ell$ Nystr{\\\"o}m approximation, regardless of the choice of test matrix. \n\n\\begin{proposition}[Nystr{\\\"o}m preconditioner: deterministic bound]\n\\label{NysPCGThm}\nLet $\\hat{A} = U \\hat{\\Lambda} U^T$ be any rank-$\\ell$ Nystr{\\\"o}m approximation, with $\\ell$th largest eigenvalue $\\hat{\\lambda}_{\\ell}$,\nand let $E = A-\\hat{A}$ be the approximation error. Construct the Nystr{\\\"o}m preconditioner $P$ as in \\eqref{eq-NysPre}.\nThen the condition number of the preconditioned matrix $P^{-1\/2}A_{\\mu}P^{-1\/2}$ satisfies\n\\begin{equation}\n \\label{eq-CondNumBnd}\n\\begin{aligned}\n \\max\\bigg\\{\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\lambda_{n}+\\mu},1\\bigg\\}\n &\\leq\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\\\\n &\\leq \\left(\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|\\right)\\min\\bigg\\{\\frac{1}{\\mu},~\n \\frac{\\hat{\\lambda}_{\\ell} + \\lambda_n + 2 \\mu}{(\\hat{\\lambda}_\\ell + \\mu)(\\lambda_n + \\mu)}\\bigg\\}.\n\\end{aligned}\n\\end{equation}\n\\end{proposition} \nFor the proof of \\cref{NysPCGThm} see \\cref{section:NysPCGThmProof}.\n\nTo interpret\nthe result, recall the expression~\\cref{eq-OptCondNumber} for the condition\nnumber induced by the optimal preconditioner. \\cref{NysPCGThm} shows that\nthe Nystr{\\\"o}m preconditioner may reduce the condition number\nalmost as well as the optimal preconditioner.\n\nIn particular, when $\\| E \\| = O(\\mu)$, \nthe condition number of the preconditioned system is bounded\nby a constant, independent of the spectrum of $A$. In this case,\nNystr{\\\"o}m PCG is guaranteed to converge quickly.\n\n\\subsubsection{The effective dimension and sketch size selection}\n\nHow should we choose the sketch size $\\ell$ to guarantee that $\\|E\\| = O( \\mu )$? \n\\cref{NysExpCorr} shows how the error in the rank-$\\ell$ randomized Nystr{\\\"o}m approximation\ndepends on the spectrum of $A$ through the eigenvalues of $A$ and the tail stable rank.\nIn this section, we present a lemma which demonstrates that the effective dimension\n$d_{\\mathrm{eff}}(\\mu)$ controls both quantities. As a consequence of this bound,\nwe will be able to choose the sketch size $\\ell$ proportional\nto the effective dimension $d_{\\mathrm{eff}}(\\mu)$.\n\nRecall from \\cref{EffDimDef} that the effective dimension of the matrix $A$\nis defined as\n\\begin{equation} \\label{eqn:deff-proof}\nd_{\\textrm{eff}}(\\mu) = \\textrm{tr}(A(A+\\mu I)^{-1}) = \\sum_{j=1}^{n}\\frac{\\lambda_j(A)}{\\lambda_j(A)+\\mu}.\n\\end{equation}\nAs previously mentioned, $d_{\\textrm{eff}}(\\mu)$ may be viewed as a smoothed count of the eigenvalues\nlarger than $\\mu$. Thus, one may expect that $\\lambda_{k}(A) \\lesssim \\mu$\nfor $k \\gtrsim d_{\\textrm{eff}}(\\mu)$. This intuition is correct, and it forms\nthe content of \\cref{KeyLemma}.\n\n\\begin{lemma}[Effective dimension]\n\\label{KeyLemma}\nLet $A\\in \\mathbb{S}_{n}^+(\\mathbb{R})$ with eigenvalues $\\lambda_{1}\\geq\\lambda_{2}\\geq\\cdots\\geq\\lambda_{n}$. Let $\\mu > 0$ be regularization parameter,\nand define the effective dimension as in~\\cref{eqn:deff-proof}. The following statements hold.\n\\begin{enumerate}\n \\item \\label{l-eff-max}\n \n Fix $\\gamma>0$. If $j\\geq (1+\\gamma^{-1})d_{\\textup{eff}}(\\mu)$, then $\\lambda_{j}\\leq \\gamma\\mu$.\n \\item \\label{l-eff-avg} If $k\\geq d_{\\textup{eff}}(\\mu)$, then\n $k^{-1} \\sum_{j>k}\\lambda_j \\leq (d_{\\textup{eff}}(\\mu)\/k) \\cdot \\mu$. \n\\end{enumerate}\n\\end{lemma}\nThe proof of \\cref{KeyLemma} may be found in \\cref{section:KeyLemmaProof}.\n\n \\cref{KeyLemma}, \\cref{l-eff-max} captures the intuitive fact that there are no more than $2 d_{\\mathrm{eff}}(\\mu)$ eigenvalues larger than $\\mu$. Similarly,\n \\cref{l-eff-avg} states that the effective dimension controls the sum\n of all the eigenvalues whose index exceeds the effective dimension.\n It is instructive to think about the meaning of these results\n when $d_{\\textrm{eff}}(\\mu)$ is small.\n\n\\subsubsection{Proof of \\cref{NysPCGEffDimThm}}\n\\label{Section:NysPCGEffDimThmProof}\n We are now prepared to prove \\cref{NysPCGEffDimThm}.\n The key ingredients in the proof are \\cref{NysExpBound}, \\cref{NysPCGThm}, and \\cref{KeyLemma}.\n \n\\begin{proof}[Proof of \\cref{NysPCGEffDimThm}]\nFix the sketch size $\\ell = 2 \\, \\lceil 1.5 \\, d_{\\mathrm{eff}}(\\mu) \\rceil + 1$.\nConstruct the rank-$\\ell$ randomized Nystr{\\\"o}m approximation $\\hat{A}_{\\mathrm{nys}}$\nwith eigenvalues $\\hat{\\lambda}_j$. Write $E = A - \\hat{A}_{\\mathrm{nys}}$ for the approximation error.\nForm the preconditioner $P$ via~\\cref{eq-NysPre}. We must bound the expected condition number\nof the preconditioned matrix $P^{-1\/2} A_{\\mu} P^{-1\/2}$\n \nFirst, we apply \\cref{NysPCGThm} to obtain a deterministic bound that is valid for any rank-$\\ell$\nNystr{\\\"o}m preconditioner:\n\\[\n\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\leq \\frac{\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|}{\\mu}\n \\leq 2 + \\frac{\\|E\\|}{\\mu}.\n\\]\nThe second inequality holds because $\\hat{\\lambda}_{\\ell} \\leq \\lambda_{\\ell} \\leq \\mu$.\nThis is a consequence of \\cref{NysPropLemma}, \\cref{it:nys-eigs}\nand \\cref{KeyLemma}, \\cref{l-eff-max} with $\\gamma = 1$.\nWe rely on the fact that $\\ell \\geq 2 \\, d_{\\mathrm{eff}}(\\mu)$.\n\nDecompose $\\ell = 2p-1$ where $p = \\lceil1.5\\,d_{\\textrm{eff}}(\\mu)\\rceil+1$.\nTake the expectation, and invoke \\cref{NysExpCorr} to obtain \n\\[\\E\\big[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\big]\n \\leq 2 + \\left(3+\\frac{4\\textrm{e}^{2}}{p}\\textrm{sr}_{p}(A)\\right) (\\lambda_{p} \/ \\mu).\\]\nBy definition, $\\textrm{sr}_{p}(A) \\cdot \\lambda_{p} = \\sum_{j \\geq p}\\lambda_{j}$.\nTo complete the bound, apply \\cref{KeyLemma} twice. We use \\cref{l-eff-max} with $\\gamma = 2$ and \\cref{l-eff-avg} with $k = p-1 = \\lceil 1.5\\,d_{\\textrm{eff}}(\\mu)\\rceil$ to reach\n\\[\n\\E\\big[\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\big]\\leq 2+\\frac{3\\cdot 2\\mu+4\\textrm{e}^{2}\\cdot 2\\mu\/3}{\\mu}<2+26 = 28,\n\\]\nwhich is the desired result.\n\\end{proof}\n\n \n\\subsection{Practical parameter selection}\n\\label{sec:adaptive-rank}\n\nIn practice, we may not know the regularization parameter $\\mu$ in advance,\nand we rarely know the effective dimension $d_{\\mathrm{eff}}(\\mu)$. As a consequence,\nwe cannot enact the theoretical recommendation for the rank of the Nystr{\\\"o}m\npreconditioner: $\\ell = 2 \\, \\lceil 1.5\\,d_{\\mathrm{eff}}(\\mu) \\rceil + 1$.\nInstead, we need an adaptive method for choosing the rank $\\ell$. Below,\nwe outline three strategies.\n\n\\subsubsection{Strategy 1: Adaptive rank selection by a posteriori error estimation}\n\\label{section:ErrorRankDoubling}\n\nThe first strategy uses the posterior condition number estimate adaptively\nin a procedure the repeatedly doubles the sketch size $\\ell$ as required.\n Recall that\n \\cref{NysPCGThm} controls the condition number\n of the preconditioned system:\n\\begin{equation}\n\\label{eq-kappa-reg-bnds}\n\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) \\leq \\frac{\\hat{\\lambda}_{\\ell}+\\mu+\\|E\\|}{\\mu}\n\\quad\\text{where $E = A - \\hat{A}_{\\mathrm{nys}}$.}\n\\end{equation} \nWe get $\\hat{\\lambda}_{\\ell}$ for free from \\cref{alg:RandNysAppx} and we can compute the error $\\|E\\|$ inexpensively with the randomized power method \\cite{kuczynski1992estimating};\nsee \\cref{alg:RandPowErrEst} in \\cref{section:AdaRankSelection}. \nThus, we can ensure the condition number is small by making $\\|E\\|$ and $\\hat{\\lambda}_{\\ell}$ fall below some desired tolerance.\nThe adaptive strategy proceeds to do this as follows.\nWe compute a randomized Nystr{\\\"o}m approximation with initial sketch size $\\ell_{0}$, and we estimate the error $\\| E \\|$ using randomized powering. \nIf $\\|E\\|$ is smaller than a prescribed tolerance, we accept the rank-$\\ell_0$ approximation. If the tolerance is not met, then we double the sketch size, update the approximation, and estimate $\\|E\\|$ again. \nThe process repeats until the estimate for $\\|E\\|$ falls below the tolerance or it breaches a threshold $\\ell_{\\textrm{max}}$ for the maximum sketch size. \\cref{alg:AdaRandNysAppx} usings the following stopping criterions $\\| E \\| \\leq \\tau\\mu$ and $\\hat{\\lambda}_{\\ell}\\leq \\tau\\mu\/11$ for a modest constant $\\tau$. The stopping criterion on $\\hat{\\lambda}_{\\ell}$ does not seem to be necessary in practice, as it is usually an order of magnitude small than $\\|E\\|$, but it is needed for \\cref{AdaNysRankThm}. \nBased on numerical experience, we recommend a choice $\\tau\\in [1,100]$. \nFor full algorithmic details of adaptive rank selection by estimating $\\|E\\|$,\n see \\ref{alg:AdaRandNysAppx} in \\ref{section:AdaRankSelection}. \n \n The following theorem shows that with high probability, \\cref{alg:AdaRandNysAppx} terminates with a modest sketch size in at most a logarithmic number of steps, and PCG with the resulting preconditioner converges rapidly.\n \n \\begin{theorem}\n \\label{AdaNysRankThm}\nRun \\cref{alg:AdaRandNysAppx} with initial sketch size $\\ell_0$ and tolerance $\\tau \\mu$ where $\\tau \\geq 1 $, and let $\\tilde{\\ell} = 2\\lceil 2d_{\\textup{eff}}\\left(\\frac{\\delta\\tau\\mu}{11}\\right)\\rceil+1$. Then with probability at least $1-\\delta$:\n\\begin{itemize}\n \\item[1.] \\cref{alg:AdaRandNysAppx} doubles the sketch size at most\n $\\lceil\\log_{2}\\left(\\frac{\\tilde{\\ell}}{\\ell_{0}}\\right)\\rceil$ times.\n \\item[2.] The final sketch size $\\ell$ satisfies\n \\[\\ell \\leq 4\\lceil2d_{\\textup{eff}}\\left(\\frac{\\delta\\tau\\mu}{11}\\right)\\rceil+2.\\]\n \\item[3.] With the preconditioner constructed from \\cref{alg:AdaRandNysAppx}, Nystr{\\\"o}m PCG converges in at most $\\lceil\\frac{\\log(2\/\\epsilon)}{\\log(1\/\\tau_{0})}\\rceil$ iterations, where $\\tau_{0} = \\frac{\\sqrt{1+12\\tau\/11}-1}{\\sqrt{1+12\\tau\/11}+1}$. \n\\end{itemize}\n\\end{theorem}\n\n\\cref{AdaNysRankThm} immediately implies the following concrete guarantee.\n\\begin{corollary}\nSet $\\tau = 44$ and $\\delta = 1\/4$ in \\cref{alg:AdaRandNysAppx} then with probability at least $3\/4$:\n\\item[1.] \\cref{alg:AdaRandNysAppx} doubles the sketch size at most\n $\\lceil\\log_{2}\\left(\\frac{\\tilde{\\ell}}{\\ell_{0}}\\right)\\rceil$ times.\n \\item[2.] The final sketch size $\\ell$ satisfies\n \\[\\ell \\leq 4\\lceil2d_{\\textup{eff}}(\\mu)\\rceil+2.\\]\n \\item[3.] With the preconditioner constructed from \\cref{alg:AdaRandNysAppx}, Nystr{\\\"o}m PCG converges in at most $\\lceil3.48\\log(2\/\\epsilon)\\rceil$ iterations. \n\\end{corollary}\n\n\\subsubsection{Strategy 2: Adaptive rank selection by monitoring $\\hat{\\lambda}_{\\ell}\/\\mu$}\n\\label{section:RatioRankDoubling}\n\nThe second strategy is almost identical to the first, except we monitor the ratio $\\hat{\\lambda}_{\\ell}\/\\mu$ instead of $\\|E\\|\/\\mu$. \nStrategy 2 doubles the approximation rank until $\\hat{\\lambda}_{\\ell}\/\\mu$ falls below some tolerance (say, 10) \nor the sample size reaches the threshold $\\ell_{\\max}$.\nThe approach is justified by the following proposition which shows that once the rank $\\ell$ is sufficiently large, with high probability, the exact condition number differs from the empirical condition number $(\\hat{\\lambda}_\\ell+\\mu)\/\\mu$ by at most a constant.\n\\begin{proposition}\n\\label{AdaRankRatProp}\nLet $\\tau\\geq 0$ denote the tolerance and $\\delta>0$ a given failure probability. Suppose the rank of the randomized Nystr{\\\"o}m approximation satisfies $\\ell \\geq 2\\lceil 2d_{\\textup{eff}}\\left(\\tau\\mu)\\right)\\rceil+1$. Then \n\\begin{equation}\n \\mathbb{P}\\left\\{\\left(\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})-\\frac{\\hat{\\lambda}_{\\ell}+\\mu}{\\mu}\\right)_{+}\\leq\\frac{\\tau}{\\delta}\\right\\}\\geq 1-\\delta,\n\\end{equation}\nwhere $X_{+} = \\max\\{X,0\\}.$\n\\end{proposition}\nThis strategy has the benefit of saving a bit of computation and is preferable when the target precision is not too important, eg, in machine learning problems where training error only loosely predicts test error.\n\n\\subsubsection{Strategy 3: Choose $\\ell$ as large as the user can afford}\n\\label{section:LargeLStrategy}\n\nThe third strategy is to choose the rank $\\ell$ as large as the user can afford.\nThis approach is coarse, and it does not yield any guarantees on the\ncost of the Nystr{\\\"o}m PCG method.\n\nNevertheless, once we have constructed a rank-$\\ell$ Nystr{\\\"o}m approximation we can combine the posterior estimate of the condition number used in strategy 1 with the standard convergence theory of PCG to obtain an upper bound for the iteration count of Nystr{\\\"o}m PCG.\nThis gives us advance warning\nabout how long it may take to solve the regularized linear system.\nAs in strategy 1 we compute the error $\\| E \\|$ in the condition number bound inexpensively with the randomized power method. \n\n\n\n\n\\section{Nystr{\\\"o}m sketch-and-solve}\n\nThe simplest mechanism for using the Nystr{\\\"o}m approximation\nis an algorithm called Nystr{\\\"o}m sketch-and-solve. This\nsection introduces the method, its implementation, and its history.\nWe also provide a general theoretical analysis that sheds light on its performance. In spite of its popularity, the Nystr{\\\"o}m sketch-and-solve method is rarely worth serious consideration.\n\n\\begin{algorithm}[t]\n\t\\caption{Nystr{\\\"o}m sketch-and-solve} \n\t\\label{alg:NysSketchSolve}\n\t\\begin{algorithmic}[1]\n\t\t\\Require{Psd matrix $A \\in \\mathbb{S}_n^+(\\R)$, right-hand side $b$, regularization $\\mu$, rank $\\ell$} \n\t\t\\Ensure{Approximate solution $\\hat{x}$ to~\\cref{eqn:reg-linsys-intro}}\n\\vspace{0.5pc}\n\t\t\\State $[U,\\hat{\\Lambda}]$ = RandomizedNystr{\\\"o}mApproximation($A,\\ell$)\n\t\t\\State Use~\\cref{eq-Woodbury} to compute $\\hat{x} = (\\hat{A}_{\\textrm{nys}}+\\mu I)^{-1}b$\n\t\\end{algorithmic}\n\\end{algorithm}\n\n\\label{Section:NystromSketchSolve}\n\\subsection{Overview}\n\nGiven a rank-$\\ell$ Nystr{\\\"o}m approximation $\\hat A_\\textrm{nys}$ of the psd matrix $A$, it is tempting to replace the regularized linear system $(A + \\mu I) x = b$ with the proxy $(\\hat{A}_{\\textrm{nys}} + \\mu I) x = b$. Indeed, we can solve the proxy linear system in $O(\\ell n)$ time using the Sherman--Morrison--Woodbury formula~\\cite[Eqn. (2.1.4)]{golubvanloan2013}:\n\n\\begin{lemma}[Approximate regularized inversion]\n\\label{SketchInv}\nConsider any rank-$\\ell$ matrix $\\hat{A}$ with eigenvalue decomposition $\\hat{A} = U \\hat \\Lambda U^T$.\nThen\n\\begin{equation}\n\\label{eq-Woodbury}\n (\\hat{A}+\\mu I)^{-1} = U(\\hat{\\Lambda}+\\mu I)^{-1}U^{T}+\\frac{1}{\\mu}(I-UU^{T}).\n\\end{equation}\n\\end{lemma}\n\n\\noindent\nWe refer to the approach in this paragraph as the Nystr{\\\"o}m sketch-and-solve algorithm\nbecause it is modeled on the sketch-and-solve paradigm that originated in~\\cite{sarlos2006improved}.\n\nSee~\\cref{alg:NysSketchSolve} for a summary of the Nystr{\\\"o}m sketch-and-solve method.\nThe algorithm produces an approximate solution $\\hat x$ to the regularized linear system~\\cref{eqn:reg-linsys-intro} in time $O(T_{\\textrm{mv}}\\ell+\\ell^{2} n)$. The arithmetic cost is much faster than a direct method, which costs $O(n^3)$. It can also be faster than running CG for a long time at a cost of $O(T_{\\textrm{mv}})$ per iteration. The method looks attractive if we only consider the runtime, and yet...\n\nNystr{\\\"o}m sketch-and-solve only has one parameter, the rank $\\ell$ of the Nystr{\\\"o}m approximation, which controls the quality of the approximate solution $\\hat x$. When $\\ell \\ll n$, the method has an appealing computational profile. As $\\ell$ increases, the approximation quality increases but the computational burden becomes heavy. We will show that, alas, an accurate solution to the linear system actually requires $\\ell\\approx n$, at which point the computational benefits of Nystr{\\\"o}m sketch-and-solve evaporate completely.\n\nIn summary, Nystr{\\\"o}m sketch-and-solve is almost never the right algorithm to use. We will see that Nystr{\\\"o}m PCG generally produces much more accurate solutions with a similar computational cost.\n\n\n\\subsection{Guarantees and deficiencies}\n\\label{NysSketchSolveAnalysis}\n\nUsing \\cref{GenInvErrBnd} together with the a priori guarantee in \\cref{NysExpBound}, we quickly obtain a performance guarantee for \\cref{alg:NysSketchSolve}. \n\n\\begin{theorem}\n\\label{NysInvBnd}\nFix $p\\geq 2$, and set $\\ell = 2p - 1$. For a psd matrix $A \\in \\mathbb{S}_n^+(\\R)$, construct a randomized Nystr{\\\"o}m approximation $\\hat{A}_{\\textup{nys}}$ using \\cref{alg:RandNysAppx}. \nThen the approximation error for the inverse satisfies\n\\begin{equation}\n \\label{eq-NysInvExpErr}\n \\mathbb{E}\\big\\|(A+\\mu I)^{-1}-(\\hat{A}_{\\textup{nys}}+\\mu I)^{-1}\\big\\|\\leq \\bigg(3+\\frac{4\\textup{e}^{2}}{p}\\textup{sr}_{p}(A)\\bigg)\\frac{\\lambda_{p}}{\\mu \\cdot (\\lambda_{p}+\\mu)}.\n\\end{equation}\nDefine $x_{\\star} = (A+\\mu I)^{-1}b$, and select $\\ell = 2\\,\\lceil 1.5 \\, d_{\\textup{eff}}(\\epsilon\\mu)\\rceil+1$.\nThen the approximate solution $\\hat{x}$ computed by \\cref{alg:NysSketchSolve} satisfies\n\\begin{equation}\n \\label{eq-NysSSRelErr}\n \\E\\bigg[\\frac{\\|\\hat{x}-x_{\\star}\\|_{2}}{\\|x_{\\star}\\|_{2}}\\bigg] \\leq 26\\epsilon. \n\\end{equation}\n\\end{theorem}\nThe proof of \\cref{NysInvBnd} may be found in \\cref{section:NysSketchSolveProof}.\n\n\\cref{NysInvBnd} tells us how accurately we can hope to solve linear systems using Nystr{\\\"o}m sketch-and-solve (\\cref{alg:NysSketchSolve}). \nTo obtain relative error $\\epsilon$, we should choose $\\ell = O(d_{\\textrm{eff}}(\\epsilon\\mu))$. When $\\epsilon \\mu$ is small, we anticipate that $d_{\\textrm{eff}}(\\epsilon\\mu)\\approx n$. In this case, Nystr{\\\"o}m sketch-and-solve has no computational value. Our analysis is sharp in its essential respects, so the pessimistic assessment is irremediable.\n\n\\subsection{History}\n\nNystr{\\\"o}m sketch-and-solve has a long history in the machine learning literature. It was introduced in \\cite{williams2001using} to speed up kernel-based learning, and it plays a role in many subsequent papers on kernel methods. In this context, the Nystr{\\\"o}m approximation is typically obtained using column sampling \\cite{el2014fast,bach2013sharp,williams2001using}, which has its limitations (\\cref{RandProjvsColSamp}). More recently, Nystr{\\\"o}m sketch-and-solve has been applied to speed up approximate cross-validation \\cite{stephenson2020LowRank}.\n\nThe analysis of Nystr{\\\"o}m sketch-and-solve presented above differs from previous analysis. Prior works~\\cite{el2014fast,bach2013sharp} focus on the kernel setting, and they use properties of column sampling schemes to derive learning guarantees. In contrast, we bound the relative error for a Nystr{\\\"om} approximation based on a random projection.\nOur overall approach extends to column sampling if we replace \\cref{NysExpBound} by an appropriate analog, such as Gittens's results~\\cite{gittens2011spectral}.\n\n\n\\section{Approximating the regularized inverse}\n\\label{section:AppxRegInverse}\n\nLet us return to the regularized linear system~\\cref{eqn:reg-linsys-intro}.\nThe solution to the problem has the form $x_{\\star} = (A+\\mu I)^{-1}b$. \nGiven a good approximation $\\hat{A}$ to the matrix $A$, it is natural to ask whether $\\hat{x} = (\\hat{A} + \\mu I)^{-1} b$ is a good approximation to the desired solution $x_{\\star}$.\n\nThere are many reasons why we might prefer to use $\\hat{A}$ in place of $A$. In particular, we may be able to solve linear systems in the matrix $\\hat{A} + \\mu I$ more efficiently. On the other hand, the utility of this approach depends on how well the inverse $(\\hat{A} + \\mu I)^{-1}$ approximates the desired inverse $(A + \\mu I)^{-1}$. The next result addresses this question for a wide class of approximations that includes the Nystr{\\\"o}m approximation. \n\n\n\n\\begin{proposition}[Regularized inverses]\n\\label{GenInvErrBnd}\nConsider psd matrices $A$, $\\hat{A}\\in \\mathbb{S}_n^+(\\R)$, and assume that the difference $E = A-\\hat{A}$ is psd. Fix $\\mu > 0$. Then\n\\begin{equation}\n \\label{eq-InvInequality}\n \\|(\\hat{A}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\|\\leq \\frac{1}{\\mu}\\frac{\\|E\\|}{\\|E\\|+\\mu}.\n\\end{equation}\nFurthermore, the bound~\\eqref{eq-InvInequality} is attained when $\\hat{A} = \\lfloor A\\rfloor_{\\ell}$ for $1\\leq \\ell \\leq n$.\n\\end{proposition}\nThe proof of \\cref{GenInvErrBnd} may be found in \\cref{section:GenInvErrBndPf}. It is based on~\\cite[Lemma~X.1.4]{bhatia2013matrix}.\n\n\n\\cref{GenInvErrBnd} has an appealing interpretation. When $\\|A - \\hat{A}\\|$ is small in comparison to the regularization parameter $\\mu$, then the approximate inverse $(\\hat{A} + \\mu I)^{-1}$ can serve in place of the inverse $(A + \\mu I)^{-1}$. Note that $\\|(A + \\mu I)^{-1}\\| \\leq 1\/\\mu$, so we can view~\\cref{eq-InvInequality} as a relative error bound.\n\n\n\n \n\n\\section*{Acknowledgments}\n\n\\bibliographystyle{siamplain}\n\n\\section{Proofs of additional propositions}\nIn this section we give the proofs for the propositions that are close to existing results but do not explicitly appear in the literature.\n\\subsubsection{Useful facts about Gaussian random matrices}\nIn this subsection we record some useful results about Gaussian random matrices that are necessary for the proof of \\cref{NysExpBound}. The proof of \\cref{NysExpBound} follows in \\cref{Section:NysExpBoundPf}.\n\\begin{proposition}[\\cite{halko2011finding,nakatsukasa2020fast}]\n\\label{GaussInvLemma}\nLet $G$ be $(\\ell-p)\\times \\ell$ standard Gaussian matrix with $\\ell\\geq 4$ and $2\\leq p \\leq \\ell-2$. Then\n\\begin{equation}\n \\left(\\E\\|G^{\\dagger}\\|^{2}_{F}\\right)^{1\/2} = \\sqrt{\\frac{\\ell-p}{p-1}},\n\\end{equation}\nand\n\\begin{equation}\n \\left(\\E\\|G^{\\dagger}\\|^{2}\\right)^{1\/2} \\leq \\textup{e}\\sqrt{\\frac{\\ell}{p^{2}-1}}.\n\\end{equation}\n\\end{proposition}\n\\begin{remark}\nThe first display in \\cref{GaussInvLemma} appears in \\cite{halko2011finding}, while the second display in \\cref{GaussInvLemma} is due to \\cite{nakatsukasa2020fast}.\n\\end{remark}\nWe also require one new result, which strengthens the improved version of Chevet's theorem due to Gordon \\cite{gordon1985some}.\n\\begin{proposition}[Squared Chevet]\n\\label{SquaredChevet}\nFix matrices $S\\in \\mathbb{R}^{r\\times m}$ and $T\\in \\mathbb{R}^{n\\times s}$ and let $G\\in\\mathbb{R}^{m\\times n}$ be a standard Gaussian matrix. Then\n\\[\\E\\|SGT\\|^{2} \\leq \\left(\\|S\\| \\|T\\|_{F}+\\|S\\|_{F}\\|T\\|\\right)^{2}.\\]\n\\end{proposition}\n\\iftutorial\nWe defer the proof of \\cref{SquaredChevet} to \\cref{section:SquaredChevetPf}.\n\\else\nAs the proof of Squared Chevet is rather technical and removed from the main ideas of this work, we have chosen to omit it. A full proof of the result may be found in \\cite{frangella2021randomized}.\n\\fi\n\\begin{remark}\n Chevet's theorem states that \\cite{halko2011finding}\n\\[\\E\\|SGT\\| \\leq \\|S\\| \\|T\\|_{F}+\\|S\\|_{F}\\|T\\|.\\]\n\\cref{SquaredChevet} immediately implies Chevet's theorem by H{\\\"o}lder's Inequality. \\end{remark}\n\n\\subsection{Proof of \\cref{NysExpBound}}\n\\label{Section:NysExpBoundPf}\n\\begin{proof}\nProposition 11.1 in \\cite[Sec. 11]{MartTroppSurvey} and the argument of Theorem 11.4 in \\cite[Sec. 11]{MartTroppSurvey} shows that\n\\[\\|A-\\hat{A}_{\\textrm{nys}}\\| \\leq \\|\\Sigma_{\\ell-p+1}\\|^{2}+\\|\\Sigma_{\\ell-p+1}\\Omega_{2}\\Omega_1^{\\dagger}\\|^{2}.\\]\nTaking expectations and using $\\|\\Sigma_{\\ell-p+1}\\|^{2} = \\lambda_{\\ell-p+1}$ gives\n\\[\\E\\|A-\\hat{A}_{\\textrm{nys}}\\| \\leq \\lambda_{\\ell-p+1}+\\E\\|\\Sigma_{\\ell-p+1}\\Omega_{2}\\Omega_1^{\\dagger}\\|^{2}.\\]\nUsing the law of total expectation, the second term may be bounded as follows\n\\begin{align*}\n \\E\\|\\Sigma_{\\ell-p+1}\\Omega_{2}\\Omega_1^{\\dagger}\\|^{2} &= \\E\\left(\\E_{\\Omega_{1}}\\left[\\|\\Sigma_{\\ell-p+1}\\Omega_{2}\\Omega_1^{\\dagger}\\|^{2}\\right] \\right) \\\\\n &\\overset{(a)}{\\leq}\\E\\left(\\|\\Sigma_{\\ell-p+1}\\|\\hspace{2pt}\\|\\Omega_{1}^{\\dagger}\\|_{F}+\\|\\Sigma_{\\ell-p+1}\\|_{F}\\hspace{2pt}\\|\\Omega_{1}^{\\dagger}\\| \\right)^{2} \\\\\n &\\overset{(b)}{\\leq} 2\\|\\Sigma_{\\ell-p+1}\\|^{2}\\E\\|\\Omega_{1}^{\\dagger}\\|^{2}_{F}+2\\|\\Sigma_{\\ell-p+1}\\|_{F}^{2}\\E\\|\\Omega_{1}^{\\dagger}\\|^{2}\\\\\n &\\overset{(c)}{\\leq} \\frac{2(\\ell-p)}{p-1}\\lambda_{\\ell-p+1}+\\frac{2\\textrm{e}^{2}\\ell}{p^{2}-1}\\left(\\sum_{j>\\ell-p}\\lambda_{j}\\right),\n\\end{align*}\n where in step $(a)$ we use Squared Chevet (\\cref{SquaredChevet}). In step $(b)$ we invoke the elementary identity $(a+b)^{2}\\leq 2a^{2}+2b^{2}$, and in step $(c)$ we apply the bounds from \\cref{GaussInvLemma}.\nInserting the above display into the bound for $\\E\\|A-\\hat{A}_{\\textrm{nys}}\\|$ yields\n\\[\\E\\|A-\\hat{A}_{\\textrm{nys}}\\| \\leq \\left(1+\\frac{2(\\ell-p)}{p-1}\\right)\\lambda_{\\ell-p+1}+\\frac{2\\textrm{e}^{2}\\ell}{p^{2}-1}\\left(\\sum_{j>\\ell-p}\\lambda_{j}\\right).\\]\nAs the bound above holds for any $2\\leq p\\leq \\ell-2$,\nwe may take the minimum over admissible $p$ to conclude the result.\n\\end{proof}\n\n\\subsubsection{Proof of \\cref{GenInvErrBnd}}\nWe require the following fact from \\cite[Chapter X]{bhatia2013matrix} ,\n\\begin{lemma}[\\cite{bhatia2013matrix} Lemma X.1.4.]\\label{fact-bhatia}\nLet $X,Y$ be psd matrices. Then\n\\[\\normiii{(X+I)^{-1}-(X+Y+I)^{-1}}\\leq \\normiii{Y(Y+I)^{-1}}\\]\nfor every unitarily invariant norm.\n\\end{lemma}\n\\label{section:GenInvErrBndPf}\n\\begin{proof}[Proof of \\cref{GenInvErrBnd}]\nWe first prove \\eqref{eq-InvInequality}.\nUnder the hypotheses of \\cref{GenInvErrBnd},\nwe may strengthen \\cref{fact-bhatia} by scaling the identity to deduce\n\\[\\|(\\hat{A}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\| \\leq \\frac{1}{\\mu}\\|(E+\\mu I)^{-1}E\\|.\\]\n\nRecall that the function $f(t) = \\frac{t}{t+\\mu}$ is matrix monotone,\nso that $A\\preceq B$ implies $f(A)\\preceq f(B)$. As $E\\preceq \\|E\\|I$, it follows that\n\\[\\|(\\hat{A}+\\mu I)^{-1}-(A+\\mu I)^{-1}\\| \\leq \\frac{1}{\\mu}\\frac{\\|E\\|}{\\|E\\|+\\mu}.\\]\nHence we have established the desired inequality.\n\nNext we show the bound is attained when $\\hat{A} = [A]_{\\ell}$.\nApplying the Woodbury identity, we may write\n\\[([A]_{\\ell}+\\mu I)^{-1} = V_{\\ell}(\\hat{\\Lambda}_{\\ell}+\\mu I)^{-1}V_{\\ell}^{T}+\\frac{1}{\\mu}(I-V_{\\ell}V_{\\ell}^{T}).\\]\nUsing the eigendecomposition of $A = V_{\\ell}\\Lambda_{\\ell}V_{\\ell}^{T}+V_{n-\\ell}\\Lambda_{n-\\ell}V_{n-\\ell}^{T}$,\nwe obtain\n\\begin{align*}\n([A]_{\\ell}+\\mu I)^{-1} - (A+\\mu I)^{-1} &= \\frac{1}{\\mu}(I-V_{\\ell}V_{\\ell}^{T})-V_{n-\\ell}(\\Lambda_{n-\\ell}+\\mu I)^{-1}V_{n-\\ell}^{T}\\\\\n &= \\frac{1}{\\mu}V_{n-\\ell}(I-(\\Lambda_{n-\\ell}+\\mu I)^{-1})V_{n-\\ell}^{T} \\\\ &=\\frac{1}{\\mu}V_{n-\\ell}\\left(\\Lambda_{n-\\ell}(\\Lambda_{n-\\ell}+\\mu I)^{-1}\\right)V_{n-\\ell}^{T}.\n\\end{align*}\nHence\n\\[\\|(A+\\mu I)^{-1}-([A]_{\\ell}+\\mu I)^{-1}\\| = \\frac{\\lambda_{\\ell+1}}{\\mu(\\lambda_{\\ell+1}+\\mu)}.\\]\n\\end{proof}\n\\subsubsection{Proof of statements for the optimal low-rank preconditioner $P_{\\star}$}\n\\label{section:PrecondPfs}\nWe show that $P_{\\star}$ is the best symmetric positive definite preconditioner\nthat is constant off $V_{\\ell}$.\n\\begin{lemma}\nLet $\\mathcal{P} = \\{P: P = V_{\\ell}MV_{\\ell}^{T}+\\beta(I-V_{\\ell}V_{\\ell}^{T})$\\ \\textrm{where}\\ $\\beta>0$\\ \\textrm{and}\\ $M\\in \\mathbb{S}^{+}_{\\ell}(\\R)\\}$.\nWith this parametrization, define $P_\\star$ by setting $M= \\frac{1}{\\lambda_{\\ell+1}+\\mu}(\\Lambda_\\ell+\\mu I)$ and $\\beta = 1$.\nThen for any symmetric psd matrix $A$ and $\\mu \\geq 0$,\n\\begin{eqnarray}\n \\min_{P\\in\\mathcal{P}} \\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) = \\frac{\\lambda_{\\ell+1}+\\mu}{\\lambda_{n}+\\mu}, \\label{eqn-optimal-prec-value} \\\\\n P_\\star = \\argmin_{P\\in\\mathcal{P}} \\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}).\n\\end{eqnarray}\n\\end{lemma}\n\\begin{proof}\nWe first prove the lefthand side of \\eqref{eqn-optimal-prec-value} is always at least as large as the righthand side,\nand then show the bound is attained by $P_{\\star}$.\nGiven $P \\in \\mathcal{P}$, we have\n\\[\nP^{-1\/2}A_{\\mu}P^{-1\/2} = V_{\\ell}M^{-1\/2}(\\Lambda_{\\ell}+\\mu I)M^{-1\/2}V_{\\ell}^{T}+\\frac{1}{\\beta}V_{n-\\ell}(\\Lambda_{n-\\ell}+\\mu I)V_{n-\\ell}^{T}.\n\\]\nFor any $1\\leq i,j\\leq n$,\n\\[\n\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2}) = \\frac{\\lambda_{1}(P^{-1\/2}A_{\\mu}P^{-1\/2})}{\\lambda_{n}(P^{-1\/2}A_{\\mu}P^{-1\/2})}\\geq \\frac{\\lambda_i(P^{-1\/2}A_{\\mu}P^{-1\/2})}{\\lambda_j(P^{-1\/2}A_{\\mu}P^{-1\/2})}.\n\\]\nFrom our expression for $P^{-1\/2}A_{\\mu}P^{-1\/2}$,\nwe see that $(\\lambda_{\\ell+1}+\\mu)\/\\gamma,(\\lambda_n+\\mu)\/\\gamma$ are eigenvalues of $P^{-1\/2}A_{\\mu}P^{-1\/2}$.\nHence for any $P\\in \\mathcal{P}$, the following inequality holds:\n\\[\n\\kappa_{2}(P^{-1\/2}A_{\\mu}P^{-1\/2})\\geq \\frac{\\lambda_{\\ell+1}+\\mu}{\\lambda_n+\\mu},\n\\]\nproving \\eqref{eqn-optimal-prec-value}.\nUsing the definition of $P_\\star$, we see\n\\begin{align*}\nP_{\\star}^{-1\/2}A_{\\mu}P^{-1\/2} &= (\\lambda_{\\ell+1}+\\mu)V_{\\ell}V_{\\ell}^{T}+V_{n-\\ell}(\\Lambda_{n-\\ell}+\\mu I)V_{n-\\ell}^{T}, \\\\\n\\kappa_2(P^{-1\/2}_{\\star}A_{\\mu}P^{-1\/2}_{\\star}) &= (\\lambda_{\\ell+1}+\\mu)\/(\\lambda_{n}+\\mu).\n\\end{align*}\n\\end{proof}\n\\iftutorial\n\\subsection{Proof of Squared Chevet}\n\\label{section:SquaredChevetPf}\nIn this subsection we provide a proof of \\cref{SquaredChevet}. The proof is based on a Gaussian comparison inequality argument, a standard technique in the high dimensional probability literature.\n\\begin{proof}\nLet \\[U = \\{S^{T}a: \\|a\\|_{2} = 1\\}\\subset \\R^{m}\\]\n\\[V = \\{Tb: \\|b\\|_{2} = 1\\}\\subset \\R^{n}\\]\nand for $u\\in U$, $v\\in V$ consider the Gaussian processes\n\\begin{equation*}\n Y_{uv} = \\langle u,Gv\\rangle +\\|S\\|\\hspace{2pt}\\|v\\|\\gamma\n\\qquad \\textup{and} \\qquad\n X_{uv} = \\|S\\|\\langle h,v \\rangle +\\|v\\|\\langle g,u\\rangle,\n\\end{equation*}\nwhere\n\\begin{itemize}\n \\item $G\\in \\R^{m\\times n}$ is a Gaussian random matrix,\n \\item $g,h$ are Gaussian random vectors in $\\R^m$ and $\\R^n$ respectively,\n \\item and $\\gamma$ is $N(0,1)$ in $\\R$.\n\\end{itemize}\nFurthermore, $G,g,h$ and $\\gamma$ are all independent.\n\nA standard calculation shows that the conditions of Slepian's lemma (\\cite[Corollary 3.12, p.~72]{ledoux2013probability}) are satisfied. Hence we conclude that\n\\begin{equation}\n\\label{eq-SlepIneq}\n \\P\\left(\\max_{u,v}Y_{uv}>t\\right)\\leq \\P\\left(\\max_{u,v}X_{uv}>t\\right).\n\\end{equation}\nWe are now ready to prove \\cref{SquaredChevet}.\nThroughout the argument below, we use the notation $X_{+} = \\max\\{X,0\\}$.\n\nWe first observe by Jensen's inequality with respect to $\\gamma$ and the variational characterization of the singular values that\n\\begin{align*}\n \\E\\max_{u,v} (Y_{uv})^{2}_{+}\n &= \\E\\max_{\\|a\\| = 1, \\|b\\| = 1} \\left( \\langle S^{T}a,GTb\\rangle+\\|S\\| \\|Tb\\|\\gamma\\right)^{2}_{+} \\\\\n &\\geq \\E_{G}\\max_{\\|a\\| = 1, \\|b\\| = 1}\\left( \\langle S^{T}a,GTb\\rangle^{2}\\right)_{+} = \\E_{G}\\|SGT\\|^{2}.\n\\end{align*}\nHence $\\E_{G}\\|SGT\\|^{2}$ is majorized by $\\E\\max_{u,v}\\hspace{2pt} (Y_{uv})^{2}_{+}.$\nFor $X_{uv}$, we note that\n\\begin{align*}\n \\E\\max_{u,v} (X_{uv})_{+}^{2}\n &\\leq\\E\\max_{u,v}X_{uv}^{2} = \\E\\max_{\\|a\\|=1,\\|b\\| = 1}\\left(\\|S\\|\\langle h,Tb \\rangle +\\|Tb\\|\\langle g,S^{T}a\\rangle\\right)^{2} \\\\\n &\\overset{(a)}{\\leq }\\E\\left(\\|S\\|^{2}\\|T^{T}h\\|^{2}+2\\|S\\|\\|T\\|\\|T^{T}h\\|\\|Sg\\|+\\|T\\|^{2}\\|Sg\\|^{2}\\right)\\\\\n &\\overset{(b)}{\\leq} \\|S\\|^{2}\\|T\\|^{2}_{F}+2\\|S\\|\\|T\\|\\|S\\|_{F}\\|T\\|_{F}+\\|T\\|^{2}\\|S\\|_{F}^{2} \\\\\n &= (\\|S\\|\\|T\\|_{F}+\\|T\\|\\|S\\|_{F})^{2},\n \\end{align*}\nwhere in step $(a)$ we expand the quadratic and use Cauchy-Schwarz. Step $(b)$ from a straightforward calculation and H{\\\"o}lder's inequality.\n\nTo conclude, we use integration by parts and \\eqref{eq-SlepIneq} to obtain\n\\begin{align*}\n\\E_{G}\\|SGT\\|^{2}\n&\\leq \\E\\max_{u,v}\\hspace{2pt} (Y_{uv})^{2}_{+} = \\int^{\\infty}_{0}t\\P\\left(\\max_{u,v}(Y_{uv})_{+}>t\\right)dt\\\\\n&= \\int^{\\infty}_{0}t\\P\\left(\\max_{u,v}Y_{uv}>t\\right)dt \\leq \\int^{\\infty}_{0}t\\P\\left(\\max_{u,v}X_{uv}>t\\right)dt \\\\\n&= \\int^{\\infty}_{0}t\\P\\left(\\max_{u,v}(X_{uv})_{+}>t\\right)dt = \\E\\max_{u,v} (X_{uv})^{2}_{+} \\\\ &\\leq (\\|S\\|\\|T\\|_{F}+\\|T\\|\\|S\\|_{F})^{2}\n\\end{align*}\ncompleting the proof.\n\\end{proof}\n\\else\n\n\\fi\n\n\\section{Additional experimental details}\n\\label{section:Experimentaldetails}\nHere we provide additional details on the experimental procedure and the methods we compared to.\n\\subsection{Ridge regression experiments}\n\\label{section:RidgeRegressionDetails}\n Most of the datasets used in our ridge regression experiments are classification datasets.\n We converted them to regression problems by using a one-hot vector encoding.\n The target vector $b$ was constructed by setting $b_i=1$ if example $i$ has the first label and 0 otherwise.\n We did no data pre-processing except on CIFAR-10,\n where we scaled the matrix by $255$ so that all entries lie in $[0,1]$.\n \nWe now give an overview of the hyperparameters of each method.\nThe R\\&T preconditioner has only one hyperparameter: the sketch size $\\ell_{\\textrm{RT}}$.\nAdaIHS has five hyperparameters: $\\rho,\\lambda_{\\rho},\\Lambda_{\\rho}, \\mu_{\\textrm{gd}}(\\rho)$, and $c_{\\textrm{gd}}(\\rho)$. The hyperparameter $\\rho\\in (0,1)$ controls the remaining four hyperparameters, which are set to the values recommended in \\cite{lacotte2020effective}.\nFor the regularization path experiments, $\\ell_{\\textrm{RT}}$ and $\\rho$ were chosen by grid search to minimize the time taken to solve the linear systems over the regularization path. We chose $m_{\\textrm{RT}}$ from the linear grid $jd$, where $j\\in\\{1,\\dots,8\\}$. Additionally, we restrict $j\\leq 4$ for Guillermo as $jd\\geq n$ when $j\\geq 5$, and hence no benefit is gained over a direct method. For AdaIHS, $\\rho$ was chosen from the linear grid $\\rho = j\\times 10^{-1}$ where $j \\in\\{1,\\dots,9\\}$. We set the initial sketch size for AdaIHS to $100$ for both sets of experiments.\n\nWe reused computation as much as possible for both R\\&T and AdaIHS, which we now detail. To construct the R\\&T preconditioner, we incur a $O(nd\\log(n)+\\ell_{\\textrm{RT}}d^{2})$ to cache the Gram matrix and pay an $O(d^{3})$ to update the preconditioner for each value of $\\mu$. In the case of AdaIHS, for each value of $\\mu$ we cache the sketch $SA$ and the corresponding Gram matrix. We then use them for the next value of $\\mu$ on the path until the adapativity criterion of the algorithm deems a new sketch necessary. For AdaIHS computing the sketch only costs $O(nd\\log(n)).$\n\nWe now give the details of the random features experiments. For Shuttle-rf we used random features corresponding to a Gaussian kernel with bandwidth parameter $\\sigma = 0.75$, we set $\\mu = 10^{-8}\/n$. For smallNORB-rf we used ReLU random features with $\\mu = 6\\times 10^{-4}$. For Higgs we normalized the features by their z-score and we used random features for a Gaussian Kernel with $\\sigma = 5$ and regularization $\\mu = 10^{-4}$. Similarly for YearMSD, we normalized the matrix by their z-score and used random features for a Gaussian kernel with $\\sigma = 8$ and $\\mu = 10^{-5}$. The sketch size for R\\&T was selected from $\\{d, 2d\\}$, to prevent the cost of the forming and applying preconditioner from becoming prohibitive. We selected the AdaIHS parameter $\\rho$ from the same grid used for the regularization path experiments. We also capped the sketch size for AdaIHS for each dataset by the sketch sized used for R\\&T. \n\nFinally, we give the details of our implementation of Nystr{\\\"o}m PCG. For both sets of experiments we used \\cref{alg:AdaRandNysAppx} initialized at $\\ell = 100$, with an error tolerance of $30\\mu$, and $q = 5$ power iterations. To avoid trivialities, the rank of the preconditioner is capped at $\\ell_{\\textrm{max}} = 0.5d$ for CIFAR-10 and $\\ell_{\\textrm{max}} = 0.4d$ for Guillermo. For the random features experiments we capped $\\ell$ at $\\ell_{\\textrm{max}} = 2000$. In the regularization path experiments, we keep track of the latest estimate $\\hat{E}$ of $\\|E\\|$, and do not compute a new Nystr{\\\"o}m approximation unless $\\hat{E}$ is larger than the error tolerance for the new regularization parameter. When we compute the new Nystr{\\\"o}m approximation, the adaptive algorithm is initialized with a target rank of twice the old one.\n\nThe values of hyperparameters used for all experiments are summarized in \\cref{t-parameters}.\n\\begin{table}[t]\n\\footnotesize\n\\begin{center}\n \\begin{tabular}{|c|c|c|c|c|}\n \\hline\n \\thead{Dataset} & \\thead{(R\\&T) sketch \\\\ size} & \\thead{AdaIHS rate} & \\thead{Initial AdaIHS \\\\sketch size} & \\thead{Initial \\\\ Nystr{\\\"o}m \\\\ sketch size} \\\\\n \\hline\n CIFAR-10 & $3d$ & $\\rho$ = 0.3 & $100$ & $100$\\\\\n \\hline\n Guillermo & $d$ & $\\rho$ = 0.3 & $100$ & $100$ \\\\\n \\hline\n shuttle-rf & $2d$ & $\\rho$ = 0.1 & $100$ & $100$ \\\\\n \\hline\n smallNORB-rf & $2d$ & $\\rho$ = 0.3 & $100$ & $100$ \\\\\n \\hline\n \\end{tabular}\n \\caption{\\label{t-parameters} Ridge regression experimental parameters.}\n\\end{center}\n\\end{table}\n\n\n\\subsection{ALOOCV}\nThe datasets were chosen so that $n$ and $d$ are both large, the challenging regime for ALOOCV. The first three datasets are binary classification problems, while SVHN has multiple classes. For SVHN we created a binary classification problem by looking at the first class vs. remaining classes.\n\nFor the large scale problems the adaptive algorithm for Nystr{\\\"o}m PCG was initialized at $\\ell_{0} = 500$ and is capped at $\\ell_{\\textrm{max}} = 4000$. We set the solve tolerances for both algorithms to $10^{-10}$. As before, we sample 100 points randomly from each dataset.\n\n\\subsection{Kernel Ridge Regression}\n\nWe converted the binary classification problem\nto a regression problem by constructing the target vector as follows:\nWe assign +1 to the first class and -1 to the second class.\nFor multi-class problems, we do one-vs-all classification; this formulation leads to multiple right hand sides, so we use block PCG for both methods. \nWe did no data pre-processing except for EMNIST, MiniBooNE, MNIST, and Santander. \nFor EMNIST and MNIST the data matrix was scaled by $255$ so that its entries lie in $[0,1]$, while for MinBooNE and Santander the features were normalized by their z-score.\nThe number of random features, $m_{\\textrm{rf}}$ from the linear grid $m_{\\textrm{rf}} = j\\times 10^{3}$ for $j = 1,\\dots,9$.\nFor adaptive Nystr{\\\"o}m PCG we capped the maximum rank for the preconditioner at $\\ell_{\\max} = \\lfloor0.1n\\rfloor$ and used a tolerance of $40$ for the ratio $\\hat{\\lambda}_{\\ell}\/{n\\mu}$ on all datasets.\n\n\\section{Additional numerical results}\n\\label{section:AddNumerics}\nHere we include some additional numerical results not appearing in the main paper.\n\\subsection{ALOOCV}\n\\cref{t-rcv1-realsim-results-part-ii} contains more details about the preconditioner and preconditioned system for the large scale ALOOCV experiments in \\cref{section:ALOOCV}. The original condition number in \\cref{t-rcv1-realsim-results-part-ii} below is estimated as follows. First we compute the top eigenvalue of the Hessian using Matlab's eigs() command, then we divide this by $\\mu$.\n\\begin{table}[H]\n\\footnotesize\n\\begin{center}\n \\begin{tabular}{|c|c|c|c|c|}\n \\hline\n \\textbf{Dataset} & \\thead{Nystr{\\\"o}m \\\\ rank} & \\thead{Preconditioner\\\\ construction \\\\ time(s)} & \\thead{Condition \\\\ number\\\\ estimate} & \\thead{Preconditioned\\\\ condition \\\\ number\\\\ estimate} \\\\\n \\hline\n rcv1 $(\\mu = \\num{1e-4})$ & $1000$ & $19.5\\hspace{2pt}(0.523)$ & $21.6$ & $2.98\\hspace{2pt} (0.081)$\\\\\n \\hline\n rcv1 $(\\mu = \\num{1e-8})$ & $4000$ & $100.6\\hspace{2pt}(3.46)$ & $5.70\\mathrm{e}{+3}$ & $17.2\\hspace{2pt} (0.218)$ \\\\\n \\hline\n realsim $(\\mu = \\num{1e-4})$ & $3100\\hspace{2pt}(1.41\\mathrm{e}{+3})$ & $82.01 (2.04)$ & $10.0$ & $1.70 \\hspace{2pt}(0.2324)$\\\\\n \\hline\n realsim $(\\mu = \\num{1e-8})$ & $4000$ & $108.3\\hspace{2pt}(6.21)$ & $2.13\\mathrm{e}{+4}$ & $62.4\\hspace{2pt}(0.945)$ \\\\\n \\hline\n \\end{tabular}\n \\caption{\\label{t-rcv1-realsim-results-part-ii} For $\\mu = 10^{-4}$ the Hessian is well-conditioned for both datasets, so there is little value to preconditioning. For $\\mu = 10^{-8}$, the ill-conditioning of the Hessian increases significantly, making preconditioning more valuable. Furthermore, as ALOOCV uses Block PCG on at least several batches of data points, the cost of constructing the preconditioner is negligible compared to the cost of solving the linear systems (see \\cref{t-rcv1-realsim-results-part-i} in \\cref{section:ALOOCV}). }\n\\end{center}\n\\end{table}\n\n\\section{Adapative rank selection via a-posteriori error estimation}\nBelow we give the pseudocode for the algorithms used to perform adaptive rank selection using the strategy proposed in \\cref{section:ErrorRankDoubling}.\n\\label{section:AdaRankSelection}\n\\subsection{Randomized Powering algorithm}\nThe pseudo-code for estimating $\\|E\\|$ by the randomized power method is given in \\cref{alg:RandPowErrEst}\n\\begin{algorithm}[t]\n\t\\caption{Randomized Power method for estimating $\\|E\\|$}\n\t\\label{alg:RandPowErrEst}\n\t\\begin{algorithmic}[1]\n\t\t\\Require{symmetric PSD matrix $A\\in \\R^{n\\times n}$, approximate eigenvectors $U$, approximate eigenvalues $\\hat{\\Lambda}$, and number of power iterations $q$.}\n\t\t\\State $g = \\textrm{randn}(n,1)$\n\t\t\\State $v_0 = \\frac{g}{\\|g\\|_{2}}$\n\t\t \\For{$i = 1,\\dots,q$}\n\t\t \\State $v = Av_0-U(\\hat{\\Lambda}(U^{T}v_{0}))$\n\t\t \\State $\\hat{E} = v_{0}^{T}v$\n\t\t \\State $v = \\frac{v}{\\|v\\|_{2}}$\n\t\t \\State $v_{0}\\leftarrow v$\n\t\t \\EndFor\n\t\t\\Ensure{estimate $\\hat{E}$ of $\\|E\\|$}\n\t\\end{algorithmic}\n\\end{algorithm}\n\n\\subsection{Adaptive rank selection algorithm}\nThe pseudocode for adaptive rank selection by a-priori error estimation is given in \\cref{alg:AdaRandNysAppx}. The code is structured to reuse use the previously computed $\\Omega$ and $Y$, resulting in significant computational savings. The error $\\|E\\|$ is estimated from $q$ iterations of the randomized power method on the error matrix $A-U\\hat{\\Lambda}U^{T}$.\n\n\\begin{algorithm}[t]\n\t\\caption{Adaptive Randomized Nystr{\\\"o}m Approximation}\n\t\\label{alg:AdaRandNysAppx}\n\t\\begin{algorithmic}[1]\n\t\t\\Require{symmetric psd matrix $A$, initial rank $\\ell_0$, maximum rank $\\ell_{\\textrm{max}}$, number of power iterations for estimating $E$, error tolerance $\\textrm{Tol}$ }\n\t\t\\State $Y = [\\hspace{5pt}], \\Omega = [\\hspace{5pt}],$ and $E = \\textrm{Inf}$\n\t\t\\State $m = \\ell_{0}$\n\t\t \\While {$E>\\textrm{Tol}$}\n\t\t \\State Generate Gaussian test matrix $\\Omega_{0}\\in \\mathbb{R}^{n\\times m}$\n\t\t \\State $[\\Omega_{0},\\sim] = \\textrm{qr}(\\Omega_{0},0)$\n\t\t \\State $Y_{0} = A\\Omega_{0}$\n\t\t \\State $\\Omega = [\\Omega\\hspace{5pt}\\Omega_{0}]$ and $Y = [Y\\hspace{5pt}Y_{0}]$\n\t\t \\State $\\nu = \\sqrt{n}\\hspace{2pt}\\textrm{eps}(\\textrm{norm}(Y,2))$\n\t\t \\State $Y_{\\nu} = Y+\\nu\\Omega,\\hspace{3pt}$\n\t\t \\State $C = \\textrm{chol}(\\Omega^{T}Y_{\\nu})$\n\t\t \\State $B = Y_{\\nu}\/C$\n\t\t \\State Compute $[U,\\Sigma,\\sim] = \\textrm{svd}(B,0)$\n\t\t \\State $\\hat{\\Lambda} = \\max\\{0,\\Sigma^{2}-\\nu I\\}$ \\Comment{remove shift}\n\t\t \\State $E = \\textrm{RandomizedPowerErrEst}(A,U,\\hat{\\Lambda},q)$\n \\Comment{estimate error}\n\t\t \\State $m\\leftarrow \\ell_{0}$, $\\ell_{0} \\leftarrow 2\\ell_{0}$\n \\Comment{double rank if tolerance is not met}\n\t\t \\If{$\\ell_{0}>\\ell_{\\textrm{max}}$}\n\t\t \\State $\\ell_{0} = \\ell_{0}-m$ \\Comment{when $\\ell_{0}>\\ell_{\\textrm{max}}$, reset to $\\ell_{0} = \\ell_{\\textrm{max}}$}\n\t\t \\State $m = \\ell_{\\textrm{max}}-\\ell_{0}$\n\t\t \\State Generate Gaussian test matrix $\\Omega_{0}\\in \\mathbb{R}^{n\\times m}$\n\t\t \\State $[\\Omega_{0},\\sim] = \\textrm{qr}(\\Omega_{0},0)$\n\t\t \\State $Y_{0} = A\\Omega_{0}$\n\t\t \\State $\\Omega = [\\Omega\\hspace{5pt}\\Omega_{0}]$ and $Y = [Y\\hspace{5pt}Y_{0}]$\n\t\t \\State $\\nu = \\sqrt{n}\\hspace{2pt}\\textrm{eps}(\\textrm{norm}(Y,2))$ \\Comment{compute final approximation and break}\n\t\t \\State $Y_{\\nu} = Y+\\nu\\Omega,\\hspace{3pt}$\n\t\t \\State $C = \\textrm{chol}(\\Omega^{T}Y_{\\nu})$\n\t\t \\State $B = Y_{\\nu}\/C$\n\t\t \\State Compute $[U,\\Sigma,\\sim] = \\textrm{svd}(B,0)$\n\t\t \\State $\\hat{\\Lambda} = \\max\\{0,\\Sigma^{2}-\\nu I\\}$\n\t\t \\State \\textbf{break}\n\t\t \\EndIf\n\t\t \\EndWhile\n\t\t\\Ensure{Nystr{\\\"o}m approximation $(U,\\hat{\\Lambda})$}\n\t\\end{algorithmic}\n\\end{algorithm}\n\n\n\\section{Motivation}\n\nIn their elegant 1997 textbook on numerical linear algebra~\\cite{trefethen1997numerical},\nTrefethen and Bau write,\n\n\\begin{quotation}\n``In ending this book with the subject of preconditioners, we find ourselves at\nthe philosophical center of the scientific computing of the future...\nNothing will be more central to computational science in the next century\nthan the art of transforming a problem that appears intractable into another\nwhose solution can be approximated rapidly. For Krylov subspace matrix iterations,\nthis is preconditioning...\nwe can only guess where this idea will take us.''\n\\end{quotation}\n\nThe next century has since arrived, and one of the most fruitful developments\nin matrix computations has been the emergence of new algorithms that use randomness\nin an essential way. This paper explores a topic at the nexus of preconditioning\nand randomized numerical linear algebra. We will show how to use a\nrandomized matrix approximation algorithm to construct a preconditioner\nfor an important class of linear systems that arises throughout\ndata analysis and scientific computing.\n\n\\subsection{The Preconditioner}\n\nConsider the regularized linear system\n\\begin{equation} \\label{eqn:reg-linsys-intro}\n(A + \\mu I) x = b\n\\quad\\text{where $A \\in \\R^{n \\times n}$ is symmetric psd and $\\mu \\geq 0$.}\n\\end{equation}\nHere and elsewhere, psd abbreviates the term ``positive semidefinite.''\nThis type of linear system emerges whenever we solve a regularized\nleast-squares problem.\nWe will design a class of preconditioners for the problem~\\cref{eqn:reg-linsys-intro}.\n\nThroughout this paper, we assume that we can access the matrix\n$A$ through matrix--vector products $x \\mapsto Ax$, commonly\nknown as \\textit{matvecs}. The algorithms that we develop\nwill economize on the number of matvecs, and they may not be\nappropriate in settings where matvecs are very expensive or\nthere are cheaper ways to interact with the matrix.\n\n\nFor a rank parameter $\\ell \\in \\mathbb{N}$, the randomized Nystr{\\\"o}m approximation of $A$ takes the form\n\\begin{equation} \\label{eqn:randnys-intro}\n\\hat{A}_{\\textrm{nys}} = (A\\Omega)(\\Omega^{T}A\\Omega)^{\\dagger}(A\\Omega)^{T}\n\\quad\\text{where $\\Omega \\in \\R^{n \\times \\ell}$ is standard normal.}\n\\end{equation}\nThis matrix provides the best psd approximation of $A$ whose range coincides with the range of the sketch $A \\Omega$. The randomness in the construction ensures that $\\hat{A}_{\\textrm{nys}}$ is a good approximation to the original matrix $A$ with high probability~\\cite[Sec.~14]{MartTroppSurvey}.\n\nWe can form the Nystr{\\\"o}m approximation with sketch size $\\ell$, using $\\ell$ matvecs with $A$,\nplus some extra arithmetic. See \\cref{alg:RandNysAppx} for the implementation details. \n\nGiven the eigenvalue decomposition $\\hat{A}_{\\textrm{nys}} = U \\hat{\\Lambda} U^T$\nof the randomized Nystr{\\\"o}m approximation, we construct the Nystr{\\\"o}m preconditioner:\n\\begin{equation} \\label{eqn:precond-intro}\nP = \\frac{1}{\\hat{\\lambda}_{\\ell}+\\mu}U(\\hat{\\Lambda}+\\mu I)U^{T}+(I-UU^T).\n\\end{equation}\nIn a slight abuse of terminology, we refer to $\\ell$ as the rank of the Nystr{\\\"o}m preconditioner.\nThe key point is that we can solve the linear system $Py = c$ very efficiently,\nand the action of $P^{-1}$ dramatically reduces the condition number of the\nregularized matrix $A_{\\mu} = A + \\mu I$.\n\nWe propose to use~\\cref{eqn:precond-intro} in conjunction with the\npreconditioned conjugate gradient (PCG) algorithm. Each iteration of PCG\ninvolves a single matvec with $A$, and a single linear solve with $P$.\nWhen the preconditioned matrix $P^{-1} A_{\\mu}$ has a modest condition\nnumber, the algorithm converges to a solution of~\\cref{eqn:reg-linsys-intro}\nvery quickly. See~\\cref{alg:NysPCG} for pseudocode for Nystr{\\\"o}m PCG.\n\nThe randomized Nystr{\\\"o}m preconditioner~\\cref{eqn:precond-intro} was suggested by P.-G.~Martinsson in the survey~\\cite[Sec.~17]{MartTroppSurvey}, but it has not been implemented or analyzed.\n\n\\subsection{Guarantees}\n\n This paper contains the first comprehensive study of the preconditioner~\\cref{eqn:precond-intro}, including theoretical analysis and testing on prototypical problems from data analysis and machine learning. One of the main contributions is a rigorous method for choosing the rank $\\ell$ to guarantee good performance, along with an adaptive rank selection procedure that performs well in practice.\n\nA key quantity in our analysis is the \\textit{effective dimension} of the regularized matrix $A+\\mu I$. That is, \n\\begin{equation}\n\\label{EffDimDef}\n d_{\\textrm{eff}}(\\mu) = \\textrm{tr}\\left(A(A+\\mu I)^{-1}\\right) = \\sum_{j=1}^{n}\\frac{\\lambda_j(A)}{\\lambda_j(A)+\\mu}.\\\n\\end{equation}\nThe effective dimension measures the degrees of freedom of the problem after regularization. \nIt may be viewed as a (smoothed) count of the eigenvalues larger than $\\mu$.\nMany real-world matrices exhibit strong spectral decay, so the effective dimension is typically much smaller than the nominal dimension $n$.\nAs we will discuss, the effective dimension also plays a role in a number of machine learning papers~\\cite{el2014fast,avron2017faster,bach2013sharp,chowdhury2018randomized,lacotte2020effective} that consider randomized algorithms for solving regularized linear systems.\n\nOur theory tells us the randomized Nystr{\\\"o}m preconditioner $P$\nis successful when its rank $\\ell$ is proportional to the effective dimension.\n\n\\begin{theorem}[Randomized Nystr{\\\"o}m Preconditioner] \n\\label{MainThm}\nLet $A\\in \\mathbb{S}_{n}^+(\\mathbb{R})$ be a psd matrix, and write $A_\\mu = A+\\mu I$ where the regularization parameter $\\mu > 0$. Define the effective dimension $d_{\\textup{eff}}(\\mu)$ as in~\\cref{EffDimDef}. Construct the randomized preconditioner $P$ from~\\cref{eqn:randnys-intro,eqn:precond-intro} with rank parameter $\\ell = 2 \\,\\lceil 1.5 \\,d_{\\textup{eff}}(\\mu)\\rceil+1$. Then the condition number of the preconditioned system satisfies\n\\begin{equation} \\label{eqn:expect-cond-intro}\n\\E\\big[ \\kappa_{2}(P^{-1\/2}A_\\mu P^{-1\/2}) \\big] < 28.\n\\end{equation}\n\\end{theorem}\n\\noindent\n\\Cref{MainThm} is a restatement of \\cref{NysPCGEffDimThm}.\n\nSimple probability bounds follow from~\\cref{eqn:expect-cond-intro} via Markov's inequality. For example,\n\\[\n\\P\\big\\{ \\kappa_{2}(P^{-1\/2}A_\\mu P^{-1\/2}) \\leq 56 \\big\\} > 1\/2.\n\\]\nThe main consequence of \\cref{MainThm} is a convergence theorem for PCG with the randomized Nystr{\\\"o}m preconditioner.\n\n\\begin{corollary}[Nystr{\\\"o}m PCG: Convergence]\nConstruct the preconditioner $P$ as in \\cref{MainThm}, and condition on the event \n$\\{ \\kappa_2(P^{-1\/2}A_\\mu P^{-1\/2}) \\leq 56 \\}$.\nSolve the regularized linear system~\\cref{eqn:reg-linsys-intro} using Nystr{\\\"o}m PCG, starting with an initial iterate $x_0 = 0$. After $t$ iterations, the relative error $\\delta_t$ satisfies\n\\[\n\\delta_t \\coloneqq \\frac{\\|x_{t}-x_{\\star}\\|_{\\rm PCG}}{\\|x_{\\star}\\|_{\\rm PCG}}< 2 \\cdot \\left(0.77 \\right)^{t}\n\\quad\\text{where $A_{\\mu} x_{\\star} = b$.}\n\\]\nThe error norm is defined as $\\| u \\|_{\\rm PCG}^2 = u^T (P^{-1\/2} A_{\\mu} P^{-1\/2} ) u$.\nIn particular, $t\\geq \\lceil 3.9 \\log(2\/\\epsilon) \\rceil$ iterations\nsuffice to achieve relative error $\\epsilon$.\n\\end{corollary}\n\nAlthough \\cref{MainThm} gives an interpretable bound for the rank $\\ell$ of the preconditioner,\nwe cannot instantiate it without knowledge of the effective dimension. To address this shortcoming,\nwe have designed adaptive methods for selecting the rank in practice (\\cref{sec:adaptive-rank}).\n\nFinally, as part of our investigation, we will also develop a detailed understanding\nof Nystr{\\\"o}m sketch-and-solve, a popular algorithm in\nthe machine learning literature \\cite{el2014fast,bach2013sharp}.\nOur analysis highlights the deficiencies of Nystr{\\\"o}m sketch-and-solve relative to Nystr{\\\"o}m PCG.\n\n\\subsection{Example: Ridge Regression}\n\\label{IntroRidgeEx}\n\nAs a concrete example, we consider the $\\ell^2$ regularized least-squares problem, also known as ridge regression.\nThis problem takes the form\n\\begin{equation}\\label{eq:ridge-intro}\n\\mathrm{minimize}_{x\\in \\mathbb{R}^{d}} \\quad \\frac{1}{2n}\\|Gx-b\\|^{2}+\\frac{\\mu}{2}\\|x\\|^{2},\n\\end{equation}\nwhere $G\\in \\R^{n\\times d}$ and $b\\in \\R^{n}$ and $\\mu>0$.\nBy calculus, the solution to \\cref{eq:ridge-intro} also satisfies the regularized system of linear equations\n\\begin{equation} \n \\label{eq-RidgeRegression}\n \\left(\\frac{1}{n}G^{T}G+\\mu I\\right)x = \\frac{1}{n}G^{T}b. \n\\end{equation}\nA direct method to solve \\cref{eq-RidgeRegression} requires $O(nd^{2})$ flops,\nwhich is prohibitive when $n$ and $d$ are both large. \nInstead, when $n$ and $d$ are large, iterative algorithms, such as the conjugate gradient method (CG), become the tools of choice.\nUnfortunately, the ridge regression linear system~\\cref{eq-RidgeRegression} is often very ill-conditioned, and CG converges very slowly. \n\nNystr{\\\"o}m PCG can dramatically accelerate the solution of \\cref{eq-RidgeRegression}. \nAs an example, consider the {shuttle-rf} dataset (\\cref{section:RidgeRegression}). The matrix $G$ has dimension $43,300 \\times 10,000$, while the preconditioner is based on a Nystr{\\\"o}m approximation with rank $\\ell = 800$.\n\\Cref{fig:shuttlerfDemo} shows the progress of the residual as a function of the iteration count. Nystr{\\\"o}m PCG converges to machine precision in 13 iterations, while CG stalls.\n\n\\begin{figure}[t]\n \\centering\n \\includegraphics[width=0.65\\textwidth]{lstsquaresfigs\/shuttle_rf_demo.pdf}\n \\caption{\\label{fig:shuttlerfDemo}\n \\textbf{Ridge regression: CG versus Nystr{\\\"o}m PCG.}\n For the {shuttle-rf} data set, Nystr{\\\"o}m PCG converges to machine precision in 13 iterations while CG stalls. See~\\cref{IntroRidgeEx,section:RidgeRegression}.}\n\\end{figure}\n\n\\subsection{Comparison to prior randomized preconditioners}\nPrior proposals for randomized preconditioners \\cite{avron2010blendenpik, meng2014lsrn, rokhlin2008fast}\naccelerate the solution of highly overdetermined or underdetermined least-squares problems using the sketch-and-precondition paradigm \\cite[Sec.~10]{MartTroppSurvey}.\nFor $n\\geq d$, these methods require $\\Omega(d^{3})$ \ncomputation to factor the preconditioner.\n\nIn contrast, the randomized Nystr{\\\"o}m preconditioner \napplies to any symmetric positive-definite linear system\nand can be significantly faster for regularized problems. \nSee \\cref{sec:preconditioner-comparison} more details.\n\n\\subsection{Roadmap}\n\\Cref{section:NystromApproximation} contains an overview of the Nystr{\\\"o}m approximation and its key properties. \\Cref{section:AppxRegInverse} studies the role of the Nystr{\\\"o}m approximation in estimating the inverse of the regularized matrix. We analyze the Nystr{\\\"o}m sketch-and-solve method in \\Cref{Section:NystromSketchSolve}, and we give a rigorous performance bound for this algorithm. \\Cref{section:NystromPCG} presents a full treatment of Nystr{\\\"o}m PCG, including theoretical results and guidance on numerical implementation. Computational experiments in \\Cref{section:NumericalExperiments} demonstrate the power of Nystr{\\\"o}m PCG for three different applications involving real data sets.\n\n\\subsection{Notation}\n\nWe write $\\mathbb{S}_{n}(\\R)$ for the linear space of $n\\times n$ real symmetric matrices, while $\\mathbb{S}_n^+(\\R)$ denotes the convex cone of real psd matrices. The symbol $\\preceq$ denotes the Loewner order on $\\mathbb{S}_{n}(\\R)$. That is, $A \\preceq B$ if and only if the eigenvalues of $B-A$ are all nonnegative.\nThe function $\\mathrm{tr}[\\cdot]$ returns the trace of a square matrix. The map $\\lambda_j(A)$ returns the $j$th largest eigenvalue of $A$; we may omit the matrix if it is clear. As usual, $\\kappa_2$ denotes the $\\ell^2$ condition number.\nWe write $\\|M\\|$ for the spectral norm of a matrix $M$. For a psd matrix $A$, we write $\\| u \\|_{A}^2 = u^T A u$ for the $A$-norm.\nGiven $A\\in \\mathbb{S}_{n}(\\R)$ and $1\\leq \\ell\\leq n$, the symbol $\\lfloor A\\rfloor_{\\ell}$ refers to any best rank-$\\ell$ approximation to $A$ relative to the spectral norm.\nFor $A \\in \\mathbb{S}_{n}^+(\\R)$ and $\\mu \\geq 0$, the regularized matrix is abbreviated $A_{\\mu} = A + \\mu I$. \nFor $A\\in \\mathbb{S}_{n}^{+}(\\R)$ and $\\mu>0$ effective dimension of $A_{\\mu}$ is defined as $d_{\\textrm{eff}}(\\mu) = \\textrm{tr}(A(A+\\mu I))^{-1}$.\nFor $A\\in \\mathbb{S}_{n}^{+}(\\R)$, the $p$-stable rank of $A$ is defined as $\\textrm{sr}_{p}(A) = \\lambda_{p}^{-1}\\sum^{n}_{j>p}\\lambda_{j}$.\nFor $A\\in \\mathbb{S}_{n}^{+}(\\R)$, we denote the time taken to compute a matvec with $A$ by $T_{\\textrm{mv}}$.","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\\label{sect1}\n\n\n\n\\begin{figure}[htbp]\n\\input{pic3.tex}\n\\caption{Multiphase Flow and Phase Transition}\n\\label{Fig1}\n\\end{figure}\n\n\n\n\n\n\nWe are interested in the motion of the fluid particles near the boundary between the atmosphere and the ocean. We call the boundary the \\emph{air-water interface}. Since evaporation and condensation phenomena occur at the interface, we have to study multiphase flow with phase transition in order to understand air-sea interaction. This paper considers the governing equations for the motion of the fluid particles in two moving domains and the interface from an energetic point of view. We employ a generalized energetic variational approach to derive our multiphase flow systems with phase transition. Of course, this paper proposes our system as one of the models for phase transition.\n\n\nLet us first introduce fundamental notations. Let $t \\geq 0$ be the time variable, and $x( = { }^t (x_1 , x_2, x_3 ) ) \\in \\mathbb{R}^3$ the spatial variable. Fix $T >0$. Let $\\Omega \\subset \\mathbb{R}^3$ be a bounded domain with a smooth boundary $\\partial \\Omega$. The symbol $n_\\Omega = n_\\Omega (x) = { }^t (n^\\Omega_1 , n^\\Omega_2 , n^\\Omega_3 )$ denotes the unit outer normal vector at $x \\in \\partial \\Omega$. Let $\\Omega_A (t) (= \\{ \\Omega_A (t) \\}_{0 \\leq t < T} )$ be a bounded domain in $\\mathbb{R}^3$ with a moving boundary $\\Gamma (t)$. Assume that $\\Gamma (t) (= \\{ \\Gamma (t) \\}_{0 \\leq t < T})$ is a smoothly evolving surface and is a closed Riemannian 2-dimensional manifold. The symbol $n_\\Gamma = n_\\Gamma ( x , t ) = { }^t (n^\\Gamma_1 , n^\\Gamma_2 , n^\\Gamma_3)$ denotes the unit outer normal vector at $x \\in \\Gamma (t)$. For each $t \\in [0,T)$, assume that $\\Omega_A (t) \\Subset \\Omega$. Set $\\Omega_B (t) = \\Omega \\setminus \\overline{\\Omega_A (t)}$. It is clear that $\\Omega = \\Omega_A (t) \\cup \\Gamma (t) \\cup \\Omega_B (t)$ (see Figure \\ref{Fig1}). Set\n\\begin{multline}\\label{eq11}\n\\Omega_{A,T} = \\bigcup_{0< t < T} \\{ \\Omega_A (t) \\times \\{ t \\} \\},{ \\ } \\Omega_{B,T} = \\bigcup_{0< t < T} \\{ \\Omega_B (t) \\times \\{ t \\} \\},\\\\\n\\Gamma_T = \\bigcup_{0< t < T} \\{ \\Gamma (t) \\times \\{ t \\} \\},{ \\ }\\Omega_T = \\Omega \\times (0,T),{ \\ }\\partial \\Omega_T = \\partial \\Omega \\times (0,T).\n\\end{multline}\n\nIn this paper we assume that the fluid in $\\Omega_{A,T}$ is a compressible one, and that the fluid in $\\Omega_{B,T}$ is an incompressible one. Let us state physical notations. Let $\\rho_A = \\rho_A ( x , t)$, $v_A = v_A ( x , t) = { }^t (v^A_1 , v^A_2 , v^A_3 )$, $p_A = p_A (x,t)$, and $\\mu_A = \\mu_A (x,t)$, $\\lambda_A = \\lambda_A (x,t)$ be the density, the velocity, the pressure, and two viscosities of the fluid in $\\Omega_A (t)$, respectively. Let $\\rho_B = \\rho_B ( x , t)$, $v_B = v_B ( x , t) = { }^t (v^B_1 , v^B_2 , v^B_3 )$, $p_B = p_B (x,t)$, and $\\mu_B = \\mu_B (x,t)$ be the density, the velocity, the pressure, and the viscosity of the fluid in $\\Omega_B (t)$, respectively. Let $v_S = v_S (x , t) = { }^t (v^S_1 , v^S_2 , v^S_3 )$ be the motion velocity of the evolving surface $\\Gamma (t)$. The symbol $\\rho_0 >0$ denotes the density of the interface $\\Gamma (t)$, and $p_0 \\in \\mathbb{R} \\setminus \\{ 0 \\}$ denotes the surface tension (coefficient) at $x \\in \\Gamma (t)$. We assume that $\\rho_A$, $v_A$, $p_A$, $\\mu_A$, $\\lambda_A$, $\\rho_B$, $v_B$, $p_B$, $\\mu_B$, $v_S$ are smooth functions in $\\mathbb{R}^4$, and that $\\rho_0$, $p_0$ are constants. \n\n\nLet us explain the key assumptions of mathematical modeling of multiphase flow systems with phase transition. Let $r_A, r_B \\in C^\\infty (\\mathbb{R}^4)$. We assume that\n\\begin{equation}\\label{eq12}\n\\begin{cases}\n{\\rm{div}} v_B =0 & \\text{ in }\\Omega_{B,T},\\\\\nv_B \\cdot n_\\Omega =0 & \\text{ on }\\partial \\Omega_T,\\\\\nv_A \\cdot n_\\Gamma = r_A v_S \\cdot n_\\Gamma & \\text{ on } \\Gamma_T,\\\\\nv_B \\cdot n_\\Gamma = r_B v_S \\cdot n_\\Gamma & \\text{ on } \\Gamma_T.\n\\end{cases}\n\\end{equation}\nThe condition ${\\rm{div}} v_B =0$ means the incompressibility condition of the fluid in $\\Omega_{B,T}$, and $v_B \\cdot n_\\Omega =0$ means that fluid particles do not go out of the domain $\\Omega$. From $v_A \\cdot n_\\Gamma = r_A v_S \\cdot n_\\Gamma$ and $v_B \\cdot n_\\Gamma = r_B v_S \\cdot n_\\Gamma$, we have $(v_A - v_B) \\cdot n_\\Gamma = (r_A - r_B) v_S \\cdot n_\\Gamma$. This condition means \\emph{phase transition} in this paper. We call the condition a \\emph{jump condition} (see Figure \\ref{Fig1}, see \\eqref{eq31}, \\eqref{eq37} for $m_A,m_B$). In general, we assume several jump conditions when we make models for multiphase flow with phase transition. This paper uses only our jump condition to derive our systems. See Slattery-Sagis-Oh \\cite{SSO07} for several jump conditions on interfacial phenomena.\n\n\nThis paper has three purposes. The first one is to make the following inviscid model for multiphase flow with phase transition:\n\\begin{equation}\\label{eq13}\n\\begin{cases}\n{\\displaystyle{D_t^A \\rho_A + ({\\rm{div}} v_A) \\rho_A = {\\rm{div}}\\left\\{ \\frac{\\rho_0}{p_0}p_A v_A \\right\\} }}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{D_t^B \\rho_B = {\\rm{div}}\\left\\{ \\frac{\\rho_0}{p_0}p_B v_B \\right\\} }}& \\text{ in } \\Omega_{B,T},\\\\\n{\\displaystyle{\\rho_A D_t^A v_A + {\\rm{grad}}p_A = - {\\rm{div}}\\left\\{ \\frac{\\rho_0}{p_0}p_A v_A \\right\\} v_A }}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{\\rho_B D_t^B v_B + {\\rm{grad}}p_B = - {\\rm{div}}\\left\\{ \\frac{\\rho_0}{p_0}p_B v_B \\right\\} v_B }}& \\text{ in } \\Omega_{B,T},\\\\\np_0 H_\\Gamma n_\\Gamma - r_A p_A n_\\Gamma + r_B p_B n_\\Gamma ={ }^t(0,0,0) & \\text{ on } \\Gamma_T,\n\\end{cases}\n\\end{equation}\nwith \\eqref{eq12}. Here $D_t^A f = \\partial_t f + (v_A,\\nabla ) f $, $D_t^B f = \\partial_t f + (v_B, \\nabla ) f $, $(v_A , \\nabla ) f = v^A_1 \\partial_1 f + v^A_2 \\partial_2 f + v^A_3 \\partial_3 f$, $(v_B , \\nabla ) f = v^B_1 \\partial_1 f + v^B_2 \\partial_2 f + v^B_3 \\partial_3 f$, ${\\rm{div}}v_A = \\nabla \\cdot v_A$, ${\\rm{div}}v_B = \\nabla \\cdot v_B$, ${\\rm{grad}} f = \\nabla f$, $\\nabla = { }^t (\\partial_1 , \\partial_2 , \\partial_3)$, $\\partial_i = \\partial\/{\\partial x_i}$, and $\\partial_t = \\partial\/{\\partial t}$. The symbol $H_\\Gamma = H_\\Gamma (x , t )$ denotes the \\emph{mean curvature in the direction} $n_\\Gamma$ defined by $H_\\Gamma = - {\\rm{div}}_\\Gamma n_\\Gamma = - (\\partial_1^\\Gamma n_1^\\Gamma + \\partial_2^\\Gamma n^\\Gamma_2 + \\partial_3^\\Gamma n^\\Gamma_3)$, where $\\partial^\\Gamma_i f := \\sum_{j=1}^3(\\delta_{ij} - n^\\Gamma_i n^\\Gamma_j ) \\partial_j f$. More precisely, under the restriction \\eqref{eq12} we apply an energetic variational approach to derive system \\eqref{eq13}. See subsection \\ref{subsec41} for details.