Finished section 2 and section 3

16 files changed, 2481 insertions, 47 deletions

diff --git a/report/.gitignore b/report/.gitignore
deleted file mode 100644
index e69de29..0000000
--- a/report/.gitignore
+++ /dev/null
diff --git a/report/figures/tracy-widom-approx/.pdf_stats.m.swp b/report/figures/tracy-widom-approx/.pdf_stats.m.swp
new file mode 100644
index 0000000..741de13
--- /dev/null
+++ b/report/figures/tracy-widom-approx/.pdf_stats.m.swp
diff --git a/report/figures/tracy-widom-approx/.plot_tracy_widom.m.swp b/report/figures/tracy-widom-approx/.plot_tracy_widom.m.swp
new file mode 100644
index 0000000..dc1d74b
--- /dev/null
+++ b/report/figures/tracy-widom-approx/.plot_tracy_widom.m.swp
diff --git a/report/figures/tracy-widom-approx/octave-workspace b/report/figures/tracy-widom-approx/octave-workspace
new file mode 100644
index 0000000..276e921
--- /dev/null
+++ b/report/figures/tracy-widom-approx/octave-workspace
diff --git a/report/figures/tracy-widom-approx/pdf_stats.m b/report/figures/tracy-widom-approx/pdf_stats.m
new file mode 100644
index 0000000..4c440db
--- /dev/null
+++ b/report/figures/tracy-widom-approx/pdf_stats.m
@@ -0,0 +1,21 @@
+function [skew, kurtosis] = pdf_stats(x,p)
+
+    % Define some useful bits
+    dx = x(2) - x(1);
+
+    % The expected value (From LibreTexts 4.1)
+    E = @(x) sum(x .* p) * dx;
+
+    % First moment (mean) (From LibreTexts 4.3)
+    mu = E(x)
+    
+    % Second moment (variance) (From LibreTexts 4.3)
+    sigma = sqrt(E((x - mu).^2))
+
+    % Third moment (skewness) (From LibreTexts 4.4)
+    skew = E(((x - mu)/sigma).^3)
+
+    % Fourth moment (excess kurtosis) (From LibreTexts 4.4)
+    kurtosis = E(((x - mu)/sigma).^4) - 3
+
+end
diff --git a/report/figures/tracy-widom-approx/plot.gnu b/report/figures/tracy-widom-approx/plot.gnu
new file mode 100644
index 0000000..a2e5194
--- /dev/null
+++ b/report/figures/tracy-widom-approx/plot.gnu
@@ -0,0 +1,31 @@
+#set term x11 persist
+set term cairolatex pdf size 6in,3in
+set output 'tracy_widom.tex'
+set linetype 1 lc rgb '#E41A1C' # red
+set linetype 2 lc rgb '#377EB8' # blue
+set linetype 3 lc rgb '#4DAF4A' # green
+
+set key samplen 2
+set grid
+set xlabel "x"
+set ylabel "p(x)"
+set lmargin at screen 0.15
+set rmargin at screen 0.85
+
+
+plot 'tracy_widom.txt' using 1:2 with lines title '$\beta=1$', \
+    'tracy_widom.txt' using 1:3 with lines title '$\beta=2$', \
+    'tracy_widom.txt' using 1:4 with lines title '$\beta=4$'
+
+set term cairolatex pdf size 6in,3in
+set output 'tracy_widom_compare.tex'
+set key samplen 2
+set grid
+set xlabel "x"
+set ylabel "p(x)"
+set lmargin at screen 0.15
+set rmargin at screen 0.85
+
+
+plot 'tracy_widom_normal.txt' using 1:2 with lines title 'TW\textsubscript{1}', \
+    'tracy_widom_normal.txt' using 1:3 with lines title 'Normal' dt 2
diff --git a/report/figures/tracy-widom-approx/plot_tracy_widom.m b/report/figures/tracy-widom-approx/plot_tracy_widom.m
new file mode 100644
index 0000000..c43e3f6
--- /dev/null
+++ b/report/figures/tracy-widom-approx/plot_tracy_widom.m
@@ -0,0 +1,41 @@
+close all;
+clear; clc;
+
+x = linspace(-6,4,1000)
+
+[pdf1,~] = tracywidom_appx(x,1)
+[pdf2,~] = tracywidom_appx(x,2)