\n\n\nThe second one is to make the following viscous model for multiphase flow with phase transition:\n\\begin{equation}\\label{eq14}\n\\begin{cases}\n{\\displaystyle{D_t^A \\rho_A + ({\\rm{div}} v_A) \\rho_A = - \\frac{\\rho_0}{p_0} {\\rm{div}}( \\mathcal{T}_A v_A) }}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{D_t^B \\rho_B = - \\frac{\\rho_0}{p_0} {\\rm{div}} ( \\mathcal{T}_B v_B )}} & \\text{ in } \\Omega_{B,T},\\\\\n{\\displaystyle{\\rho_A D_t^A v_A = {\\rm{div}} \\mathcal{T}_A + \\frac{\\rho_0}{p_0} {\\rm{div}}( \\mathcal{T}_A v_A) v_A }}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{\\rho_B D_t^B v_B = {\\rm{div}} \\mathcal{T}_B + \\frac{\\rho_0}{p_0} {\\rm{div}}( \\mathcal{T}_B v_B)v_B }}& \\text{ in } \\Omega_{B,T},\\\\\np_0 H_\\Gamma n_\\Gamma + r_A \\widetilde{\\mathcal{T}}_A n_\\Gamma - r_B \\widetilde{\\mathcal{T}}_B n_\\Gamma= { }^t( 0,0,0) & \\text{ on } \\Gamma_T,\n\\end{cases}\n\\end{equation}\nwith\n\\begin{equation}\\label{eq15}\n\\begin{cases}\n{\\rm{div}} v_B =0 & \\text{ in }\\Omega_{B,T},\\\\\nv_B = { }^t (0,0,0) & \\text{ in }\\partial \\Omega_T,\\\\\nv_A \\cdot n_\\Gamma = r_A v_S \\cdot n_\\Gamma & \\text{ on } \\Gamma_T,\\\\\nv_B \\cdot n_\\Gamma = r_B v_S \\cdot n_\\Gamma & \\text{ on } \\Gamma_T,\\\\\nP_\\Gamma v_A = { }^t (0,0,0) & \\text{ on } \\Gamma_T,\\\\\nP_\\Gamma v_B = { }^t (0,0,0) & \\text{ on } \\Gamma_T,\n\\end{cases}\n\\end{equation}\nwhere\n\\begin{equation}\\label{eq16}\n\\begin{cases}\n\\mathcal{T}_A =\\mathcal{T}_A (p_A , v_A) :=\\mu_A D (v_A) + \\lambda_A ({\\rm{div}} v_A)I_{3\\times 3} - p_A I_{3 \\times 3} ,\\\\\n\\mathcal{T}_B = \\mathcal{T}_B (p_B, v_B ) :=\\mu_B D (v_B) - p_B I_{3 \\times 3},\\\\ \n\\widetilde{\\mathcal{T}}_A =\\widetilde{\\mathcal{T}}_A (p_A , v_A) :=\\mu_A (n_\\Gamma \\cdot (n_\\Gamma , \\nabla ) v_A)+ \\lambda_A ({\\rm{div}} v_A) - p_A ,\\\\\n\\widetilde{\\mathcal{T}}_B = \\widetilde{\\mathcal{T}}_B (p_B, v_B ) :=\\mu_B (n_\\Gamma \\cdot (n_\\Gamma , \\nabla ) v_B) - p_B . \n\\end{cases}\n\\end{equation}\nHere $D (v_A) =\\{ { }^t(\\nabla v_A) +(\\nabla v_A) \\}\/2$ and $D (v_B) =\\{ { }^t(\\nabla v_B) +(\\nabla v_B) \\}\/2$. The symbol $I_{3\\times 3}$ denotes the $3 \\times 3$ identity matrix, and $P_\\Gamma = P_\\Gamma (x ,t)$ an \\emph{orthogonal projection to a tangent space} defined by $P_\\Gamma = I_{3 \\times 3} - n_\\Gamma \\otimes n_\\Gamma$, where $\\otimes$ is the tensor product. More precisely, under the restriction \\eqref{eq15} we apply an energetic variational approach to derive system \\eqref{eq14}. See subsection \\ref{subsec42} for details.\n\n\nThe third one is to investigate the conservative form, the conservation and energy laws of our systems \\eqref{eq13} and \\eqref{eq14}. In fact, any solution to system \\eqref{eq14} with \\eqref{eq15} satisfies that for $t_1 < t_2$,\n\\begin{multline}\\label{eq17}\n\\int_{\\Omega_A (t_2)} \\rho_A (x,t_2) { \\ } d x + \\int_{\\Omega_B (t_2)} \\rho_B (x,t_2) { \\ } d x + \\int_{\\Gamma (t_2)} \\rho_0 { \\ }d \\mathcal{H}_x^2 \\\\\n= \\int_{\\Omega_A (t_1)} \\rho_A (x,t_1) { \\ } d x + \\int_{\\Omega_B (t_1)} \\rho_B (x,t_1) { \\ } d x + \\int_{\\Gamma (t_1)} \\rho_0 { \\ }d \\mathcal{H}_x^2,\n\\end{multline}\nand\n\\begin{multline}\\label{eq18}\n\\int_{\\Omega_A (t_2)} \\frac{1}{2} \\rho_A \\vert v_A \\vert^2{ \\ }d x + \\int_{\\Omega_B (t_2)} \\frac{1}{2} \\rho_B \\vert v_B \\vert^2{ \\ }d x\\\\\n+ \\int_{t_1}^{t_2 } \\int_{\\Omega_A (t)}(\\mu_A \\vert D (v_A) \\vert^2+ \\lambda_A \\vert { \\rm{div} }v_A \\vert ^2) { \\ }d x d t + \\int_{t_1}^{t_2} \\int_{\\Omega_B (t)} \\mu_B \\vert D (v_B) \\vert^2{ \\ }d x dt\\\\\n= \\int_{\\Omega_A (t_1)} \\frac{1}{2} \\rho_A \\vert v_A \\vert^2{ \\ }d x + \\int_{\\Omega_B (t_1)} \\frac{1}{2} \\rho_B \\vert v_B \\vert^2{ \\ }d x\\\\\n+ \\int_{t_1}^{t_2} \\int_{\\Omega_B (t)} \\left( \\frac{\\rho_0}{2 p_0} {\\rm{div}}(\\mathcal{T}_B v_B) \\vert v_B \\vert^2\\right) { \\ }d x dt + \\int_{t_1}^{t_2} \\int_{\\Gamma (t)} ({\\rm{div}}_\\Gamma v_S )p_0 { \\ }d \\mathcal{H}^2_x d t\\\\\n+ \\int_{t_1}^{t_2 } \\int_{\\Omega_A (t)}\\left( ({\\rm{div}} v_A) p_A + \\frac{\\rho_0}{2 p_0} {\\rm{div}} ( \\mathcal{T}_A v_A) \\vert v_A \\vert^2\\right) { \\ }d x d t.\n\\end{multline}\nMoreover, any solution to system \\eqref{eq13} with \\eqref{eq12} satisfies \\eqref{eq17}, \\eqref{eq18} when $\\mu_A \\equiv \\lambda_A \\equiv \\mu_B \\equiv 0$, and\n\\begin{multline}\\label{eq19}\n\\int_{\\Omega_A (t_2)} \\rho_A v_A (x,t) { \\ }d x + \\int_{\\Omega_B (t_2)} \\rho_B v_B (x,t) { \\ }d x\\\\\n= \\int_{\\Omega_A (t_1)} \\rho_A v_A { \\ }d x + \\int_{\\Omega_B (t_1)} \\rho_B v_B { \\ }d x\\\\\n+ \\int_{t_1}^{t_2} \\int_{\\Gamma (t)} (p_B - p_A) n_\\Gamma { \\ }d \\mathcal{H}^2_x d t - \\int_{t_1}^{t_2} \\int_{\\partial \\Omega} p_B n_\\Omega { \\ } d \\mathcal{H}^2_x d t.\n\\end{multline}\nHere $ \\vert D (v_A) \\vert^2= D(v_A): D (v_A)$, $ \\vert D (v_B) \\vert^2= D(v_B): D (v_B)$, and $d \\mathcal{H}^2_x$ denotes \\emph{2-dimensional Hausdorff measure}. We often call \\eqref{eq17}, \\eqref{eq19}, and \\eqref{eq18}, the \\emph{law of conservation of mass}, the \\emph{law of conservation of momentum}, and the \\emph{energy equality}, respectively. We easily check that system \\eqref{eq14} satisfies the following conservative form:\n\\begin{equation*}\n\\begin{cases}\n{\\displaystyle{\\partial_t \\rho_A + {\\rm{div}}\\left( \\rho_A v_A + \\frac{\\rho_0}{p_0} \\mathcal{T}_A v_A \\right) = 0}}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{\\partial_t \\rho_B + {\\rm{div}}\\left( \\rho_B v_B + \\frac{\\rho_0}{p_0} \\mathcal{T}_B v_B \\right) = 0}}& \\text{ in } \\Omega_{B,T},\\\\\n{\\displaystyle{\\partial_t (\\rho_A v_A) + {\\rm{div}} \\left( \\rho_A v_A \\otimes v_A - \\mathcal{T}_A \\right) = 0}}& \\text{ in } \\Omega_{A,T},\\\\\n{\\displaystyle{\\partial_t (\\rho_B v_B) + {\\rm{div}}\\left( \\rho_B v_B \\otimes v_B - \\mathcal{T}_B \\right) = 0}}& \\text{ in } \\Omega_{B,T}.\n\\end{cases}\n\\end{equation*}\n\n\\begin{remark}\\label{rem11}$(\\rm{i})$ If we change \\eqref{eq12} or \\eqref{eq15} to another restriction, then we can derive another system by applying our approaches.\\\\\n$(\\rm{ii})$ If $r_A \\equiv r_B \\equiv 1 $, then we choose $\\rho_0 =0$ to derive the usual Euler and Navier-Stokes systems, or a two-phase flow system with surface tension by our approaches.\n\\end{remark}\n\nLet us explain three key ideas of deriving our multiphase flow systems with phase transition. The first point is to acknowledge the existence of the interface, that is, we assume that the density of the interface is a positive constant $\\rho_0$. The second point is to divide the jump condition $(v_A - v_B) \\cdot n_\\Gamma = (r_A - r_B) v_S \\cdot n_\\Gamma$ into $v_A \\cdot n_\\Gamma = r_A v_S \\cdot n_\\Gamma$ and $v_B \\cdot n_\\Gamma = r_B v_S \\cdot n_\\Gamma$. The third point is to make use of a generalized energetic variational approach. More precisely, we apply an energetic variational approach in order to look for functions $F_A$ and $F_B$ satisfying\n\\begin{equation*}\n\\begin{cases}\nD_t^A \\rho_A + ({\\rm{div}} v_A) \\rho_A = F_A & \\text{ in } \\Omega_{A,T},\\\\\nD_t^B \\rho_B = F_B & \\text{ in } \\Omega_{B,T},\n\\end{cases}\n\\end{equation*}\nand\n\\begin{equation*}\n\\frac{d }{d t} \\left( \\int_{\\Omega_A (t)} \\rho_A (x,t) { \\ }d x + \\int_{\\Omega_B(t)} \\rho_B (x,t) { \\ }d x + \\int_{\\Gamma (t)} \\rho_0 { \\ }d \\mathcal{H}^2_x \\right) =0 .\n\\end{equation*}\n\n\nAn energetic variational approach is a method for deriving PDEs by using the forces derived from a variation of energies. Gyarmati \\cite{Gya70} applied an energetic variational approach, which had been studied by Strutt \\cite{Str73} and Onsager \\cite{Ons31a, Ons31b}, to make several models for fluid dynamics in domains. Hyon-Kwak-Liu \\cite{HKL10} made use of their energetic variational approach to study complex fluid in domains. Koba-Sato \\cite{KS17} applied their energetic variational approach to make their non-Newtonian fluid systems in domains. Koba-Liu-Giga \\cite{KLG17} and Koba \\cite{K18} employed their energetic variational approaches to derive their fluid systems on an evolving closed surface. However, these papers \\cite{HKL10,KS17,KLG17,K18} did not consider multiphase flow. This paper improves and modifies their methods in \\cite{HKL10,KS17,KLG17,K18} to derive our multiphase flow systems. See Section \\ref{sect4} for details.\n\n\n\nFinally, we introduce the results related to this paper. Bothe-Pr\\\"{u}ss \\cite{BP12,BP17} considered multiphase flow with interface effects. In \\cite{BP12}, they made models for multiphase flow with surface tension and viscosities by applying the \\emph{Boussinesq-Scriven law}. In \\cite{BP17}, they made use of their jump conditions to make models for multi-component two-phase flow system with phase transition, and to study the individual mass densities of an isothermal mixture of $N$-species in a domain. Although this paper does not consider surface viscosity (surface flow), this paper considers interface effects such as surface tension and phase transition. Note that our models are different from the ones in \\cite{BP12, BP17}. See also \\cite{KLG17, K18} for models for surface flow.\n\n\n\nThe outline of this paper is as follows: In Section \\ref{sect2} we state the main results of this paper. In Section \\ref{sect3} we study the law of conservation of mass for multiphase flow with phase transition. In Section \\ref{sect4} we apply an energetic variational approach to make mathematical models for multiphase flow with phase transition. In Section \\ref{sect5} we investigate the conservation and energy laws of our systems. In Appendix, we provide two useful lemmas to derive our systems.\n\n\n\n\\section{Main Results}\\label{sect2}\nWe first introduce the transport theorems. Then we state the main results.\n\\begin{definition}[$\\Omega_T$ is flowed by the velocity fields $(v_A,v_B,v_S)$]\\label{def21}{ \\ }\\\\\n$(\\rm{i})$ We say that $\\Omega_{A,T}$ is \\emph{flowed by the velocity field} $v_A = v_A (x,t)$ if for each $0< t 4\\sigma$ lower than expectations from the MARLEY prediction.\n\nAs this result is discrepant with expectations, several checks were subsequently performed. First, to verify the transparency to neutrons of the lead, the lead used for the target was checked for impurities. The presence of lighter atoms in the surrounding lead may increase the neutron scattering cross section and would also decrease the density of the neutrino target. The lead is stamped as $99.99\\%$ natural lead. The density of lead used to cast the targets was measured and determined to be $11.48\\pm0.21$\\,$\\mbox{g\/cm}^3$, within uncertainty of the nominal value of $11.29$\\,$\\mbox{g\/cm}^3$. Second, the prompt neutron event rate was compared to the delivered proton beam power as a function of time. This was done to check the stability of the neutron selection efficiency during detector operations. The excess of neutron events in the prompt window was observed to follow the delivered POT exposure. Third, the PSD cut was extended to include lower energy recoils. This increases both the expected number of detected neutrons and the sensitivity to lower energy neutrons. Extending the PSD cut down to 50~keV increased the number of expected NINs by a factor of 1.43. However, these lower energy recoil events were not included in the original fit as the uncertainty on their selection efficiency is large. Fitting this low recoil energy sideband gave a NIN rate consistent with that observed in the analysis sample.\n\n\n\\begin{figure}[!bt]\n\\centering\n\\includegraphics[width=\\linewidth]{images\/combinedFit.png}\n\\caption{Likelihood profiles from the lead neutrino cube and Eljen cell detector updated analysis. A value of 1 corresponds to the predicted signal from the MARLEY event generator.}\n\\label{fig:LL}\n\\end{figure}\n\nThe analysis of the Eljen cell data in reference~\\cite{akimov2017} has been updated in three ways. The previous analysis assumed that the emitted NINs followed an evaporative neutron spectrum, and assumed the spectra of neutron emission events of all multiplicities were identical. The updated analysis has used MARLEY to generate a neutron energy distribution that depends on the multiplicity of the event along with new calculations of the number of neutrinos produced per incident POT from reference~\\cite{PhysRevD.106.032003}. Finally, time broadening of the beam-related neutron population was incorporated into the fit and allowed to float, as was done in the analysis of the lead neutrino cube, to incorporate dispersion effects due to time-of-flight varying with incident neutron energy. The influence of this additional uncertainty is detailed in supplementary materials~\\cite{nubesSupMat}.\n\nCombining the results yields a cross section scaling factor of $0.29^{+0.17}_{-0.16}$ relative to predictions from MARLEY (see Tab.~\\ref{marleyTable}) from a joint fit. For the neutrino cube sample, this corresponds to 100$^{+57}_{-54}$ events, consistent with the NIN fit using only data from this detector.\n\nThe lead neutrino cube was designed to measure the ${}^{nat}\\mbox{Pb}(\\nu_e,e^{-}+\\mbox{X}n)$ cross section using electron neutrinos produced at the SNS. The origin of the observed reduction in the signal expectations is unknown. It should be noted that while the suppression is observed in the measured results compared to the MARLEY model, the current result cannot provide meaningful data on charged-current events on lead without neutron emission, as the detector is not designed to measure the emitted electron.\n\nOne possible explanation could be that the inclusive charged-current cross section is lower than expected for lead, affecting both neutron emitting and non-neutron emitting interactions. This could be tested by a dedicated detector measuring the electromagnetic energy deposited in charged-current events on lead. This can be done within COHERENT, and there are also external plans (see reference~\\cite{pidar}). Additionally, a detector measuring the electromagnetic component of charged-current neutrino interactions on ${}^{127}$I has collected data for several years at the SNS, and may help to test theoretical predictions.\n\nAnother possibility is that the neutrons emitted by the charged-current interaction have energies lower than theoretically predicted in MARLEY. If this is the case, the sensitivity of the HALO experiment would be unaffected by the observed reduction in the charged-current cross section. However, there are no models predicting the emission of low energy neutrons from charged-current events on lead. A measurement of the NIN cross section with a capture-gated detector would test this possibility.\n\nMeasuring the NIN cross section on a lighter target may also provide understanding for the current result. In 2017, a similar detector to the lead neutrino cube was deployed to the SNS, seeking to measure the NIN cross section on iron with a $\\sim$700-kg target. The results described herein reduce the likelihood that the iron neutrino cube will successfully measure the NIN cross section, but analysis is still under way on the data it has collected. \n\nThere are several implications of a reduced lead NIN cross section for existing experiments. For CEvNS detectors at the SNS and ESS, this measurement impacts the expected backgrounds and design of detector shielding. This result has negative implications for HALO's potential to study supernova neutrinos. However, the HALO data continues to be vital for understanding the next galactic core-collapse supernova as HALO is sensitive to the $\\nu_e$ component of the supernova flux, while most large detectors are primarily sensitive to the $\\bar{\\nu}_e$ component through inverse beta decay.\n\nA separate analysis of the 2$n$ NIN emission cross section on lead is planned using the data collected by the lead neutrino cube. While the rate of observed events is expected to be lower, steady-state backgrounds are also significantly reduced.\n\n\\textit{Conclusion:} Five years of data have been recorded and analyzed to study NINs produced from electron neutrino charged-current interactions on lead at the SNS. Combining the results of this analysis with an updated analysis of the Eljen cell detector yields a cross section suppressed by a factor of $0.29^{+0.17}_{-0.16}$ compared to the MARLEY prediction. The cause of the apparent reduction in the NIN cross section is unknown, but future experiments will help to determine its origin. Within COHERENT, updated measurements of the neutrino flux with a heavy-water detector will improve systematic uncertainties on the existing measurements \\cite{COHERENT:2021xhx}, and measurements of charged-current cross sections on other targets may help to determine whether a similar suppression is seen for other nuclei.\n\n\\textit{Acknowledgements:} The COHERENT collaboration would like to thank the Duke Machine Shop for its help casting the lead targets used for this detector, Steven Gardiner for his assistance in adapting MARLEY for use with iron and lead, and the authors of reference~\\cite{wakasa2012} for providing the ${}^{208}\\mbox{Pb}(p,n)$ data used for generating predictions with MARLEY.\n\nThe COHERENT collaboration acknowledges the Kavli Institute at the University of Chicago for Eljen cell detector contributions. The COHERENT collaboration acknowledges the generous resources provided by the ORNL Spallation Neutron Source, a DOE Office of Science User Facility, and thanks Fermilab for the continuing loan of the CENNS-10 detector. We also acknowledge support from the Alfred~P. Sloan Foundation, the Consortium for Nonproliferation Enabling Capabilities, the National Science Foundation, the Korea National Research Foundation (NRF 2022R1A3B1078756), and the U.S. Department of Energy, Office of Science. Laboratory Directed Research and Development funds from ORNL also supported this project. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. This research used the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility. The work was supported by the Ministry of Science and Higher Education of the Russian Federation, Project Fundamental properties of elementary particles and cosmology No. 0723-2020-0041.\n\n\\nocite{*}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\n\\section{Introduction}\\label{sec:intro}\n\t\t\n\n\tIn variational calculations of molecular rotation-vibration energies and wavefunctions, a matrix representation\n\tof the molecular rotation-vibration Hamiltonian, constructed in terms of suitable basis functions, is diagonalized\n\tnumerically. It is well known that this type of calculation can be facilitated by the introduction of symmetrized\n\tbasis functions, i.e., basis functions that generate irreducible representations of a symmetry group for the molecule\n\tin question (see, for example, Ref.~\\cite{98BuJexx}). Even though the calculation of energies and wavefunctions\n\tcan, in principle, be carried out without the use of symmetry, the subsequent simulation of molecular spectra, involving\n\tthe computation of transition intensities, would be impossible in practice without the consideration of symmetry~\\cite{18ChJeYu}.\n\tWe implement the symmetry information in the variational calculation by defining groups of matrices that are\n\tisomorphic or homomorphic to the original symmetry group of the molecule and that are associated with the various\n\tirreducible representations (irreps) of this symmetry group~\\cite{98BuJexx}. When suitable matrix group elements are known, projection\n\toperator techniques are employed to obtain the desired symmetrized basis functions for the variational calculation~\\cite{98BuJexx}.\n\tIn a recent paper~\\cite{18ChJeYu}, we described an example of such a symmetry adaption, in that we\n\tpresented character tables and irreducible representation transformation matrices for \\Dh{n} groups with arbitrary $n$-values.\n\tWith these results, we could practically utilize the linear-molecule symmetry properties described by the \\Dh{\\infty} point group\n\tin numerical calculations with the variational nuclear motion program {{\\sc TROVE}}~\\cite{07YuThJe.method}, the acetylene molecule $^{12}$C$_2$H$_2$\\ serving as an example.\n\tIn the present work, we report an analogous analysis for the molecular symmetry (MS) group~{\\itshape\\bfseries G}$_{36}$\\ and the extended molecular symmetry (EMS) group {\\itshape\\bfseries G}$_{36}$(EM) \\cite{98BuJexx} of the ethane molecule H$_3$$^{12}$C$^{12}$CH$_3$, shown in \\fig{fig:ethane_equilibrium}, with the aim of facilitating the solution of the rotation-vibration Schr\\\"{o}dinger equation for ethane and related molecules.\n\n\n\nThe MS group {\\itshape\\bfseries G}$_{36}$\\ has been the subject of a number of studies (see, for example, \\citep{81SmBexx,12CaAlSe}). The EMS group {\\itshape\\bfseries G}$_{36}$(EM) was studied in detail by Di Lauro and Lattanzi~\\citep{10LaDixx,05LaDixx}. Examples of the application of the {\\itshape\\bfseries G}$_{36}$(EM) group include studies of the rotation-torsional spectra of various ethane-type molecules \\citep{80Hougen,99LaLaxx,96LaLaVa,04LaDiHo,06LaDiHo}. {\\sc TROVE}\\ (Theoretical ROVibrational Energies) \\cite{07YuThJe.method,15YaYuxx.method} is a general variational program for computing ro-vibrational spectra and properties for small to medium-size polyatomic molecules of arbitrary structure. It has been applied to a large number of polyatomic species \\cite{09YuBaYa.NH3,11YaYuJe.H2CO,14SoHeYu.PH3,15SoAlTe.PH3,14UnYuTe.SO3,15AlYuTe.H2CO,14YuTexx.CH4,15YaYuxx.method,15AlOvPo.H2O2,15OwYuYa.CH3Cl,15OwYuYa.SiH4,15AdYaYuJe.CH3,15OwYuTh.NH3,16AlPoOv.HOOH,16UnTeYu.SO2,16OwYuYa,16OwYuYa1.CH4,18OwYaTh,18MaYaTe,15OwYuYa1.SiH4,19CoYuKo,19MaChYa}, most of which have considerable symmetry [e.g., with molecular symmetry groups~\\cite{98BuJexx} such as \\Cv{3}(M), \\Dh{n}(M) and {\\itshape\\bfseries T}$_{\\rm d}$(M)]. TROVE is an efficient computer program for simulating hot spectra of polyatomic molecules; it is one of the main tools of the ExoMol project \\cite{12TeYuxx.db,17TeYuxx}. The most recent updates of TROVE have been reported in Refs.~\\citenum{17TeYuxx,GAIN}. TROVE uses an automatic approach for constructing a symmetry-adapted basis set to be used in setting up a matrix representation of the molecular rotation-vibration Hamiltonian. As mentioned above, we require towards this end, for each irrep of the symmetry group in question~\\cite{98BuJexx}, a group of matrices constituting that irrep. However, for {\\itshape\\bfseries G}$_{36}$\\ or {\\itshape\\bfseries G}$_{36}$(EM), these matrices have not been available in the literature thus far. The present work aims at describing fully the groups {\\itshape\\bfseries G}$_{36}$\\ and {\\itshape\\bfseries G}$_{36}$(EM) and, in particular, determining matrix groups that define the irreps. The matrix groups obtained are used for symmetrizing the potential energy surface and the rotation-vibration basis functions for ethane.\n\n\n\n\t\\begin{figure}[htbp!]\n\t\t\\centering\n\t\t\\chemfig{{C}([:120]-{H})([:-100]<{H})([:-130]<:{H})-C([:-60]-H)([:80]<:H)([:50]] (0,0.2) -- (0.5,0.2) node[above] {$R$} -- (1,0.2);\n\\draw[<->] (-0.2,-0.1) -- ++ (120:0.5) node[below left] {$r$} -- ++(120:0.5);\n\\draw [domain=180:240] plot ({1 + 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[below] {$\\alpha$};\n\\draw [domain=240:300] plot ({1 + 0.3*cos(\\x)}, {0.3*sin(\\x)}) ;\n\\end{tikzpicture}\n\\caption{Representative members of three of the vibrational coordinate subsets. Here $R$ is the \\ce{C-C} bond length, $r$ is one of the six C--H$_k$ bond lengths $r_k$, and $\\alpha$ is one of the six $\\angle$({H$_k$-C-C}) bond angles $\\alpha_k$.}\n\\label{fig:three_vibrational_classes}\n\\end{figure}\nThe last vibrational subset is obtained form\nsix dihedral angles\n$\\theta_{12}$, $\\theta_{23}$, $\\theta_{31}$,\n$\\theta_{45}$, $\\theta_{56}$, $\\theta_{64}$,\none of which is labelled $\\theta$ in \\fig{fig:dihedrals}.\n$\\theta_{ij}$ is the angle between\nthe \\ce{H$_i$-C-C} and \\ce{H$_j$-C-C} planes, where protons $i$ and $j$ belong to the same \\ce{CH3} group. Only four of the six angles are linearly independent due to the constraints\n$\\theta_{12} + \\theta_{23} + \\theta_{31}$ $=$\n$\\theta_{45} + \\theta_{56} +\\theta_{64}$ $=$\n$2 \\pi$. The positive directions of rotation for the $\\theta_{ij}$ angles\nare from proton 1 $\\rightarrow$ 2 $\\rightarrow$ 3 for\nthe one \\ce{CH3} group, and from proton 4 $\\rightarrow$ 5 $\\rightarrow$ 6 for\nthe other.\nThe independent coordinates constructed from the six $\\theta_{ij}$ angles are\n\\begin{equation}\n\\begin{split}\n{\\gamma}_1 &= \\frac{1}{\\sqrt{6}}(2\\theta_{23}- \\theta_{31} - \\theta_{12}), \\\\\n{\\gamma}_2 &= \\frac{1}{\\sqrt{2}}(\\theta_{31} - \\theta_{12}), \\\\\n{\\delta}_1 &= \\frac{1}{\\sqrt{6}}(2\\theta_{56} - \\theta_{64} - \\theta_{45}), \\\\\n{\\delta}_2 &= \\frac{1}{\\sqrt{2}}(\\theta_{64} - \\theta_{45}),\n\\end{split}\n\\label{eq:gamma-delta}\n\\end{equation}\nwhich transform as the $G$ representation of {\\itshape\\bfseries G}$_{36}$.\n\nTo describe the orientation of the ethane molecule with Euler angles, one approach is to attach coordinate axes on each \\ce{CH3} group. Here, the $z$ axis is the same for both and points from \\ce{C_$b$} to \\ce{C_$a$}, while the $x_a$ and $x_b$ axes point in the direction of \\ce{C_$a$}-\\ce{H1} and \\ce{C_$b$}-\\ce{H4}, respectively, when the molecule is viewed in the Newman projection of \\fig{fig:coordinate_axes}. The $y$ axes ensure that the Cartesian axes are right handed. With this construction, the $\\theta$ and $\\phi$ Euler angles describing the direction of the $z$ axis for \\ce{CH3} group are the same while the $\\chi$ angles describing the rotation about the $z$ axis are different and are denoted by $\\chi_a$ and $\\chi_b$. These increase in the counterclockwise direction due to the right hand rule. This essentially follows Section 15.4.4 of \\cite{98BuJexx} in the definition of the Euler angles according to the convention described in Section 10.1.1 of \\cite{98BuJexx}.\n\n\\begin{figure}[htbp!]\n\\centering\n\\begin{tikzpicture}[scale=1.8]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 2};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {3};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {1};\n\n\t\\draw [dashed] (0,0) -- ++ (40+20:1) circle(2pt)[fill] node[above right] {5};\n\t\\draw [dashed] (0,0) -- ++(160+20:1) circle(2pt)[fill] node[above left] {4};\n\\draw [dashed] (0,0) -- ++(280+20:1) circle(2pt)[fill] ++ (280:0.15) circle(0pt) node {6};\n\\draw[->] (0,0) -- ++ (240:0.8) node[left] {$x_a$};\n\\draw[->] (0,0) -- ++ (240+90:0.8) node[right] {$y_a$};\n\\draw[->] (0,0) -- ++ (160+20:0.8) node[above] {$x_b$};\n\t\\draw[->] (0,0) -- ++ (160+90+20:0.8) node[below] {$y_b$};\n\n\n\\end{tikzpicture}\n\t\\caption{A Newman projection of ethane, with the CH$_3$ group containing protons 1, 2, and 3, indicated by solid \\ce{C-H} bonds, being closest to the viewer. The $x$ and $y$ components of the coordinate axes attached to each \\ce{CH3} group is shown, the subscript $a$ signifying that the coordinate axes are for the \\ce{C_$a$H3} group. To ensure the coordinate system is right handed, the $z$ axis (the same for both groups) points from \\ce{C_$b$} to \\ce{C_$a$}. With this construction, the $\\theta$ and $\\phi$ Euler describing the direction of the $z$ axis are the same for \\ce{CH3} group are the same while the $\\chi$ angle describing the rotation about the $z$ axis different and are denoted by $\\chi_a$ and $\\chi_b$. These increase in the counterclockwise direction due to the right hand rule.}\n\\label{fig:coordinate_axes}\n\\end{figure}\n\nAs described in \\cite{98BuJexx}, to achieve maximum separation of the torsional and rotational motion, it is expedient to define two new coordinates from $\\chi_a$ and $\\chi_b$. We set the rotational coordinate $\\chi$ to\n\\begin{equation}\\label{eq:chichiachib}\n\t\\chi = \\frac12 ( \\chi_a + \\chi_b)\n\\end{equation}\nand hence our $x$ axis shown in \\fig{fig:dihedrals} halves the angle between \\ce{H1-C-C} and \\ce{H4-C-C} and increases in the counterclockwise direction. The torsional angle $\\tau$ could be defined as\n\\begin{equation}\\label{eq:tau=chia-chib}\n\\tau = \\chi_a - \\chi_b\n\\end{equation}\nand hence, as indicated in \\fig{fig:dihedrals}, is the angle from \\ce{H4-C-C} to \\ce{H1-C-C} in the counterclockwise direction.\nIn the TROVE calculations, we use a different choice and define $\\tau$ as the average of three dihedral angles. To define these, we form three pairs of protons $(4,1)$, $(6,2)$, and $(5,3)$ with the two members belonging to different \\ce{CH3} groups. The pairs are chosen such that the protons $i$ and $j$ in each $(i,j)$ pair form a dihedral angle $\\tau_{ij}$ of $\\pi$ in the staggered equilibrium geometry of \\fig{fig:ethane_equilibrium} and $\\tau_{ij}=0$ for the eclipsed geometry (see \\fig{fig:ethane_eclipsed}), using the labelling of \\fig{fig:ethane_labelling}. In a general instantaneous geometry, each $(i,j)$ pair defines a dihedral angle $\\tau_{ij}$ (where the positive direction of rotation for the $\\tau_{ij}$ angles\nis from proton 1 $\\rightarrow$ 2 $\\rightarrow$ 3)\nand the torsional angle is then given by a symmetric combination\n\\begin{equation}\n\\tau =\n\\frac13 ( \\tau_{41} + \\tau_{62} + \\tau_{53}).\n\n\\label{eq:taudef}\n\\end{equation}\nWith this definition, $\\tau=0$, $2\\pi\/3$ and $4\\pi\/3$ correspond to eclipsed configurations, while at $\\tau = \\pi\/3$, $\\pi$, $5\\pi\/3$ the molecule is in one of its three equilibrium geometries. The torsional angle $\\tau$ has definite transformation\nproperties under the operations of {\\itshape\\bfseries G}$_{36}$\\ (see also \\ref{sect:appenix_b}). As discussed in Section~\\ref{sec:extenedGTS}, the two coordinate-pair values ($\\tau$, $\\chi$) and ($\\tau + 2\\pi$, $\\chi + \\pi$) describe the same physical situation. However, the coordinate which $\\tau$ is based on, $\\chi_a - \\chi_b$, has a range of $4\\pi$. Although a given geometry can be described by a value of $\\tau$ in the interval $[0, 2\\pi]$, we must allow $\\tau$ to range over $[0, 4\\pi]$ to obtain a correct correlation with $\\chi_a - \\chi_b$ (see Section~\\ref{sec:extenedGTS} below).\n\n\\begin{figure}[htbp!]\n\\centering\n\\begin{tikzpicture}[scale=1.8]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 2};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {3};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {1};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {5};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {4};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] ++ (280:0.15) circle(0pt) node {6};\n\\draw[->] (0,0) -- ++ (200:0.8) node[left] {$x$};\n\\draw[->] (0,0) -- ++ (200+90:0.8) node[right] {$y$};\n\n\\draw [domain=0:60] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[above] {$\\theta$};\n\\draw [domain=60:120] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)});\n\n\\draw[-] [domain=160:200] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[above left] {$\\tau$};\n\t\\draw[->] [domain=200:240] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)});\n\\end{tikzpicture}\n\t\\caption{A Newman projection of ethane, with the CH$_3$ group containing protons 1, 2, 3, indicated by solid \\ce{C-H} bonds, being closest to the viewer. One of the dihedral angles used in the vibrational subsets is labelled by $\\theta$ and the torsional angle is labelled by $\\tau$ and is measured in the counterclockwise direction. The $x$ axis halves the dihedral angle between the \\ce{H$_1$-C-C} and \\ce{H$_4$-C-C} planes.\n}\n\\label{fig:dihedrals}\n\\end{figure}\n\n\\begin{figure}[htbp!]\n\t\t\\centering\n\t\t\\chemfig{{\\it a}([:120]-{1})([:-100]<{3})([:-130]<:{2})-{\\it b}([:60]-4)([:-50]<5)([:-80]<:6)}\n\t\t\\caption{Ethane in the eclipsed configuration.}\n\t\t\\label{fig:ethane_eclipsed}\n\t\\end{figure}\nIn conclusion, the coordinate subsets, for which we initially diagonalize reduced Hamiltonians, are\n\\begin{enumerate}\n\\item the \\ce{C-C} bond length $R$,\n\\item six \\ce{C-H} bond lengths $r_k$, $k$ $=$ 1, 2, \\ldots, 6,\n\\item six bond angles $\\angle$({H$_k$-C-C}) $=$ $\\alpha_k$, $k$ $=$ 1, 2, \\ldots, 6,\n\\item four dihedral-angle coordinates\n${\\gamma}_1$,\n${\\gamma}_2$,\n${\\delta}_1$, and\n${\\delta}_2$,\n\\item the torsional angle $\\tau$, and\n\\item the three rotational angles $(\\theta, \\phi, \\chi)$.\n\\end{enumerate}\nThe primitive basis functions for subsets 1, 2, 3, and 5 are obtained using the Numerov-Cooley approach \\citep{07YuThJe.method,24Numerov.method,61Coxxxx.method}, while we use harmonic-oscillator eigenfunctions~\\cite{98BuJexx} for subset 4.\nThe primitive basis set 5 is obtained by solving the 1D torsional Schr\\\"{o}dinger equation\n\\begin{equation}\n\\label{eq:torsion-schr-eq}\n \\left[-\\frac{1}{2}\\frac{\\partial}{\\partial \\tau} g_{\\tau,\\tau}^{\\rm 1D}(\\tau) \\frac{\\partial}{\\partial \\tau} + V^{\\rm 1D}(\\tau) \\right] | n \\rangle = E_n | n \\rangle\n\\end{equation}\nusing the basis set constructed from the normalised, $4\\pi$-periodic Fourier series functions $\\sqrt{1\/2\\pi} \\cos(k \\tau \/ 2 )$ and $\\sqrt{1\/2\\pi} \\sin(k \\tau \/ 2 )$. Here $g_{\\tau,\\tau}^{\\rm 1D}(\\tau)$ is the purely torsional element of the TROVE kinetic-energy $g$-matrix (see \\cite{07YuThJe.method}) and $V^{\\rm 1D}(\\tau)$ is the 1-dimensional, $2\\pi\/3$-periodic torsional part of the 18D potential energy function of ethane with the remaining 17 vibrational coordinates set to their equilibrium values. For both the kinetic-energy function $g_{\\tau,\\tau}^{\\rm 1D}(\\tau)$ and the potential function $V^{\\rm 1D}(\\tau)$ we must consider $\\tau$-values in the extended interval $[0, 4\\pi]$ as detailed in Section~\\ref{sec:extenedGTS} below.\n\n\n\\subsection{Transformation of the vibrational coordinates under {\\itshape\\bfseries G}$_{36}$\\ }\n\nAs described in \\sect{sect:irrep_g36}, one can construct every operation of {\\itshape\\bfseries G}$_{36}$\\ with only four generating operations. In the {\\sc TROVE}\\ calculations, we use the generators $R_2^{(-)} = (132)(456)$, $R_2^{(+)} = (123)(456)$, $R_3^{(+)} = (14)(26)(35)(ab)^*$ and $R_4^{(-)} = (14)(25)(36)(ab)$. Then, to describe the transformation properties of a coordinate for all elements in {\\itshape\\bfseries G}$_{36}$, we need only determine these properties for the four generating operations. We have implemented in {\\sc TROVE}\\ the procedure to generate the irreducible representations of {\\itshape\\bfseries G}$_{36}$\\ based on these four group generators and the multiplication rules from Table~\\ref{tab:multiplicationtable}. The latter can be conveniently represented as the following recursive rule:\n\\begin{equation}\nT_i = T_j \\, T_k,\\\n\\end{equation}\nwhere the operations $T_i$, $T_j$ and $T_k$ ($i,j,k = 1,\\ldots,36$) are as organised in Table~\\ref{tab:recurrence_prod}. \n\n\\begin{table}[hbtp!]\n\\caption{\\label{tab:recurrence_prod} The recursive rules to generate the elements of {\\itshape\\bfseries G}$_{36}$\\ using the four generators $T_2 = R_2^{(+)} = (123)(465)$, $T_{4} = R_4^{(-)}$ = $(14)(25)(36)(ab)$, $T_7 = R_2^{(-)}$ $=$ $(132)(456)$, and $ T_{19} = R_4^{(+)}$ $=$ $(14)(26)(35)(ab)^*$. See also Table~\\protect\\ref{tab:multiplicationtable} for the class structure of {\\itshape\\bfseries G}$_{36}$\\ and Fig.~\\protect\\ref{fig:4pi} for an illustration of the effects of the generators.}\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.35}\n\\begin{tabular}{lllclll}\n\\hline\\hline\n$T_{1\\phantom{0}}=$ & $E$ & \\phantom{\\huge l} && $T_{19}=$ &\n$(14)(25)(36)(ab)$ & $=R_4^{(-)}$ \\\\\n$T_{2\\phantom{0}}=$ & $(123)(456)$ & $=R_2^{(+)}$ && $T_{20}=$ & (16)(24)(34)$(ab)$ & $= T_{7} \\, T_{21}$ \\\\\n$T_{3\\phantom{0}}=$ & $(132)(465)$ & $={T_2}^2 $ && $T_{21}=$ & (15)(26)(34)$(ab)$ & $= T_{7}\\, T_{19}$ \\\\\n$T_{4\\phantom{0}}=$ & $(14)(26)(35)(ab)^*$ & $=R_4^{(+)}$ && $T_{22}=$ & (153426)$(ab)$ & $= T_{19} \\, T_2$ \\\\\n$T_{5\\phantom{0}}=$ & $(16)(25)(34)(ab)^*$ & $=T_2 \\, T_{6}$ && $T_{23}=$ & (162435)$(ab)$ & $=T_{19} \\, T_3 $ \\\\\n$T_{6\\phantom{0}}=$ & $(15)(24)(36)(ab)^*$ & $=T_{2} \\, T_{4}$ && $T_{24}=$ & (143624)$(ab)$ & $= T_{20} \\, T_2 $ \\\\\n$T_{7\\phantom{0}}=$ & $(132)(456)$ & $=R_2^{(-)}$ && $T_{25}=$ & (152634)$(ab)$ & $= T_{20} \\, T_3$ \\\\\n$T_{8\\phantom{0}}=$ & $(123)(465)$ & $={T_7}^2 $ && $T_{26}=$ & (163524)$(ab)$ & $= T_{21} \\,T_2 $ \\\\\n$T_{9\\phantom{0}}=$ & $(465)$ & $=T_7 \\, T_{2}$ && $T_{27}=$ & (142536)$(ab)$ & $= T_{21} \\, T_3 $ \\\\\n$T_{10}=$ & (123) & $=T_7 \\, T_{3}$ && $T_{28}=$ & (23)(56)$^*$ & $=T_{19} \\, T_4 $ \\\\\n$T_{11}=$ & $(132)$ & $=T_8 \\, T_{2}$ && $T_{29}=$ & (13)(46)$^*$ & $= T_{19} \\, T_{5} $ \\\\\n$T_{12}=$ & $(456)$ & $=T_8 \\, T_{3}$ && $T_{30}=$ & (12)(45)$^*$ & $= T_{19} \\, T_{6} $ \\\\\n$T_{13}=$ & (152436)$(ab)^*$ & $=T_7 \\, T_{4}$ && $T_{31}=$ & (12)(46)$^*$ & $= T_{20} \\, T_4 $ \\\\\n$T_{14}=$ & (142635)$(ab)^*$ & $=T_{7} \\, T_{5}$ && $T_{32}=$ & (23)(45)$^*$ & $=T_{20} \\, T_{5} $ \\\\\n$T_{15}=$ & (162534)$(ab)^*$ & $=T_{7} \\, T_{6}$ && $T_{33}=$ & (13)(56)$^*$ & $= T_{20} \\, T_{6} $ \\\\\n$T_{16}=$ & (163425)$(ab)^*$ & $=T_8 \\, T_{4}$ && $T_{34}=$ & (13)(45)$^*$ & $= T_{21} \\, T_4 $ \\\\\n$T_{17}=$ & (153624)$(ab)^*$ & $=T_{8} \\, T_{5}$ && $T_{35}=$ & (12)(56)$^*$ & $= T_{21} \\, T_{5} $ \\\\\n$T_{18}=$ & (143526)$(ab)^*$ & $=T_{8} \\, T_{6}$ && $T_{36}=$ & (23)(46)$^*$ & $=T_{21} \\, T_{6} $ \\\\\n\\hline\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\nEach of the vibrational coordinates and the torsional coordinate can be expressed as a function of the nuclear Cartesian coordinates. In the following, and in \\ref{sec:appendixB}, we describe the procedure in determining the transformation of these coordinates under the {\\itshape\\bfseries G}$_{36}$\\ operations in a systematic way, although in the majority of cases the result is intuitive.\n\nThe \\ce{C-C} bond length $R$ is invariant\nunder all {\\itshape\\bfseries G}$_{36}$\\ operations. We label the six \\ce{C-H_k} bond lengths $r_k$,\nand the six bond angles $\\angle${H$_k$-C-C} $=$ $\\alpha_k$, by the generic labels $\\beta_k$, as the two subsets transform identically. The transformation properties are determined by recognizing\n that after the operation $O_i$ $\\in$ {\\itshape\\bfseries G}$_{36}$\\ has been carried out, the proton 1, say, occupies the position\npreviously occupied by the proton $k$ (and the C nucleus to which it is bound has\nmoved with it), and therefore the transformed value of the \\ce{C-H$_1$} bond length is $r_{1}^{\\prime}$ $=$ $r_k$, the original value of the \\ce{C-H$_k$} bond length, with analogous considerations\n for the bond lengths $r_2$, \\dots, $r_6$, and the $\\alpha_i$ angles.\n\nFor ($\\beta_1$, $\\beta_2$, $\\beta_3$), we obtain the following transformation properties under the generating operations:\n\\begin{center}\n\\begin{tabbing}\n\\parbox[l]{7.4truecm}{\n$\n\\begin{pmatrix}\n\\beta_1^\\prime \\\\\n\\beta_2^\\prime \\\\\n\\beta_3^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n0 & 0 & 1 \\\\\n1 & 0 & 0 \\\\\n0 & 1 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_1 \\\\\n\\beta_2 \\\\\n\\beta_3\n\\end{pmatrix}\n\t$\nfor (123)(456),}\n\\parbox[l]{8.1truecm}{\n$\n\\begin{pmatrix}\n\\beta_1^\\prime \\\\\n\\beta_2^\\prime \\\\\n\\beta_3^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 & 0 \\\\\n0 & 0 & 1 \\\\\n0 & 1 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_4 \\\\\n\\beta_5 \\\\\n\\beta_6\n\\end{pmatrix}\n$\nfor $(14)(26)(35)(ab)^*,$}\n\\end{tabbing}\n\\begin{tabbing}\n\\parbox[l]{7.4truecm}{\n$\n\\begin{pmatrix}\n\\beta_1^\\prime \\\\\n\\beta_2^\\prime \\\\\n\\beta_3^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n0 & 1 & 0 \\\\\n0 & 0 & 1 \\\\\n1 & 0 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_1\\\\\n\\beta_2 \\\\\n\\beta_3\n\\end{pmatrix}\n$\nfor $(132)(456)$,}\n\\parbox[l]{8.0truecm}{\n$\n\\begin{pmatrix}\n\\beta_1^\\prime \\\\\n\\beta_2^\\prime \\\\\n\\beta_3^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 & 0 \\\\\n0 & 1 & 0 \\\\\n0 & 0 & 1\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_4 \\\\\n\\beta_5 \\\\\n\\beta_6\n\\end{pmatrix}\n$\nfor $(14)(25)(36)(ab)$}\n\\end{tabbing}\n\\end{center}\nwhile for $(\\beta_4, \\beta_5, \\beta_6)$ they are given by\n\\begin{center}\n\\begin{tabbing}\n\\parbox[l]{7.4truecm}{\n\t$\n\\begin{pmatrix}\n\\beta_4^\\prime \\\\\n\\beta_5^\\prime \\\\\n\\beta_6^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n0 & 0 & 1 \\\\\n1 & 0 & 0 \\\\\n0 & 1 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_4 \\\\\n\\beta_5 \\\\\n\\beta_6\n\\end{pmatrix}\n$\n\tfor $(123)(456)$,}\n\\parbox[l]{8.1truecm}{\n\t$\n\\begin{pmatrix}\n\\beta_4^\\prime \\\\\n\\beta_5^\\prime \\\\\n\\beta_6^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 & 0 \\\\\n0 & 0 & 1 \\\\\n0 & 1 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_1 \\\\\n\\beta_2 \\\\\n\\beta_3\n\\end{pmatrix}\n$\nfor $(14)(26)(35)(ab)^*,$}\n\\end{tabbing}\n\n\\begin{tabbing}\n\\parbox[l]{7.4truecm}{\n$\n\\begin{pmatrix}\n\\beta_4^\\prime \\\\\n\\beta_5^\\prime \\\\\n\\beta_6^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n0 & 0 & 1 \\\\\n1 & 0 & 0 \\\\\n0 & 1 & 0\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_4 \\\\\n\\beta_5 \\\\\n\\beta_6\n\\end{pmatrix}\n\t$\nfor $(132)(456)$,}\n\\parbox[l]{8.0truecm}{\n$\n\\begin{pmatrix}\n\\beta_4^\\prime \\\\\n\\beta_5^\\prime \\\\\n\\beta_6^\\prime\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 & 0 \\\\\n0 & 1 & 0 \\\\\n0 & 0 & 1\n\\end{pmatrix}\n\\begin{pmatrix}\n\\beta_1 \\\\\n\\beta_2 \\\\\n\\beta_3\n\\end{pmatrix}\n\t$\n\tfor $(14)(25)(36)(ab)$.}\n\\end{tabbing}\n\\end{center}\n\n\nThe dihedral-angle coordinates\n$({\\gamma}_1, {\\gamma}_2, {\\delta}_1,\n{\\delta}_2)$ are mixed by the {\\itshape\\bfseries G}$_{36}$\\ operations. The transformation properties are most easily determined by using the correspondence with the transformation of the\n$r_k$ and $\\alpha_k$ coordinates.\nFor $({\\gamma}_1, {\\gamma}_2)$ we write\n\\begin{equation}\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2 \\\\\n2\\pi \\\\\n\\end{pmatrix} =\n{\\mathbf Z} \\,\n\\begin{pmatrix}\n\\theta_{12} \\\\ \\theta_{23} \\\\ \\theta_{31} \\\\\n\\end{pmatrix}\n\\end{equation}\nwith\n\\begin{equation}\n{\\mathbf Z} =\n\\begin{pmatrix}\n-\\frac{1}{\\sqrt{6}}& \\frac{2}{\\sqrt{6}} &-\\frac{1}{\n \\sqrt{6}}\\\\ -{\\frac{1}{\\sqrt{2}}}&0&{\\frac{1}{\\sqrt{2}}}\n \\\\\n1 & 1 & 1 \\\\\n\\end{pmatrix}\n\\end{equation}\nwhere we have taken into account the constraint $\\theta_{12} + \\theta_{23} + \\theta_{31}$ $=$\n$2 \\pi$ in the third row of ${\\mathbf Z}$.\n\nAfter we have carried out the operation $(123)(456)$, the protons 1, 2, and 3 are found at the positions initially occupied by the protons 3, 1, and 2, respectively, and so\nthe angles\n $\\theta_{12}$,\n$\\theta_{23}$, $\\theta_{31}$\nare permuted as follows\n\\begin{equation}\n\\begin{pmatrix}\n\\theta_{12}' \\\\ \\theta_{23}' \\\\ \\theta_{31}' \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n\\theta_{31} \\\\ \\theta_{12} \\\\ \\theta_{23} \\\\\n\\end{pmatrix} =\n{\\mathbf S} \\,\n\\begin{pmatrix}\n\\theta_{12} \\\\ \\theta_{23} \\\\ \\theta_{31} \\\\\n\\end{pmatrix}\n= {\\mathbf S}\\, {\\mathbf Z}^{-1} \\,\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2 \\\\\n2\\pi \\\\\n\\end{pmatrix}\n\\end{equation}\nwith\n\\begin{equation}\n{\\mathbf S} =\n\\begin{pmatrix}\n0 & 0 & 1 \\\\\n1 & 0 & 0 \\\\\n0 & 1 & 0 \\\\\n\\end{pmatrix}\n\\end{equation}\nand we can finally calculate the transformed values of\n$({\\gamma}_1, {\\gamma}_2)$ as\n\\begin{equation}\n\\begin{pmatrix}\n{\\gamma}_1' \\\\\n{\\gamma}_2' \\\\\n2\\pi \\\\\n\\end{pmatrix} =\n{\\mathbf Z}\\,\n\\begin{pmatrix}\n\\theta_{12}' \\\\ \\theta_{23}' \\\\ \\theta_{31}' \\\\\n\\end{pmatrix} =\n{\\mathbf Z}\\, {\\mathbf S}\\, {\\mathbf Z}^{-1} \\,\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2 \\\\\n2\\pi \\\\\n\\end{pmatrix}\n\\end{equation}\nwhere\n\\begin{equation}\n{\\mathbf Z}\\, {\\mathbf S}\\, {\\mathbf Z}^{-1} =\n\\begin{pmatrix}\n-\\frac12 & -\\frac{\\sqrt{3}}{2} & 0 \\\\\n\\frac{\\sqrt{3}}{2} & -\\frac12 & 0 \\\\\n0 & 0 & 1 \\\\\n\\end{pmatrix}.\n\\end{equation}\nWith the upper 2~$\\times$~2 corner of this matrix we can express the transformed values $({\\gamma}_1', {\\gamma}_2')$ in terms of $({\\gamma}_1, {\\gamma}_2)$.\n The transformation matrix for $({\\gamma}_1, {\\gamma}_2)$ for $(123)(456)$, and the ones for the other generating operations, obtained in a similar manner, are\n\\begin{center}\n\\begin{tabbing}\n\\parbox[l]{7.3truecm}{\n$\n\\begin{pmatrix}\n{\\gamma}_1^\\prime \\\\\n{\\gamma}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n-\\frac12 & -\\frac{\\sqrt{3}}{2} \\\\\n\\frac{\\sqrt{3}}{2} & -\\frac12 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2\\\\\n\\end{pmatrix}\n$ for $(123)(456)$,}\n\\parbox[l]{8.2truecm}{\n$\n\\begin{pmatrix}\n{\\gamma}_1^\\prime \\\\\n{\\gamma}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 \\\\\n0 & -1 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\delta}_1 \\\\\n{\\delta}_2\\\\\n\\end{pmatrix}\n$ for $(14)(26)(35)(ab)^*,$}\n\\end{tabbing}\n\\begin{tabbing}\n\\parbox[l]{7.3truecm}{\n$\n\\begin{pmatrix}\n{\\gamma}_1^\\prime \\\\\n{\\gamma}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n-\\frac12 & \\frac{\\sqrt{3}}{2} \\\\\n-\\frac{\\sqrt{3}}{2} & -\\frac12 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2\\\\\n\\end{pmatrix}\n$ for $(132)(456)$,}\n\\parbox[l]{8.2truecm}{\n$\n\\begin{pmatrix}\n{\\gamma}_1^\\prime \\\\\n{\\gamma}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\delta}_1 \\\\\n{\\delta}_2\\\\\n\\end{pmatrix}\n$ for $(14)(25)(36)(ab),$}\n\\end{tabbing}\n\\end{center}\nand those for ($\\delta_1$, $\\delta_2$) are given by\n\\begin{center}\n\\begin{tabbing}\n\\parbox[l]{7.3truecm}{\n$\n\\begin{pmatrix}\n{\\delta}_1^\\prime \\\\\n{\\delta}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n-{\\frac{1}{2}}&{-\\frac{\\sqrt{3}}{2}}\\\\ {\\frac{\n \\sqrt{3}}{2}}&-{\\frac{1}{2}}\\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\delta}_1 \\\\\n{\\delta}_2\\\\\n\\end{pmatrix}\n$ for $(123)(456)$,}\n\\parbox[l]{8.2truecm}{\n$\n\\begin{pmatrix}\n{\\delta}_1^\\prime \\\\\n{\\delta}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 \\\\\n0 & -1 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2\\\\\n\\end{pmatrix}\n$ for $(14)(26)(35)(ab)^*,$}\n\\end{tabbing}\n\n\\begin{tabbing}\n\\parbox[l]{7.3truecm}{\n$\n\\begin{pmatrix}\n{\\delta}_1^\\prime \\\\\n{\\delta}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n-{\\frac{1}{2}}&{-\\frac{\\sqrt{3}}{2}}\\\\ {\\frac{\n \\sqrt{3}}{2}}&-{\\frac{1}{2}}\\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\delta}_1 \\\\\n{\\delta}_2\\\\\n\\end{pmatrix}\n$ for $(132)(456)$,}\n\\parbox[l]{8.2truecm}{\n$\n\\begin{pmatrix}\n{\\delta}_1^\\prime \\\\\n{\\delta}_2^\\prime \\\\\n\\end{pmatrix} =\n\\begin{pmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{pmatrix}\n\\begin{pmatrix}\n{\\gamma}_1 \\\\\n{\\gamma}_2\\\\\n\\end{pmatrix}\n$ for $(14)(25)(36)(ab).$}\n\\end{tabbing}\n\\end{center}\n\n\\subsection{The extended molecular symmetry group {\\itshape\\bfseries G}$_{36}$(EM) and the transformation of the torsional coordinate}\n\\label{sec:extenedGTS}\nAs explained in Section~{15.4.4} of \\cite{98BuJexx}, our separation of the rotational and torsional degrees of freedom has led $\\chi$ and $\\tau$ being double-valued. That is, there are two sets of\n$(\\chi,\\tau)$ values associated with the same physical situation.\nThis is most straightforwardly seen\nby considering Eq.~(\\ref{eq:chichiachib}) and the three angles\n$\\chi_a$, $\\chi_b$, and $\\chi$ appearing in it. The angle $\\chi_a$ is determined entirely by the positions in space of the protons 1, 2, 3 and their carbon nucleus C$_a$; $\\chi_b$ is determined by the positions of the protons 4, 5, 6 and their carbon nucleus C$_b$; and $\\chi$ is the average of the two. Due to the $2\\pi$ periodicity of $\\chi_a$, increasing it by $2\\pi$ does not change the positions in space of the nuclei in \\ce{C_$a$H3}, however in this case $\\chi$ $\\rightarrow$ $\\chi+\\pi$ and $\\tau \\rightarrow \\tau + 2\\pi$.\nThat is, the two coordinate pairs ($\\chi$,$\\tau$) and ($\\chi+\\pi$,$\\tau+2\\pi$) describe identical physical situations.\n\nOne way of avoiding the ambiguity described above would be to use a molecule-fixed axis system with, for example, $\\chi$ $=$ $\\chi_a$. This molecule-axis system is attached to the \\ce{CH3} group with the protons 1, 2, 3, and not influenced by the other \\ce{CH3} group. A $\\chi$ coordinate chosen in this manner has no ambiguity. However, as already mentioned it is advantageous to choose $\\chi$ according to Eq.~(\\ref{eq:chichiachib}) since this choice\n(called the Internal Axis Method (IAM), see Section~{15.2.2} of \\cite{98BuJexx}) yields a particularly useful form of the rotation-torsion-vibration Hamiltonian with minimized coupling between rotation and torsion. It is desirable to keep the definition of $\\chi$ from Eq.~(\\ref{eq:chichiachib}) and find a way of treating the ambiguity. We use here the procedure first proposed by Hougen~\\cite{64Hougen} in 1964, primarily for dimethylacetylene H$_3$CCCCH$_3$, whose internal rotation is essentially free, but generally applicable to other molecules such as ethane H$_3$CCH$_3$, hydrogen peroxide HOOH, and disulfane HSSH with two identical moieties carrying out internal rotation. Recently, these ideas have been extended to molecules with two different moieties and applied to oxadisulfane (a.k.a. hydrogen thio-peroxide) HSOH~\\cite{04YAMADA,09YAMADA}, and more recently they have been applied to computation of the rotation-torsion-vibrational spectra of hydrogen peroxide HOOH in Ref.~\\cite{15AlOvPo.H2O2,16AlPoOv.HOOH}, where the HOOH kinetic energy operator was built using the $x$-axis chosen to halve the dihedral angle between the \\ce{H$_1$-O-O} and \\ce{H$_4$-O-O} planes, as well as in Ref.~\\cite{18SzViRe}.\n\nWe consider the effect of {\\itshape\\bfseries G}$_{36}$\\ operations on $\\chi_a$, described thoroughly in Section 12.1.1 of \\cite{98BuJexx}, where the axes are rotated in such a way that the coordinates of the nuclei -- measured in a space-fixed axis system -- remain the same after the operation, assuming the \\ce{C_$a$H3} group is in the equilibrium configuration. Considering the operation (123), we see that, using our convention, $\\chi_a$ becomes $\\chi_a + 4\\pi\/3$ or, equivalently, $\\chi_a - 2\\pi\/3$. This would correspond to the pair $(\\tau, \\chi)$ becoming $(\\tau + 4\\pi\/3, \\chi + 2\\pi\/3)$ or $(\\tau - 2\\pi\/3, \\chi - \\pi\/3)$, which are no longer equivalent but correspond to the same physical situation as noted before. For $(123)^3 = E$, the changes become $(\\tau + 4\\pi, \\chi + 2\\pi) = (\\tau, \\chi)$ or $(\\tau -2\\pi, \\chi - \\pi) = (\\tau + 2\\pi, \\chi + \\pi)$. These are illustrated in \\fig{fig:4pi}(A) and \\fig{fig:4pi}(F), respectively. \n\n\n\n\n\n\n\nIn order to deal with the double-valuedness of ($\\tau$, $\\chi$), we extend the symmetry description in the manner first introduced by Hougen~\\cite{64Hougen}, by extending {\\itshape\\bfseries G}$_{36}$\\ to the extended molecular symmetry group {\\itshape\\bfseries G}$_{36}$(EM) as explained in Section~15.4.4 of \\cite{98BuJexx}.\nTo appreciate the definition of {\\itshape\\bfseries G}$_{36}$(EM), we note that the\ninternal coordinates $R$, $r_k$ and $\\alpha_k$ ($k$ $=$ 1, 2, \\ldots, 6),\n${\\gamma}_1$,\n${\\gamma}_2$,\n${\\delta}_1$,\n${\\delta}_2$,\n $\\theta$, and $ \\phi$ used for ethane in the present work are all ``space-fixed'' in the sense of Section~15.4.4 in~\\cite{98BuJexx}; the instantaneous values of these coordinates can be unambiguously obtained from the instantaneous coordinate values of the nuclei in a Cartesian, space-fixed axis system~\\cite{98BuJexx}, $XYZ$ say. \\ref{sec:appendixB} explains in detail how the internal coordinates values are determined from the Cartesian coordinate values.\n\n We present here the ideas of\nHougen~\\cite{64Hougen}, using the more modern notation of\nSection~15.4.4 in~\\cite{98BuJexx}. The extension of\n{\\itshape\\bfseries G}$_{36}$\\ to {\\itshape\\bfseries G}$_{36}$(EM) involves the introduction of\n a fictitious operation $E'$ (taken to be different from the identity $E$) which, for ethane, we can think of as letting the \\ce{C_$a$H3} do a full torsional revolution relative to the \\ce{C_$b$H3}. That is, $E'$ has the effect of transforming $\\chi$ $\\rightarrow$ $\\chi+\\pi$ and $\\tau$ $\\rightarrow$ $\\tau + 2\\pi$. After the application of $(E')^2$ the molecule-fixed axis system is back where it started, and so we take $(E')^2$ $=$ $E$. $E'$ does not affect the space-fixed nuclear coordinates; it has the same effect as the identity operation\non the complete rotation-torsion-vibration wavefunction of ethane.\n\nWe now define four generating operations $a$, $b$, $c$ and $d$\nthat transform $\\chi$ and $\\tau$ unambiguously and\n have the same effect on the space-fixed\ncoordinates [$R$, $r_k$ and $\\alpha_k$ ($k$ $=$ 1, 2, \\ldots, 6),\n${\\gamma}_1$,\n${\\gamma}_2$,\n${\\delta}_1$,\n${\\delta}_2$,\n $\\theta$, and $ \\phi$]\nas the {\\itshape\\bfseries G}$_{36}$\\ operations (123), (456), (14)(26)(35)($ab$)$^*$ and (23)(56)$^*$, respectively.\n Tables~A-28 and~A-33 of~\\cite{98BuJexx} are the character tables of {\\itshape\\bfseries G}$_{36}$\\ and {\\itshape\\bfseries G}$_{36}$(EM), respectively.\n Comparison of the two tables shows that\nthe four generating operations\n$R_2^{(-)} = (132)(456)$, $R_2^{(+)} = (123)(456)$, $R_4^{(+)} = (14)(26)(35)(ab)^*$ and $R_4^{(-)} = (14)(25)(36)(ab)$\nchosen for {\\itshape\\bfseries G}$_{36}$\\ in the present work correspond to $ab$, $a^5\\, b$, $c$, and $d\\, c$, respectively.\nFollowing Section~15.4.4 of~\\cite{98BuJexx},\nwe \\textit{define} in Table~\\ref{tab:torsion_transformations}\nthe effect on $\\chi$ and $\\tau$ of the {\\itshape\\bfseries G}$_{36}$(EM)\ngenerators. The approach of~\\cite{98BuJexx} to simply postulate, by definition, the\neffect of the {\\itshape\\bfseries G}$_{36}$(EM)\ngenerators on $\\chi$ and $\\tau$ may appear arbitrary. It is not, however.\nWe show in\nFig.~\\ref{fig:4pi} how, for each of the four {\\itshape\\bfseries G}$_{36}$(EM) generators\n$ab$, $a^5\\, b$, $c$, and $d\\, c$, the effect on\n$\\chi$ and $\\tau$ can be explained as the effect of the {\\itshape\\bfseries G}$_{36}$\\ partner\nof the {\\itshape\\bfseries G}$_{36}$(EM) generator in question (Table~\\ref{tab:torsion_transformations}).\n\n\n\\begin{table}[hbtp!]\n\\caption{\\label{tab:torsion_transformations} Transformation of the torsion angle $\\tau$ and the rotation angle $\\chi$ under the generators of {\\itshape\\bfseries G}$_{36}$(EM).}\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\\hline\nTransformed $\\tau$ &Transformed $\\chi$ &\n{\\itshape\\bfseries G}$_{36}$(EM) generator & {\\itshape\\bfseries G}$_{36}$\\ generator \\\\\n\\hline\n$\\tau - 4\\pi\/3$ & $\\chi$ & $ab$ & (123)(456) \\\\\n$\\tau$ & $\\chi + 2\\pi\/3$ & $a^5\\, b$ &(132)(456) \\\\\n$2\\pi- \\tau$ &$\\chi + \\pi$ & $c$ & (14)(26)(35)($ab$)$^*$ \\\\\n$\\tau$ & $\\chi$ & $d\\, c$ &(14)(25)(36)($ab$) \\\\\n$\\tau+2\\pi$ &$\\chi + \\pi$& $E'$ & \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nThe group generated by the five operations\n$a$, $b$, $c$, $d$, and $E'$ has 72 elements and, as mentioned above, it is denoted\n{\\itshape\\bfseries G}$_{36}$(EM), called an extended molecular symmetry (EMS)\ngroup, and its\ncharacter table is given as Table~A-33\nof~\\cite{98BuJexx}. This character table shows that we can think of {\\itshape\\bfseries G}$_{36}$(EM) as a direct product\n\\begin{equation}\n \\text{{\\itshape\\bfseries G}$_{36}$(EM)} = \\text{{\\itshape\\bfseries G}$_{36}$} \\times \\{ E,E' \\},\n\\end{equation}\nwhere the group $\\mathcal{G}_{36}$ is constructed from\nthe generating operations $a$, $b$, $c$ and $d$; it is isomorphic to {\\itshape\\bfseries G}$_{36}$, so that it has the irreducible representations given in Table~\\ref{tab:chartab}.\nThe two-element group $\\{ E,E' \\}$ is cyclic of order 2 and has two irreps $A'$ and $A''$, both one-dimensional, with the representation matrices $1$ or $-1$, respectively, under $E'$. The irreps of {\\itshape\\bfseries G}$_{36}$(EM) are straightforwardly constructed from those of {\\itshape\\bfseries G}$_{36}$.\n Each irrep $\\Gamma$ of {\\itshape\\bfseries G}$_{36}$\\ in Table~\\ref{tab:chartab} gives rise to two irreps of {\\itshape\\bfseries G}$_{36}$(EM),\n $\\Gamma_s$ $=$ $(\\Gamma,A')$ and\n $\\Gamma_d$ $=$ $(\\Gamma,A'')$ as given in Table~{A-33} of \\cite{98BuJexx}.\n An irrep $\\Gamma_s$ has identical characters for the operations $E$ and $E'$, $\\chi_s [E']$ $=$ $\\chi_s [E]$, whereas for the irrep\n $\\Gamma_d$, $\\chi_d [E']$ $=$ $-\\chi_d [E]$.\nAs long as we pretend that $E'$ $\\ne$ $E$, we must also pretend that the coordinate values $(\\tau,\\chi)$ and $E'\\, (\\tau,\\chi)$ $=$ $(\\tau+2\\pi,\\chi+\\pi)$ describe different physical situations. As a consequence, we must allow $\\tau$ to be periodic with a period of $4\\pi$ as already mentioned in connection with Eq.~(\\ref{eq:torsion-schr-eq}). The torsional potential energy function $V^{\\rm 1D}(\\tau)$ is periodic with period $2\\pi$, $V^{\\rm 1D}(\\tau)$ $=$ $V^{\\rm 1D}(\\tau+2\\pi)$ for $\\tau$ $\\in$ $[0, 2\\pi]$, and this symmetry causes the torsional wavefunctions $| n \\rangle$\nfrom Eq.~(\\ref{eq:torsion-schr-eq}) to be either symmetric (of $\\Gamma_s$ symmetry) or antisymmetric (of $\\Gamma_d$ symmetry) under $E'$.\n\n\nWe know that in reality, $E'$ $=$ $E$, and so only functions and coordinates with $\\Gamma_s$ symmetries occur in nature. Since we can form, for example, basis functions of an allowed $\\Gamma_s$ symmetry as products of an even number of factors, each with a forbidden symmetry $\\Gamma_d'$, say, we need to consider also the $\\Gamma_d$ symmetries initially for the torsional and rotational basis functions. The final wavefunctions resulting from our theoretical calculations should be subjected to a `reality check': They must necessarily have a $\\Gamma_s$ symmetry in {\\itshape\\bfseries G}$_{36}$(EM). In particular, torsional basis functions of $d$ symmetry must be combined with rotational basis functions of $d$ symmetry to produce a torsion-rotation basis function of an allowed $s$ symmetry.\n\n\n\\begin{figure}[htbp!]\n\\centering\n\n\\parbox{3.5cm}{(A)\n\\begin{tikzpicture}[scale=1.1]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 2};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {3};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {1};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {5};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {4};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] node[below] {6};\n\\draw[->] (0,0) -- ++ (200:1) node[left] {$x$};\n\n\\draw [domain=0:60] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[above] {$\\theta$};\n\\draw [domain=60:120] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)});\n\n\\draw [domain=160:180] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[left] {$\\tau$};\n\\draw[->] [domain=180:240] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)});\n\\end{tikzpicture}\n}\n \\parbox{3.5cm}{(B)\n \\begin{tikzpicture}[scale=1.1]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 3};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {1};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {2};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {6};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {5};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] node[below] {4};\n\\draw[->] (0,0) -- ++ (200:1) node[left] {$x$};\n\n\\draw [domain=280:400] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)}) node[above] {$\\tau$};\n\\draw[->] [domain=400:840] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)});\n\\end{tikzpicture}\n}\n\\parbox{3.5cm}{(C)\n\\begin{tikzpicture}[scale=1.1]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 1};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {2};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {3};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {6};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {5};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] node[below] {4};\n\\draw[->] (0,0) -- ++ (320:1) node[right] {$x$};\n\n\\draw [domain=280:320] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)}) node[right] {$\\tau$};\n\\draw[->] [domain=320:360] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)});\n\\end{tikzpicture}\n}\n\\parbox{3.5cm}{(D)\n\\begin{tikzpicture}[scale=1.1]\n\\draw[dashed] (0,0) circle(2pt)[fill] -- ++ (0+180:1) circle(2pt)[fill] node[left] {\\ 6};\n\\draw[dashed] (0,0) -- ++(120+180:1) circle(2pt)[fill] node[below right] {5};\n\\draw[dashed] (0,0) -- ++(240+180:1) circle(2pt)[fill] node[above right] {4};\n\n\\draw [] (0,0) -- ++ (40+180:1) circle(2pt)[fill] node[below left] {3};\n\\draw [] (0,0) -- ++(160+180:1) circle(2pt)[fill] node[below right] {1};\n\\draw [] (0,0) -- ++(280+180:1) circle(2pt)[fill] node[above] {2};\n\\draw[->] (0,0) -- ++ (200+180:1) node[right] {$x$};\n\n\n\\draw [domain=60:200] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[left] {$\\tau$};\n\\draw[->] [domain=200:340] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) ;\n\\end{tikzpicture}\n}\n\n\\parbox{3.5cm}{(E)\n\\begin{tikzpicture}[scale=1.1]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 5};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {6};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {4};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {2};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {1};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] node[below] {3};\n\\draw[->] (0,0) -- ++ (200:1) node[left] {$x$};\n\n\\draw[<-] [domain=160:180] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) node[left] {$\\tau$};\n\\draw [domain=180:240] plot ({ 0.3*cos(\\x)}, {0.3*sin(\\x)}) ;\n\\end{tikzpicture}\n}\n\\parbox{3.5cm}{(F)\n\\begin{tikzpicture}[scale=1.1]\n\\draw (0,0) circle(2pt)[fill] -- ++ (0:1) circle(2pt)[fill] node[right] {\\ 2};\n\\draw (0,0) -- ++(120:1) circle(2pt)[fill] node[above left] {3};\n\\draw (0,0) -- ++(240:1) circle(2pt)[fill] node[below left] {1};\n\n\\draw [dashed] (0,0) -- ++ (40:1) circle(2pt)[fill] node[above right] {5};\n\\draw [dashed] (0,0) -- ++(160:1) circle(2pt)[fill] node[above left] {4};\n\\draw [dashed] (0,0) -- ++(280:1) circle(2pt)[fill] node[below] {6};\n\\draw[->] (0,0) -- ++ (200+180:1) node[right] {$x$};\n\n\\draw [domain=160:330] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)}) node[right] {$\\tau$};Fa\n\\draw[->][domain=330:240+360] plot ({ e^((\\x+200)\/(3000))*0.3*cos(\\x)}, {e^((\\x+200)\/(3000))*0.3*sin(\\x)});\n\\end{tikzpicture}\n}\n\n\\caption{Newman projections of ethane showing the effects of the {\\itshape\\bfseries G}$_{36}$(EM) generators (and their {\\itshape\\bfseries G}$_{36}$\\ partners; see Table~\\protect\\ref{tab:torsion_transformations})\non $\\tau$ and $\\chi$; the change of $\\tau$ is represented by the curved arrow\nencircling the C--C axis and the change of $\\chi$ is illustrated by the change in $x$-axis orientation. (A): Starting configuration with $\\tau = 4\\pi\/9$ and the $x$-axis forming the clockwise angle $8\\pi\/9$ with the horizontal. (B): The effect of $ab$ $\\sim$ (123)(465) which causes $\\tau$ to decrease by $4\\pi\/3$ (equivalent to an increase of $8\\pi\/3$ ) and $\\chi$ to remain constant. (C): The effect of $a^5 \\, b$ $\\sim$ (132)(456) with $\\tau$ remaining constant and $\\chi$ changing by $+2\\pi\/3$. (D): The effect of $c$ $\\sim$ (14)(26)(35)$(ab)^*$ with $\\tau$ $\\rightarrow$ $2\\pi - \\tau$ and $\\chi$ $\\rightarrow$ $\\chi + \\pi$. (E): The effect of $d\\, c$ $\\sim$ (14)(25)(36)$(ab)$ under which $\\tau$ and $\\chi$ are both invariant. (F): The effect of $E'$ which has no {\\itshape\\bfseries G}$_{36}$\\ partner, $E'\\, \\tau$ $=$ $\\tau+2\\pi$ and $E'\\, \\chi$ $=$ $\\chi+\\pi$. }\n\\label{fig:4pi}\n\n\\end{figure}\n\n\n\n\n\n\n\\subsection{Rigid-symmetric-rotor function representations}\nAs mentioned above, we use the rigid-symmetric-rotor eigenfunctions $\\vert J, k, m \\rangle$~\\cite{98BuJexx} as primitive rotational basis functions. For $K\\neq 0$ (where $K = \\abs{k}$), the corresponding symmetrized functions\n are defined as\n\\begin{equation}\n\\ket{JKm\\eta} = \\frac{i^{\\eta}(-1)^\\sigma}{\\sqrt{2}}(\\ket{J, k, m } + (-1)^{J+K}\\ket{J, -k, m})\n\\end{equation}\nwhere\n\\begin{equation}\n\\begin{cases}\n\\sigma = K \\ \\text{mod} \\ 3 & \\eta = 1 \\\\\n\\sigma = 0 & \\eta = 0, \\\\\n\\end{cases}\n\\end{equation}\nwhile for $K=0$ it is $\\ket{J 0 0 \\eta} = i^{\\eta}\\ket{J,0,0}$ where $\\eta= J \\ \\text{mod} \\ 2 $. Using the rigid rotor transformation properties given in Eqs. (12-46) and (12-47) of \\cite{98BuJexx}, along with Tables~{12-1} and~{15-6} of \\cite{98BuJexx}, we can determine the irreps of the rigid rotor basis functions; the results are summarised in \\tabl{tab:rotation_irreps}.\n\n\\begin{table}[hbtp!]\n\\caption{\\label{tab:rotation_irreps} The irreps of the rigid rotor wavefunctions. For $K > 0$, the two functions with $\\eta$ $=$ 0, 1 generate a two-dimensional irrep or the direct sum of two one-dimensional irreps. For a given $K$ value, we list first the $\\eta=0$ function and then the $\\eta=1$ one. $n$ is a positive integer.}\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\\hline\n$K$ & $\\Gamma$ \\\\\n\\hline\n0 ($J$ even) & $A_{1s}$ \\\\\n0 ($J$ odd) & $A_{2s}$ \\\\\n$K=3n$ ($K$ even) & $A_{1s} \\oplus A_{2s}$ \\\\\n$K=3n$ ($K$ odd) & $A_{4d} \\oplus A_{3d}$ \\\\\n$K=3n+1$ ($K$ even) & $E_{1s}$ \\\\\n$K=3n+1$ ($K$ odd) & $E_{2d}$ \\\\\n$K=3n+2$ ($K$ even) & $E_{1s}$ \\\\\n$K=3n+2$ ($K$ odd) & $E_{2d}$ \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\n\n\\subsection{Symmetrisation of the basis set}\n\nOnce a set of basis functions has been constructed for one of the subsets mentioned above as eigenfunctions of a 1D Schr\\\"odinger equation, the degenerate eigenfunctions (which in general transform reducibly) are symmetrised by a sampling and projection procedure described in sections 4 and 5 of \\cite{17YuYaOv.methods}. Briefly, a set of geometries is sampled (typically around 50) and each MS operation is applied to the eigenfunctions to obtain an overdetermined set of linear equations which are solved for the transformation matrix effecting the operation on the degenerate eigenfunctions. Using the traces of these matrices and the irrep matrices, one can obtain the irreducible coefficients of the reducible matrix as well as projection operators onto the irreps. These operators are then applied to the eigenfunctions to generate the symmetrized basis functions.\n\nOne then produces the basis functions for the complete TROVE calculation as products of the symmetrised 1D basis functions, one 1D basis function from each of the sets defined above. In general, these total basis functions do not transform irreducibly, and so a further application of the symmetrisation procedure is required, although the sampling step can be omitted as the transformation properties of the `factor' functions are already known.\n\n\n\n\n\\section{Potential Energy Function of Ethane in a Symmetry Adapted Representation}\n\n\nTo represent the PES analytically, an on-the-fly symmetrization procedure has been implemented (see, e.g., \\citep{15OwYuYa.CH3Cl}). We first introduce the stretching coordinates\n\\begin{equation}\\label{eq:stretch1}\n\\xi_1=1-\\exp\\left(-a(R - R_{\\mathrm{e}})\\right)\n\\end{equation}\n\\begin{equation}\\label{eq:stretch2}\n\\xi_j=1-\\exp\\left(-b(r_i - r_{\\mathrm{e}})\\right){\\,};\\hspace{2mm}j=2,3,4,5,6,7{\\,}, \\hspace{2mm} i=j-1,\n\\end{equation}\n($a$ is used for the C--C internal coordinate $R$, and $b$ is used for the six C--H internal coordinates $r_1,r_2$, $r_3$, $r_4$, $r_5$ and $r_6$) the bending angular coordinates\n\\begin{equation}\\label{eq:angular1}\n\\xi_k = (\\alpha_i - \\alpha_{\\mathrm{e}}){\\,};\\hspace{2mm}k=8,9,10,11,12,13{\\,}, \\hspace{2mm} i=k-7,\n\\end{equation}\nthe dihedral coordinates from Eq.~(\\ref{eq:gamma-delta})\n\\begin{equation}\n\\left( \\xi_{14}, \\xi_{15}, \\xi_{16}, \\xi_{17} \\right) =\n\\left( {\\gamma}_1, {\\gamma}_2, {\\delta}_1, {\\delta}_2 \\right)\n\\end{equation}\nand, finally, the torsional term\n\\begin{equation}\\label{eq:angular3}\n\\xi_{18} = 1 + \\cos 3\\tau\n\\end{equation}\nwhere $\\tau$ is defined in Eq.~(\\ref{eq:taudef}).\nThe quantities\n $R_{\\mathrm{e}}$, $r_{\\mathrm{e}}$ and $\\alpha_{\\mathrm{e}}$ are the equilibrium structural parameter values of C$_2$H$_6$.\n\n\nTaking an initial potential term of the form\n\\begin{equation}\\label{eq:V_i}\nV_{\\bm k}^{\\mathrm{initial}}=\\prod_{i=1}^{18} \\xi_{i}^{\\,k_i}\n\\end{equation}\nwith maximum expansion order $\\sum_{i} k_i =6$, each symmetry operation $T_{X}$ of {\\itshape\\bfseries G}$_{36}$\\ (see Table~\\ref{tab:recurrence_prod}) is independently applied to $V_{\\bm k}^{\\mathrm{initial}}$, i.e.\n\\begin{equation}\\label{eq:V_op}\nV_{\\bm k}^{T_{X}} = T_{X}{\\,} V_{\\bm k}^{\\mathrm{initial}}(\\bm \\xi) = T_{X}\\left(\\prod_{i=1}^{18} \\xi_{i}^{\\,k_i}\\right)\n\\end{equation}\nwhere $T_{X}$ is one of the 36 operators of {\\itshape\\bfseries G}$_{36}$, to create 36 new terms. Here ${\\bm k}$ denotes the 18-dimensional hyper-index ${k_1, k_2, \\ldots , k_{18}}$ and $(\\bm \\xi)$ denotes $\\{\\xi_1,\\xi_2,\\ldots,\\xi_{18}\\}$. The results are summed up to produce a final term\n\\begin{equation}\\label{eq:V_f}\nV_{\\bm k}^{\\mathrm{final}}= \\sum_{T_{X}} V_{\\bm k}^{T_{X}},\n\\end{equation}\nwhich is itself subjected to the 36 {\\itshape\\bfseries G}$_{36}$\\ symmetry operations $T_{X}$ to check its invariance. The total potential function is then given by the expression\n\\begin{equation}\nV_{\\mathrm{total}}(\\bm \\xi)= \\sum_{\\bm k} {\\,} f_{\\bm k} V_{\\bm k}^{\\mathrm{final}}(\\bm \\xi)\n\\end{equation}\nwhere $f_{\\bm k}$ are the corresponding expansion coefficients determined through a least-squares fitting to the \\textit{ab initio}\\ data generated at the CCSD(T)-F12b\/aug-cc-pVTZ level of theory. The details of the PES will be given elsewhere. The symmetry operations are represented as matrices and are generated from the four chosen generators as described above (see also~\\ref{sec:appendixa}).\n\n\n\n\n\n\\section{Numerical Example}\n\nIn this section we will apply the symmetrisation procedure on a small test basis set for the ethane molecule. We will demonstrate how the method works for subsets 2 (six C$-$H$_i$ stretching modes), 4 (four dihedral-angle modes ${\\gamma}_1$, ${\\gamma}_2$, ${\\delta}_1$, ${\\delta}_2$), and 5 (the torsional mode $\\tau$). In subset 1 (C$-$C stretch), the symmetrised wavefunctions are of $A_{1s}$ symmetry only as each {\\itshape\\bfseries G}$_{36}$\\ operation leaves the bond length $R$ invariant; in subset 3 (six C$-$C$-$H$_i$ bending modes), each {\\itshape\\bfseries G}$_{36}$\\ element has the same effect on the coordinates as in subset 2, and so the irreps obtained for subset 3 are identical to those obtained for subset 2.\n\nIn TROVE calculations, the size of the primitive basis set is determined by the maximum polyad number $P_{\\text{max}}$, which occurs in the inequality\n\\begin{equation}\nP = a_1 n_1 + a_2 n_2 + a_3 n_3 + \\ldots \\leq P_{\\text{max}}\n\\end{equation}\nwhere $n_i$ is the excitation number for the primitive basis function of coordinate $i$ and $a_i$ is its polyad coefficient. In our example all $a_i$ $=$ 1.\n\n\\subsection{Subset 2 symmetrisation}\n\nFor the six-member subset 2, we set the maximum polyad number to be 1, so the space is seven-dimensional. We consider here the 7 unsymmetrised eigenfunctions at lowest energy, the latter 4 being degenerate. As the first three of these eigenfunctions eigenfunctions are non-degenerate, they are already symmetrised and no further work is required. The first one-dimensional energy solution (at $\\SI{0.0}{\\per\\centi\\meter}$) is essentially the primitive ground-state wavefunction with small contributions from the other primitives:\n\\begin{equation}\n\\label{eq:subset_1:no_1}\n\\Psi_1 = 0.9999374\\ket{000000} + \\ldots\n\\end{equation}\nwhere $\\ldots$ signifies small (of the order $10^{-14}$) contributions from other primitive functions (omitted in the following). For simplicity we give only 5--7 significant digits here, while the actual calculations are done in quadruple precision. The eigenfunction in Eq.~(\\ref{eq:subset_1:no_1}) has $A_{1s}$ symmetry.\n\nThe second one-dimensional solution (at $\\SI{2929.16}{\\per\\centi\\meter}$) is\n\\begin{equation}\n \\Psi_2 = \\frac{1}{\\sqrt{6}}(-\\ket{000001} -\\ket{000010} -\\ket{000100} +\\ket{001000} +\\ket{010000} +\\ket{100000})\n\\end{equation}\nand has $A_{4s}$ symmetry.\n\nThe final one-dimensional solution (at $\\SI{2940.44}{\\per\\centi\\meter}$) is\n\\begin{equation}\n \\Psi_3 = \\frac{1}{\\sqrt{6}}(\\ket{000001} +\\ket{000010} +\\ket{000100} +\\ket{001000} +\\ket{010000} + \\ket{100000})\n\\end{equation}\nwhich is totally symmetric and so of $A_{1s}$ symmetry.\n\nThe four unsymmetrised, degenerate solutions (at $\\SI{3007.21}{\\per\\centi\\meter}$) are\n\\begin{equation}\n\\begin{split}\n \\Psi_4 =& +0.565540\\ket{000001} -0.209498\\ket{000010} -0.356041\\ket{000100} -0.482230\\ket{001000} \\\\\n & -4.233691\\ket{010000} +0.524567\\ket{100000} \\\\\n \\Psi_5 =& -0.536788\\ket{000010} +0.446199\\ket{000100} +0.330258\\ket{001000} -0.578016\\ket{010000} \\\\\n &+0.247758\\ket{100000} \\\\\n \\Psi_6 =& +0.581276\\ket{000001} -0.308888\\ket{000010}-0.272388\\ket{000100} +0.398602\\ket{001000} \\\\\n &+0.157199\\ket{010000} -0.555801\\ket{100000} \\\\\n \\Psi_7 =& -0.489104\\ket{000010} +0.516345\\ket{000100} -0.407635\\ket{001000}+ 0.553226\\ket{010000} \\\\\n &-0.145592\\ket{100000}\n\\end{split}\n\\end{equation}\nwhich turns out to be of $G_s$ symmetry, and thus also already symmetrised. However,\n in this case there is ambiguity in the group matrices describing the transformation properties of the degenerate wavefunctions. We therefore find and apply a unitary transformation on the wavefunctions to produce functions with transformation properties described by our `standard' $G$ representation matrices collected in Section~\\ref{sec:finalmatrices}.\n To this end, we follow the sampling procedure from Ref.~\\cite{17YuYaOv.methods}, derive the transformation properties of the above wavefunctions and convert them to have our `standard' transformation properties. For this work, we modified the sampling procedure in TROVE by applying it to the five group generators only (out of 72). This simple modification led to a significant speedup of the sampling part of the code and is now the standard part of TROVE.\n The reduced symmetrised wavefunctions become\n\\begin{equation}\n\\begin{split}\n \\Psi_4 &= \\frac{1}{2\\sqrt{3}}( -\\ket{000001} -\\ket{000010} + 2\\ket{000100} -\\ket{001000} -\\ket{010000} + 2\\ket{100000}) \\\\\n \\Psi_5 &= \\frac{1}{2}(-\\ket{000001} + \\ket{000010} - \\ket{001000} + \\ket{010000})\\\\\n \\Psi_6 &= \\frac{1}{2\\sqrt{3}}(-\\ket{000001}-\\ket{000010} +2\\ket{000100} + \\ket{001000} +\\ket{010000} - 2\\ket{100000}) \\\\\n \\Psi_7 &= \\frac12 ( -\\ket{000001} +\\ket{000010} +\\ket{001000} - \\ket{010000})\n\\end{split}\n\\end{equation}\nwhich are recognised as the linear combinations (defined by the matrix ${\\mathbf V}$) of bond lengths $r_k$ that transform as the $G_s$ irrep [Eq.~\\eqref{eq:gtransform}].\n\n\\subsection{Subset 4 symmetrisation}\n\nFor subset 4, we use a maximum polyad number of 1 and thus we have 5 eigenfunctions, one non-degenerate and four degenerate ones.\n$\\ket{0000}$ is the first eigenfunction (at $\\SI{0.0}{\\per\\centi\\meter})$; it has $A_{1s}$ symmetry. The other four unsymmetrised eigenfunctions (at $\\SI{1469.30}{\\per\\centi\\meter})$ are\n\\begin{equation}\n\\begin{split}\n\\Psi_2 &= \\frac{1}{\\sqrt{2}}(\\ket{0001} -\\ket{0100}) \\\\\n\\Psi_3 &= -\\frac{1}{\\sqrt{2}}(\\ket{0001} + \\ket{0100}) \\\\\n\\Psi_4 &= -\\frac{1}{\\sqrt{2}}(\\ket{0010} + \\ket{1000}) \\\\\n\\Psi_5 &= \\frac{1}{\\sqrt{2}}(-\\ket{0010} + \\ket{1000})\n\\end{split}\n\\end{equation}\nwhich again turns out to be of $G_s$ symmetry. Here and in the following, $\\frac{1}{\\sqrt{2}}$ stands for the numerical value $0.707106781186545$ ($\\pm 10^{-15})$. The desired symmetrised functions are\n\\begin{equation}\n\\begin{split}\n\\Psi_2 &= \\frac{1}{\\sqrt{2}}(\n\\ket{0010} + \\ket{1000}) \\\\\n\\Psi_3 &=\n\\frac{1}{\\sqrt{2}}(\n\\ket{0001} + \\ket{0100}) \\\\\n\\Psi_4 &=\n\\frac{1}{\\sqrt{2}}(\n\\ket{0010} -\\ket{1000}\n) \\\\\n\\Psi_5 &= \\frac{1}{\\sqrt{2}}(\n\t\\ket{0001} -\\ket{0100}).\n\\end{split}\n\\end{equation}\n\\subsection{Subset 5 symmetrisation}\n\nFor the one dimensional subset 5 we use a maximum polyad number of 29 and show, for illustrative purposes, the symmetrisation of the first three eigenfunctions. The lowest energy solution (at $\\SI{0.0}{\\per\\centi\\meter}$ with $A_{1s}$ symmetry) is:\n\\begin{equation}\n\\Psi_1 = 0.999958\\ket{0} + \\ldots.\n\\end{equation}\n The second and third eigenfunctions (at $\\SI{0.0029}{\\per\\centi\\meter})$ are degenerate, and the unsymmetrised wavefunctions are\n\\begin{equation}\n\\begin{split}\n\\Psi_2 = & +0.0272058\\ket{1} + 0.999588\\ket{2} + \\ldots \\\\\n\\Psi_3 = &-0.999588\\ket{1} + 0.0272058\\ket{2} + \\ldots.\n\\end{split}\n\\end{equation}\nThese turn out to be of $E_{3d}$ symmetry, which we then convert to\n\\begin{equation}\n\\begin{split}\n\\Psi_2 = & -0.75926\\ket{1} - 0.65072\\ket{2} + \\ldots \\\\\n\\Psi_3 = &-0.65072\\ket{1} + 0.75926\\ket{2} + \\ldots\n\\end{split}\n\\end{equation}\nto obey our `standard' transformation properties imposed by the matrices in~\\ref{sec:appendixa}.\n\n\\subsection{Torsional basis function symmetries}\n\n\n\\fig{fig:irrep_energies} shows the torsional potential energy as a function of $\\tau$. In order for the torsional basis functions to transform according to the irreps of the extended MS group {\\itshape\\bfseries G}$_{36}$(EM), we obtain them as solutions of the 1D torsional Schr\\\"odinger equation in Eq.~\\eqref{eq:torsion-schr-eq}. In solving this Schr\\\"odinger equation in a Fourier-series basis [see the discussion of Eq.~\\eqref{eq:torsion-schr-eq}], we let $\\tau$ vary from 0 to $4\\pi$ so that the potential energy curve in \\fig{fig:irrep_energies} has six minima. In the figure, we indicate the lowest allowed torsional energies. Some of these energies are degenerate, i.e., associated with more than one eigenfunction of a given irreducible representation. In the limit of an infinite barrier height, we expect the energies to be six-fold degenerate. With the actual, finite height of the barrier, the energies form near-degenerate clusters with a total multiplicity of 6 as shown in \\fig{fig:zoomed_plot}. However, since our description of the torsional angle $\\tau$ $\\in$ $[0, 4 \\pi]$ is unphysical, only three of the states in the cluster (of $s$ symmetry) exist in nature if they are combined with rigid-rotor basis functions of $s$ symmetry. The other three states (of $d$ symmetry) must be combined with\nrigid-rotor basis functions of $d$ symmetry in order that the total rotation-torsion state can exist in nature.\nFor $J$ $=$ 0, only the $s$-type torsional states will exist since only $s$-type rigid-rotor basis functions are available.\n\n\\begin{figure}[htbp!]\n \\centering\n \\begin{tikzpicture}\n \\begin{axis}[\n xtick={\n0, 1.5708, 3.14159, 4.7123889, 6.28318,\n 7.85398, 9.42477, 10.9955689, 12.56636\n },\n xticklabels={\n $0$, $\\frac{\\pi}{2}$, $\\pi$, $\\frac{3\\pi}{2}$, $2\\pi$,\n $\\frac{5\\pi}{2}$, $3\\pi$, $\\frac{7\\pi}{2}$, $4\\pi$\n },\n xlabel={$\\tau$ (\\SI{}{\\radian})},\n ylabel={Energy\/$hc$ (\\SI{}{\\per\\centi\\meter})}]\n \\addplot[smooth] table[x=angle,y=energy] {\n angle energy\n 0\t1003.77951556\n0.069813170079778\t992.60301469816\n0.139626340159556\t959.590813837953\n0.209439510239333\t906.266645428049\n0.279252680319111\t835.078568736274\n0.349065850398889\t749.26978315875\n0.418879020478667\t652.712557344184\n0.488692190558445\t549.717316998068\n0.558505360638222\t444.8292039328\n0.628318530718\t342.623379896951\n0.698131700797778\t247.50848945125\n0.767944870877556\t163.545565412708\n0.837758040957333\t94.287710200816\n0.907571211037111\t42.6443703823134\n0.977384381116889\t10.7729746917228\n1.04719755119667\t4.10521118250522E-28\n1.11701072127644\t10.7729746917228\n1.18682389135622\t42.6443703823134\n1.256637061436\t94.287710200816\n1.32645023151578\t163.545565412708\n1.39626340159556\t247.50848945125\n1.46607657167533\t342.623379896951\n1.53588974175511\t444.8292039328\n1.60570291183489\t549.717316998068\n1.67551608191467\t652.712557344184\n1.74532925199444\t749.26978315875\n1.81514242207422\t835.078568736274\n1.884955592154\t906.266645428049\n1.95476876223378\t959.590813837953\n2.02458193231356\t992.60301469816\n2.09439510239333\t1003.77951556\n2.16420827247311\t992.60301469816\n2.23402144255289\t959.590813837953\n2.30383461263267\t906.266645428049\n2.37364778271244\t835.078568736274\n2.44346095279222\t749.26978315875\n2.513274122872\t652.712557344184\n2.58308729295178\t549.717316998069\n2.65290046303156\t444.829203932801\n2.72271363311133\t342.623379896951\n2.79252680319111\t247.50848945125\n2.86233997327089\t163.545565412708\n2.93215314335067\t94.2877102008161\n3.00196631343044\t42.6443703823134\n3.07177948351022\t10.7729746917228\n3.14159265359\t4.16074439846136E-28\n3.21140582366978\t10.7729746917228\n3.28121899374956\t42.6443703823133\n3.35103216382933\t94.287710200816\n3.42084533390911\t163.545565412708\n3.49065850398889\t247.50848945125\n3.56047167406867\t342.623379896951\n3.63028484414844\t444.8292039328\n3.70009801422822\t549.717316998068\n3.769911184308\t652.712557344184\n3.83972435438778\t749.26978315875\n3.90953752446756\t835.078568736274\n3.97935069454733\t906.266645428049\n4.04916386462711\t959.590813837953\n4.11897703470689\t992.60301469816\n4.18879020478667\t1003.77951556\n4.25860337486644\t992.60301469816\n4.32841654494622\t959.590813837953\n4.398229715026\t906.266645428049\n4.46804288510578\t835.078568736274\n4.53785605518556\t749.26978315875\n4.60766922526533\t652.712557344184\n4.67748239534511\t549.717316998069\n4.74729556542489\t444.829203932801\n4.81710873550467\t342.623379896951\n4.88692190558445\t247.50848945125\n4.95673507566422\t163.545565412708\n5.026548245744\t94.2877102008161\n5.09636141582378\t42.6443703823134\n5.16617458590356\t10.7729746917229\n5.23598775598333\t4.27181083037364E-28\n5.30580092606311\t10.7729746917228\n5.37561409614289\t42.6443703823133\n5.44542726622267\t94.2877102008159\n5.51524043630244\t163.545565412708\n5.58505360638222\t247.50848945125\n5.654866776462\t342.623379896951\n5.72467994654178\t444.8292039328\n5.79449311662156\t549.717316998068\n5.86430628670133\t652.712557344184\n5.93411945678111\t749.26978315875\n6.00393262686089\t835.078568736274\n6.07374579694067\t906.266645428049\n6.14355896702045\t959.590813837953\n6.21337213710022\t992.60301469816\n6.28318530718\t1003.77951556\n6.35299847725978\t992.60301469816\n6.42281164733956\t959.590813837953\n6.49262481741933\t906.266645428049\n6.56243798749911\t835.078568736274\n6.63225115757889\t749.26978315875\n6.70206432765867\t652.712557344184\n6.77187749773844\t549.717316998069\n6.84169066781822\t444.829203932801\n6.911503837898\t342.623379896951\n6.98131700797778\t247.50848945125\n7.05113017805756\t163.545565412708\n7.12094334813733\t94.2877102008161\n7.19075651821711\t42.6443703823134\n7.26056968829689\t10.7729746917229\n7.33038285837667\t4.43841047824206E-28\n7.40019602845644\t10.7729746917228\n7.47000919853622\t42.6443703823133\n7.539822368616\t94.2877102008159\n7.60963553869578\t163.545565412708\n7.67944870877556\t247.50848945125\n7.74926187885533\t342.623379896951\n7.81907504893511\t444.8292039328\n7.88888821901489\t549.717316998068\n7.95870138909467\t652.712557344184\n8.02851455917445\t749.26978315875\n8.09832772925422\t835.078568736274\n8.168140899334\t906.266645428049\n8.23795406941378\t959.590813837953\n8.30776723949356\t992.60301469816\n8.37758040957333\t1003.77951556\n8.44739357965311\t992.603014698161\n8.51720674973289\t959.590813837953\n8.58701991981267\t906.266645428049\n8.65683308989244\t835.078568736274\n8.72664625997222\t749.26978315875\n8.796459430052\t652.712557344184\n8.86627260013178\t549.717316998069\n8.93608577021156\t444.829203932801\n9.00589894029133\t342.623379896951\n9.07571211037111\t247.50848945125\n9.14552528045089\t163.545565412708\n9.21533845053067\t94.2877102008162\n9.28515162061044\t42.6443703823135\n9.35496479069022\t10.7729746917229\n9.42477796077\t4.66054334206662E-28\n9.49459113084978\t10.7729746917228\n9.56440430092956\t42.6443703823133\n9.63421747100933\t94.2877102008159\n9.70403064108911\t163.545565412708\n9.77384381116889\t247.50848945125\n9.84365698124867\t342.623379896951\n9.91347015132845\t444.8292039328\n9.98328332140822\t549.717316998068\n10.053096491488\t652.712557344184\n10.1229096615678\t749.26978315875\n10.1927228316476\t835.078568736274\n10.2625360017273\t906.266645428049\n10.3323491718071\t959.590813837953\n10.4021623418869\t992.60301469816\n10.4719755119667\t1003.77951556\n10.5417886820464\t992.603014698161\n10.6116018521262\t959.590813837953\n10.681415022206\t906.26664542805\n10.7512281922858\t835.078568736274\n10.8210413623656\t749.26978315875\n10.8908545324453\t652.712557344184\n10.9606677025251\t549.717316998069\n11.0304808726049\t444.829203932801\n11.1002940426847\t342.623379896951\n11.1701072127644\t247.50848945125\n11.2399203828442\t163.545565412708\n11.309733552924\t94.2877102008162\n11.3795467230038\t42.6443703823135\n11.4493598930836\t10.7729746917229\n11.5191730631633\t4.93820942184732E-28\n11.5889862332431\t10.7729746917228\n11.6587994033229\t42.6443703823132\n11.7286125734027\t94.2877102008159\n11.7984257434824\t163.545565412708\n11.8682389135622\t247.50848945125\n11.938052083642\t342.623379896951\n12.0078652537218\t444.8292039328\n12.0776784238016\t549.717316998068\n12.1474915938813\t652.712557344184\n12.2173047639611\t749.26978315875\n12.2871179340409\t835.078568736274\n12.3569311041207\t906.266645428049\n12.4267442742004\t959.590813837953\n12.4965574442802\t992.60301469816\n12.56637061436\t1003.77951556\n};\n\n \\addplot[mark=none,,blue,style=ultra thin] coordinates {(0.786555, 145.221) (1.30784, 145.221)};\n \\addplot[mark=none,blue,dashed, style=ultra thin] coordinates {(0.786553, 145.224) (1.30784, 145.224)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.786547, 145.23) (1.30785, 145.23)};\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.786544, 145.233) (1.30785, 145.233)};\n\n \\addplot[mark=none,blue,dashed, style=ultra thin] coordinates {(0.576294, 421.286) (1.5181, 421.286)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.576223, 421.391) (1.51817, 421.391)};\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.576073, 421.613) (1.51832, 421.613)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.575998, 421.725) (1.5184, 421.725)};\n\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.41252, 663.551) (1.68187, 663.551)};\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.411362, 665.193) (1.68303, 665.193)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.408908, 668.661) (1.68549, 668.661)};\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.407645, 670.445) (1.68675, 670.445)};\n\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.265027, 850.114) (1.82937, 850.114)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.256877, 858.736) (1.83752, 858.736)};\n \\addplot[mark=none,blue,dashed,style=ultra thin] coordinates {(0.235004, 880.801) (1.85939, 880.801)};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.217873, 896.944) (1.87652, 896.944)};\n\n\\end{axis}\n \\end{tikzpicture}\n \\caption{The torsional potential energy as a function of the torsion angle $\\tau$. The allowed energy values are marked by blue horizontal lines. Each energy may correspond to more than one eigenfunction of a given irreducible representation. Dashed lines indicate states of $d$-type symmetry.}\n \\label{fig:irrep_energies}\n\\end{figure}\n\n\\begin{figure}[htbp!]\n \\centering\n \\begin{tikzpicture}\n \\begin{axis}[\n ylabel style={yshift=0.4cm},\n xlabel={$\\tau$ (\\SI{}{\\radian})},\n ylabel={Energy\/$hc$ (\\SI{}{\\per\\centi\\meter})},\n yticklabel style={\/pgf\/number format\/.cd,fixed zerofill,precision=3}]\n \\addplot[smooth] table[x=angle,y=energy] {\n angle energy\n0.786557 145.22\n0.786538 145.24\n };\n \\addplot[smooth] table[x=angle,y=energy] {\n angle energy\n1.30784 145.22\n1.30786 145.24\n };\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.786555, 145.221) (1.30784, 145.221)} node[above left]{$A_{1s}$};\n \\addplot[mark=none,blue,dashed, style=ultra thin] coordinates {(0.786553, 145.224) (1.30784, 145.224)} node[above left]{$E_{3d}$};\n \\addplot[mark=none,blue,style=ultra thin] coordinates {(0.786547, 145.23) (1.30785, 145.23)} node[above left]{$E_{3s}$};\n \\addplot[mark=none,blue, dashed, style=ultra thin] coordinates {(0.786544, 145.233) (1.30785, 145.233)} node[above left]{$A_{1d}$};\n \\end{axis}\n \\end{tikzpicture}\n \\caption{A enlarged detail of \\protect\\fig{fig:irrep_energies}, showing the lowest energy cluster with the {\\itshape\\bfseries G}$_{36}$(EM) symmetry labels indicated.}\n \\label{fig:zoomed_plot}\n\\end{figure}\n\n\\fig{fig:torsion_ground} shows the ground state torsional wavefunction which, as always, is totally symmetric (of $A_{1s}$ symmetry) in {\\itshape\\bfseries G}$_{36}$(EM). The effect of the {\\itshape\\bfseries G}$_{36}$(EM) generators on $\\tau$ is shown in \\tabl{tab:torsion_transformations}. In \\fig{fig:torsion_first} (left display) we show the doubly-degenerate wavefunctions of the first excited state. They span the $E_{3d}$ irrep but must be transformed to obtain the transformation properties imposed by the $E_{3d}$ matrices described in \\sect{sec:Einalmatrices}. The transformed functions, with the desired transformation properties are shown in \\fig{fig:torsion_first} (right display).\n\n\n\\begin{figure}[htbp!]\n\t \\centering\n\t\t \\begin{tikzpicture}\n\t\t\t\t \\begin{axis}[\n\t\t\t\t\t\t\t xtick={\n\t\t\t\t\t\t\t\t 0, 1.5708, 3.14159, 4.7123889, 6.28318,\n\t\t\t\t\t\t\t\t 7.85398, 9.42477, 10.9955689, 12.56636\n\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t xticklabels={\n\t\t\t\t\t\t\t\t\t\t\t $0$, $\\frac{\\pi}{2}$, $\\pi$, $\\frac{3\\pi}{2}$, $2\\pi$,\n\t\t\t\t\t\t\t\t\t\t\t\t $\\frac{5\\pi}{2}$, $3\\pi$, $\\frac{7\\pi}{2}$, $4\\pi$\n\t\t\t\t\t\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t xlabel={$\\tau$ (\\SI{}{\\radian})},\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t ylabel={Amplitude}]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\addplot[smooth] table[x=angle,y=energy] {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t angle energy\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0\t-0.00277264\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.006981317\t-0.002778\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.013962634\t-0.00279411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.020943951\t-0.002821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.027925268\t-0.0028588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.034906585\t-0.00290762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.041887902\t-0.00296766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0488692191\t-0.00303911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0558505361\t-0.00312224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0628318531\t-0.00321734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0698131701\t-0.00332474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0767944871\t-0.00344484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0837758041\t-0.00357805\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0907571211\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0977384381\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1047197551\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1117010721\t-0.00425195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1186823891\t-0.00445859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1256637061\t-0.00468183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1326450232\t-0.00492241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1396263402\t-0.00518113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1466076572\t-0.00545886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1535889742\t-0.00575648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1605702912\t-0.00607498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1675516082\t-0.00641537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1745329252\t-0.00677873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1815142422\t-0.0071662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1884955592\t-0.00757898\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1954768762\t-0.00801835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2024581932\t-0.00848562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2094395102\t-0.00898219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2164208272\t-0.00950953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2234021443\t-0.01006918\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2303834613\t-0.01066272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2373647783\t-0.01129184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2443460953\t-0.01195829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2513274123\t-0.01266388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2583087293\t-0.01341051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2652900463\t-0.01420016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2722713633\t-0.01503487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2792526803\t-0.01591677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2862339973\t-0.01684806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2932153143\t-0.01783102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3001966313\t-0.01886802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3071779484\t-0.01996149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3141592654\t-0.02111394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3211405824\t-0.02232796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3281218994\t-0.02360623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3351032164\t-0.02495147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3420845334\t-0.0263665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3490658504\t-0.0278542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3560471674\t-0.02941753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3630284844\t-0.03105949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3700098014\t-0.03278316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3769911184\t-0.03459168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3839724354\t-0.03648824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3909537524\t-0.03847606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3979350695\t-0.04055844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4049163865\t-0.04273869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4118977035\t-0.04502017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4188790205\t-0.04740625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4258603375\t-0.04990033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4328416545\t-0.05250581\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4398229715\t-0.0552261\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4468042885\t-0.05806461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4537856055\t-0.06102472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4607669225\t-0.06410978\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4677482395\t-0.06732312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4747295565\t-0.070668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4817108736\t-0.07414764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4886921906\t-0.07776517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.4956735076\t-0.08152364\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5026548246\t-0.085426\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5096361416\t-0.08947509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5166174586\t-0.0936736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5235987756\t-0.09802411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5305800926\t-0.10252901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5375614096\t-0.10719052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5445427266\t-0.11201069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5515240436\t-0.11699133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5585053606\t-0.12213405\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5654866776\t-0.12744021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5724679947\t-0.13291091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5794493117\t-0.13854696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5864306287\t-0.14434891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5934119457\t-0.15031697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6003932627\t-0.15645104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6073745797\t-0.16275067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6143558967\t-0.16921505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6213372137\t-0.17584299\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6283185307\t-0.18263294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6352998477\t-0.18958291\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6422811647\t-0.19669052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6492624817\t-0.20395293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6562437987\t-0.21136688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6632251158\t-0.21892865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6702064328\t-0.22663407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6771877498\t-0.23447847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6841690668\t-0.24245672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6911503838\t-0.25056321\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.6981317008\t-0.25879184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7051130178\t-0.26713601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7120943348\t-0.27558862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7190756518\t-0.2841421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7260569688\t-0.29278839\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7330382858\t-0.30151892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7400196028\t-0.31032467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7470009199\t-0.31919614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7539822369\t-0.32812338\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7609635539\t-0.33709597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7679448709\t-0.34610308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7749261879\t-0.35513346\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7819075049\t-0.36417547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7888888219\t-0.37321708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.7958701389\t-0.38224592\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.8028514559\t-0.39124929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.8098327729\t-0.40021419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.8168140899\t-0.40912734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.8237954069\t-0.41797525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.8307767239\t-0.42674418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.837758041\t-0.43542024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.844739358\t-0.44398941\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.851720675\t-0.45243756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.858701992\t-0.46075048\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.865683309\t-0.46891397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.872664626\t-0.47691383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.879645943\t-0.48473591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.88662726\t-0.4923662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.893608577\t-0.49979079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.900589894\t-0.506996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.907571211\t-0.51396833\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.914552528\t-0.52069461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9215338451\t-0.52716196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9285151621\t-0.53335785\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9354964791\t-0.53927018\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9424777961\t-0.54488727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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3.9863320116\t-0.00848562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9933133286\t-0.00801835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0002946456\t-0.00757898\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0072759626\t-0.0071662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0142572796\t-0.00677873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0212385966\t-0.00641537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0282199136\t-0.00607498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0352012306\t-0.00575648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0421825476\t-0.00545886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0491638646\t-0.00518113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0561451816\t-0.00492241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0631264986\t-0.00468183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0701078157\t-0.00445859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0770891327\t-0.00425195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0840704497\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0910517667\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0980330837\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1050144007\t-0.00357805\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1119957177\t-0.00344484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1189770347\t-0.00332474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1259583517\t-0.00321734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1329396687\t-0.00312224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1399209857\t-0.00303911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1469023027\t-0.00296766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1538836197\t-0.00290762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1608649368\t-0.0028588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1678462538\t-0.002821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1748275708\t-0.00279411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1818088878\t-0.002778\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1887902048\t-0.00277264\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1957715218\t-0.002778\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2027528388\t-0.00279411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2097341558\t-0.002821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2167154728\t-0.0028588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2236967898\t-0.00290762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2306781068\t-0.00296766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2376594238\t-0.00303911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2446407409\t-0.00312224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2516220579\t-0.00321734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2586033749\t-0.00332474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2655846919\t-0.00344484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2725660089\t-0.00357805\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2795473259\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2865286429\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2935099599\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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4.5099307872\t-0.02232796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5169121042\t-0.02360623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5238934212\t-0.02495147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5308747382\t-0.0263665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5378560552\t-0.0278542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5448373722\t-0.02941753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5518186892\t-0.03105949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5588000062\t-0.03278316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5657813232\t-0.03459168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5727626402\t-0.03648824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5797439572\t-0.03847606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5867252742\t-0.04055844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5937065912\t-0.04273869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6006879083\t-0.04502017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6076692253\t-0.04740625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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4.7193702974\t-0.10252901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7263516144\t-0.10719052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7333329314\t-0.11201069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7403142484\t-0.11699133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7472955654\t-0.12213405\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7542768824\t-0.12744021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7612581994\t-0.13291091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7682395164\t-0.13854696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7752208335\t-0.14434891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7822021505\t-0.15031697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7891834675\t-0.15645104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7961647845\t-0.16275067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8031461015\t-0.16921505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8101274185\t-0.17584299\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8171087355\t-0.18263294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8240900525\t-0.18958291\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8310713695\t-0.19669052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8380526865\t-0.20395293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8450340035\t-0.21136688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8520153205\t-0.21892865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8589966376\t-0.22663407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8659779546\t-0.23447847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8729592716\t-0.24245672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8799405886\t-0.25056321\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8869219056\t-0.25879184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8939032226\t-0.26713601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9008845396\t-0.27558862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9078658566\t-0.2841421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9148471736\t-0.29278839\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9218284906\t-0.30151892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9288098076\t-0.31032467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9357911246\t-0.31919614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9427724416\t-0.32812338\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9497537587\t-0.33709597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9567350757\t-0.34610308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9637163927\t-0.35513346\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9706977097\t-0.36417547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9776790267\t-0.37321708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9846603437\t-0.38224592\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9916416607\t-0.39124929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9986229777\t-0.40021419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0056042947\t-0.40912734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0125856117\t-0.41797525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0195669287\t-0.42674418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0265482457\t-0.43542024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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9.7459185431\t-0.29278839\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7528998601\t-0.2841421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7598811772\t-0.27558862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7668624942\t-0.26713601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7738438112\t-0.25879184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7808251282\t-0.25056322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7878064452\t-0.24245672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7947877622\t-0.23447847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8017690792\t-0.22663407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8087503962\t-0.21892865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8157317132\t-0.21136688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8227130302\t-0.20395293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8296943472\t-0.19669052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8366756642\t-0.18958292\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8436569812\t-0.18263294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8506382983\t-0.175843\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8576196153\t-0.16921505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8646009323\t-0.16275067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8715822493\t-0.15645104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8785635663\t-0.15031697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8855448833\t-0.14434891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8925262003\t-0.13854696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8995075173\t-0.13291091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9064888343\t-0.12744021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9134701513\t-0.12213405\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9204514683\t-0.11699133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9274327853\t-0.11201069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9344141024\t-0.10719052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9413954194\t-0.10252901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9483767364\t-0.09802411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9553580534\t-0.0936736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9623393704\t-0.08947509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9693206874\t-0.085426\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9763020044\t-0.08152364\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9832833214\t-0.07776517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9902646384\t-0.07414764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9972459554\t-0.070668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0042272724\t-0.06732312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0112085894\t-0.06410978\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0181899064\t-0.06102472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0251712235\t-0.05806461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0321525405\t-0.0552261\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0391338575\t-0.05250581\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0461151745\t-0.04990033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0530964915\t-0.04740625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0600778085\t-0.04502017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0670591255\t-0.04273869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0740404425\t-0.04055844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0810217595\t-0.03847606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0880030765\t-0.03648824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0949843935\t-0.03459168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1019657105\t-0.03278316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1089470276\t-0.03105949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1159283446\t-0.02941753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1229096616\t-0.0278542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1298909786\t-0.0263665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1368722956\t-0.02495147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1438536126\t-0.02360623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1508349296\t-0.02232796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1578162466\t-0.02111394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1647975636\t-0.01996149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1717788806\t-0.01886802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1787601976\t-0.01783102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1857415146\t-0.01684806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1927228316\t-0.01591677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1997041487\t-0.01503487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2066854657\t-0.01420016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2136667827\t-0.01341051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2206480997\t-0.01266388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2276294167\t-0.01195829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2346107337\t-0.01129184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2415920507\t-0.01066272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2485733677\t-0.01006918\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2555546847\t-0.00950953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2625360017\t-0.00898219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2695173187\t-0.00848562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2764986357\t-0.00801835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2834799528\t-0.00757898\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2904612698\t-0.0071662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2974425868\t-0.00677873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3044239038\t-0.00641537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3114052208\t-0.00607498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3183865378\t-0.00575648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3253678548\t-0.00545886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3323491718\t-0.00518113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3393304888\t-0.00492241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3463118058\t-0.00468183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3532931228\t-0.00445859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3602744398\t-0.00425195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3672557568\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3742370739\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3812183909\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3881997079\t-0.00357805\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3951810249\t-0.00344484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4021623419\t-0.00332474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4091436589\t-0.00321734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4161249759\t-0.00312224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4231062929\t-0.00303911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4300876099\t-0.00296766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4370689269\t-0.00290762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4440502439\t-0.0028588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4510315609\t-0.002821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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10.5627326331\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5697139501\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5766952671\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5836765841\t-0.00425195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5906579011\t-0.00445859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5976392181\t-0.00468183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6046205351\t-0.00492241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6116018521\t-0.00518113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6185831691\t-0.00545886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6255644861\t-0.00575648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6325458031\t-0.00607498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6395271202\t-0.00641537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6465084372\t-0.00677873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6534897542\t-0.0071662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6604710712\t-0.00757898\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6674523882\t-0.00801835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6744337052\t-0.00848562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6814150222\t-0.00898219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6883963392\t-0.00950953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6953776562\t-0.01006918\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7023589732\t-0.01066272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7093402902\t-0.01129184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7163216072\t-0.01195829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7233029243\t-0.01266388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7302842413\t-0.01341051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7372655583\t-0.01420016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7442468753\t-0.01503487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7512281923\t-0.01591677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7582095093\t-0.01684806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7651908263\t-0.01783102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7721721433\t-0.01886802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7791534603\t-0.01996149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7861347773\t-0.02111394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7931160943\t-0.02232796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8000974113\t-0.02360623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8070787283\t-0.02495147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8140600454\t-0.0263665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8210413624\t-0.0278542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8280226794\t-0.02941753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8350039964\t-0.03105949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8419853134\t-0.03278316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8489666304\t-0.03459168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8559479474\t-0.03648824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8629292644\t-0.03847606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8699105814\t-0.04055844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8768918984\t-0.04273869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8838732154\t-0.04502017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8908545324\t-0.04740625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8978358495\t-0.04990033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9048171665\t-0.05250581\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9117984835\t-0.0552261\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9187798005\t-0.05806461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9257611175\t-0.06102472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9327424345\t-0.06410978\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9397237515\t-0.06732312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9467050685\t-0.070668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9536863855\t-0.07414764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9606677025\t-0.07776517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9676490195\t-0.08152364\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9746303365\t-0.085426\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9816116535\t-0.08947509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9885929706\t-0.0936736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9955742876\t-0.09802411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0025556046\t-0.10252901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0095369216\t-0.10719052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0165182386\t-0.11201069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0234995556\t-0.11699133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0304808726\t-0.12213406\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0374621896\t-0.12744021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0444435066\t-0.13291091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0514248236\t-0.13854697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0584061406\t-0.14434891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0653874576\t-0.15031697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0723687747\t-0.15645104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0793500917\t-0.16275067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0863314087\t-0.16921505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0933127257\t-0.175843\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1002940427\t-0.18263294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1072753597\t-0.18958292\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1142566767\t-0.19669052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1212379937\t-0.20395293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1282193107\t-0.21136688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1352006277\t-0.21892865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1421819447\t-0.22663407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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11.344640138\t-0.47691383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.351621455\t-0.48473592\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.358602772\t-0.4923662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.365584089\t-0.4997908\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.372565406\t-0.506996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.379546723\t-0.51396834\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.38652804\t-0.52069462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.393509357\t-0.52716196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.400490674\t-0.53335786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.407471991\t-0.53927019\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.414453308\t-0.54488727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4214346251\t-0.55019794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4284159421\t-0.5551915\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4353972591\t-0.55985787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4423785761\t-0.56418752\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4493598931\t-0.56817156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4563412101\t-0.57180178\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4633225271\t-0.57507064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4703038441\t-0.57797131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4772851611\t-0.58049773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4842664781\t-0.58264457\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4912477951\t-0.58440732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4982291121\t-0.58578224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5052104291\t-0.58676641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5121917462\t-0.58735776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5191730632\t-0.58755501\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5261543802\t-0.58735776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5331356972\t-0.58676641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5401170142\t-0.58578224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5470983312\t-0.58440732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5540796482\t-0.58264457\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5610609652\t-0.58049773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5680422822\t-0.57797131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5750235992\t-0.57507064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5820049162\t-0.57180178\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5889862332\t-0.56817156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5959675503\t-0.56418752\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6029488673\t-0.55985787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6099301843\t-0.5551915\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6169115013\t-0.55019794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6238928183\t-0.54488727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6308741353\t-0.53927019\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6378554523\t-0.53335786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6448367693\t-0.52716196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6518180863\t-0.52069462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6587994033\t-0.51396834\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6657807203\t-0.506996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6727620373\t-0.4997908\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6797433543\t-0.4923662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6867246714\t-0.48473592\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6937059884\t-0.47691383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7006873054\t-0.46891397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7076686224\t-0.46075048\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7146499394\t-0.45243756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7216312564\t-0.44398942\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7286125734\t-0.43542025\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7355938904\t-0.42674418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7425752074\t-0.41797525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7495565244\t-0.40912735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7565378414\t-0.40021419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7635191584\t-0.39124929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7705004754\t-0.38224592\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7774817925\t-0.37321708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7844631095\t-0.36417547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7914444265\t-0.35513346\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7984257435\t-0.34610308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8054070605\t-0.33709597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8123883775\t-0.32812338\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8193696945\t-0.31919615\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8263510115\t-0.31032467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8333323285\t-0.30151892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8403136455\t-0.29278839\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8472949625\t-0.2841421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8542762795\t-0.27558862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8612575966\t-0.26713601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8682389136\t-0.25879184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8752202306\t-0.25056322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8822015476\t-0.24245672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8891828646\t-0.23447847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8961641816\t-0.22663407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9031454986\t-0.21892865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9101268156\t-0.21136688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9171081326\t-0.20395293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9240894496\t-0.19669052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9310707666\t-0.18958292\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9380520836\t-0.18263294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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12.1474915939\t-0.04740625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1544729109\t-0.04502017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1614542279\t-0.04273869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1684355449\t-0.04055844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1754168619\t-0.03847606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1823981789\t-0.03648824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1893794959\t-0.03459168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1963608129\t-0.03278316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2033421299\t-0.03105949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.210323447\t-0.02941753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.217304764\t-0.0278542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.224286081\t-0.0263665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.231267398\t-0.02495147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.238248715\t-0.02360623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.245230032\t-0.02232796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.252211349\t-0.02111394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.259192666\t-0.01996149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.266173983\t-0.01886802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2731553\t-0.01783102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.280136617\t-0.01684806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.287117934\t-0.01591677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.294099251\t-0.01503487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3010805681\t-0.01420016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3080618851\t-0.01341051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3150432021\t-0.01266388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3220245191\t-0.01195829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3290058361\t-0.01129184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3359871531\t-0.01066272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3429684701\t-0.01006918\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3499497871\t-0.00950953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3569311041\t-0.00898219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3639124211\t-0.00848562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3708937381\t-0.00801835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3778750551\t-0.00757898\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3848563722\t-0.0071662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3918376892\t-0.00677873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3988190062\t-0.00641537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4058003232\t-0.00607498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4127816402\t-0.00575648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4197629572\t-0.00545886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4267442742\t-0.00518113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4337255912\t-0.00492241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4407069082\t-0.00468183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4476882252\t-0.00445859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4546695422\t-0.00425195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4616508592\t-0.0040612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4686321762\t-0.00388569\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4756134933\t-0.00372483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4825948103\t-0.00357805\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4895761273\t-0.00344484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4965574443\t-0.00332474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5035387613\t-0.00321734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5105200783\t-0.00312224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5175013953\t-0.00303911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5244827123\t-0.00296766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5314640293\t-0.00290762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5384453463\t-0.0028588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5454266633\t-0.002821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5524079803\t-0.00279411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5593892974\t-0.002778\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5663706144\t-0.00277264\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t };\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{axis}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{tikzpicture}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\caption{The ground state torsional wavefunction.}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\label{fig:torsion_ground}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{figure}\n\n\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\begin{figure}[htbp!]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\centering\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\begin{tikzpicture}[scale=0.9]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\begin{axis}[\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xtick={\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0, 1.5708, 3.14159, 4.7123889, 6.28318,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.85398, 9.42477, 10.9955689, 12.56636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xticklabels={\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $0$, $\\frac{\\pi}{2}$, $\\pi$, $\\frac{3\\pi}{2}$, $2\\pi$,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $\\frac{5\\pi}{2}$, $3\\pi$, $\\frac{7\\pi}{2}$, $4\\pi$\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xlabel={$\\tau$ (\\SI{}{\\radian})},\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t ylabel={Amplitude}]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\addplot[smooth, red] table[x=angle,y=energy] {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t angle energy\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0\t0.00257847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.006981317\t0.0025048\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.013962634\t0.00244081\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.020943951\t0.00238625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.027925268\t0.00234091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.034906585\t0.00230461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.041887902\t0.00227718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0488692191\t0.00225852\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0558505361\t0.00224853\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0628318531\t0.00224717\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0698131701\t0.0022544\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0767944871\t0.00227024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0837758041\t0.00229472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0907571211\t0.0023279\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.0977384381\t0.00236989\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1047197551\t0.0024208\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1117010721\t0.0024808\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1186823891\t0.00255008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1256637061\t0.00262885\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1326450232\t0.00271735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1396263402\t0.00281587\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1466076572\t0.00292471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1535889742\t0.00304422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1605702912\t0.00317477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1675516082\t0.00331676\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1745329252\t0.00347062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1815142422\t0.00363683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1884955592\t0.00381589\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.1954768762\t0.00400832\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2024581932\t0.00421471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2094395102\t0.00443565\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2164208272\t0.00467179\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2234021443\t0.0049238\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2303834613\t0.00519238\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2373647783\t0.00547829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2443460953\t0.0057823\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2513274123\t0.00610525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2583087293\t0.00644798\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2652900463\t0.00681139\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2722713633\t0.00719642\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2792526803\t0.00760403\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2862339973\t0.00803525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.2932153143\t0.0084911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3001966313\t0.00897269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3071779484\t0.00948113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3141592654\t0.01001758\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3211405824\t0.01058325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3281218994\t0.01117937\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t0.3351032164\t0.01180721\n\t\t\t\t\t\t\t\t\t\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};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\addplot[smooth, blue] table[x=angle,y=energy] {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t angle energy\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1125850088\t-0.01592123\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1195663258\t-0.01515312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1265476429\t-0.01441673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1335289599\t-0.01371121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1405102769\t-0.01303567\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1474915939\t-0.01238923\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1544729109\t-0.01177102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1614542279\t-0.01118015\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1684355449\t-0.01061576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1754168619\t-0.010077\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1823981789\t-0.00956299\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1893794959\t-0.00907291\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.1963608129\t-0.00860591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.2033421299\t-0.00816119\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.210323447\t-0.00773794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.217304764\t-0.00733538\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.224286081\t-0.00695273\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.231267398\t-0.00658924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.238248715\t-0.00624418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.245230032\t-0.00591684\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.252211349\t-0.00560653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.259192666\t-0.00531256\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.266173983\t-0.00503429\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.2731553\t-0.00477109\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.280136617\t-0.00452234\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.287117934\t-0.00428747\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.294099251\t-0.0040659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3010805681\t-0.00385709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3080618851\t-0.00366052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3150432021\t-0.0034757\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3220245191\t-0.00330213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3290058361\t-0.00313938\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3359871531\t-0.00298701\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3429684701\t-0.0028446\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3499497871\t-0.00271177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3569311041\t-0.00258814\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3639124211\t-0.00247339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3708937381\t-0.00236718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3778750551\t-0.0022692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3848563722\t-0.00217918\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3918376892\t-0.00209687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.3988190062\t-0.00202201\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4058003232\t-0.00195439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4127816402\t-0.00189381\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4197629572\t-0.0018401\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4267442742\t-0.0017931\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4337255912\t-0.00175267\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4407069082\t-0.0017187\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4476882252\t-0.0016911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4546695422\t-0.0016698\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4616508592\t-0.00165473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4686321762\t-0.00164588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4756134933\t-0.00164323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4825948103\t-0.00164679\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4895761273\t-0.00165661\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.4965574443\t-0.00167272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5035387613\t-0.00169522\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5105200783\t-0.0017242\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5175013953\t-0.0017598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5244827123\t-0.00180216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5314640293\t-0.00185145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5384453463\t-0.00190788\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5454266633\t-0.00197167\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5524079803\t-0.00204307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5593892974\t-0.00212237\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t12.5663706144\t-0.00220988\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{axis}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{tikzpicture}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\begin{tikzpicture}[scale=0.9]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\begin{axis}[\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xtick={\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0, 1.5708, 3.14159, 4.7123889, 6.28318,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.85398, 9.42477, 10.9955689, 12.56636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xticklabels={\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $0$, $\\frac{\\pi}{2}$, $\\pi$, $\\frac{3\\pi}{2}$, $2\\pi$,\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $\\frac{5\\pi}{2}$, $3\\pi$, $\\frac{7\\pi}{2}$, $4\\pi$\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t },\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t xlabel={$\\tau$ (\\SI{}{\\radian})},\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t ylabel={Amplitude}]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\addplot[smooth, blue] table[x=angle,y=energy] {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t angle energy\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0\t1.14903999997532E-008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.006981317\t0.000120877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.013962634\t0.0002422161\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.020943951\t0.0003644876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.027925268\t0.0004881698\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.034906585\t0.0006137216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.041887902\t0.000741656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0488692191\t0.0008724328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0558505361\t0.0010065727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0628318531\t0.0011445648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0698131701\t0.0012869364\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0767944871\t0.001434221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0837758041\t0.001586961\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0907571211\t0.0017457247\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0977384381\t0.0019110784\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1047197551\t0.0020836489\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1117010721\t0.0022640319\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1186823891\t0.002452878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1256637061\t0.0026508479\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1326450232\t0.0028586433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1396263402\t0.0030769791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1466076572\t0.0033065939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1535889742\t0.0035482622\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1605702912\t0.0038027911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1675516082\t0.0040710286\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1745329252\t0.0043538492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1815142422\t0.0046521477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1884955592\t0.0049668743\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1954768762\t0.0052990269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2024581932\t0.0056496262\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2094395102\t0.0060197309\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2164208272\t0.0064104517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2234021443\t0.0068229395\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2303834613\t0.0072584091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2373647783\t0.0077180972\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2443460953\t0.0082032945\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2513274123\t0.008715345\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2583087293\t0.0092556458\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2652900463\t0.0098256308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2722713633\t0.0104267916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2792526803\t0.0110606825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2862339973\t0.0117288883\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2932153143\t0.0124330762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3001966313\t0.0131749382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3071779484\t0.0139562274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3141592654\t0.0147787628\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3211405824\t0.0156443916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3281218994\t0.0165550316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3351032164\t0.0175126352\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3420845334\t0.0185192342\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.3490658504\t0.0195768656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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0.5235987756\t0.0692673668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5305800926\t0.0724541067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5375614096\t0.0757515121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5445427266\t0.0791610462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5515240436\t0.0826839857\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5585053606\t0.0863214674\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5654866776\t0.0900744719\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.5724679947\t0.0939437671\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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0.9704030641\t0.3989253208\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9773843811\t0.4017428481\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9843656981\t0.4043101825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9913470151\t0.4066220024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9983283321\t0.4086734821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0053096491\t0.4104603389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0122909662\t0.4119787895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0192722832\t0.4132256471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0262536002\t0.4141982767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0332349172\t0.414894611\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0402162342\t0.4153131748\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0471975512\t0.415453084\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0541788682\t0.415314037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0611601852\t0.414896329\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0681415022\t0.4142008439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0751228192\t0.4132290624\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0821041362\t0.411983053\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0890854532\t0.4104654451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0960667703\t0.4086794439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1030480873\t0.4066287994\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1100294043\t0.4043178146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1170107213\t0.4017513088\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1239920383\t0.3989346026\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1309733553\t0.3958735273\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1379546723\t0.3925743536\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1449359893\t0.3890438145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1519173063\t0.3852890537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1588986233\t0.381317609\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1658799403\t0.3771374062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1728612573\t0.3727566806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1798425743\t0.3681840067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1868238914\t0.3634282446\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1938052084\t0.3584984937\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2007865254\t0.3534040686\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2077678424\t0.3481545158\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2147491594\t0.3427595163\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2217304764\t0.3372288747\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2287117934\t0.3315725381\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2356931104\t0.3258004985\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2426744274\t0.3199227811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2496557444\t0.313949442\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2566370614\t0.307890528\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2636183784\t0.3017560226\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2705996955\t0.295555851\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2775810125\t0.2892998266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2845623295\t0.2829976597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2915436465\t0.2766589\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2985249635\t0.2702929478\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3055062805\t0.2639089644\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3124875975\t0.257515954\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3194689145\t0.2511226649\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3264502315\t0.244737599\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3334315485\t0.2383689729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3404128655\t0.2320247637\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3473941825\t0.2257126217\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3543754995\t0.2194399112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3613568166\t0.2132136697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3683381336\t0.2070406148\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3753194506\t0.20092713\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3823007676\t0.1948792681\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3892820846\t0.1889027335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3962634016\t0.1830028858\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4032447186\t0.1771847406\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4102260356\t0.1714529612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4172073526\t0.1658118538\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4241886696\t0.1602654081\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4311699866\t0.1548172436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4381513036\t0.1494706547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4451326207\t0.1442286048\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4521139377\t0.1390937059\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4590952547\t0.1340682868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4660765717\t0.1291543369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4730578887\t0.1243535571\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4800392057\t0.1196673389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4870205227\t0.1150967944\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4940018397\t0.110642752\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5009831567\t0.1063058042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5079644737\t0.1020862492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5149457907\t0.0979841673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5219271077\t0.0939994174\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5289084247\t0.0901316157\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5358897418\t0.0863801806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5428710588\t0.0827443344\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5498523758\t0.0792231193\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5568336928\t0.0758153987\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5638150098\t0.0725199076\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5707963268\t0.0693351849\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5777776438\t0.0662596591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5847589608\t0.0632916562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5917402778\t0.0604293389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5987215948\t0.0576708283\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6057029118\t0.0550140973\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6126842288\t0.052457075\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6196655459\t0.0499976061\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6266468629\t0.0476334812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6336281799\t0.0453624189\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6406094969\t0.0431821307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6475908139\t0.0410902551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6545721309\t0.0390844306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6615534479\t0.0371622688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6685347649\t0.0353213692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6755160819\t0.0335593258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6824973989\t0.0318737382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6894787159\t0.0302622017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6964600329\t0.0287223461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.7034413499\t0.0272517915\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.710422667\t0.0258482178\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.717403984\t0.0245092928\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.724385301\t0.0232327452\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.731366618\t0.0220163252\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.738347935\t0.0208578266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.745329252\t0.0197550799\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.752310569\t0.0187059699\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.759291886\t0.0177084152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.766273203\t0.0167603991\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.77325452\t0.0158599302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.780235837\t0.0150050907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.787217154\t0.0141940171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.7941984711\t0.0134248816\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8011797881\t0.0126959205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8081611051\t0.0120054275\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8151424221\t0.0113517658\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8221237391\t0.0107333213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8291050561\t0.0101485787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8360863731\t0.0095960303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8430676901\t0.0090742659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8500490071\t0.0085819069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8570303241\t0.0081176352\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8640116411\t0.0076802047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8709929581\t0.0072683981\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8779742751\t0.0068810593\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8849555922\t0.0065171046\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8919369092\t0.0061754634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8989182262\t0.0058551474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9058995432\t0.0055552196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9128808602\t0.005274761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9198621772\t0.0050129377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9268434942\t0.004768949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9338248112\t0.0045420357\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9408061282\t0.0043314916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9477874452\t0.0041366463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9547687622\t0.0039568891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9617500792\t0.0037916376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9687313962\t0.0036403678\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9757127133\t0.0035025763\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9826940303\t0.0033778206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9896753473\t0.0032656897\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9966566643\t0.0031658254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0036379813\t0.0030778828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0106192983\t0.0030015757\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0176006153\t0.0029366706\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0245819323\t0.0028829236\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0315632493\t0.0028401936\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0385445663\t0.0028083212\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0455258833\t0.0027872129\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0525072003\t0.0027768277\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0594885174\t0.0027771143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0664698344\t0.0027881066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0734511514\t0.0028098575\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0804324684\t0.0028424636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0874137854\t0.0028860582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0943951024\t0.0029407997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1013764194\t0.0030069256\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1083577364\t0.0030846668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1153390534\t0.0031743369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1223203704\t0.0032762623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1293016874\t0.0033908289\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1362830044\t0.0035184686\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1432643214\t0.003659639\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1502456385\t0.0038148802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1572269555\t0.0039847465\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1642082725\t0.0041698506\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1711895895\t0.0043708692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1781709065\t0.0045885238\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1851522235\t0.0048235864\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1921335405\t0.0050768922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1991148575\t0.0053493219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2060961745\t0.0056418343\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2130774915\t0.0059554305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2200588085\t0.0062911983\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2270401255\t0.0066502625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2340214426\t0.0070338399\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2410027596\t0.0074432104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2479840766\t0.007879721\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2549653936\t0.0083448024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2619467106\t0.0088399502\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2689280276\t0.0093667534\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2759093446\t0.0099268714\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2828906616\t0.0105220482\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2898719786\t0.0111541374\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2968532956\t0.0118250393\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3038346126\t0.0125367787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3108159296\t0.0132914697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3177972466\t0.0140912922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3247785637\t0.0149385683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3317598807\t0.0158356832\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3387411977\t0.0167851368\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3457225147\t0.0177895419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3527038317\t0.0188516047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3596851487\t0.0199741299\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3666664657\t0.0211600361\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3736477827\t0.0224123636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3806290997\t0.0237342371\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3876104167\t0.0251289005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3945917337\t0.0265997152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4015730507\t0.0281501388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4085543678\t0.0297837505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4155356848\t0.0315042011\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4225170018\t0.033315303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4294983188\t0.0352209282\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4364796358\t0.0372250594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4434609528\t0.0393318019\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4504422698\t0.0415453236\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4574235868\t0.0438699003\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4644049038\t0.0463098843\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4713862208\t0.0488697214\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4783675378\t0.0515539422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4853488548\t0.0543671127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4923301718\t0.0573138837\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4993114889\t0.060398957\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5062928059\t0.0636270886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5132741229\t0.0670030595\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5202554399\t0.0705316613\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5272367569\t0.0742177315\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5342180739\t0.07806609\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5411993909\t0.08208156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5481807079\t0.0862689129\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5551620249\t0.0906329066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5621433419\t0.095178257\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5691246589\t0.0999095727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5761059759\t0.1048314069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.583087293\t0.1099481835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.59006861\t0.1152642432\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.597049927\t0.1207837325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.604031244\t0.1265106818\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.611012561\t0.1324489033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.617993878\t0.138602036\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.624975195\t0.1449734704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.631956512\t0.1515663529\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.638937829\t0.1583835706\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.645919146\t0.1654276986\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.652900463\t0.1727010111\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.65988178\t0.180205417\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.666863097\t0.1879424891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6738444141\t0.1959133847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6808257311\t0.2041188618\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6878070481\t0.2125592241\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6947883651\t0.2212343383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7017696821\t0.2301435644\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7087509991\t0.239285755\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7157323161\t0.248659257\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7227136331\t0.2582618286\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7296949501\t0.2680906976\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7366762671\t0.2781424593\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7436575841\t0.2884131431\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7506389011\t0.2988981101\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7576202182\t0.309592127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7646015352\t0.3204892503\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7715828522\t0.3315829278\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7785641692\t0.342865884\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7855454862\t0.3543301883\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7925268032\t0.3659671975\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7995081202\t0.377767585\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8064894372\t0.3897213312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8134707542\t0.4018177269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8204520712\t0.4140453467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8274333882\t0.4263921081\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8344147052\t0.4388452238\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8413960222\t0.4513912824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8483773393\t0.4640161875\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8553586563\t0.4767052296\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8623399733\t0.4894430833\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8693212903\t0.5022138427\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8763026073\t0.5150010405\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8832839243\t0.527787672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8902652413\t0.540556233\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8972465583\t0.5532887754\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9042278753\t0.5659669031\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9112091923\t0.578571859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9181905093\t0.5910845303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9251718263\t0.6034855155\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9321531434\t0.6157551616\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9391344604\t0.6278736419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9461157774\t0.6398209641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9530970944\t0.651577052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9600784114\t0.6631218079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9670597284\t0.6744351548\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9740410454\t0.6854971011\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9810223624\t0.6962878051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9880036794\t0.7067876149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9949849964\t0.7169771637\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0019663134\t0.7268373962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0089476304\t0.7363496539\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0159289474\t0.7454957252\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0229102645\t0.7542579104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0298915815\t0.7626190814\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0368728985\t0.770562723\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0438542155\t0.7780730206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0508355325\t0.7851348818\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0578168495\t0.7917340192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0647981665\t0.7978569707\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0717794835\t0.8034911787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0787608005\t0.8086250043\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0857421175\t0.8132477891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0927234345\t0.8173499029\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0997047515\t0.8209227372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1066860685\t0.8239587952\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1136673856\t0.8264516518\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1206487026\t0.8283960519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1276300196\t0.8297878687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1346113366\t0.8306241379\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1415926536\t0.8309030939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1485739706\t0.83062414\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1555552876\t0.8297878653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1625366046\t0.8283960506\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1695179216\t0.8264516526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1764992386\t0.8239587917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1834805556\t0.8209227369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1904618726\t0.8173498993\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1974431897\t0.8132477952\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2044245067\t0.8086250071\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2114058237\t0.8034911781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2183871407\t0.7978569755\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2253684577\t0.7917340218\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2323497747\t0.7851348833\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2393310917\t0.7780730209\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2463124087\t0.7705627233\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2532937257\t0.7626190751\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2602750427\t0.7542579051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2672563597\t0.745495722\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2742376767\t0.7363496529\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2812189937\t0.7268373984\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2882003108\t0.7169771626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2951816278\t0.7067876181\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3021629448\t0.6962877995\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3091442618\t0.6854971085\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3161255788\t0.6744351545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3231068958\t0.6631218076\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3300882128\t0.6515770528\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3370695298\t0.6398209594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3440508468\t0.6278736394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3510321638\t0.6157551687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3580134808\t0.6034855183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3649947978\t0.5910845298\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3719761149\t0.5785718552\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3789574319\t0.5659669035\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3859387489\t0.5532887736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3929200659\t0.5405562356\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3999013829\t0.5277876659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4068826999\t0.5150010473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4138640169\t0.5022138473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4208453339\t0.4894430856\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4278266509\t0.4767052298\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4348079679\t0.464016192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4417892849\t0.4513912771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4487706019\t0.4388452216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4557519189\t0.4263921027\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.462733236\t0.4140453509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.469714553\t0.4018177246\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.47669587\t0.3897213365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.483677187\t0.3777675826\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.490658504\t0.3659671929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.497639821\t0.3543301804\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.504621138\t0.3428658847\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.511602455\t0.3315829296\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.518583772\t0.3204892498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.525565089\t0.3095921222\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.532546406\t0.2988981128\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.539527723\t0.2884131371\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5465090401\t0.278142463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5534903571\t0.2680906925\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5604716741\t0.2582618267\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5674529911\t0.2486592539\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5744343081\t0.2392857551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5814156251\t0.2301435634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5883969421\t0.2212343372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5953782591\t0.2125592273\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6023595761\t0.2041188627\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6093408931\t0.1959133866\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6163222101\t0.187942492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6233035271\t0.180205422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6302848441\t0.1727010051\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6372661612\t0.1654277022\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6442474782\t0.1583835709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6512287952\t0.1515663541\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6582101122\t0.1449734716\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6651914292\t0.1386020436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6721727462\t0.1324489064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6791540632\t0.1265106781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6861353802\t0.1207837331\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6931166972\t0.1152642426\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7000980142\t0.1099481924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7070793312\t0.1048314047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7140606482\t0.0999095672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7210419653\t0.0951782545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7280232823\t0.090632906\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7350045993\t0.0862689121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7419859163\t0.0820815493\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7489672333\t0.0780660931\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7559485503\t0.0742177289\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7629298673\t0.0705316617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7699111843\t0.067003053\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7768925013\t0.0636270895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7838738183\t0.0603989597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7908551353\t0.0573138774\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7978364523\t0.0543671114\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8048177693\t0.0515539383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8117990864\t0.0488697248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8187804034\t0.0463098828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8257617204\t0.0438698929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8327430374\t0.0415453234\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8397243544\t0.0393317957\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8467056714\t0.0372250614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8536869884\t0.0352209209\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8606683054\t0.0333153016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8676496224\t0.0315042034\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8746309394\t0.0297837445\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8816122564\t0.0281501428\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8885935734\t0.0265997174\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8955748905\t0.025128904\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9025562075\t0.0237342353\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9095375245\t0.0224123598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9165188415\t0.0211600422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9235001585\t0.0199741305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9304814755\t0.018851601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9374627925\t0.0177895435\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9444441095\t0.0167851328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9514254265\t0.0158356767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9584067435\t0.0149385625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9653880605\t0.0140912892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9723693775\t0.013291464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9793506945\t0.0125367767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9863320116\t0.0118250397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9933133286\t0.0111541402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0002946456\t0.0105220533\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0072759626\t0.009926871\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0142572796\t0.0093667517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0212385966\t0.0088399514\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0282199136\t0.0083447966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0352012306\t0.0078797199\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0421825476\t0.0074432094\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0491638646\t0.0070338325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0561451816\t0.0066502603\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0631264986\t0.0062911859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0701078157\t0.0059554294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0770891327\t0.0056418301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0840704497\t0.005349322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0910517667\t0.0050768907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0980330837\t0.004823582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1050144007\t0.0045885227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1119957177\t0.004370869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1189770347\t0.0041698464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1259583517\t0.0039847369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1329396687\t0.0038148692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1399209857\t0.0036596369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1469023027\t0.0035184597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1538836197\t0.0033908269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1608649368\t0.0032762545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1678462538\t0.003174323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1748275708\t0.0030846656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1818088878\t0.0030069223\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1887902048\t0.0029408023\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1957715218\t0.0028860486\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2027528388\t0.0028424584\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2097341558\t0.0028098559\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2167154728\t0.0027880924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2236967898\t0.0027771008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2306781068\t0.0027768127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2376594238\t0.0027872063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2446407409\t0.0028083076\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2516220579\t0.0028401817\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2586033749\t0.0028829131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2655846919\t0.0029366483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2725660089\t0.0030015704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2795473259\t0.0030778617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2865286429\t0.0031657997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2935099599\t0.003265673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3004912769\t0.0033778014\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3074725939\t0.0035025525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3144539109\t0.0036403439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3214352279\t0.0037916192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3284165449\t0.0039568608\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.335397862\t0.0041366165\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.342379179\t0.0043314588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.349360496\t0.0045420038\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.356341813\t0.0047689151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.36332313\t0.0050129042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.370304447\t0.0052747237\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.377285764\t0.0055551739\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.384267081\t0.0058551095\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.391248398\t0.0061754207\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.398229715\t0.006517062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.405211032\t0.0068810115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.412192349\t0.0072683462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.419173666\t0.0076801451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4261549831\t0.0081175795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4331363001\t0.0085818423\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4401176171\t0.0090741969\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4470989341\t0.0095959589\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4540802511\t0.010148499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4610615681\t0.0107332521\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4680428851\t0.0113516811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4750242021\t0.0120053412\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4820055191\t0.0126958244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4889868361\t0.013424777\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4959681531\t0.0141939114\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5029494701\t0.0150049877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5099307872\t0.0158598096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5169121042\t0.0167602791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5238934212\t0.017708293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5308747382\t0.0187058328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5378560552\t0.0197549362\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5448373722\t0.0208576725\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5518186892\t0.0220161596\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5588000062\t0.0232325666\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5657813232\t0.0245091079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5727626402\t0.025848021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5797439572\t0.0272515876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5867252742\t0.0287221285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5937065912\t0.0302619819\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6006879083\t0.0318734979\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6076692253\t0.0335590809\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6146505423\t0.0353211037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6216318593\t0.0371619967\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6286131763\t0.0390841403\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6355944933\t0.0410899422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6425758103\t0.0431818002\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6495571273\t0.0453620773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6565384443\t0.0476331195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6635197613\t0.0499972279\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6705010783\t0.0524566876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6774823953\t0.055013685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6844637124\t0.0576703922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6914450294\t0.0604288862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6984263464\t0.0632911755\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7054076634\t0.0662591675\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7123889804\t0.0693346562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7193702974\t0.0725193572\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7263516144\t0.0758148343\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7333329314\t0.079222519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7403142484\t0.082743714\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7472955654\t0.0863795307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7542768824\t0.0901309397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7612581994\t0.093998709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7682395164\t0.097983435\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7752208335\t0.1020854864\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7822021505\t0.1063050042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7891834675\t0.1106419211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7961647845\t0.1150959239\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8031461015\t0.1196664353\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8101274185\t0.124352626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8171087355\t0.1291533722\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8240900525\t0.1340672794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8310713695\t0.1390926655\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8380526865\t0.1442275198\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8450340035\t0.1494695269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8520153205\t0.1548160862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8589966376\t0.1602642034\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8659779546\t0.1658106065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8729592716\t0.1714516669\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8799405886\t0.1771834044\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8869219056\t0.1830015146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8939032226\t0.1889013147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9008845396\t0.1948777997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9078658566\t0.2009256208\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9148471736\t0.2070390574\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9218284906\t0.2132120633\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9288098076\t0.2194382585\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9357911246\t0.2257109212\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9427724416\t0.2320230195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9497537587\t0.2383671789\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9567350757\t0.2447357492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9637163927\t0.2511207768\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9706977097\t0.2575140206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9776790267\t0.2639069824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9846603437\t0.2702909157\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9916416607\t0.2766568269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9986229777\t0.2829955301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0056042947\t0.2892976467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0125856117\t0.2955536287\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0195669287\t0.3017537558\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0265482457\t0.3078882111\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0335295628\t0.3139470843\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0405108798\t0.3199203755\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0474921968\t0.3257980464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0544735138\t0.3315700491\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0614548308\t0.3372263467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0684361478\t0.3427569324\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0754174648\t0.3481518962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0823987818\t0.35340142\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0893800988\t0.3584957975\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0963614158\t0.3634255113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1033427328\t0.3681812465\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1103240498\t0.3727538772\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1173053668\t0.3771345624\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1242866839\t0.3813147433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1312680009\t0.3852861527\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1382493179\t0.389040888\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1452306349\t0.3925713956\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1522119519\t0.3958705438\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1591932689\t0.3989316065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1661745859\t0.4017482862\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1731559029\t0.4043147709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1801372199\t0.4066257357\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1871185369\t0.4086763699\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1940998539\t0.4104623614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.2010811709\t0.4119799547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.208062488\t0.4132259537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.215043805\t0.4141977307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.222025122\t0.4148932067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.229006439\t0.4153109122\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.235987756\t0.4154499655\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.242969073\t0.4153100586\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.24995039\t0.414891493\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.256931707\t0.4141951634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.263913024\t0.4132225469\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.270894341\t0.4119756877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.277875658\t0.4104572484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.284856975\t0.4086704185\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.291838292\t0.4066189448\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.2988196091\t0.4043071415\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3058009261\t0.4017398325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3127822431\t0.398922322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3197635601\t0.3958604501\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3267448771\t0.3925604928\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3337261941\t0.3890291695\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3407075111\t0.3852736327\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3476888281\t0.3813014293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3546701451\t0.3771204685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3616514621\t0.372738997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3686327791\t0.3681656017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3756140961\t0.3634091094\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3825954132\t0.358478632\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3895767302\t0.353383505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3965580472\t0.3481332458\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4035393642\t0.3427375543\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4105206812\t0.3372062418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4175019982\t0.3315492316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4244833152\t0.3257765163\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4314646322\t0.3198981404\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4384459492\t0.3139241594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4454272662\t0.3078646028\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4524085832\t0.3017294577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4593899002\t0.2955286549\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4663712172\t0.2892720047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4733525343\t0.2829692135\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4803338513\t0.2766298421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4873151683\t0.2702632639\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4942964853\t0.2638786765\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5012778023\t0.2574850542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5082591193\t0.2510911499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5152404363\t0.2447054617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5222217533\t0.2383362308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5292030703\t0.2319914033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5361843873\t0.2256786304\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5431657043\t0.2194052854\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5501470213\t0.2131784145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5571283383\t0.2070047101\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5641096554\t0.2008905696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5710909724\t0.1948420499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5780722894\t0.1888648306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5850536064\t0.1829642811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5920349234\t0.1771454279\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5990162404\t0.1714129116\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6059975574\t0.1657710497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6129788744\t0.1602238298\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6199601914\t0.1547748601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6269415084\t0.1494274461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6339228254\t0.1441845268\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6409041424\t0.1390487376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6478854595\t0.1340223938\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6548667765\t0.1291074703\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6618480935\t0.1243056773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6688294105\t0.1196184107\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6758107275\t0.115046756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6827920445\t0.1105915732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6897733615\t0.1062534176\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6967546785\t0.1020326004\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7037359955\t0.0979292062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7107173125\t0.0939430551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7176986295\t0.0900737933\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7246799465\t0.0863208191\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7316612635\t0.0826833624\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7386425806\t0.0791604451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7456238976\t0.0757509425\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7526052146\t0.0724535586\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7595865316\t0.0692668456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7665678486\t0.0661892419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7735491656\t0.063219023\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7805304826\t0.0603543812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7875117996\t0.0575934088\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7944931166\t0.0549340886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8014744336\t0.0523743233\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8084557506\t0.0499119545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8154370676\t0.0475447734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8224183847\t0.0452704882\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8293997017\t0.0430867749\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8363810187\t0.0409912953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8433623357\t0.0389816559\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8503436527\t0.0370554536\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8573249697\t0.0352102849\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8643062867\t0.0334437207\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8712876037\t0.0317533512\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8782689207\t0.0301367515\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8852502377\t0.0285915389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8922315547\t0.0271153134\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8992128717\t0.0257057206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9061941887\t0.0243604255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9131755058\t0.0230771376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9201568228\t0.0218535688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9271381398\t0.0206874968\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9341194568\t0.0195767158\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9411007738\t0.0185190849\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9480820908\t0.0175125057\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9550634078\t0.0165549036\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9620447248\t0.0156442731\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9690260418\t0.0147786537\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9760073588\t0.0139561257\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9829886758\t0.0131748358\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9899699928\t0.0124329836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9969513099\t0.0117288079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0039326269\t0.0110605941\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0109139439\t0.0104267068\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0178952609\t0.0098255518\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0248765779\t0.0092555718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0318578949\t0.0087152776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0388392119\t0.0082032335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0458205289\t0.0077180415\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0528018459\t0.0072583503\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0597831629\t0.0068228845\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0667644799\t0.0064103981\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0737457969\t0.0060196797\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0807271139\t0.0056495764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.087708431\t0.0052989852\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.094689748\t0.0049668402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.101671065\t0.0046521099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.108652382\t0.0043538064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.115633699\t0.0040710024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.122615016\t0.0038027619\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.129596333\t0.0035482283\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.13657765\t0.0033065566\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.143558967\t0.0030769433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.150540284\t0.0028586162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.157521601\t0.0026508323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.164502918\t0.0024528596\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1714842351\t0.0022640095\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1784655521\t0.0020836258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1854468691\t0.0019110654\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1924281861\t0.0017457057\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1994095031\t0.0015869471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2063908201\t0.0014341984\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2133721371\t0.0012869163\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2203534541\t0.0011445498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2273347711\t0.0010065556\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2343160881\t0.000872424\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2412974051\t0.0007416386\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2482787221\t0.0006137125\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2552600391\t0.000488148\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2622413562\t0.0003644655\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2692226732\t0.0002421955\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2762039902\t0.0001208641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2831853072\t-1.14903999997532E-008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2901666242\t-0.000120877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2971479412\t-0.0002422161\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3041292582\t-0.0003644876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3111105752\t-0.0004881698\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3180918922\t-0.0006137216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3250732092\t-0.000741656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3320545262\t-0.0008724328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3390358432\t-0.0010065727\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3460171603\t-0.0011445648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3529984773\t-0.0012869364\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3599797943\t-0.001434221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3669611113\t-0.001586961\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3739424283\t-0.0017457247\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3809237453\t-0.0019110784\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3879050623\t-0.0020836489\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3948863793\t-0.0022640319\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4018676963\t-0.002452878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4088490133\t-0.0026508479\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4158303303\t-0.0028586433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4228116473\t-0.0030769791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4297929643\t-0.0033065939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4367742814\t-0.0035482622\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4437555984\t-0.0038027911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4507369154\t-0.0040710286\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4577182324\t-0.0043538492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4646995494\t-0.0046521477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4716808664\t-0.0049668743\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4786621834\t-0.0052990269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4856435004\t-0.0056496186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4926248174\t-0.0060197309\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4996061344\t-0.0064104517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5065874514\t-0.006822946\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5135687684\t-0.0072584091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5205500855\t-0.0077180972\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5275314025\t-0.0082032945\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5345127195\t-0.008715345\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5414940365\t-0.0092556382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5484753535\t-0.0098256308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5554566705\t-0.0104267916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5624379875\t-0.0110606825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5694193045\t-0.0117288948\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5764006215\t-0.0124330762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5833819385\t-0.0131749382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5903632555\t-0.0139562274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5973445725\t-0.0147787628\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6043258895\t-0.0156443916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6113072066\t-0.0165550316\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6182885236\t-0.0175126352\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6252698406\t-0.0185192266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6322511576\t-0.0195768656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6392324746\t-0.0206876511\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6462137916\t-0.0218537341\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6531951086\t-0.0230773112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6601764256\t-0.0243606135\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6671577426\t-0.0257059147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6741390596\t-0.0271155186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6811203766\t-0.0285917487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6881016936\t-0.0301369816\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6950830107\t-0.0317535907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7020643277\t-0.0334439721\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7090456447\t-0.0352105511\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7160269617\t-0.0370557348\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7230082787\t-0.0389819508\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7299895957\t-0.0409916038\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7369709127\t-0.0430871062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7439522297\t-0.0452708227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7509335467\t-0.0475451311\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7579148637\t-0.0499123384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7648961807\t-0.0523747193\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7718774977\t-0.0549344996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7788588147\t-0.0575938434\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7858401318\t-0.0603548398\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7928214488\t-0.0632194987\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7998027658\t-0.0661897434\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8067840828\t-0.0692673733\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8137653998\t-0.0724541056\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8207467168\t-0.0757515121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8277280338\t-0.0791610451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8347093508\t-0.0826839846\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8416906678\t-0.0863214739\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8486719848\t-0.0900744708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8556533018\t-0.0939437736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8626346188\t-0.0979299432\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8696159358\t-0.1020333754\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8765972529\t-0.1062542199\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8835785699\t-0.1105924107\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8905598869\t-0.1150476276\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8975412039\t-0.1196193131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9045225209\t-0.1243066245\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9115038379\t-0.1291084499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9184851549\t-0.1340234052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9254664719\t-0.1390497949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9324477889\t-0.1441856168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9394291059\t-0.1494285702\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9464104229\t-0.1547760343\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9533917399\t-0.1602250415\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.960373057\t-0.1657723083\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.967354374\t-0.171414203\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.974335691\t-0.1771467633\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.981317008\t-0.1829656699\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.988298325\t-0.1888662573\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.995279642\t-0.194843525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.002260959\t-0.2008920995\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.009242276\t-0.2070062838\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.016223593\t-0.2131800242\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.02320491\t-0.2194069587\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.030186227\t-0.2256803482\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.037167544\t-0.231993155\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.044148861\t-0.2383380301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0511301781\t-0.244707321\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0581114951\t-0.2510930529\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0650928121\t-0.2574870079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0720741291\t-0.263880669\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0790554461\t-0.2702653108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0860367631\t-0.2766319355\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0930180801\t-0.2829713534\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0999993971\t-0.2892741928\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1069807141\t-0.2955308896\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1139620311\t-0.3017317467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1209433481\t-0.307866931\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1279246651\t-0.3139265381\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1349059822\t-0.3199005626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1418872992\t-0.3257789861\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1488686162\t-0.3315517393\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1558499332\t-0.337208795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1628312502\t-0.3427401491\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1698125672\t-0.3481358894\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1767938842\t-0.353386183\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1837752012\t-0.3584813467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1907565182\t-0.3634118654\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1977378352\t-0.3681683879\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2047191522\t-0.3727418296\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2117004692\t-0.3771233285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2186817862\t-0.3813043186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2256631033\t-0.3852765508\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2326444203\t-0.3890321131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2396257373\t-0.3925634602\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2466070543\t-0.3958634494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2535883713\t-0.3989253458\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2605696883\t-0.401742873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2675510053\t-0.4043102074\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2745323223\t-0.4066220274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2815136393\t-0.408673507\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2884949563\t-0.4104603639\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2954762733\t-0.4119788145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3024575903\t-0.413225672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3094389074\t-0.4141983016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3164202244\t-0.4148946425\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3234015414\t-0.4153132062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3303828584\t-0.4154531089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3373641754\t-0.4153140619\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3443454924\t-0.4148963539\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3513268094\t-0.4142008688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3583081264\t-0.4132290873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3652894434\t-0.4119830779\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3722707604\t-0.41046547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3792520774\t-0.4086794689\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3862333944\t-0.4066288244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3932147114\t-0.4043178395\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4001960285\t-0.4017513337\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4071773455\t-0.3989346275\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4141586625\t-0.3958735522\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4211399795\t-0.3925743786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4281212965\t-0.3890438394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4351026135\t-0.3852890722\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4420839305\t-0.3813176339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4490652475\t-0.3771374246\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4560465645\t-0.372756699\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4630278815\t-0.3681840317\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4700091985\t-0.3634282695\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4769905155\t-0.3584985122\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4839718326\t-0.3534040946\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4909531496\t-0.3481545342\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4979344666\t-0.3427595347\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5049157836\t-0.3372289008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5118971006\t-0.3315725641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5188784176\t-0.325800517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5258597346\t-0.3199227995\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5328410516\t-0.3139494604\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5398223686\t-0.3078905464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5468036856\t-0.301756041\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5537850026\t-0.2955558694\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5607663196\t-0.289299845\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5677476366\t-0.2829976781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5747289537\t-0.2766589261\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5817102707\t-0.2702929597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5886915877\t-0.2639089828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5956729047\t-0.2575159735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6026542217\t-0.2511226844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6096355387\t-0.2447376109\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6166168557\t-0.2383689924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6235981727\t-0.2320247756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6305794897\t-0.2257126337\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6375608067\t-0.2194399231\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6445421237\t-0.2132136751\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6515234407\t-0.2070406202\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6585047578\t-0.200927142\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6654860748\t-0.1948792811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6724673918\t-0.1889027465\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6794487088\t-0.1830028988\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6864300258\t-0.177184746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6934113428\t-0.1714529666\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7003926598\t-0.1658118668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7073739768\t-0.1602654211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7143552938\t-0.154817249\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7213366108\t-0.1494706677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7283179278\t-0.1442286037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7352992448\t-0.1390937189\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7422805618\t-0.1340682998\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7492618789\t-0.1291543499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7562431959\t-0.1243535701\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7632245129\t-0.1196673379\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7702058299\t-0.1150967933\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7771871469\t-0.1106427575\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7841684639\t-0.1063058031\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7911497809\t-0.1020862557\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7981310979\t-0.0979841803\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8051124149\t-0.0939994305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8120937319\t-0.0901316222\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8190750489\t-0.0863801795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8260563659\t-0.0827443333\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.833037683\t-0.0792231258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.840019\t-0.0758154052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.847000317\t-0.0725199141\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.853981634\t-0.0693351839\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.860962951\t-0.0662596656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.867944268\t-0.0632916551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.874925585\t-0.0604293454\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.881906902\t-0.0576708348\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.888888219\t-0.0550140973\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.895869536\t-0.0524570815\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.902850853\t-0.0499976126\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.90983217\t-0.0476334812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.916813487\t-0.0453624255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9237948041\t-0.0431821307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9307761211\t-0.0410902616\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9377574381\t-0.0390844306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9447387551\t-0.0371622753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9517200721\t-0.0353213692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9587013891\t-0.0335593258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9656827061\t-0.0318737382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9726640231\t-0.0302622082\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9796453401\t-0.0287223461\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9866266571\t-0.0272517915\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9936079741\t-0.0258482178\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0005892911\t-0.0245092993\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0075706081\t-0.0232327452\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0145519252\t-0.0220163252\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0215332422\t-0.0208578266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0285145592\t-0.0197550799\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0354958762\t-0.0187059765\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0424771932\t-0.0177084217\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0494585102\t-0.0167604056\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0564398272\t-0.0158599302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0634211442\t-0.0150050907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0704024612\t-0.0141940171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0773837782\t-0.013424874\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0843650952\t-0.0126959205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0913464122\t-0.0120054275\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0983277293\t-0.0113517658\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1053090463\t-0.0107333213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1122903633\t-0.0101485787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1192716803\t-0.0095960303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1262529973\t-0.0090742659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1332343143\t-0.0085819069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1402156313\t-0.0081176417\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1471969483\t-0.0076802047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1541782653\t-0.0072684046\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1611595823\t-0.0068810658\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1681408993\t-0.0065171046\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1751222163\t-0.0061754634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1821035333\t-0.0058551474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1890848504\t-0.0055552196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1960661674\t-0.005274761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2030474844\t-0.0050129377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2100288014\t-0.004768949\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2170101184\t-0.0045420357\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2239914354\t-0.0043314916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2309727524\t-0.0041366463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2379540694\t-0.0039568891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2449353864\t-0.0037916376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2519167034\t-0.0036403678\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2588980204\t-0.0035025763\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2658793374\t-0.0033778206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2728606545\t-0.0032656897\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2798419715\t-0.0031658254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2868232885\t-0.0030778828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2938046055\t-0.0030015757\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3007859225\t-0.0029366706\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3077672395\t-0.0028829236\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3147485565\t-0.0028401936\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3217298735\t-0.0028083212\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3287111905\t-0.0027872129\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3356925075\t-0.0027768277\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3426738245\t-0.0027771143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3496551415\t-0.0027881066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3566364585\t-0.0028098575\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3636177756\t-0.0028424701\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3705990926\t-0.0028860582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3775804096\t-0.0029407997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3845617266\t-0.0030069256\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3915430436\t-0.0030846668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3985243606\t-0.0031743369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4055056776\t-0.0032762623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4124869946\t-0.0033908289\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4194683116\t-0.0035184686\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4264496286\t-0.003659639\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4334309456\t-0.0038148802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4404122626\t-0.0039847465\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4473935797\t-0.0041698506\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4543748967\t-0.0043708692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4613562137\t-0.0045885238\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4683375307\t-0.0048235864\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4753188477\t-0.0050768922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4823001647\t-0.0053493219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4892814817\t-0.0056418343\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4962627987\t-0.0059554305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5032441157\t-0.0062911983\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5102254327\t-0.0066502625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5172067497\t-0.0070338399\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5241880667\t-0.0074432104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5311693837\t-0.007879721\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5381507008\t-0.0083448024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5451320178\t-0.0088399502\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5521133348\t-0.0093667534\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5590946518\t-0.0099268714\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5660759688\t-0.0105220482\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5730572858\t-0.0111541374\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5800386028\t-0.0118250393\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5870199198\t-0.0125367787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5940012368\t-0.0132914697\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6009825538\t-0.0140912922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6079638708\t-0.0149385683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6149451878\t-0.0158356832\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6219265049\t-0.0167851368\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6289078219\t-0.0177895419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6358891389\t-0.0188516047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6428704559\t-0.0199741299\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6498517729\t-0.0211600361\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6568330899\t-0.0224123636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6638144069\t-0.0237342371\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6707957239\t-0.0251289081\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6777770409\t-0.0265997152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6847583579\t-0.0281501388\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6917396749\t-0.0297837505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6987209919\t-0.0315042011\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.7057023089\t-0.033315303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.712683626\t-0.0352209282\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.719664943\t-0.0372250594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.72664626\t-0.0393318019\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.733627577\t-0.0415453236\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.740608894\t-0.0438699003\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.747590211\t-0.0463098843\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.754571528\t-0.048869729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.761552845\t-0.0515539422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.768534162\t-0.0543671127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.775515479\t-0.0573138837\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.782496796\t-0.0603989635\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.789478113\t-0.0636270962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.7964594301\t-0.0670030595\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8034407471\t-0.0705316689\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8104220641\t-0.0742177315\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8174033811\t-0.0780660976\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8243846981\t-0.08208156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8313660151\t-0.0862689129\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8383473321\t-0.0906329142\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8453286491\t-0.095178257\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8523099661\t-0.0999095803\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8592912831\t-0.1048314069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8662726001\t-0.1099481976\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8732539171\t-0.1152642497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8802352341\t-0.1207837401\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8872165512\t-0.1265106883\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8941978682\t-0.1324489174\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9011791852\t-0.1386020436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9081605022\t-0.1449734769\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9151418192\t-0.1515663605\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9221231362\t-0.1583835782\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9291044532\t-0.1654277127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9360857702\t-0.1727010186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9430670872\t-0.1802054311\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9500484042\t-0.1879424967\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9570297212\t-0.1959133988\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9640110382\t-0.2041188759\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9709923553\t-0.2125592382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9779736723\t-0.2212343524\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9849549893\t-0.230143572\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9919363063\t-0.2392857691\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9989176233\t-0.2486592711\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0058989403\t-0.2582618427\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0128802573\t-0.2680907052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0198615743\t-0.2781424734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0268428913\t-0.2884131572\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0338242083\t-0.2988981318\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0408055253\t-0.3095921411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0477868423\t-0.320489272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0547681593\t-0.331582943\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0617494764\t-0.3428658981\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0687307934\t-0.3543302024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0757121104\t-0.3659672116\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0826934274\t-0.3777676066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0896747444\t-0.3897213594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0966560614\t-0.4018177486\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1036373784\t-0.4140453684\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1106186954\t-0.4263921298\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1176000124\t-0.438845252\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1245813294\t-0.4513913041\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1315626464\t-0.4640162092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1385439634\t-0.4767052578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1455252805\t-0.4894431115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1525065975\t-0.5022138785\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1594879145\t-0.5150010698\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1664692315\t-0.5277877002\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1734505485\t-0.5405562612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1804318655\t-0.5532888036\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1874131825\t-0.5659669389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1943944995\t-0.5785718948\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2013758165\t-0.5910845596\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2083571335\t-0.6034855437\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2153384505\t-0.6157551974\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2223197675\t-0.6278736777\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2293010845\t-0.6398209934\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2362824016\t-0.6515770878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2432637186\t-0.6631218437\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2502450356\t-0.6744351906\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2572263526\t-0.6854971369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2642076696\t-0.6962878409\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2711889866\t-0.7067876507\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2781703036\t-0.7169771995\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2851516206\t-0.726837432\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2921329376\t-0.7363496897\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2991142546\t-0.745495761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3060955716\t-0.7542579462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3130768886\t-0.7626191172\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3200582056\t-0.7705627588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3270395227\t-0.7780730564\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3340208397\t-0.7851349252\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3410021567\t-0.791734055\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3479834737\t-0.7978570141\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3549647907\t-0.8034912145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3619461077\t-0.8086250401\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3689274247\t-0.8132478325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3759087417\t-0.8173499463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3828900587\t-0.8209227806\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3898713757\t-0.823958831\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3968526927\t-0.8264517017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4038340097\t-0.8283960953\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4108153268\t-0.8297879121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4177966438\t-0.8306241813\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4247779608\t-0.8309031362\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4317592778\t-0.8306241758\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4387405948\t-0.8297879087\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4457219118\t-0.828396094\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4527032288\t-0.826451696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4596845458\t-0.8239588351\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4666658628\t-0.8209227803\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4736471798\t-0.8173499492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4806284968\t-0.8132478386\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4876098138\t-0.8086250429\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4945911308\t-0.8034912215\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5015724479\t-0.7978570113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5085537649\t-0.7917340576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5155350819\t-0.7851349267\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5225163989\t-0.7780730567\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5294977159\t-0.7705627667\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5364790329\t-0.7626191185\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5434603499\t-0.7542579485\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5504416669\t-0.7454957654\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5574229839\t-0.7363496887\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5644043009\t-0.7268374342\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5713856179\t-0.7169771984\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5783669349\t-0.7067876473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.585348252\t-0.6962878353\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.592329569\t-0.6854971378\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.599310886\t-0.6744351903\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.606292203\t-0.6631218434\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.61327352\t-0.651577082\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.620254837\t-0.6398209952\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.627236154\t-0.6278736751\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.634217471\t-0.6157551904\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.641198788\t-0.6034855399\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.648180105\t-0.5910845591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.655161422\t-0.578571891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.662142739\t-0.5659669328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.669124056\t-0.5532888094\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6761053731\t-0.5405562648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6830866901\t-0.5277877017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6900680071\t-0.5150010689\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6970493241\t-0.5022138755\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7040306411\t-0.4894431073\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7110119581\t-0.476705258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7179932751\t-0.4640162136\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7249745921\t-0.4513913063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7319559091\t-0.4388452433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7389372261\t-0.4263921244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7459185431\t-0.414045365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7528998601\t-0.4018177463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7598811772\t-0.3897213582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7668624942\t-0.3777676043\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7738438112\t-0.3659672146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7808251282\t-0.3543302021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7878064452\t-0.3428659064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7947877622\t-0.3315829437\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8017690792\t-0.3204892715\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8087503962\t-0.3095921439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8157317132\t-0.298898128\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8227130302\t-0.2884131512\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8296943472\t-0.2781424771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8366756642\t-0.2680907066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8436569812\t-0.2582618408\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8506382983\t-0.2486592615\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8576196153\t-0.2392857692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8646009323\t-0.2301435775\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8715822493\t-0.2212343513\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8785635663\t-0.2125592414\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8855448833\t-0.2041188703\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8925262003\t-0.1959134007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8995075173\t-0.1879424996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9064888343\t-0.1802054296\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9134701513\t-0.1727010192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9204514683\t-0.1654277098\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9274327853\t-0.1583835775\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9344141024\t-0.1515663617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9413954194\t-0.1449734792\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9483767364\t-0.1386020436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9553580534\t-0.1324489139\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9623393704\t-0.1265106922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9693206874\t-0.1207837407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9763020044\t-0.1152642502\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9832833214\t-0.1099481924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9902646384\t-0.1048314047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9972459554\t-0.0999095813\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0042272724\t-0.0951782545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0112085894\t-0.0906329136\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0181899064\t-0.0862689121\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0251712235\t-0.0820815634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0321525405\t-0.0780660931\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0391338575\t-0.0742177365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0461151745\t-0.0705316682\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0530964915\t-0.0670030606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0600778085\t-0.063627096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0670591255\t-0.0603989597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0740404425\t-0.057313885\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0810217595\t-0.0543671114\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0880030765\t-0.0515539448\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0949843935\t-0.0488697248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1019657105\t-0.0463098828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1089470276\t-0.0438699005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1159283446\t-0.0415453234\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1229096616\t-0.0393318033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1298909786\t-0.0372250614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1368722956\t-0.0352209285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1438536126\t-0.0333153016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1508349296\t-0.0315042034\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1578162466\t-0.0297837445\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1647975636\t-0.0281501428\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1717788806\t-0.0265997174\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1787601976\t-0.025128904\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1857415146\t-0.0237342353\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1927228316\t-0.0224123598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1997041487\t-0.0211600422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2066854657\t-0.0199741305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2136667827\t-0.018851601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2206480997\t-0.0177895435\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2276294167\t-0.0167851328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2346107337\t-0.0158356767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2415920507\t-0.0149385625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2485733677\t-0.0140912892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2555546847\t-0.013291464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2625360017\t-0.0125367767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2695173187\t-0.0118250397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2764986357\t-0.0111541402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2834799528\t-0.0105220533\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2904612698\t-0.009926871\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2974425868\t-0.0093667517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3044239038\t-0.0088399514\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3114052208\t-0.0083447966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3183865378\t-0.0078797199\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3253678548\t-0.0074432094\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3323491718\t-0.0070338325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3393304888\t-0.0066502603\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3463118058\t-0.0062911859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3532931228\t-0.0059554294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3602744398\t-0.0056418301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3672557568\t-0.005349322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3742370739\t-0.0050768907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3812183909\t-0.004823582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3881997079\t-0.0045885227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3951810249\t-0.004370869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4021623419\t-0.0041698464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4091436589\t-0.0039847369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4161249759\t-0.0038148692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4231062929\t-0.0036596369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4300876099\t-0.0035184597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4370689269\t-0.0033908269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4440502439\t-0.0032762545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4510315609\t-0.003174323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.458012878\t-0.0030846656\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.464994195\t-0.0030069223\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.471975512\t-0.0029408023\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.478956829\t-0.0028860486\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.485938146\t-0.0028424584\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.492919463\t-0.0028098559\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.49990078\t-0.0027880924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.506882097\t-0.0027771008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.513863414\t-0.0027768127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.520844731\t-0.0027872063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.527826048\t-0.0028083076\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.534807365\t-0.0028401817\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.541788682\t-0.0028829066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5487699991\t-0.0029366483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5557513161\t-0.0030015704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5627326331\t-0.0030778617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5697139501\t-0.0031657997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5766952671\t-0.003265673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5836765841\t-0.0033778014\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5906579011\t-0.0035025525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5976392181\t-0.0036403439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6046205351\t-0.0037916192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6116018521\t-0.0039568608\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6185831691\t-0.0041366165\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6255644861\t-0.0043314588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6325458031\t-0.0045420038\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6395271202\t-0.0047689151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6465084372\t-0.0050129042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6534897542\t-0.0052747237\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6604710712\t-0.0055551739\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6674523882\t-0.0058551029\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6744337052\t-0.0061754207\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6814150222\t-0.0065170555\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6883963392\t-0.0068810115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6953776562\t-0.0072683462\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7023589732\t-0.0076801451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7093402902\t-0.0081175795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7163216072\t-0.0085818423\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7233029243\t-0.0090741904\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7302842413\t-0.0095959524\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7372655583\t-0.010148499\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7442468753\t-0.0107332456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7512281923\t-0.0113516811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7582095093\t-0.0120053347\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7651908263\t-0.0126958244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7721721433\t-0.0134247705\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7791534603\t-0.0141939049\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7861347773\t-0.0150049736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7931160943\t-0.0158598096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8000974113\t-0.016760265\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8070787283\t-0.0177082865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8140600454\t-0.0187058328\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8210413624\t-0.0197549297\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8280226794\t-0.0208576725\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8350039964\t-0.0220161596\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8419853134\t-0.0232325666\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8489666304\t-0.0245091014\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8559479474\t-0.025848021\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8629292644\t-0.0272515876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8699105814\t-0.0287221285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8768918984\t-0.0302619678\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8838732154\t-0.0318734914\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8908545324\t-0.0335590668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8978358495\t-0.0353211037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9048171665\t-0.0371619826\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9117984835\t-0.0390841327\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9187798005\t-0.0410899357\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9257611175\t-0.0431817937\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9327424345\t-0.0453620708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9397237515\t-0.047633113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9467050685\t-0.0499972214\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9536863855\t-0.0524566735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9606677025\t-0.0550136709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9676490195\t-0.0576703857\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9746303365\t-0.0604288797\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9816116535\t-0.063291169\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9885929706\t-0.0662591534\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9955742876\t-0.0693346497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0025556046\t-0.0725193507\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0095369216\t-0.0758148213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0165182386\t-0.0792225125\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0234995556\t-0.0827436934\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0304808726\t-0.08637951\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0374621896\t-0.0901309191\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0444435066\t-0.093998696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0514248236\t-0.097983422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0584061406\t-0.1020854658\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0653874576\t-0.1063049836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0723687747\t-0.1106419005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0793500917\t-0.1150959032\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0863314087\t-0.1196664158\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0933127257\t-0.1243526054\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1002940427\t-0.1291533516\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1072753597\t-0.1340672588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1142566767\t-0.1390926384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1212379937\t-0.1442274927\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1282193107\t-0.1494695063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1352006277\t-0.1548160526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1421819447\t-0.1602641687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1491632617\t-0.1658105794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1561445787\t-0.1714516333\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1631258958\t-0.1771833773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1701072128\t-0.1830014734\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1770885298\t-0.1889012811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1840698468\t-0.194877766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1910511638\t-0.2009255872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1980324808\t-0.2070390162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2050137978\t-0.2132120232\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2119951148\t-0.2194382184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2189764318\t-0.2257108876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2259577488\t-0.2320229783\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2329390658\t-0.2383671387\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2399203828\t-0.2447357156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2469016999\t-0.2511207367\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2538830169\t-0.2575139729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2608643339\t-0.2639069347\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2678456509\t-0.2702908615\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2748269679\t-0.2766567792\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2818082849\t-0.2829954824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2887896019\t-0.289297599\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2957709189\t-0.2955535745\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3027522359\t-0.3017537016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3097335529\t-0.3078881568\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3167148699\t-0.3139470301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3236961869\t-0.3199203137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3306775039\t-0.3257979922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.337658821\t-0.3315699884\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.344640138\t-0.3372262784\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.351621455\t-0.3427568782\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.358602772\t-0.348151842\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.365584089\t-0.3534013451\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.372565406\t-0.3584957292\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.379546723\t-0.3634254506\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.38652804\t-0.3681811782\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.393509357\t-0.3727538088\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.400490674\t-0.3771345016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.407471991\t-0.3813146684\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.414453308\t-0.3852860779\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4214346251\t-0.3890408132\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4284159421\t-0.3925713348\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4353972591\t-0.3958704765\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4423785761\t-0.3989315317\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4493598931\t-0.4017482113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4563412101\t-0.404314696\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4633225271\t-0.4066256685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4703038441\t-0.4086762886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4772851611\t-0.4104622866\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4842664781\t-0.4119798799\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4912477951\t-0.4132258789\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4982291121\t-0.4141976494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5052104291\t-0.4148931254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5121917462\t-0.4153108308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5191730632\t-0.4154498841\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5261543802\t-0.4153099772\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5331356972\t-0.4148914181\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5401170142\t-0.4141950885\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5470983312\t-0.413222472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5540796482\t-0.4119756129\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5610609652\t-0.4104571736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5680422822\t-0.4086703436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5750235992\t-0.4066188775\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5820049162\t-0.4043070667\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5889862332\t-0.4017397576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5959675503\t-0.3989222472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6029488673\t-0.3958603753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6099301843\t-0.3925604179\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6169115013\t-0.3890290947\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6238928183\t-0.3852735579\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6308741353\t-0.3813013545\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6378554523\t-0.3771203937\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6448367693\t-0.3727389363\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6518180863\t-0.3681655269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6587994033\t-0.3634090345\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6657807203\t-0.3584785637\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6727620373\t-0.3533834366\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6797433543\t-0.3481331851\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6867246714\t-0.3427374935\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6937059884\t-0.3372061735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7006873054\t-0.3315491633\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7076686224\t-0.3257764555\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7146499394\t-0.3198980861\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7216312564\t-0.3139241052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7286125734\t-0.3078645486\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7355938904\t-0.3017294035\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7425752074\t-0.2955285931\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7495565244\t-0.2892719505\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7565378414\t-0.2829691658\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7635191584\t-0.2766297944\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7705004754\t-0.2702632162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7774817925\t-0.2638786223\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7844631095\t-0.2574850065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7914444265\t-0.2510911022\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7984257435\t-0.2447054216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8054070605\t-0.2383361831\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8123883775\t-0.2319913556\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8193696945\t-0.2256785968\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8263510115\t-0.2194052518\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8333323285\t-0.2131783733\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8403136455\t-0.2070046765\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8472949625\t-0.200890536\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8542762795\t-0.1948420087\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8612575966\t-0.1888647894\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8682389136\t-0.182964254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8752202306\t-0.1771453943\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8822015476\t-0.171412878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8891828646\t-0.1657710226\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8961641816\t-0.1602238027\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9031454986\t-0.154774833\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9101268156\t-0.149427419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9171081326\t-0.1441844997\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9240894496\t-0.1390487105\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9310707666\t-0.1340223667\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9380520836\t-0.1291074497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9450334006\t-0.1243056643\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9520147177\t-0.1196183836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9589960347\t-0.115046743\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9659773517\t-0.1105915526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9729586687\t-0.106253397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9799399857\t-0.1020325874\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9869213027\t-0.0979291856\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9939026197\t-0.093943042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0008839367\t-0.0900737803\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0078652537\t-0.0863207985\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0148465707\t-0.0826833418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0218278877\t-0.0791604321\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0288092047\t-0.0757509295\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0357905218\t-0.0724535445\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0427718388\t-0.0692668391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0497531558\t-0.0661892213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0567344728\t-0.0632190089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0637157898\t-0.0603543747\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0706971068\t-0.0575933947\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0776784238\t-0.0549340745\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0846597408\t-0.0523743103\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0916410578\t-0.049911948\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0986223748\t-0.0475447669\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1056036918\t-0.0452704741\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1125850088\t-0.0430867683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1195663258\t-0.0409912812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1265476429\t-0.0389816494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1335289599\t-0.037055447\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1405102769\t-0.0352102784\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1474915939\t-0.0334437142\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1544729109\t-0.0317533372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1614542279\t-0.030136745\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1684355449\t-0.0285915324\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1754168619\t-0.0271152993\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1823981789\t-0.0257057141\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1893794959\t-0.0243604255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1963608129\t-0.0230771376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2033421299\t-0.0218535688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.210323447\t-0.0206874903\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.217304764\t-0.0195767093\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.224286081\t-0.0185190849\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.231267398\t-0.0175124992\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.238248715\t-0.0165549036\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.245230032\t-0.0156442666\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.252211349\t-0.0147786396\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.259192666\t-0.0139561192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.266173983\t-0.0131748358\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2731553\t-0.0124329771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.280136617\t-0.0117288014\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.287117934\t-0.0110605941\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.294099251\t-0.0104267068\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3010805681\t-0.0098255518\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3080618851\t-0.0092555718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3150432021\t-0.0087152776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3220245191\t-0.0082032335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3290058361\t-0.007718035\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3359871531\t-0.0072583503\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3429684701\t-0.0068228845\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3499497871\t-0.0064103905\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3569311041\t-0.0060196797\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3639124211\t-0.0056495764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3708937381\t-0.0052989787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3778750551\t-0.0049668402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3848563722\t-0.0046521099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3918376892\t-0.0043538064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3988190062\t-0.0040709948\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4058003232\t-0.0038027543\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4127816402\t-0.0035482283\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4197629572\t-0.0033065566\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4267442742\t-0.0030769433\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4337255912\t-0.0028586162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4407069082\t-0.0026508323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4476882252\t-0.0024528531\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4546695422\t-0.0022640095\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4616508592\t-0.0020836258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4686321762\t-0.0019110654\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4756134933\t-0.0017456992\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4825948103\t-0.0015869471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4895761273\t-0.0014341984\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4965574443\t-0.0012869163\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5035387613\t-0.0011445498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5105200783\t-0.0010065556\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5175013953\t-0.000872424\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5244827123\t-0.0007416386\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5314640293\t-0.0006137125\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5384453463\t-0.000488148\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5454266633\t-0.0003644655\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5524079803\t-0.0002421955\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5593892974\t-0.0001208641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5663706144\t1.14903999997532E-008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t };\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\addplot[smooth, red] table[x=angle,y=energy] {\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t angle energy\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0\t0.0033957422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.006981317\t0.0034023092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.013962634\t0.0034220302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.020943951\t0.0034549693\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.027925268\t0.0035012598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.034906585\t0.0035610578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.041887902\t0.0036345792\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0488692191\t0.0037220864\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0558505361\t0.0038238939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0628318531\t0.0039403683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0698131701\t0.0040719088\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0767944871\t0.0042189989\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0837758041\t0.004382143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0907571211\t0.0045619073\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.0977384381\t0.0047589218\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1047197551\t0.0049738688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1117010721\t0.0052074825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1186823891\t0.0054605709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1256637061\t0.0057339766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1326450232\t0.0060286173\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1396263402\t0.0063454874\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1466076572\t0.0066856152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1535889742\t0.0070501253\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1605702912\t0.0074401966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1675516082\t0.0078570829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1745329252\t0.0083020998\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1815142422\t0.0087766463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1884955592\t0.0092821954\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.1954768762\t0.009820287\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2024581932\t0.010392573\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2094395102\t0.0110007377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2164208272\t0.0116465891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2234021443\t0.0123319959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2303834613\t0.0130589211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2373647783\t0.0138294255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2443460953\t0.0146456293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2513274123\t0.0155097907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2583087293\t0.0164242132\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.2652900463\t0.0173913112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 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0.9424777961\t0.6673296917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9494591131\t0.6738335647\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9564404301\t0.6799490751\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9634217471\t0.6856638588\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9704030641\t0.6909662437\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9773843811\t0.6958453591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9843656981\t0.7002911435\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9913470151\t0.7042943477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 0.9983283321\t0.7078466345\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0053096491\t0.7109405541\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0122909662\t0.713569611\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0192722832\t0.7157282424\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0262536002\t0.7174118856\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0332349172\t0.7186169908\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0402162342\t0.7193409766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0471975512\t0.7195823085\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0541788682\t0.7193404776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0611601852\t0.7186160004\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0681415022\t0.7174104115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0751228192\t0.7157262704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0821041362\t0.7135671411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0890854532\t0.710937608\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.0960667703\t0.707843197\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1030480873\t0.7042904275\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1100294043\t0.7002867407\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1170107213\t0.6958404812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1239920383\t0.6909608841\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1309733553\t0.6856580177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1379546723\t0.679942774\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1449359893\t0.6738267972\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1519173063\t0.6673224653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1588986233\t0.6604428497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1658799403\t0.653201644\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1728612573\t0.6456131495\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1798425743\t0.6376922084\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1868238914\t0.6294541447\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.1938052084\t0.6209147247\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2007865254\t0.6120901095\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2077678424\t0.6029968042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2147491594\t0.5936515871\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2217304764\t0.5840714609\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2287117934\t0.5742736161\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2356931104\t0.5642753744\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2426744274\t0.5540941115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2496557444\t0.5437472436\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2566370614\t0.5332521519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2636183784\t0.5226261375\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2705996955\t0.5118863854\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2775810125\t0.501049919\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2845623295\t0.4901335285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2915436465\t0.4791537612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.2985249635\t0.468126878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3055062805\t0.4570688037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3124875975\t0.445995078\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3194689145\t0.4349208631\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3264502315\t0.4238608865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3334315485\t0.4128293939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3404128655\t0.4018401887\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3473941825\t0.3909065177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3543754995\t0.3800411323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3613568166\t0.3692562274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3683381336\t0.3585634339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3753194506\t0.3479738199\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3823007676\t0.3374978405\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3892820846\t0.3271453892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.3962634016\t0.3169257477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4032447186\t0.3068476003\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4102260356\t0.2969190128\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4172073526\t0.2871474688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4241886696\t0.277539838\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4311699866\t0.2681024227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4381513036\t0.2588408909\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4451326207\t0.2497603901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4521139377\t0.2408654634\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4590952547\t0.2321601086\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4660765717\t0.2236477822\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4730578887\t0.2153314168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4800392057\t0.2072134301\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4870205227\t0.1992957362\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.4940018397\t0.1915797961\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5009831567\t0.1840665782\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5079644737\t0.1767566412\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5149457907\t0.1696501065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5219271077\t0.1627467084\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5289084247\t0.1560457886\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5358897418\t0.1495463351\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5428710588\t0.1432469966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5498523758\t0.1371461093\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5568336928\t0.1312417113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5638150098\t0.1255315597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5707963268\t0.1200131643\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5777776438\t0.1146837952\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5847589608\t0.1095405035\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5917402778\t0.1045801473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.5987215948\t0.0997994174\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6057029118\t0.0951948248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6126842288\t0.0907627774\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6196655459\t0.0864995053\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6266468629\t0.0824011788\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6336281799\t0.0784638675\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6406094969\t0.0746835422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6475908139\t0.071056151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6545721309\t0.0675775496\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6615534479\t0.0642436103\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6685347649\t0.0610501422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6755160819\t0.0579929762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6824973989\t0.0550679217\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6894787159\t0.0522708236\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.6964600329\t0.0495975171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.7034413499\t0.047043895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.710422667\t0.044605888\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.717403984\t0.042279456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.724385301\t0.0400606112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.731366618\t0.0379454631\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.738347935\t0.0359301322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.745329252\t0.0340108497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.752310569\t0.0321839063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.759291886\t0.0304456612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.766273203\t0.0287925819\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.77325452\t0.0272211836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.780235837\t0.0257281108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.787217154\t0.0243100673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.7941984711\t0.0229638538\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8011797881\t0.021686365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8081611051\t0.0204745979\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8151424221\t0.0193256219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8221237391\t0.0182366182\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8291050561\t0.0172048526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8360863731\t0.0162276897\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8430676901\t0.0153025643\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8500490071\t0.0144270438\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8570303241\t0.0135987476\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8640116411\t0.012815396\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8709929581\t0.0120748131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8779742751\t0.0113748756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8849555922\t0.0107135746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8919369092\t0.0100889787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.8989182262\t0.0094992137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9058995432\t0.008942515\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9128808602\t0.0084171732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9198621772\t0.0079215648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9268434942\t0.0074541346\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9338248112\t0.007013402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9408061282\t0.0065979322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9477874452\t0.0062063868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9547687622\t0.0058374653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9617500792\t0.0054899576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9687313962\t0.0051626769\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9757127133\t0.0048545202\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9826940303\t0.0045644367\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9896753473\t0.0042914155\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 1.9966566643\t0.0040344913\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0036379813\t0.0037927758\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0106192983\t0.0035654047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0176006153\t0.003351559\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0245819323\t0.0031504633\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0315632493\t0.0029613909\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0385445663\t0.002783652\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0455258833\t0.0026165872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0525072003\t0.0024595685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0594885174\t0.0023120254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0664698344\t0.0021733808\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0734511514\t0.0020431272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0804324684\t0.0019207679\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0874137854\t0.0018058244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.0943951024\t0.0016978663\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1013764194\t0.0015964781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1083577364\t0.0015012519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1153390534\t0.0014118375\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1223203704\t0.0013278692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1293016874\t0.0012490196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1362830044\t0.001175\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1432643214\t0.0011054917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1502456385\t0.0010402331\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1572269555\t0.0009789618\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1642082725\t0.0009214391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1711895895\t0.0008674286\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1781709065\t0.0008167186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1851522235\t0.0007691151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1921335405\t0.0007244118\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.1991148575\t0.0006824418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2060961745\t0.0006430389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2130774915\t0.000606034\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2200588085\t0.0005712796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2270401255\t0.0005386463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2340214426\t0.0005080052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2410027596\t0.0004792151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2479840766\t0.0004521795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2549653936\t0.0004267811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2619467106\t0.000402919\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2689280276\t0.0003805063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2759093446\t0.0003594508\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2828906616\t0.0003396535\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2898719786\t0.000321057\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.2968532956\t0.0003035646\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3038346126\t0.0002871339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3108159296\t0.0002716802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3177972466\t0.0002571491\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3247785637\t0.0002434896\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3317598807\t0.0002306384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3387411977\t0.0002185523\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3457225147\t0.0002071789\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3527038317\t0.0001964801\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3596851487\t0.0001864102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3666664657\t0.0001769289\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3736477827\t0.0001680079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3806290997\t0.0001596123\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3876104167\t0.0001516908\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.3945917337\t0.0001442402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4015730507\t0.000137221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4085543678\t0.000130606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4155356848\t0.0001243767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4225170018\t0.0001184946\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4294983188\t0.0001129598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4364796358\t0.000107735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4434609528\t0.0001028092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4504422698\t9.81593874000014E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4574235868\t9.37755360000021E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4644049038\t8.96346342000032E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4713862208\t8.57277544000015E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4783675378\t8.20394565999999E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4853488548\t7.85586372000005E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4923301718\t7.52676802000009E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.4993114889\t7.21663204000002E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5062928059\t6.9221751399999E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5132741229\t6.64488880000036E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5202554399\t6.38192602000071E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5272367569\t6.13434411999986E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5342180739\t5.89907902000045E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5411993909\t0.000056773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5481807079\t5.4670176000006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5551620249\t5.26778140000073E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5621433419\t5.07945292000031E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5691246589\t0.000049006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.5761059759\t4.7316193400003E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.583087293\t4.57108746000009E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.59006861\t4.41962682000072E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.597049927\t4.27439405999985E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.604031244\t0.000041384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.611012561\t4.00783704000013E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.617993878\t3.88375924000039E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.624975195\t3.7670185000005E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.631956512\t3.65466863999908E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.638937829\t3.54788644000015E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.645919146\t3.4474166000012E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.652900463\t3.35064324000073E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.65988178\t3.25918250000112E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.666863097\t3.17085629999991E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6738444141\t3.0873934800002E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6808257311\t3.00792208000056E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6878070481\t2.93081347999963E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.6947883651\t0.000028578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7017696821\t2.78672744000175E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7087509991\t2.71932623999993E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7157323161\t2.65485030000179E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7227136331\t2.59211920000113E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7296949501\t2.53190779999912E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7366762671\t2.47347608000048E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7436575841\t2.41760565999893E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7506389011\t2.36312963999841E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7576202182\t2.31061984000136E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7646015352\t2.25902518000143E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7715828522\t2.20914184000109E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7785641692\t2.16166162000098E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7855454862\t2.11380928000215E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7925268032\t2.06758585999944E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.7995081202\t2.02174244000042E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8064894372\t1.97752860000289E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8134707542\t0.000019337\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8204520712\t1.88957152000291E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8274333882\t1.84737085999753E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8344147052\t1.80554645999864E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8413960222\t1.7630893600018E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8483773393\t1.72213982000124E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8553586563\t1.68104544000236E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8623399733\t1.63935036000262E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8693212903\t1.59822890000161E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8763026073\t0.000015568\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8832839243\t1.51688834000296E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8902652413\t1.47567082000033E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.8972465583\t1.434439539999E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9042278753\t1.39297288000439E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9112091923\t0.000013517\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9181905093\t1.30954170000641E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9251718263\t1.2683367200006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9321531434\t1.22548642000342E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9391344604\t1.18327184000511E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9461157774\t1.14028730000548E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9530970944\t1.09718833999906E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9600784114\t1.05408832000164E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9670597284\t1.01023280000834E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9740410454\t9.65626080001725E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9810223624\t9.21247760005128E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9880036794\t8.75907160002853E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 2.9949849964\t8.30472740004362E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0019663134\t7.84835059997047E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0089476304\t7.38665520000348E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0159289474\t6.91741460001616E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0229102645\t6.45572700003205E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0298915815\t5.97978180000291E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0368728985\t5.50569500007425E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0438542155\t5.0311048000462E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0508355325\t4.54059339999313E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0578168495\t4.0631664001145E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0647981665\t3.57138340001395E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0717794835\t3.08872939996929E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0787608005\t2.59633799998271E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0857421175\t2.0991488000055E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0927234345\t0.000001601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.0997047515\t0.000001112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1066860685\t6.20809600004879E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1136673856\t1.2553580008845E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1206487026\t-3.73510000040156E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1276300196\t-8.70672000052863E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1346113366\t-1.36469840000819E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1415926536\t-1.85440500000134E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1485739706\t-2.35060420000766E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1555552876\t-0.000002849\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1625366046\t-3.33773459992859E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1695179216\t-3.82459459996598E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1764992386\t-4.30763400000034E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1834805556\t-4.78823460003941E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1904618726\t-5.26350420004817E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.1974431897\t-5.74471279995992E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2044245067\t-6.21173699999478E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2114058237\t-6.68355899996476E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2183871407\t-7.14451139999239E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2253684577\t-7.60284199990968E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2323497747\t-8.06142880005467E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2393310917\t-8.5069311999697E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2463124087\t-8.95425499991553E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2532937257\t-9.39448959996758E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2602750427\t-9.82635859997361E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2672563597\t-1.02583853999749E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2742376767\t-1.0682859199973E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2812189937\t-1.11007783999972E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2882003108\t-1.15164235999776E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.2951816278\t-1.19275941999897E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3021629448\t-1.23245177999776E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3091442618\t-1.27256424000133E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3161255788\t-1.31158049999081E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3231068958\t-0.000013507\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3300882128\t-1.38915949999263E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3370695298\t-1.42686355999455E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3440508468\t-1.46403131999762E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3510321638\t-1.50131831999634E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3580134808\t-1.53786105999698E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3649947978\t-1.57463913999512E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3719761149\t-1.6104618799917E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3789574319\t-1.64652335999937E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3859387489\t-1.68162977999819E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3929200659\t-1.71773084000071E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.3999013829\t-1.75232713999773E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4068826999\t-1.78768931999307E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4138640169\t-1.82283129999405E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4208453339\t-1.85828292000034E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4278266509\t-1.89316091999681E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4348079679\t-0.000019294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4417892849\t-1.96567314000029E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4487706019\t-2.00195835999839E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.4557519189\t-2.0381170199979E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.462733236\t-2.07541793999788E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.469714553\t-0.000021135\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.47669587\t-0.00002152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.483677187\t-0.000021914\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.490658504\t-2.23135333999869E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.497639821\t-2.27233211999855E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.504621138\t-2.31461048000037E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.511602455\t-2.35791168000099E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.518583772\t-2.40303969999966E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.525565089\t-2.44927636000036E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.532546406\t-2.49752637999923E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.539527723\t-2.5465215999998E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5465090401\t-2.59781017999949E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5534903571\t-2.65206884000058E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5604716741\t-2.70747631999912E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5674529911\t-0.00002766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5744343081\t-2.82636609999914E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5814156251\t-2.88944284000114E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5883969421\t-2.95665357999963E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.5953782591\t-3.02551021999775E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6023595761\t-3.09872782000009E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6093408931\t-3.17457181999853E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6163222101\t-3.25564353999969E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6233035271\t-3.33966103999994E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6302848441\t-3.42824461999902E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6372661612\t-0.000035216\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6442474782\t-3.6189645599996E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6512287952\t-3.72281259999885E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6582101122\t-3.83172209999921E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6651914292\t-3.94621912000043E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6721727462\t-4.06747887999881E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6791540632\t-4.19428924000043E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6861353802\t-4.32923279999886E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.6931166972\t-0.000044712\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7000980142\t-0.000046205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7070793312\t-0.000047783\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7140606482\t-4.94544533999955E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7210419653\t-5.12190511999938E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7280232823\t-5.3087414200001E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7350045993\t-5.50592824000024E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7419859163\t-5.71398123999992E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7489672333\t-5.93482606000006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7559485503\t-6.16756785999928E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7629298673\t-6.41358957999966E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7699111843\t-6.67535852000023E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7768925013\t-6.95056986000017E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7838738183\t-7.24331795999983E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7908551353\t-7.55292505999969E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.7978364523\t-7.88055753999997E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8048177693\t-8.22673105999941E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8117990864\t-8.5947817600001E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8187804034\t-8.98414145999969E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8257617204\t-0.000093976\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8327430374\t-9.83438707999988E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8397243544\t-0.0001029837\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8467056714\t-0.0001079018\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8536869884\t-0.0001131152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8606683054\t-0.0001186509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8676496224\t-0.000124513\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8746309394\t-0.000130736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8816122564\t-0.0001373478\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8885935734\t-0.0001443558\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.8955748905\t-0.0001518119\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9025562075\t-0.0001597116\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9095375245\t-0.0001681089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9165188415\t-0.0001770242\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9235001585\t-0.0001864986\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9304814755\t-0.0001965687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9374627925\t-0.0002072659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9444441095\t-0.000218628\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9514254265\t-0.0002307101\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9584067435\t-0.0002435522\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9653880605\t-0.0002572171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9723693775\t-0.0002717404\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9793506945\t-0.0002871924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9863320116\t-0.0003036177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 3.9933133286\t-0.0003211016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0002946456\t-0.0003396941\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0072759626\t-0.0003594892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0142572796\t-0.000380551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0212385966\t-0.0004029651\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0282199136\t-0.0004268223\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0352012306\t-0.0004522149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0421825476\t-0.0004792533\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0491638646\t-0.000508033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0561451816\t-0.0005386785\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0631264986\t-0.0005713092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0701078157\t-0.000606054\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0770891327\t-0.0006430647\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0840704497\t-0.0006824649\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0910517667\t-0.000724439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.0980330837\t-0.0007691332\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1050144007\t-0.0008167427\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1119957177\t-0.0008674509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1189770347\t-0.0009214605\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1259583517\t-0.0009789786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1329396687\t-0.0010402513\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1399209857\t-0.0011055086\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1469023027\t-0.0011750108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1538836197\t-0.0012490377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1608649368\t-0.0013278852\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1678462538\t-0.0014118474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1748275708\t-0.0015012647\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1818088878\t-0.0015964854\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1887902048\t-0.001697877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.1957715218\t-0.0018058311\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2027528388\t-0.0019207718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2097341558\t-0.0020431394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2167154728\t-0.0021733906\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2236967898\t-0.0023120306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2306781068\t-0.0024595791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2376594238\t-0.0026165947\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2446407409\t-0.0027836608\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2516220579\t-0.0029614065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2586033749\t-0.0031504838\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2655846919\t-0.0033515703\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2725660089\t-0.0035654179\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2795473259\t-0.0037927922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2865286429\t-0.0040345089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.2935099599\t-0.0042914271\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3004912769\t-0.0045644577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3074725939\t-0.0048545368\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3144539109\t-0.0051626895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3214352279\t-0.005489971\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.3284165449\t-0.0058374822\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.335397862\t-0.0062064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.342379179\t-0.0065979457\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.349360496\t-0.007013422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.356341813\t-0.0074541563\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.36332313\t-0.0079215935\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.370304447\t-0.0084171956\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.377285764\t-0.0089425419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.384267081\t-0.0094992441\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.391248398\t-0.0100890018\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.398229715\t-0.0107136048\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.405211032\t-0.0113749013\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.412192349\t-0.0120748391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.419173666\t-0.0128154305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4261549831\t-0.0135987794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4331363001\t-0.014427077\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4401176171\t-0.0153026118\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4470989341\t-0.0162277331\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4540802511\t-0.017204901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4610615681\t-0.0182366653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4680428851\t-0.0193256704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4750242021\t-0.0204746529\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4820055191\t-0.021686423\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4889868361\t-0.0229639159\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.4959681531\t-0.0243101284\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5029494701\t-0.0257281744\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5099307872\t-0.0272212493\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5169121042\t-0.0287926483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5238934212\t-0.030445737\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5308747382\t-0.0321839797\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5378560552\t-0.0340109372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5448373722\t-0.0359302227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5518186892\t-0.0379455519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5588000062\t-0.0400607157\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5657813232\t-0.0422795582\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5727626402\t-0.0446059958\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5797439572\t-0.0470440126\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5867252742\t-0.0495976379\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.5937065912\t-0.0522709521\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6006879083\t-0.055068065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6076692253\t-0.0579931188\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6146505423\t-0.0610502959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6216318593\t-0.0642437688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6286131763\t-0.0675777135\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6355944933\t-0.0710563221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6425758103\t-0.0746837291\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6495571273\t-0.0784640596\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6565384443\t-0.0824013874\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6635197613\t-0.0864997192\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6705010783\t-0.0907629965\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6774823953\t-0.0951950612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6844637124\t-0.0997996617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6914450294\t-0.1045804045\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.6984263464\t-0.1095407702\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7054076634\t-0.1146840757\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7123889804\t-0.1200134587\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7193702974\t-0.1255318739\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7263516144\t-0.1312420372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7333329314\t-0.1371464487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7403142484\t-0.1432473503\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7472955654\t-0.1495466999\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7542768824\t-0.1560461676\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7612581994\t-0.1627471106\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7682395164\t-0.1696505319\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7752208335\t-0.1767570771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7822021505\t-0.1840670335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7891834675\t-0.1915802612\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.7961647845\t-0.1992962254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8031461015\t-0.2072139458\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8101274185\t-0.2153319471\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8171087355\t-0.2236483344\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8240900525\t-0.2321606815\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8310713695\t-0.2408660577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8380526865\t-0.2497610105\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8450340035\t-0.2588415322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8520153205\t-0.2681030825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8589966376\t-0.2775405234\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8659779546\t-0.287148178\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8729592716\t-0.2969197532\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8799405886\t-0.3068483614\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8869219056\t-0.3169265372\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.8939032226\t-0.3271462043\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9008845396\t-0.3374986801\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9078658566\t-0.3479746812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9148471736\t-0.3585643212\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9218284906\t-0.3692571495\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9288098076\t-0.3800420799\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9357911246\t-0.3909074896\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9427724416\t-0.4018411785\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9497537587\t-0.4128304237\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9567350757\t-0.4238619351\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9637163927\t-0.4349219455\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9706977097\t-0.4459961831\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9776790267\t-0.457069938\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9846603437\t-0.4681280416\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9916416607\t-0.4791549444\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 4.9986229777\t-0.4901347348\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0056042947\t-0.5010511529\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0125856117\t-0.5118876494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0195669287\t-0.5226274274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0265482457\t-0.53325347\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0335295628\t-0.5437485901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0405108798\t-0.55409548\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0474921968\t-0.5642767725\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0544735138\t-0.5742750429\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0614548308\t-0.5840729097\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0684361478\t-0.5936530578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0754174648\t-0.6029983\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0823987818\t-0.6120916335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0893800988\t-0.6209162626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.0963614158\t-0.629455704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1033427328\t-0.637693788\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1103240498\t-0.6456147492\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1173053668\t-0.6532032629\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1242866839\t-0.6604444867\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1312680009\t-0.6673241187\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1382493179\t-0.6738284663\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1452306349\t-0.6799444597\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1522119519\t-0.6856597208\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1591932689\t-0.690962591\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1661745859\t-0.6958422031\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1731559029\t-0.7002884723\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1801372199\t-0.7042921737\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1871185369\t-0.7078449587\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.1940998539\t-0.7109393683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.2010811709\t-0.7135689154\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.208062488\t-0.7157280421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.215043805\t-0.7174121919\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.222025122\t-0.7186177866\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.229006439\t-0.7193422665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.235987756\t-0.7195840956\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.242969073\t-0.719342761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.24995039\t-0.7186187681\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.256931707\t-0.7174136679\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.263913024\t-0.7157300137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.270894341\t-0.7135713739\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.277875658\t-0.7109423149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.284856975\t-0.7078483868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.291838292\t-0.7042960974\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.2988196091\t-0.7002928776\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3058009261\t-0.695847091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3127822431\t-0.6909679538\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3197635601\t-0.6856655532\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3267448771\t-0.6799507617\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3337261941\t-0.6738352304\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3407075111\t-0.6673313458\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3476888281\t-0.6604521704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3546701451\t-0.6532114042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3616514621\t-0.6456233406\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3686327791\t-0.637702824\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3756140961\t-0.6294651782\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3825954132\t-0.6209261673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3895767302\t-0.6121019699\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.3965580472\t-0.6030090691\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4035393642\t-0.5936642531\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4105206812\t-0.5840845171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4175019982\t-0.5742870635\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4244833152\t-0.5642892063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4314646322\t-0.5541083205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4384459492\t-0.5437618242\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4454272662\t-0.5332671054\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4524085832\t-0.5226414565\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4593899002\t-0.5119020732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4663712172\t-0.501065965\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4733525343\t-0.4901499276\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4803338513\t-0.4791705254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4873151683\t-0.4681439967\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.4942964853\t-0.4570862825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5012778023\t-0.4460129093\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5082591193\t-0.4349390535\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5152404363\t-0.4238794248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5222217533\t-0.4128482951\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5292030703\t-0.4018594382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5361843873\t-0.39092613\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5431657043\t-0.3800611075\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5501470213\t-0.3692765717\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5571283383\t-0.3585841578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5641096554\t-0.3479949104\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5710909724\t-0.3375193235\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5780722894\t-0.3271672663\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5850536064\t-0.3169480309\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5920349234\t-0.3068702943\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.5990162404\t-0.2969421297\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6059975574\t-0.2871710176\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6129788744\t-0.2775638391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6199601914\t-0.2681268786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6269415084\t-0.2588658369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6339228254\t-0.2497858336\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6409041424\t-0.2408914187\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6478854595\t-0.2321866\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6548667765\t-0.2236748342\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6618480935\t-0.2153590541\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6688294105\t-0.2072416721\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6758107275\t-0.1993246155\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6827920445\t-0.1916093333\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6897733615\t-0.1840968117\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.6967546785\t-0.1767876133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7037359955\t-0.1696818371\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7107173125\t-0.1627792421\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7176986295\t-0.15607917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7246799465\t-0.1495805959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7316612635\t-0.1432821909\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7386425806\t-0.1371822914\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7456238976\t-0.1312789243\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7526052146\t-0.1255698552\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7595865316\t-0.1200526113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7665678486\t-0.1147244483\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7735491656\t-0.1095824323\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7805304826\t-0.1046234244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7875117996\t-0.0998441077\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.7944931166\t-0.0952410222\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8014744336\t-0.0908105528\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8084557506\t-0.0865489522\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8154370676\t-0.0824523979\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8224183847\t-0.0785169409\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8293997017\t-0.0747385939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8363810187\t-0.0711132767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8433623357\t-0.0676368903\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8503436527\t-0.0643052783\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8573249697\t-0.0611142846\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8643062867\t-0.0580597222\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8712876037\t-0.0551374274\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8782689207\t-0.0523432491\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8852502377\t-0.0496730398\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8922315547\t-0.047122693\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.8992128717\t-0.0446881553\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9061941887\t-0.0423653962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9131755058\t-0.0401504526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9201568228\t-0.038039425\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9271381398\t-0.0360284761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9341194568\t-0.0341138334\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9411007738\t-0.0322918005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9480820908\t-0.0305587764\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9550634078\t-0.0289112187\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9620447248\t-0.0273456966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9690260418\t-0.0258588467\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9760073588\t-0.0244474151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9829886758\t-0.0231082096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9899699928\t-0.021838177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 5.9969513099\t-0.0206343095\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0039326269\t-0.0194937308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0109139439\t-0.0184136413\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0178952609\t-0.0173913512\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0248765779\t-0.0164242443\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0318578949\t-0.0155098302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0388392119\t-0.0146456653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0458205289\t-0.0138294577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0528018459\t-0.0130589547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0597831629\t-0.0123320226\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0667644799\t-0.0116466083\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0737457969\t-0.0110007606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.0807271139\t-0.0103925964\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.087708431\t-0.0098203219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.094689748\t-0.0092822166\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.101671065\t-0.0087766624\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.108652382\t-0.0083021224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.115633699\t-0.0078570996\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.122615016\t-0.0074402102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.129596333\t-0.007050147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.13657765\t-0.0066856324\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.143558967\t-0.0063454983\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.150540284\t-0.0060286285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.157521601\t-0.0057339872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.164502918\t-0.0054605818\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1714842351\t-0.0052075015\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1784655521\t-0.0049738729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1854468691\t-0.0047589303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1924281861\t-0.0045619166\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.1994095031\t-0.0043821474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2063908201\t-0.0042190099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2133721371\t-0.0040719162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2203534541\t-0.0039403771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2273347711\t-0.0038238968\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2343160881\t-0.0037220959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2412974051\t-0.0036345869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2482787221\t-0.003561063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2552600391\t-0.003501266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2622413562\t-0.0034549746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2692226732\t-0.003422025\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2762039902\t-0.0034023098\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2831853072\t-0.0033957422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2901666242\t-0.0034023092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.2971479412\t-0.0034220302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3041292582\t-0.0034549693\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3111105752\t-0.0035012598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3180918922\t-0.0035610578\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3250732092\t-0.0036345792\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3320545262\t-0.0037220864\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3390358432\t-0.0038238939\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3460171603\t-0.0039403683\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3529984773\t-0.0040719088\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3599797943\t-0.0042189989\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3669611113\t-0.004382143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3739424283\t-0.0045619073\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3809237453\t-0.0047589218\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3879050623\t-0.0049738688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.3948863793\t-0.0052074825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4018676963\t-0.0054605709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4088490133\t-0.0057339766\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4158303303\t-0.0060286173\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4228116473\t-0.0063454874\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4297929643\t-0.0066856152\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4367742814\t-0.0070501253\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4437555984\t-0.0074401966\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4507369154\t-0.0078570829\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4577182324\t-0.0083020998\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4646995494\t-0.0087766463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4716808664\t-0.0092821954\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4786621834\t-0.009820287\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4856435004\t-0.0103925665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4926248174\t-0.0110007377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.4996061344\t-0.0116465891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5065874514\t-0.0123319883\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5135687684\t-0.0130589211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5205500855\t-0.0138294255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5275314025\t-0.0146456293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5345127195\t-0.0155097907\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5414940365\t-0.0164242067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5484753535\t-0.0173913112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5554566705\t-0.0184136007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5624379875\t-0.0194936783\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5694193045\t-0.0206342511\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5764006215\t-0.0218381139\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5833819385\t-0.0231081561\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5903632555\t-0.0244473494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.5973445725\t-0.0258587804\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6043258895\t-0.027345626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6113072066\t-0.0289111494\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6182885236\t-0.0305586968\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6252698406\t-0.0322917147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6322511576\t-0.0341137464\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6392324746\t-0.036028382\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6462137916\t-0.038039335\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6531951086\t-0.040150358\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6601764256\t-0.0423652859\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6671577426\t-0.0446880429\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6741390596\t-0.0471225788\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6811203766\t-0.0496729131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6881016936\t-0.0523431108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.6950830107\t-0.0551372868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7020643277\t-0.0580595753\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7090456447\t-0.0611141227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7160269617\t-0.0643051123\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7230082787\t-0.0676367184\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7299895957\t-0.0711130961\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7369709127\t-0.0747384069\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7439522297\t-0.078516745\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7509335467\t-0.0824521895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7579148637\t-0.0865487327\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7648961807\t-0.0908103127\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7718774977\t-0.0952407861\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7788588147\t-0.0998438514\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7858401318\t-0.104623156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7928214488\t-0.1095821478\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.7998027658\t-0.1147241606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8067840828\t-0.1200523039\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8137653998\t-0.1255695376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8207467168\t-0.1312785915\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8277280338\t-0.1371819352\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8347093508\t-0.1432818245\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8416906678\t-0.1495802139\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8486719848\t-0.1560787671\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8556533018\t-0.1627788267\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8626346188\t-0.1696814135\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8696159358\t-0.1767871563\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8765972529\t-0.1840963416\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8835785699\t-0.1916088468\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8905598869\t-0.1993241079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.8975412039\t-0.2072411466\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9045225209\t-0.2153585032\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9115038379\t-0.2236742632\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9184851549\t-0.2321860158\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9254664719\t-0.2408908066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9324477889\t-0.2497851942\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9394291059\t-0.2588651787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9464104229\t-0.2681261963\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.9533917399\t-0.2775631354\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.960373057\t-0.2871702846\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.967354374\t-0.2969413709\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.974335691\t-0.3068695082\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.981317008\t-0.3169472283\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.988298325\t-0.3271664369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 6.995279642\t-0.337518463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.002260959\t-0.3479940259\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.009242276\t-0.3585832386\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.016223593\t-0.3692756318\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.02320491\t-0.380060143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.030186227\t-0.3909251357\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.037167544\t-0.401858415\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.044148861\t-0.4128472428\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0511301781\t-0.4238783438\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0581114951\t-0.434937943\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0650928121\t-0.4460117804\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0720741291\t-0.4570851156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0790554461\t-0.4681428059\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0860367631\t-0.479169304\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0930180801\t-0.4901486873\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.0999993971\t-0.5010646927\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1069807141\t-0.5119007741\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1139620311\t-0.5226401259\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1209433481\t-0.5332657477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1279246651\t-0.5437604456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1349059822\t-0.5541069133\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1418872992\t-0.5642877672\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1488686162\t-0.5742856065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1558499332\t-0.5840830272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1628312502\t-0.5936627369\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1698125672\t-0.6030075353\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1767938842\t-0.6121004219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1837752012\t-0.6209245901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1907565182\t-0.6294635752\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.1977378352\t-0.6377011974\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2047191522\t-0.6456217035\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2117004692\t-0.6532097414\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2186817862\t-0.6604504893\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2256631033\t-0.6673296472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2326444203\t-0.6738335202\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2396257373\t-0.6799490306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2466070543\t-0.6856638144\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2535883713\t-0.6909661992\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2605696883\t-0.6958453146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2675510053\t-0.700291099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2745323223\t-0.7042943032\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2815136393\t-0.70784659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2884949563\t-0.7109405096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.2954762733\t-0.7135695665\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3024575903\t-0.715728198\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3094389074\t-0.7174118412\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3164202244\t-0.7186169387\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3234015414\t-0.7193409245\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3303828584\t-0.719582264\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3373641754\t-0.7193404332\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3443454924\t-0.718615956\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3513268094\t-0.717410367\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3583081264\t-0.715726226\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3652894434\t-0.7135670967\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3722707604\t-0.7109375636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3792520774\t-0.7078431526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3862333944\t-0.704290383\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.3932147114\t-0.7002866962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4001960285\t-0.6958404367\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4071773455\t-0.6909608397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4141586625\t-0.6856579732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4211399795\t-0.6799427295\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4281212965\t-0.6738267527\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4351026135\t-0.6673224284\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4420839305\t-0.6604428052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4490652475\t-0.6532016072\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4560465645\t-0.6456131126\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4630278815\t-0.637692164\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4700091985\t-0.6294541002\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4769905155\t-0.6209146878\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4839718326\t-0.6120900791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4909531496\t-0.6029967674\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.4979344666\t-0.5936515502\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5049157836\t-0.5840714306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5118971006\t-0.5742735858\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5188784176\t-0.5642753375\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5258597346\t-0.5540940746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5328410516\t-0.5437472067\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5398223686\t-0.533252115\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5468036856\t-0.5226261006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5537850026\t-0.5118863485\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5607663196\t-0.5010498821\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5677476366\t-0.4901334916\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5747289537\t-0.4791537308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5817102707\t-0.4681268487\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5886915877\t-0.4570687668\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.5956729047\t-0.4459950552\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6026542217\t-0.4349208403\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6096355387\t-0.4238608572\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6166168557\t-0.4128293711\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6235981727\t-0.4018401594\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6305794897\t-0.3909064884\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6375608067\t-0.3800411031\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6445421237\t-0.3692562058\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6515234407\t-0.3585634123\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6585047578\t-0.3479737906\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6654860748\t-0.3374978253\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6724673918\t-0.327145374\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6794487088\t-0.3169257325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6864300258\t-0.3068475786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.6934113428\t-0.2969189911\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7003926598\t-0.2871474536\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7073739768\t-0.2775398228\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7143552938\t-0.268102401\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7213366108\t-0.2588408758\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7283179278\t-0.249760376\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7352992448\t-0.2408654482\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7422805618\t-0.2321600934\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7492618789\t-0.223647767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7562431959\t-0.2153314017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7632245129\t-0.207213416\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7702058299\t-0.1992957221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7771871469\t-0.1915797744\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7841684639\t-0.1840665641\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7911497809\t-0.1767566336\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.7981310979\t-0.1696500914\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8051124149\t-0.1627466933\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8120937319\t-0.156045781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8190750489\t-0.149546321\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.8260563659\t-0.1432469825\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.833037683\t-0.1371461017\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.840019\t-0.1312417038\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.847000317\t-0.1255315521\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.853981634\t-0.1200131502\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.860962951\t-0.1146837876\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.867944268\t-0.1095404894\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.874925585\t-0.1045801397\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.881906902\t-0.0997994098\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.888888219\t-0.0951948248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.895869536\t-0.0907627698\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.902850853\t-0.0864994977\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.90983217\t-0.0824011788\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.916813487\t-0.0784638599\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9237948041\t-0.0746835422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9307761211\t-0.0710561434\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9377574381\t-0.0675775496\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9447387551\t-0.0642436027\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9517200721\t-0.0610501422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9587013891\t-0.0579929762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9656827061\t-0.0550679217\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9726640231\t-0.052270816\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9796453401\t-0.0495975171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9866266571\t-0.047043895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 7.9936079741\t-0.044605888\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0005892911\t-0.0422794484\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0075706081\t-0.0400606112\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0145519252\t-0.0379454631\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0215332422\t-0.0359301322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0285145592\t-0.0340108497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0354958762\t-0.0321838988\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0424771932\t-0.0304456536\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0494585102\t-0.0287925743\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0564398272\t-0.0272211836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0634211442\t-0.0257281108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0704024612\t-0.0243100673\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0773837782\t-0.0229638473\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0843650952\t-0.021686365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0913464122\t-0.0204745979\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.0983277293\t-0.0193256219\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1053090463\t-0.0182366182\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1122903633\t-0.0172048526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1192716803\t-0.0162276897\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1262529973\t-0.0153025643\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1332343143\t-0.0144270438\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1402156313\t-0.0135987401\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1471969483\t-0.012815396\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1541782653\t-0.0120748055\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1611595823\t-0.011374868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1681408993\t-0.0107135746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1751222163\t-0.0100889787\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1821035333\t-0.0094992137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1890848504\t-0.008942515\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.1960661674\t-0.0084171732\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2030474844\t-0.0079215648\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2100288014\t-0.0074541346\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2170101184\t-0.007013402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2239914354\t-0.0065979322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2309727524\t-0.0062063868\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2379540694\t-0.0058374653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2449353864\t-0.0054899576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2519167034\t-0.0051626769\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2588980204\t-0.0048545202\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2658793374\t-0.0045644367\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2728606545\t-0.0042914155\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2798419715\t-0.0040344913\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2868232885\t-0.0037927758\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.2938046055\t-0.0035654047\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3007859225\t-0.003351559\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3077672395\t-0.0031504633\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3147485565\t-0.0029613909\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3217298735\t-0.002783652\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3287111905\t-0.0026165872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3356925075\t-0.0024595685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3426738245\t-0.0023120254\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3496551415\t-0.0021733808\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3566364585\t-0.0020431272\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3636177756\t-0.0019207603\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3705990926\t-0.0018058244\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3775804096\t-0.0016978663\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3845617266\t-0.0015964781\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3915430436\t-0.0015012519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.3985243606\t-0.0014118375\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4055056776\t-0.0013278692\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4124869946\t-0.0012490196\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4194683116\t-0.001175\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4264496286\t-0.0011054917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4334309456\t-0.0010402331\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4404122626\t-0.0009789618\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4473935797\t-0.0009214391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4543748967\t-0.0008674286\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4613562137\t-0.0008167186\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4683375307\t-0.0007691151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4753188477\t-0.0007244118\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4823001647\t-0.0006824418\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4892814817\t-0.0006430389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.4962627987\t-0.000606034\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5032441157\t-0.0005712796\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5102254327\t-0.0005386463\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5172067497\t-0.0005080052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5241880667\t-0.0004792151\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5311693837\t-0.0004521795\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5381507008\t-0.0004267811\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5451320178\t-0.000402919\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5521133348\t-0.0003805063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5590946518\t-0.0003594508\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5660759688\t-0.0003396535\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5730572858\t-0.000321057\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5800386028\t-0.0003035646\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5870199198\t-0.0002871339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.5940012368\t-0.0002716802\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6009825538\t-0.0002571491\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6079638708\t-0.0002434896\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6149451878\t-0.0002306384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6219265049\t-0.0002185523\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6289078219\t-0.0002071789\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6358891389\t-0.0001964801\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6428704559\t-0.0001864102\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6498517729\t-0.0001769289\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6568330899\t-0.0001680079\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6638144069\t-0.0001596123\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6707957239\t-0.0001516974\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6777770409\t-0.0001442402\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6847583579\t-0.000137221\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6917396749\t-0.000130606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.6987209919\t-0.0001243767\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.7057023089\t-0.0001184946\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.712683626\t-0.0001129598\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.719664943\t-0.000107735\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.72664626\t-0.0001028092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.733627577\t-9.81593874000014E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.740608894\t-9.37755360000021E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.747590211\t-8.96346342000032E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.754571528\t-8.57342616000026E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.761552845\t-8.20394565999999E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.768534162\t-7.85586372000005E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.775515479\t-7.52676802000009E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.782496796\t-7.21587277999966E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.789478113\t-6.92282586000001E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.7964594301\t-6.64488880000036E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8034407471\t-6.38257674000081E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8104220641\t-6.13434411999986E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8174033811\t-5.89972974000055E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8243846981\t-0.000056773\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8313660151\t-5.4670176000006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8383473321\t-5.26843212000014E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8453286491\t-5.07945292000031E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8523099661\t-4.90124690000066E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8592912831\t-4.7316193400003E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8662726001\t-4.57097892000019E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8732539171\t-4.41886756000001E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8802352341\t-4.27504477999996E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8872165512\t-4.13764408000103E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.8941978682\t-4.00772849999953E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9011791852\t-3.8844099600005E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9081605022\t-3.76625924000118E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9151418192\t-3.65531936000057E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9221231362\t-3.54853716000025E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9291044532\t-3.4473080600006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9360857702\t-3.35129396000083E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9430670872\t-3.25907396000052E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9500484042\t-3.17150702000002E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9570297212\t-3.0872849399996E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9640110382\t-3.00781354000135E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9709923553\t-0.000029307\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9779736723\t-0.000028577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9849549893\t-2.78737816000046E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9919363063\t-2.71921770000072E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 8.9989176233\t-2.65474176000258E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0058989403\t-2.59201066000192E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0128802573\t-2.53255851999923E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0198615743\t-2.47336754000127E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0268428913\t-0.000024175\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0338242083\t-2.36367182000208E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0408055253\t-2.31051129999937E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0477868423\t-2.25956735999955E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0547681593\t-2.21044328000131E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0617494764\t-2.16155307999899E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0687307934\t-0.000021137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0757121104\t-2.06747732000023E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0826934274\t-2.02228462000409E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0896747444\t-1.97731151999891E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.0966560614\t-1.9342453999982E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1036373784\t-1.89011370000103E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1106186954\t-1.8479130400012E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1176000124\t-1.80532938000022E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1245813294\t-1.76363154000547E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1315626464\t-1.72268200000214E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1385439634\t-1.68082836000116E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1455252805\t-1.63913328000143E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1525065975\t-1.59866254000329E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1594879145\t-1.55799070000739E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1664692315\t-1.51667125999899E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1734505485\t-1.47545374000191E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1804318655\t-1.43422246000058E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1874131825\t-1.39340652000608E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.1943944995\t-1.35213566000436E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2013758165\t-1.31073460000186E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2083571335\t-1.26811964000217E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2153384505\t-1.22592005999955E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2223197675\t-1.18370548000124E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2293010845\t-1.14148020000093E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2362824016\t-1.09762198000074E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2432637186\t-1.05452195999778E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2502450356\t-1.01066643999892E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2572263526\t-9.66059720003409E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2642076696\t-9.21681400001262E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2711889866\t-8.76340799998987E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2781703036\t-8.30906380006047E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2851516206\t-7.85268699998731E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2921329376\t-0.000007391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.2991142546\t-6.92175099997749E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3060955716\t-6.4600634000489E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3130768886\t-5.98411819996425E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3200582056\t-0.00000551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3270395227\t-5.03544120006305E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3340208397\t-4.55143700001104E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3410021567\t-4.06750280007584E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3479834737\t-3.58222700008737E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3549647907\t-3.09306580004165E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3619461077\t-2.60067440005507E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3689274247\t-0.00000211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3759087417\t-1.61180239999226E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3828900587\t-1.12285860004446E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3898713757\t-6.25146000021726E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.3968526927\t-1.28786800057679E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4038340097\t3.62666400022249E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4108153268\t8.59828400034957E-007\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4177966438\t1.35385479999028E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4247779608\t1.85766119992214E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4317592778\t2.34626779999081E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4387405948\t2.83814719997943E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4457219118\t3.32689099996619E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4527032288\t3.81375100000358E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4596845458\t4.29679039998243E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4666658628\t4.7773910000215E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4736471798\t5.26025320002344E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4806284968\t5.73386919999752E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4876098138\t6.20740059997793E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.4945911308\t6.67271540000236E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5015724479\t7.14017499997555E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5085537649\t7.59850560000386E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5155350819\t8.05058520003676E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5225163989\t8.50259480000837E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5294977159\t8.94341139989763E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5364790329\t9.38364600000519E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5434603499\t9.81551500001121E-006\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5504416669\t1.0247541799957E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5574229839\t1.06785228000117E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5644043009\t1.10964419999249E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5713856179\t1.15120871999608E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.5783669349\t1.19156651999797E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.585348252\t1.23201813999607E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.592329569\t1.27137133999478E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.599310886\t1.31114685999467E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.606292203\t1.35026359999735E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.61327352\t1.38796659999718E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.620254837\t1.42642991999842E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.627236154\t0.000014636\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.634217471\t1.50077614000099E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.641198788\t1.53731887999609E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.648180105\t1.57344623999967E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.655161422\t1.61002823999556E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.662142739\t1.64533045999837E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.669124056\t0.000016812\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6761053731\t1.71653793999971E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6830866901\t1.7518935000016E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6900680071\t1.78714713999772E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.6970493241\t1.82304837999803E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7040306411\t1.85774073999945E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7110119581\t1.89337800000078E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7179932751\t1.92885669999809E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7249745921\t1.96448024000206E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7319559091\t2.00141617999472E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7389372261\t2.037574839997E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7459185431\t2.07552647999709E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7528998601\t2.11295705999648E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7598811772\t2.15145321999788E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7668624942\t2.19086235999644E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7738438112\t2.23081116000057E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7808251282\t2.27178993999766E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7878064452\t2.31406830000225E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.7947877622\t2.3580202200002E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8017690792\t0.000024025\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8087503962\t2.44873417999947E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8157317132\t2.49622493999901E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8227130302\t2.54663013999901E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8296943472\t2.5979187199987E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8366756642\t2.65217737999701E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8436569812\t2.70758486000111E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8506382983\t2.76535329999938E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8576196153\t2.82647463999974E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8646009323\t2.88955137999897E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8715822493\t2.95676211999885E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8785635663\t3.02561876000112E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8855448833\t3.09807709999998E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8925262003\t3.17468035999913E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.8995075173\t3.25499282000097E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9064888343\t3.33901032000122E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9134701513\t3.42835315999962E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9204514683\t3.52095179999845E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9274327853\t3.61972382000031E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9344141024\t3.72216188000013E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9413954194\t3.83107138000049E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9483767364\t3.94621912000043E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9553580534\t4.0668281599987E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9623393704\t0.000041944\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9693206874\t4.32858207999945E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9763020044\t4.4705526399999E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9832833214\t0.000046205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9902646384\t0.000047783\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 9.9972459554\t4.94555387999945E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0042272724\t5.12190511999938E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0112085894\t5.3080906999993E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0181899064\t5.50592824000024E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0251712235\t5.71408977999913E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0321525405\t5.93482606000006E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0391338575\t6.16691713999917E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0461151745\t6.41434883999967E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0530964915\t6.67470780000012E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0600778085\t6.95132911999949E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0670591255\t7.24331795999983E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0740404425\t7.55227433999993E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0810217595\t7.88055753999997E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0880030765\t8.22749031999977E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.0949843935\t8.5947817600001E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1019657105\t8.98414145999969E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1089470276\t9.39695392000034E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1159283446\t9.83438707999988E-005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1229096616\t0.0001029772\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1298909786\t0.0001079018\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1368722956\t0.0001131087\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1438536126\t0.0001186509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1508349296\t0.000124513\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1578162466\t0.000130736\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1647975636\t0.0001373478\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1717788806\t0.0001443558\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1787601976\t0.0001518119\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1857415146\t0.0001597116\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1927228316\t0.0001681089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.1997041487\t0.0001770242\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2066854657\t0.0001864986\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2136667827\t0.0001965687\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2206480997\t0.0002072659\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2276294167\t0.000218628\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2346107337\t0.0002307101\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2415920507\t0.0002435522\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2485733677\t0.0002572171\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2555546847\t0.0002717404\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2625360017\t0.0002871924\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2695173187\t0.0003036177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2764986357\t0.0003211016\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2834799528\t0.0003396941\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2904612698\t0.0003594892\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.2974425868\t0.000380551\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3044239038\t0.0004029651\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3114052208\t0.0004268223\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3183865378\t0.0004522149\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3253678548\t0.0004792533\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3323491718\t0.000508033\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3393304888\t0.0005386785\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3463118058\t0.0005713092\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3532931228\t0.000606054\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3602744398\t0.0006430647\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3672557568\t0.0006824649\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3742370739\t0.000724439\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3812183909\t0.0007691332\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3881997079\t0.0008167427\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.3951810249\t0.0008674509\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4021623419\t0.0009214605\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4091436589\t0.0009789786\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4161249759\t0.0010402513\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4231062929\t0.0011055086\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4300876099\t0.0011750108\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4370689269\t0.0012490377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4440502439\t0.0013278852\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.4510315609\t0.0014118474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.458012878\t0.0015012647\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.464994195\t0.0015964854\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.471975512\t0.001697877\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.478956829\t0.0018058311\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.485938146\t0.0019207718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.492919463\t0.0020431394\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.49990078\t0.0021733906\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.506882097\t0.0023120306\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.513863414\t0.0024595791\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.520844731\t0.0026165947\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.527826048\t0.0027836608\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.534807365\t0.0029614065\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.541788682\t0.0031504762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5487699991\t0.0033515703\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5557513161\t0.0035654179\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5627326331\t0.0037927922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5697139501\t0.0040345089\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5766952671\t0.0042914271\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5836765841\t0.0045644577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5906579011\t0.0048545368\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.5976392181\t0.0051626895\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6046205351\t0.005489971\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6116018521\t0.0058374822\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6185831691\t0.0062064\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6255644861\t0.0065979457\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6325458031\t0.007013422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6395271202\t0.0074541563\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6465084372\t0.0079215935\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6534897542\t0.0084171956\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6604710712\t0.0089425419\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6674523882\t0.0094992365\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6744337052\t0.0100890018\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6814150222\t0.0107135972\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6883963392\t0.0113749013\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.6953776562\t0.0120748391\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7023589732\t0.0128154305\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7093402902\t0.0135987794\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7163216072\t0.014427077\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7233029243\t0.0153026042\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7302842413\t0.0162277255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7372655583\t0.017204901\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7442468753\t0.0182366577\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7512281923\t0.0193256704\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7582095093\t0.0204746453\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7651908263\t0.021686423\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7721721433\t0.0229639083\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7791534603\t0.0243101208\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7861347773\t0.0257281733\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.7931160943\t0.0272212493\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8000974113\t0.0287926472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8070787283\t0.0304457294\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8140600454\t0.0321839797\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8210413624\t0.0340109296\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8280226794\t0.0359302227\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8350039964\t0.0379455519\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8419853134\t0.0400607157\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8489666304\t0.0422795506\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8559479474\t0.0446059958\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8629292644\t0.0470440126\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8699105814\t0.0495976379\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8768918984\t0.052270951\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8838732154\t0.0550680574\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8908545324\t0.0579931177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.8978358495\t0.0610502959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9048171665\t0.0642437677\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9117984835\t0.06757772\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9187798005\t0.0710563145\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9257611175\t0.0746837215\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9327424345\t0.078464052\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9397237515\t0.0824013798\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9467050685\t0.0864997116\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9536863855\t0.0907629954\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9606677025\t0.0951950601\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9676490195\t0.0997996541\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9746303365\t0.1045803969\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9816116535\t0.1095407626\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9885929706\t0.1146840746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 10.9955742876\t0.1200134511\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0025556046\t0.1255318663\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0095369216\t0.131242022\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0165182386\t0.1371464411\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0234995556\t0.1432473416\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0304808726\t0.1495466912\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0374621896\t0.156046159\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0444435066\t0.1627470954\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0514248236\t0.1696505168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0584061406\t0.1767570684\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0653874576\t0.1840670248\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0723687747\t0.1915802525\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0793500917\t0.1992962168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0863314087\t0.207213923\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.0933127257\t0.2153319384\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1002940427\t0.2236483257\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1072753597\t0.2321606729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1142566767\t0.2408660414\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1212379937\t0.2497609942\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1282193107\t0.2588415235\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1352006277\t0.2681030586\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1421819447\t0.2775405137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1491632617\t0.2871481618\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1561445787\t0.2969197293\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1631258958\t0.3068483452\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1701072128\t0.3169265199\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1770885298\t0.3271461804\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1840698468\t0.3374986562\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1910511638\t0.3479746574\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.1980324808\t0.3585643038\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2050137978\t0.369257118\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2119951148\t0.3800420485\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2189764318\t0.3909074657\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2259577488\t0.4018411611\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2329390658\t0.4128303922\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2399203828\t0.4238619113\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2469016999\t0.434921914\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2538830169\t0.4459961581\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2608643339\t0.4570699131\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2678456509\t0.4681280091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2748269679\t0.4791549195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2818082849\t0.4901347099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2887896019\t0.501051128\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.2957709189\t0.5118876168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3027522359\t0.5226273948\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3097335529\t0.5332534375\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3167148699\t0.5437485576\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3236961869\t0.554095454\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.3306775039\t0.56427674\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.337658821\t0.5742750027\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.344640138\t0.5840728761\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.351621455\t0.5936530253\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.358602772\t0.6029982675\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.365584089\t0.6120915923\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.372565406\t0.620916229\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.379546723\t0.6294556639\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.38652804\t0.6376937544\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.393509357\t0.6456147156\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.400490674\t0.6532032228\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.407471991\t0.6604444455\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.414453308\t0.6673240775\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4214346251\t0.6738284251\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4284159421\t0.6799444195\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4353972591\t0.6856596731\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4423785761\t0.6909625498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4493598931\t0.6958421619\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4563412101\t0.7002884311\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4633225271\t0.7042921259\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4703038441\t0.7078449099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4772851611\t0.7109393271\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4842664781\t0.7135688741\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4912477951\t0.7157280009\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.4982291121\t0.7174121431\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5052104291\t0.7186177378\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5121917462\t0.7193422177\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5191730632\t0.7195840468\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5261543802\t0.7193427122\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5331356972\t0.7186187269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5401170142\t0.7174136267\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5470983312\t0.7157299725\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5540796482\t0.7135713327\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5610609652\t0.7109422737\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5680422822\t0.7078483456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5750235992\t0.7042960497\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5820049162\t0.7002928363\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5889862332\t0.6958470498\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.5959675503\t0.6909679126\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6029488673\t0.685665512\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6099301843\t0.6799507205\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6169115013\t0.6738351891\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6238928183\t0.6673313046\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6308741353\t0.6604521292\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6378554523\t0.653211363\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6448367693\t0.6456233005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6518180863\t0.6377027828\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6587994033\t0.629465137\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6657807203\t0.6209261337\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6727620373\t0.6121019362\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6797433543\t0.603009029\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6867246714\t0.593664213\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.6937059884\t0.5840844835\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7006873054\t0.5742870298\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7076686224\t0.5642891662\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7146499394\t0.5541082879\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7216312564\t0.5437617917\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7286125734\t0.5332670729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7355938904\t0.5226414239\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7425752074\t0.5119020472\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7495565244\t0.5010659325\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7565378414\t0.4901499026\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7635191584\t0.4791705005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7705004754\t0.4681439718\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7774817925\t0.45708625\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7844631095\t0.4460128844\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7914444265\t0.4349390285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.7984257435\t0.4238793934\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8054070605\t0.4128482702\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8123883775\t0.4018594132\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8193696945\t0.3909261061\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8263510115\t0.3800610836\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8333323285\t0.3692765544\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8403136455\t0.3585841339\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8472949625\t0.3479948865\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8542762795\t0.3375193062\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8612575966\t0.327167249\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8682389136\t0.3169480146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8752202306\t0.3068702705\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8822015476\t0.2969421058\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8891828646\t0.2871710013\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.8961641816\t0.2775638228\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9031454986\t0.2681268623\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9101268156\t0.2588658206\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9171081326\t0.2497858173\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9240894496\t0.2408914024\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9310707666\t0.2321865837\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9380520836\t0.2236748255\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9450334006\t0.2153590389\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9520147177\t0.2072416558\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9589960347\t0.1993246003\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9659773517\t0.1916093247\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9729586687\t0.184096803\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9799399857\t0.1767875981\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9869213027\t0.1696818284\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 11.9939026197\t0.1627792269\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0008839367\t0.1560791548\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0078652537\t0.1495805872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0148465707\t0.1432821823\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0218278877\t0.1371822762\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0288092047\t0.1312789091\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0357905218\t0.1255698542\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0427718388\t0.1200526037\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0497531558\t0.1147244396\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0567344728\t0.1095824312\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0637157898\t0.1046234168\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0706971068\t0.0998441066\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0776784238\t0.0952410211\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0846597408\t0.0908105377\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0916410578\t0.0865489446\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.0986223748\t0.0824523903\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1056036918\t0.0785169398\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1125850088\t0.0747385863\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1195663258\t0.0711132756\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1265476429\t0.0676368827\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1335289599\t0.0643052708\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1405102769\t0.061114277\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1474915939\t0.0580597146\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1544729109\t0.0551374263\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1614542279\t0.0523432415\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1684355449\t0.0496730322\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1754168619\t0.0471226919\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1823981789\t0.0446881477\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1893794959\t0.0423653962\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.1963608129\t0.0401504526\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2033421299\t0.038039425\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.210323447\t0.0360284685\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.217304764\t0.0341138258\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.224286081\t0.0322918005\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.231267398\t0.0305587688\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.238248715\t0.0289112187\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.245230032\t0.027345689\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.252211349\t0.0258588456\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.259192666\t0.0244474075\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.266173983\t0.0231082096\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.2731553\t0.0218381694\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.280136617\t0.0206343019\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.287117934\t0.0194937308\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.294099251\t0.0184136413\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3010805681\t0.0173913512\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3080618851\t0.0164242443\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3150432021\t0.0155098302\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3220245191\t0.0146456653\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3290058361\t0.0138294501\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3359871531\t0.0130589547\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3429684701\t0.0123320226\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3499497871\t0.0116466148\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3569311041\t0.0110007606\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3639124211\t0.0103925964\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3708937381\t0.0098203143\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3778750551\t0.0092822166\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3848563722\t0.0087766624\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3918376892\t0.0083021224\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.3988190062\t0.0078571061\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4058003232\t0.0074402167\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4127816402\t0.007050147\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4197629572\t0.0066856324\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4267442742\t0.0063454983\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4337255912\t0.0060286285\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4407069082\t0.0057339872\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4476882252\t0.0054605743\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4546695422\t0.0052075015\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4616508592\t0.0049738729\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4686321762\t0.0047589303\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4756134933\t0.004561909\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4825948103\t0.0043821474\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4895761273\t0.0042190099\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.4965574443\t0.0040719162\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5035387613\t0.0039403771\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5105200783\t0.0038238968\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5175013953\t0.0037220959\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5244827123\t0.0036345869\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5314640293\t0.003561063\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5384453463\t0.003501266\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5454266633\t0.0034549746\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5524079803\t0.003422025\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5593892974\t0.0034023098\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t 12.5663706144\t0.0033957422\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t };\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{axis}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \\end{tikzpicture}\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\caption{The degenerate first excited state torsional wavefunctions. Left display: The two wavefunctions which generate the $E_{3d}$ irrep, but which do not transform as given by the transformation matrices of \\protect\\sect{sec:Einalmatrices}, displayed as a red and a blue curve, respectively. Right display: The corresponding two $E_{3d}$ wavefunctions obtained as transforming according to the transformation matrices of \\protect\\sect{sec:Einalmatrices} and displayed as a red and a blue curve, respectively.}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\label{fig:torsion_first}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\\end{figure} \n\n\n\n\nThe symmetry adapted ro-vibrational basis set functions are constructed as direct products of the symmetrized component\nfunctions from the different subspaces as $ \\Psi_{\\lambda_0}^{(0),\\Gamma_0} \\otimes\n\\Psi_{\\lambda_1}^{(1),\\Gamma_1} \\otimes \\Psi_{\\lambda_2}^{(2),\\Gamma_2} \\cdots \\otimes\n\\Psi_{\\lambda_L}^{(L),\\Gamma_L}$, where $L$ is the number of vibrational subspaces. The symmetry of a product basis function is the direct product of the irreducible representations of the component functions. This symmetry must be further reduced, but this is rather straightforward when each component function generates one of the irreps of the group and has defined, `standard' transformation properties. In this case we use the same projection operator symmetrization technique described above without further sampling of the symmetry properties of the corresponding components. The $d$-symmetry components are unphysical and must be disregarded. Some $s$ symmetry ro-vibrational basis functions will necessarily contain products of the $d$ components, underpinning the importance of the {\\itshape\\bfseries G}$_{36}$(EM) extended symmetry group. The nuclear spin statistical weights of the ro-vibrational states can be deduced using the procedure from \\cite{98BuJexx}. We obtain nuclear spin statistical weights of 6, 10, 6, 10, 4, 4, 2, 6, 12 for the {\\itshape\\bfseries G}$_{36}$(EM) symmetries $A_{1s}, A_{2s}, A_{3s}, A_{4s}, E_{1s}, E_{2s}, E_{3s}, E_{4s}$, and $G_s$, respectively.\n\n\n\n\n\n\n\n\\section{Conclusion}\n\nWe have presented a detailed description of the {\\itshape\\bfseries G}$_{36}$\\ and {\\itshape\\bfseries G}$_{36}$(EM) molecular symmetry groups. A full set of irreducible representation matrices have been derived and tested for constructing symmetry-adapted potential energy functions and basis functions of ethane C$_2$H$_6$. Both the construction of the transformation matrices and the symmetry adaption can be implemented as numerical procedures as part of computational approaches to the solution of the ro-vibrational Schr\\\"odinger equation. A self-consistent choice of the vibrational, torsional and rotational coordinates for ethane, satisfying the {\\itshape\\bfseries G}$_{36}$(EM) symmetry requirements have been introduced and analyzed in full detail. The irreducible representation matrices as well as the coordinate choice made for ethane in the present work have been implemented as part of\nthe program system TROVE, and we have discussed a few examples of symmetrized wavefunctions. These results of the present work will be important in our planned line-list calculations for ethane.\n\nThe results of the present work are, of course, not only applicable to\nethane H$_3$CCH$_3$, but also to other molecules with MS groups {\\itshape\\bfseries G}$_{36}$\\ and {\\itshape\\bfseries G}$_{36}$(EM).\nA prominent molecule of this kind is dimethylacetylene\nH$_3$CCCCH$_3$. Also, subgroups of the \n matrix groups constructed can be applied to molecules whose MS groups are subgroups of {\\itshape\\bfseries G}$_{36}$\\ and {\\itshape\\bfseries G}$_{36}$(EM), such as D$_3$CCH$_3$. The general ideas used for generating the matrix groups can be applied to other MS groups. In particular, generation of matrix groups in a manner similar to that of the present work will be required for MS groups with irreps of dimension 4 and higher.\n\n\n\n\n\\section{Acknowledgements}\n\n\nThis work was supported by the STFC Projects No. ST\/M001334\/1 and ST\/R000476\/1, and by the COST action MOLIM (CM1405). The authors acknowledge the use of the UCL Legion High Performance Computing Facility (Legion@UCL) and associated support services in the completion of this work, along with the Cambridge Service for Data Driven Discovery (CSD3), part of which is operated by the University of Cambridge Research Computing on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC component of CSD3 was funded by BIS capital funding via STFC capital grants ST\/P002307\/1 and ST\/R002452\/1 and STFC operations grant ST\/R00689X\/1. DiRAC is part of the National e-Infrastructure. The present work was supported in part by the Deutsche Forschungsgemeinschaft.\n\n\n\n\\setcounter{section}{0}\n\\setcounter{equation}{0}\n\\setcounter{table}{0}\n\\renewcommand\\thesection{Appendix \\Alph{section}}\n\\renewcommand\\thesubsection{\\Alph{section}.\\arabic{subsection}}\n\\renewcommand\\theequation{\\Alph{section}.\\arabic{equation}}\n\\renewcommand\\thetable{\\Alph{section}.\\arabic{table}}\n\\renewcommand\\thesubsubsection{\\Alph{section}.\\arabic{subsection}.\\arabic{subsubsection}}\n\n\\section{Character table of the isomorphic groups\n{\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ and {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$.}\\label{sec:appendixC3vgroups}\n\n{\\itshape\\bfseries G}$_{36}$ is the direct product of\n{\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ and {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$, \n{\\itshape\\bfseries G}$_{36}$ $=$\n{\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ $\\times$ {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$,\nand so the irreps of {\\itshape\\bfseries G}$_{36}$ are obtained from those of\n{\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ and {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$.\nThese latter irreps are given in Table~\\ref{tab:C3vchartab}. \n\n\\begin{table}[h]\n\\caption{\\label{tab:C3vchartab}Common character tables of \n{\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ and {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$. }\n\\begin{center}\n\\renewcommand{\\arraystretch}{1.5}\n\\begin{tabular}{lrrr}\n\\hline\\hline\n$\\Gamma$ &\n${\\mathcal C}_1^{(\\pm)}$ & ${\\mathcal C}_2^{(\\pm)}$ & ${\\mathcal C}_3^{(\\pm)}$ \\\\\n& 1 & 2 & 3 \\\\\n\\hline\n$A_1$ & 1 & 1 & 1 \\\\\n$A_2$ & 1 & 1 & $-$1 \\\\\n$E$ & 2 & $-$1 & 0 \\\\\n\\hline\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\nWe label\n\tthe elements of {\\itshape\\bfseries C}$_{3{\\rm v}}^{(\\pm)}$ as\n\t$R_j^{(\\pm)}$, $j$ $=$ 1, 2, \\dots, 6 (see \\tabl{tab:multiplicationtable}). The nuclei are labelled as in \\fig{fig:ethane_labelling}.\n\t {\\itshape\\bfseries C}$_{3{\\rm v}}^{(\\pm)}$ has three\nclasses,\n${\\mathcal C}_1^{(\\pm)}$ $=$ $\\{ E \\}$ $=$ $\\{ R_1^{(\\pm)} \\}$,\n${\\mathcal C}_2^{(\\pm)}$ $=$ $\\{ R_2^{(\\pm)}, R_3^{(\\pm)} \\}$, and\n${\\mathcal C}_3^{(\\pm)}$ $=$ $\\{ R_4^{(\\pm)}, R_5^{(\\pm)}, R_6^{(\\pm)} \\}$.\n\n\\section{The {\\itshape\\bfseries G}$_{36}$\\ Transformation Matrices}\\label{sec:appendixa}\n\\setcounter{equation}{0}\n\nIn Sections~\\ref{sec:Einalmatrices}\nand~\\ref{sec:finalmatrices}, we have abbreviated some of the operations\n$R$ $\\in$ {\\itshape\\bfseries G}$_{36}$\\ as $R$ $=$ $R_j^{(-)} \\, R_k^{(+)}$ $=$ $R_k^{(+)} \\, R_j^{(-)}$, where $R_j^{(-)}$ $\\in$ {\\itshape\\bfseries C}$_{3{\\rm v}}^{(-)}$ and\n$R_k^{(+)}$ $\\in$ {\\itshape\\bfseries C}$_{3{\\rm v}}^{(+)}$ (since, if we used the complete labels such as (15)(24)(36)$(ab)^*$ and (143526)$(ab)^*$, the text would not fit on the page). All such products, and the complete classes of {\\itshape\\bfseries G}$_{36}$, are given in\n \\tabl{tab:multiplicationtable}.\n\n\n\\subsection{$E_i$ transformation matrices in {\\itshape\\bfseries G}$_{36}$}\\label{sec:Einalmatrices}\nFor each operation $R$ $\\in$ {\\itshape\\bfseries G}$_{36}$, we list here the four matrices\n$ {\\mathbf M}_{E_1}\\left[ R \\right]$,\n$ {\\mathbf M}_{E_2}\\left[ R \\right]$,\n$ {\\mathbf M}_{E_3}\\left[ R \\right]$, and\n$ {\\mathbf M}_{E_4}\\left[ R \\right]$ in that order.\n\\subsubsection{One-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing $E$}\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ E \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\\\[5pt]\n\\end{tabbing}}\n\\end{center}\n\\subsubsection{Two-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (123)(456) and (132)(465)}\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_2^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}}} \\\\[5pt]\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\[5pt]\n\\end{tabbing}}\n\\end{center}\n\\subsubsection{Three-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (14)(26)(35)($ab$)$^*$}\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_4^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{-1}{0}{0}{-1} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{-1}{0}{0}{-1} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n\\end{tabbing}}\n\\end{center}\n\\subsubsection{Two-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing (123)(456) and (132)(456)}\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} } \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{1}{0}{0}{1} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsubsection{Four-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (123) and (456)}\n\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)}R_2^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} } \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} } \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)}R_3^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)}R_2^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)}R_3^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsubsection{Six-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (142635)($ab$)$^*$ }\n\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)} R_4^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{ \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} } \\=\n\\parbox[b]{3.0truecm}{ \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1} } \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1} } \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)} R_5^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_2^{(-)} R_6^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)} R_4^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{1}{0}{0}{-1} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)} R_5^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_3^{(-)} R_6^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsubsection{Three-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing (14)(25)(36)($ab$) }\n\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-1}{0}{0}{-1}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{-1}{0}{0}{-1} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{1} \\> \\twobytwo{-1}{0}{0}{-1} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsubsection{Six-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (142536)($ab$) }\n\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} R_2^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} } \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} } \\\\[5pt]\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} R_2^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} R_2^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} R_3^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} R_3^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} R_3^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsubsection{Nine-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (12)(45)$^*$}\n\n\\begin{center}\n{\\small\\baselineskip=32pt\n\\begin{tabbing}\n\\parbox[b]{3.5truecm}{$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} R_4^{(+)} \\right]$}\n\\= \\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-1}{0}{0}{1}} \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{1}{0}{0}{-1} } \\=\n\\parbox[b]{3.0truecm}{\\twobytwo{-1}{0}{0}{1} } \\\\[5pt]\n$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} R_5^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{-1}{0}{0}{1} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_4^{(-)} R_6^{(+)} \\right] $ \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{-1}{0}{0}{1} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} R_4^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{-1}{0}{0}{1} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} R_5^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_5^{(-)} R_6^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} R_4^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{1}{0}{0}{-1} \\> \\twobytwo{-1}{0}{0}{1} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} R_5^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n$ {\\mathbf M}_{E_i}\\left[ R_6^{(-)} R_6^{(+)} \\right] $ \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\> \\twobytwo{-\\frac{1}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{\\sqrt{3}}{2}}{\\frac{1}{2}} \\> \\twobytwo{\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{\\sqrt{3}}{2}}{-\\frac{1}{2}} \\\\\n\\end{tabbing}}\n\\end{center}\n\n\\subsection{$G$ transformation matrices in {\\itshape\\bfseries G}$_{36}$}\n\\label{sec:finalmatrices}\n\n\\subsubsection{One-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing $E$}\n\\begin{displaymath}\n{\\mathbf M}_G\\left[ R_1^{(-)} R_1^{(+)} \\right] =\n\\left( \\begin{array}{rrrr} 1&0&0&0\\\\ 0&1&0&0\\\\ 0&0&1&0\\\\ 0&0&0&1\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Two-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (123)(456) and (132)(465)}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_1^{(-)} R_2^{(+)} \\right] =\n \\left( \\begin{array}{rrrr} -{\\frac{1}{2}}&-{\\frac{\\sqrt{3}}{2}}&0&0\\\\ {\\frac{\\sqrt{3}\n }{2}}&-{\\frac{1}{2}}&0&0\\\\ 0&0&-{\\frac{1}{2}}&-{\\frac{\\sqrt{3}\n }{2}}\\\\ 0&0&{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_1^{(-)} R_3^{(+)} \\right] =\n \\left( \\begin{array}{rrrr}-{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{2}}&0&0\\\\ -{\\frac{\\sqrt{3}\n }{2}}&-{\\frac{1}{2}}&0&0\\\\ 0&0&-{\\frac{1}{2}}&{\\frac{\\sqrt{3}\n }{2}}\\\\ 0&0&-{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Three-member class ${\\mathcal C}_1^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (14)(26)(35)($ab$)$^*$}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_1^{(-)} R_4^{(+)} \\right] =\n \\left( \\begin{array}{cccc}1&0&0&0\\\\ 0&-1&0&0\\\\ 0&0&-1&0\\\\ 0&0&0&1\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_1^{(-)} R_5^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&-{\\frac{\\sqrt{3}}{2}}&0&0\\\\ -{\\frac{\\sqrt{3}\n }{2}}&{\\frac{1}{2}}&0&0\\\\ 0&0&{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{2\n }}\\\\ 0&0&{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_1^{(-)} R_6^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{2}}&0&0\\\\ {\\frac{\\sqrt{3}\n }{2}}&{\\frac{1}{2}}&0&0\\\\ 0&0&{\\frac{1}{2}}&-{\\frac{\\sqrt{3}}{\n 2}}\\\\ 0&0&-{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Two-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing (123)(456) and (132)(456)}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)} R_1^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&-{\\frac{\\sqrt{3}}{2}}\\\\ 0&-{\\frac{1}{2\n }}&{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&-{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}&\n 0\\\\ {\\frac{\\sqrt{3}}{2}}&0&0&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)} R_1^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&{\\frac{\\sqrt{3}}{2}}\\\\ 0&-{\\frac{1}{2\n }}&-{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}&\n 0\\\\ -{\\frac{\\sqrt{3}}{2}}&0&0&-{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Four-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (123) and (456)}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)}R_2^{(+)} \\right] =\n\\left( \\begin{array}{cccc} {\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&-{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{\n 4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)}R_3^{(+)} \\right] =\n\\left( \\begin{array}{cccc} {\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&-{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{\n 4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)}R_2^{(+)} \\right] =\n\\left( \\begin{array}{cccc} {\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&-{\\frac{\\sqrt{\n 3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4\n }}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)}R_3^{(+)} \\right] =\n\\left( \\begin{array}{cccc} {\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&-{\\frac{\n \\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{\n 1}{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&-{\\frac{3\n }{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\n\n\n\n\\subsubsection{Six-member class ${\\mathcal C}_2^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (142635)($ab$)$^*$ }\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)} R_4^{(+)} \\right] =\n\\left( \\begin{array}{cccc} -{\\frac{1 }{2}}&0&0&-{\\frac{\\sqrt{3} }{2}}\\\\ 0&{\\frac{1 }{2\n }}&-{\\frac{\\sqrt{3} }{2}}&0\\\\ 0&{\\frac{\\sqrt{3} }{2}}&{\\frac{1 }{2}}&0\n \\\\ {\\frac{\\sqrt{3} }{2}}&0&0&-{\\frac{1 }{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)} R_4^{(+)} \\right] =\n\\left( \\begin{array}{cccc} -{\\frac{1 }{2}}&0&0&{\\frac{\\sqrt{3} }{2}}\\\\ 0&{\\frac{1 }{2}}\n &{\\frac{\\sqrt{3} }{2}}&0\\\\ 0&-{\\frac{\\sqrt{3} }{2}}&{\\frac{1 }{2}}&0\n \\\\ -{\\frac{\\sqrt{3} }{2}}&0&0&-{\\frac{1 }{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)} R_5^{(+)} \\right] =\n\\left( \\begin{array}{cccc }{\\frac{1 }{4}}&{\\frac{\\sqrt{3} }{4}}&-{\\frac{3 }{4}}&{\\frac{\\sqrt{\n 3} }{4}}\\\\ {\\frac{\\sqrt{3} }{4}}&-{\\frac{1 }{4}}&{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3 }{4}}\\\\ {\\frac{3 }{4}}&-{\\frac{\\sqrt{3} }{4}}&-{\\frac{1\n }{4}}&-{\\frac{\\sqrt{3} }{4}}\\\\ -{\\frac{\\sqrt{3} }{4}}&-{\\frac{3\n }{4}}&-{\\frac{\\sqrt{3} }{4}}&{\\frac{1 }{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)} R_5^{(+)} \\right] =\n\\left( \\begin{array}{cccc }{\\frac{1 }{4}}&{\\frac{\\sqrt{3} }{4}}&{\\frac{3 }{4}}&-{\\frac{\\sqrt{\n 3} }{4}}\\\\ {\\frac{\\sqrt{3} }{4}}&-{\\frac{1 }{4}}&-{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3 }{4}}\\\\ -{\\frac{3 }{4}}&{\\frac{\\sqrt{3} }{4}}&-{\\frac{\n 1 }{4}}&-{\\frac{\\sqrt{3} }{4}}\\\\ {\\frac{\\sqrt{3} }{4}}&{\\frac{3 }{\n 4}}&-{\\frac{\\sqrt{3} }{4}}&{\\frac{1 }{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_2^{(-)} R_6^{(+)} \\right] =\n\\left( \\begin{array}{cccc }{\\frac{1 }{4}}&-{\\frac{\\sqrt{3} }{4}}&{\\frac{3 }{4}}&{\\frac{\\sqrt{\n 3} }{4}}\\\\ -{\\frac{\\sqrt{3} }{4}}&-{\\frac{1 }{4}}&{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3 }{4}}\\\\ -{\\frac{3 }{4}}&-{\\frac{\\sqrt{3} }{4}}&-\n {\\frac{1 }{4}}&{\\frac{\\sqrt{3} }{4}}\\\\ -{\\frac{\\sqrt{3} }{4}}&{\\frac{3\n }{4}}&{\\frac{\\sqrt{3} }{4}}&{\\frac{1 }{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_3^{(-)} R_6^{(+)} \\right] =\n\\left( \\begin{array}{cccc }{\\frac{1 }{4}}&-{\\frac{\\sqrt{3} }{4}}&-{\\frac{3 }{4}}&-{\\frac{\n \\sqrt{3} }{4}}\\\\ -{\\frac{\\sqrt{3} }{4}}&-{\\frac{1 }{4}}&-{\\frac{\\sqrt{\n 3} }{4}}&{\\frac{3 }{4}}\\\\ {\\frac{3 }{4}}&{\\frac{\\sqrt{3} }{4}}&-{\\frac{\n 1 }{4}}&{\\frac{\\sqrt{3} }{4}}\\\\ {\\frac{\\sqrt{3} }{4}}&-{\\frac{3 }{\n 4}}&{\\frac{\\sqrt{3} }{4}}&{\\frac{1 }{4}}\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Three-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_1^{(+)}$ containing (14)(25)(36)($ab$) }\n\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} \\right] =\n\\left( \\begin{array}{cccc}1&0&0&0\\\\ 0&1&0&0\\\\ 0&0&-1&0\\\\ 0&0&0&-1\\end{array} \\right) \\end{displaymath}\n\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} \\right] =\n\\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&-{\\frac{\\sqrt{3}}{2}}\\\\ 0&-{\\frac{1}{2\n }}&{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}&0\n \\\\ -{\\frac{\\sqrt{3}}{2}}&0&0&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} \\right] =\n\\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&{\\frac{\\sqrt{3}}{2}}\\\\ 0&-{\\frac{1}{2\n }}&-{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&-{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}&\n 0\\\\ {\\frac{\\sqrt{3}}{2}}&0&0&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\n\\subsubsection{Six-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_2^{(+)}$ containing (142536)($ab$) }\n\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} R_2^{(+)} \\right] =\n\\left( \\begin{array}{cccc}-{\\frac{1}{2}}&-{\\frac{\\sqrt{3}}{2}}&0&0\\\\ {\\frac{\\sqrt{3}\n }{2}}&-{\\frac{1}{2}}&0&0\\\\ 0&0&{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{\n 2}}\\\\ 0&0&-{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} R_2^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&-{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{\n 1}{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{3}{\n 4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} R_2^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&-{\\frac{\\sqrt{\n 3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1\n }{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&-{\\frac{3\n }{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} R_3^{(+)} \\right] =\n\\left( \\begin{array}{cccc}-{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{2}}&0&0\\\\ -{\\frac{\\sqrt{3}\n }{2}}&-{\\frac{1}{2}}&0&0\\\\ 0&0&{\\frac{1}{2}}&-{\\frac{\\sqrt{3}\n }{2}}\\\\ 0&0&{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} R_3^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&-{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{\n 1}{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{\n 4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} R_3^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&-{\\frac{\n \\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1\n }{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4\n }}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\n\n\\subsubsection{Nine-member class ${\\mathcal C}_3^{(-)} \\times {\\mathcal C}_3^{(+)}$ containing (12)(45)$^*$}\n\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} R_4^{(+)} \\right] =\n\\left( \\begin{array}{cccc}1&0&0&0\\\\ 0&-1&0&0\\\\ 0&0&1&0\\\\ 0&0&0&-1\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} R_5^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&-{\\frac{\\sqrt{3}}{2}}&0&0\\\\ -{\\frac{\\sqrt{3}\n }{2}}&{\\frac{1}{2}}&0&0\\\\ 0&0&-{\\frac{1}{2}}&-{\\frac{\\sqrt{3}\n }{2}}\\\\ 0&0&-{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_4^{(-)} R_6^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{2}}&0&0\\\\ {\\frac{\\sqrt{3}\n }{2}}&{\\frac{1}{2}}&0&0\\\\ 0&0&-{\\frac{1}{2}}&{\\frac{\\sqrt{3}}{\n 2}}\\\\ 0&0&{\\frac{\\sqrt{3}}{2}}&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} R_4^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&-{\\frac{\\sqrt{3}}{2}}\\\\ 0&{\\frac{1}{2\n }}&-{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&-{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}\n &0\\\\ -{\\frac{\\sqrt{3}}{2}}&0&0&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} R_5^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4\n }}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_5^{(-)} R_6^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&{\\frac{\\sqrt{\n 3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}&{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{\n 4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} R_4^{(+)} \\right] =\n \\left( \\begin{array}{cccc}-{\\frac{1}{2}}&0&0&{\\frac{\\sqrt{3}}{2}}\\\\ 0&{\\frac{1}{2}}\n &{\\frac{\\sqrt{3}}{2}}&0\\\\ 0&{\\frac{\\sqrt{3}}{2}}&-{\\frac{1}{2}}&0\n \\\\ {\\frac{\\sqrt{3}}{2}}&0&0&{\\frac{1}{2}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} R_5^{(+)} \\right] =\n \\left( \\begin{array}{cccc}{\\frac{1}{4}}&{\\frac{\\sqrt{3}}{4}}&{\\frac{3}{4}}&-{\\frac{\\sqrt{\n 3}}{4}}\\\\ {\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}&-{\\frac{\\sqrt{3}\n }{4}}&-{\\frac{3}{4}}\\\\ {\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&{\\frac{1\n }{4}}&{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{\n 4}}&{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\\begin{displaymath} {\\mathbf M}_G\\left[ R_6^{(-)} R_6^{(+)} \\right] =\n\\left( \\begin{array}{cccc}{\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{3}{4}}&-{\\frac{\n \\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}&-{\\frac{\\sqrt{\n 3}}{4}}&{\\frac{3}{4}}\\\\ -{\\frac{3}{4}}&-{\\frac{\\sqrt{3}}{4}}&\n {\\frac{1}{4}}&-{\\frac{\\sqrt{3}}{4}}\\\\ -{\\frac{\\sqrt{3}}{4}}&{\\frac{3\n }{4}}&-{\\frac{\\sqrt{3}}{4}}&-{\\frac{1}{4}}\\end{array} \\right) \\end{displaymath}\n\n\n\n\t\\section{Derivation of the transformation of internal coordinates}\\label{sec:appendixB}\n\\setcounter{equation}{0}\n\n\tIn the following we will describe the procedure with which to calculate the transformation of the internal coordinates due to the molecular symmetry group operations. If $f$ is a function of the Cartesian coordinates $\\vect{X}_1$, $\\vect{X}_2,$ and $\\vect{X}_3$ of three nuclei 1, 2, and 3, respectively, then, after the operation (123), nucleus 1 is at the position nucleus 3 was previously, 2 is at 1, and 3 is at 2. We thus have $(123)f(\\vect{X}_1,\\vect{X}_2,\\vect{X}_3) = f(\\vect{X}_3,\\vect{X}_1,\\vect{X}_2)$. Also, $E^*f(\\vect{X}_1,\\vect{X}_2,\\vect{X}_3) = f(-\\vect{X}_1,-\\vect{X}_2,-\\vect{X}_3)$. Since any curvilinear coordinate can be written as a function of the Cartesian coordinates, this defines the coordinate change due to the operation. We will now go through the three types of internal coordinates that TROVE uses.\n\n\t\\subsection{Bond Lengths}\n\t\\renewcommand{\\vect}[1]{\\mathbf{#1}}\n\t\n\n\tThe bond length between nuclei 1 and 2 (with position vectors $\\vect{r}_1$ and $\\vect{r}_2$, respectively in the space-fixed axis system) is defined by $|\\vect{r}_1 - \\vect{r}_2|.$ We see that this value is unaffected by $E^*$ and the other operations simply result in the relabelling of the bond lengths. For example, the \\ce{H1-C_$a$} bond length is given by $r_1$ $=$ $|\\vect{r}_1 - \\vect{r}_a|$ and the operation (123) transforms $r_1$ to $r_1'$ $=$ $|\\vect{r}_3 - \\vect{r}_a|$ $=$ $r_3$, and we obtain, once again, an obvious result. The operation $(14)(26)(35)(ab)^*$ yields $r_1'$ $=$ $|-\\vect{r}_4 + \\vect{r}_b| = |\\vect{r}_4 - \\vect{r}_b| = r_4$\n\n\t\\subsection{Bond Angles}\n\n\tTo obtain the angle between nuclei 1 and $b$ via nucleus $a$ we define $\\vect{r}_{1a} = \\vect{r}_1 - \\vect{r}_a$ and likewise for $\\vect{r}_{ba}$. Then the sought angle is\n\t\\begin{equation}\n\t\\alpha_1 =\n\t\t\\arccos \\left(\\frac{\\vect{r}_{1a}\\cdot \\vect{r}_{ba}}{|\\vect{r}_{1a}|| \\vect{r}_{ba}|} \\right).\n\t\t\\end{equation}\n\t\tDespite the expression for $\\alpha_1$ being more complex than the expression for $r_1$,\n\t\tthe effect of MS group operations can be determined completely analogously.\n\t\t $E^*$ produces no effect and the other operations relabel. For $(123)$, we have\n\t\t\\begin{equation}\n\t\t\\alpha_1' =\n\t\t\t\\arccos \\left(\\frac{\\vect{r}_{3a}\\cdot \\vect{r}_{ba}}{|\\vect{r}_{3a}|| \\vect{r}_{ba}|} \\right) = \\alpha_3,\n\t\t\t\\end{equation}\n\t\t\twhile for $(14)(26)(35)(ab)^*$\n\t\t\t\\begin{equation}\n\t\t\t\\alpha_1' =\n\t\t\t\t\\arccos \\left(\\frac{(-\\vect{r}_{4b})\\cdot (-\\vect{r}_{ab})}{|-\\vect{r}_{4b}|| -\\vect{r}_{ab}|} \\right) =\\arccos \\left(\\frac{\\vect{r}_{4b}\\cdot \\vect{r}_{ab}}{|\\vect{r}_{4b}|| \\vect{r}_{ab}|} \\right) = \\alpha_4.\n\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\n\t\t\t\t\\subsection{Dihedral Angles}\n\\def\\vect{e}_{z}{\\vect{e}_{z}}\n\\def\\mathrm{arctan2}{\\mathrm{arctan2}}\n\t\t\t\tThe expressions involving the dihedral angles are the most complicated. Consider the four nuclei labelled 1, a, b, and 4 in \\fig{fig:dihedral-atoms}. The dihedral angle between the plane spanned by 1, $a$, and $b$ and that spanned by $a$, $b$, and 4 is shown in \\fig{fig:dihedral-atoms} and \\fig{fig:dihedral-angle}. We define\n\t\t\t\t$\\normvec{\\vect{v}}$ as the unit vector obtained by normalization of $\\vect{v}$,\n\t\t\t\t$\\normvec{\\vect{v}}$ $=$ $\\vect{v}\/\\vert \\vect{v} \\vert$. The orientation of the $z$ axis is defined by $\\vect{e}_{z}$ $=$ $ \\normvec{\\vect{r}_{ab}}$. We need two further axes $x$ and $y$ (whose orientations are defined by the unit vectors $\\vect{e}_{x}$ and $\\vect{e}_{y}$, respectively) which, together with $z$, form a right-handed axis system.\n\t\t\t\t\n\t\t\t\tTo simplify the discussion, we take the $xy$ plane to be horizontal and the $z$ axis to be vertical.\n\t\t\t\tWe aim at obtaining the $x$ and $y$ components of $\\vect{r}_{1a}$ in order to determine the ``horizontal'' angle $\\theta$ it makes with $\\vect{r}_{4b}$ as shown in \\fig{fig:dihedral-angle}. We require the $x$ axis to be directed along the horizontal component (i.e., the component perpendicular to $\\vect{e}_{z}$)\n\t\t\t\tof $\\vect{r}_{4b}$. Thus, the $y$ axis is perpendicular to the plane defined by $\\vect{e}_{z}$ and $\\vect{r}_{4b}$, so that we have $\\vect{e}_{y} = \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}$ and therefore $\\vect{e}_{x} = \\vect{e}_{z} \\times \\vect{e}_{y} = \\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}$ as shown in \\fig{fig:dihedral-cross}. The unit vector $\\vect{e}_{x'} = \\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}$ defines an $x'$ axis in the 1--$a$--$b$ plane; this axis is analogous to the $x$ axis in the 4--$a$--$b$ plane. The dihedral angle between the two planes is the angle between the $x$ and $x'$ axes.\n\t\t\t\t\n\t\t\t\t\n\t\t\t\tThe $x$ and $y$ components of $\\vect{e}_{x'}$ are $\\vect{e}_{x} \\cdot \\vect{e}_{x'}$ and $\\vect{e}_{y} \\cdot \\vect{e}_{x'}$, respectively. In order to obtain the dihedral angle in the range $[-\\pi,\\pi]$ with the correct sign, we use the standard trigonometric\n\t\t\t\tfunction\\footnote{For $(x,y)$ $=$ $(r\\,\\cos\\varphi, r\\,\\sin\\varphi)$, the function\n\t\t\t\t$\\mathrm{arctan2} (y,x) = \\varphi \\in [-\\pi,\\pi]$.}\n\t\t\t\t$\\mathrm{arctan2}$ to obtain\n\t\t\t\t\\begin{eqnarray}\n\t\t\t\\theta =\t\\tau_{41} & = &\n\t\t\t\t\\mathrm{arctan2}(\\vect{e}_{y} \\cdot \\vect{e}_{x'}, \\vect{e}_{x} \\cdot \\vect{e}_{x'})\n\t\t\t\t\\nonumber\\\\ & = &\n\t\t\t\t\\mathrm{arctan2}(\\vect{e}_{y} \\cdot \\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}},\\vect{e}_{x} \\cdot \\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}})\n\t\t\t\t\\end{eqnarray}\n\t\t\t\twhich, written more explicitly, is\n\t\t\t\t\\begin{equation}\n\t\t\t\t\t\\begin{split}\n\t\t\t\t\\theta =\t\\tau_{41} =\n\t\t\t\t\t\t\\mathrm{arctan2} [& \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}} \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}), \\\\\n\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}) ] \\\\\n\t\t\t\t\t\t=\t\\mathrm{arctan2} [& \\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}), \\\\\n\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}) ]\n\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\\label{eq:died-def}\n\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\twhere the last expression emphasizes the equivalence of nuclei 1 and 4.\n\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\\begin{figure}[htbp!]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\centering\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tdplotsetmaincoords{70}{110}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{tikzpicture}[tdplot_main_coords]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,o-o] (0,0,0) node[above left]{$b$} -- (0,0,1) node[left]{$a$};\n\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,-o] (0,0,1) -- (0.353553,0.612372,1.707107) node[right]{1};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,-o] (0,0,0) -- (-0.700629,-0.509037,-0.866025) node[left]{4};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{tikzpicture}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\caption{Four nuclei 1, 4, $a$, and $b$. The dihedral angle\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t$\\theta$ is the angle between\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tthe 1--$a$--$b$ and 4--$a$--$b$ planes. We define the positive direction of the angle by the right hand rule with the thumb pointing in the $\\vect{r}_{ab}$ direction.}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\label{fig:dihedral-atoms}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{figure}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{figure}[htbp!]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\centering\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tdplotsetmaincoords{0}{0}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{tikzpicture}[tdplot_main_coords]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick] (0,0,0) -- (0,0,1) ;\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,-o] (0,0,1) -- (0.353553,0.612372,1.707107) node[right]{1};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,-o] (0,0,0) -- (-0.700629,-0.509037,-0.866025) node[left]{4};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tdplotdrawarc[->]{(0,0,0)}{0.3}{-145}{60}{anchor = west}{$\\theta$};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{tikzpicture}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\caption{Top down view of \\fig{fig:dihedral-atoms} with the dihedral angle (with the defined direction) marked as $\\theta$.}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\label{fig:dihedral-angle}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{figure}\n\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{figure}[htbp!]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\centering\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tdplotsetmaincoords{0}{0}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{tikzpicture}[tdplot_main_coords]\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick] (0,0,0) -- (0,0,1) ;\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,->] (0,0,1) -- (0.353553,0.612372,1.707107) node[right]{$\\vect{r}_{1a}$};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,->] (0,0,0) -- (-0.700629,-0.509037,-0.866025) node[left]{$\\vect{r}_{4b}$};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,->] (0,0,0) -- (-0.700629,-0.509037,-0.866025);\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\draw[thick,->] (0,0,0) -- (0.573576,-0.819152, 0) node[below right]{$\\vect{e}_{y} = \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}$};\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{tikzpicture}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\caption{The $y$ axis.}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\label{fig:dihedral-cross}\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{figure}\n\nWe define the dihedral angles $\\theta_{ij}$ and $\\tau_{ij}$ in terms of Eq.~\\eqref{eq:died-def} and, by means of this equation,\nwe can determine their transformation properties under the generating operations of {\\itshape\\bfseries G}$_{36}$.\n\t\t\t\t\t\t We note that generally $E^*\\mathrm{arctan2}(y,x) = \\mathrm{arctan2}(-y,x) = 2\\pi - \\mathrm{arctan2}(y,x).$\n\t\t\t\t\t\t The dihedral angle $\\theta_{23}$, for example, is defined by\n\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\\theta_{23} = \\mathrm{arctan2} [& \\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{3a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{2a}}), \\\\\n\t\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{3a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{2a}}) ]\n\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\tUnder (123) we obtain\n\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\\theta_{23}' =\n\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& \\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{2a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}), \\\\\n\t\t\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{2a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}) ] = \\theta_{12}.\n\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\tTo obtain the effect of (14)(26)(35)$(ab)^*$, we initially apply (14)(26)(35)$(ab)$ with the result\n\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{6b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t&(-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}}) \\cdot (-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{6b}}) ].\n\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\tApplying $E^*$ reverses $\\vect{e}_{z}$, and by swapping $\\vect{r}_{5b}$ and $\\vect{r}_{6b}$ we obtain the final result:\n\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\\theta_{23}' =\t\t\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{6b}} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t&(-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{6b}}) \\cdot (-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}}) ] = \\theta_{56}.\n\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\twhere the positive direction of the dihedral angle is in the sense of the proton numbering.\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tFinally, applying (14)(25)(36)$(ab)$ to $\\theta_{23}$ gives\n\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\\theta_{23}' =\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{6b}} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t&(-\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{6b}}) \\cdot (-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{5b}}) ] = \\theta_{56}.\n\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\t\tFor $\\tau_{41}$, which is defined by going counterclockwise from 4 to 1, the equation is\n\t\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& \\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}) ] = \\tau_{41}.\n\t\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\t\t\tUnder operation (123)(456), this becomes\n\t\t\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\\tau_{41}' =\t\t\\mathrm{arctan2} [& \\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{3a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{6b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{3a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{6b}}) ] = \\tau_{63}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\tTo determine the effect of (14)(26)(35)$(ab)^*$, we first apply (14)(26)(35)$(ab)$ to $\\tau_{41}$\nand obtain\n\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{4b}} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{1a}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t&(-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{4b}}) \\cdot (-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{1a}}) ].\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\tApplying $E^*$ reverses $\\vect{e}_{z}$. After swapping the order of $\\vect{r}_{1a}$ and $\\vect{r}_{4b}$, we have\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tau_{41}' =\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t&(\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{1a}}) \\cdot (\\vect{e}_{z} \\times \\normvec{\\vect{e}_{z} \\times \\vect{r}_{4b}}) ] = 2\\pi - \\tau_{41}.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tFinally, applying (14)(25)(36)$(ab)$ to $\\tau_{41}$ gives\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{equation}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\begin{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\tau_{41}' =\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\mathrm{arctan2} [& -\\vect{e}_{z} \\cdot ( \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{4b}} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{1a}}), \\\\\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t&(-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{4b}}) \\cdot (-\\vect{e}_{z} \\times \\normvec{-\\vect{e}_{z} \\times \\vect{r}_{1a}}) ] = \\tau_{41}.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{split}\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\\end{equation}\n\t\n\t\t\t\t\n\\section{Transformation of $\\tau$ under the generating operations of {\\itshape\\bfseries G}$_{36}$}\n\\setcounter{equation}{0}\n\\label{sect:appenix_b}\n\nThe torsional coordinate $\\tau$ is defined by\nEq.~(\\ref{eq:taudef}):\n\\begin{equation}\n\\tau =\n\\frac13 ( \\tau_{41} + \\tau_{62} + \\tau_{53}),\n\\end{equation}\nand we will investigate how this coordinate transforms under the generating operations of {\\itshape\\bfseries G}$_{36}$, $R_2^{(+)} = (123)(456)$, $R_2^{(-)} = (132)(456)$, $R_4^{(+)} = (14)(26)(35)(ab)^*$, and $R_4^{(-)} = (14)(25)(36)(ab)$ used in the {\\sc TROVE}\\ calculations. The transformation properties of the dihedral angles $\\tau_{ij}$ are derived as outlined in \\ref{sec:appendixB}.\n\nThe operation (123)(456) permutes the protons 1, 2, 3, 4, 5, 6 to the positions previously occupied by the protons labelled\n3, 1, 2, 6, 4, 5, and the transformed value of $\\tau$ is given by\n\\begin{equation}\n\\tau^\\prime =\n\\frac13 ( \\tau_{63} +\\tau_{51} + \\tau_{42})\n\\end{equation}\nwhere\n\\begin{align}\n\\tau_{63} & = \\tau_{62} + \\theta_{23} \\\\\n\t\\tau_{51} & = \\tau_{53} + \\theta_{31} \\\\\n\\tau_{42} & = \\tau_{41} + \\theta_{12}. \\\\\n\\end{align}\nFor example, $\\tau_{51}$ $=$ $\\tau_{53}$ $+$ $\\theta_{31}$, the plus sign coming about because the positive direction of rotation for the $\\tau_{ij}$ dihedral angles (proton 1 $\\rightarrow$ 2 $\\rightarrow$ 3) is the same as that of\n$\\theta_{12}$, $\\theta_{23}$, and $\\theta_{31}$.\nHence\n\\begin{align}\n \\tau^\\prime\n & = \\frac13 \\left(\n \\tau_{41} + \\tau_{62} +\n\\tau_{53}\n+ \\left[ \\theta_{12} + \\theta_{23} + \\theta_{31} \\right] \\right) \\\\\n & = \\frac13 \\left(\n \\tau_{41} + \\tau_{62} + \\tau_{53}\n + 2\\pi \\right) = \\tau + 2\\pi\/3\n\\end{align}\nor, equivalently, $\\tau^\\prime$ $=$ $\\tau - 4\\pi\/3$ as given in \\tabl{tab:torsion_transformations}, to ensure that $(123)^3(456)^3 = E$.\n\n\nAfter carrying out the operation (132)(456), the protons 1, 2, 3, 4, 5, 6 are found at the positions previously occupied by the protons labelled\n2, 3, 1, 6, 4, 5, respectively. Consequently, the transformed value of $\\tau$ is given by\n\\begin{equation}\n\\tau^\\prime =\n\\frac13 ( \\tau_{62} + \\tau_{53} + \\tau_{41})\n= \\tau.\n\\end{equation}\n\n\nFor $(14)(26)(35)(ab)^*$,\n\\begin{align}\n\\tau^\\prime & =\n\\frac13 ( \\tau_{14} + \\tau_{26} + \\tau_{35}) \\\\\n & =\n\\frac13 ( -\\tau_{41} - \\tau_{62} - \\tau_{53}) = -\\tau\n\\end{align}\nor, equivalently, $2\\pi - \\tau$ as given in \\tabl{tab:torsion_transformations}.\n\nFinally, for (14)(25)(36)$(ab)$\n\\begin{align}\n\\tau^\\prime & =\n\\frac13 ( -\\tau_{14} -\\tau_{26} - \\tau_{35}) \\\\\n & =\n\\frac13 ( \\tau_{41} + \\tau_{62} + \\tau_{53}) = \\tau.\n\\end{align}\nThe transformation properties derived here are summarized in\n\\tabl{tab:torsion_transformations}.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}