+[pdf4,~] = tracywidom_appx(x,4)
+
+% Fig. 1 Tracy-Widoms
+figure(1)
+hold on
+plot(x,pdf1)
+plot(x,pdf2)
+plot(x,pdf4)
+
+A = [x', pdf1', pdf2', pdf4']
+save -ascii tracy_widom.txt A
+
+% Fig 2. Compare to Normal
+normpdf = @(x,mu,sigma) 1/(sigma*sqrt(2*pi)).*exp(-0.5*((x-mu)/sigma).^2)
+npdf = normpdf(x,-1.38,1.268)
+
+figure(2)
+hold on
+plot(x,pdf1)
+plot(x,npdf,'--')
+
+B = [x', pdf1', npdf']
+save -ascii tracy_widom_normal.txt B
+
+% Skewness and Excess Kurtosis
+x_stat = linspace(-9,9,50e3)
+[pdf1_stat,~] = tracywidom_appx(x_stat,1)
+npdf_stat = normpdf(x_stat, -1.38, 1.268)
+
+fprintf("Tracy Widom\n")
+[~,~] = pdf_stats(x_stat, pdf1_stat)
+fprintf("Normal Distribution\n")
+[~,~] = pdf_stats(x_stat, npdf_stat)
+
diff --git a/report/figures/tracy-widom-approx/tracy_widom.pdf b/report/figures/tracy-widom-approx/tracy_widom.pdf
new file mode 100644
index 0000000..ac8fd64
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom.pdf
diff --git a/report/figures/tracy-widom-approx/tracy_widom.tex b/report/figures/tracy-widom-approx/tracy_widom.tex
new file mode 100644
index 0000000..4897f0d
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom.tex
@@ -0,0 +1,128 @@
+% GNUPLOT: LaTeX picture with Postscript
+\begingroup
+  \makeatletter
+  \providecommand\color[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package color not loaded in conjunction with
+      terminal option `colourtext'%
+    }{See the gnuplot documentation for explanation.%
+    }{Either use 'blacktext' in gnuplot or load the package
+      color.sty in LaTeX.}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \@ifundefined{ifGPcolor}{%
+    \newif\ifGPcolor
+    \GPcolortrue
+  }{}%
+  \@ifundefined{ifGPblacktext}{%
+    \newif\ifGPblacktext
+    \GPblacktexttrue
+  }{}%
+  % define a \g@addto@macro without @ in the name:
+  \let\gplgaddtomacro\g@addto@macro
+  % define empty templates for all commands taking text:
+  \gdef\gplbacktext{}%
+  \gdef\gplfronttext{}%
+  \makeatother
+  \ifGPblacktext
+    % no textcolor at all
+    \def\colorrgb#1{}%
+    \def\colorgray#1{}%
+  \else
+    % gray or color?
+    \ifGPcolor
+      \def\colorrgb#1{\color[rgb]{#1}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
+      \expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
+      \expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
+      \expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
+      \expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
+      \expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
+      \expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
+      \expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
+      \expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
+    \else
+      % gray
+      \def\colorrgb#1{\color{black}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color{black}}%
+      \expandafter\def\csname LT1\endcsname{\color{black}}%
+      \expandafter\def\csname LT2\endcsname{\color{black}}%
+      \expandafter\def\csname LT3\endcsname{\color{black}}%
+      \expandafter\def\csname LT4\endcsname{\color{black}}%
+      \expandafter\def\csname LT5\endcsname{\color{black}}%
+      \expandafter\def\csname LT6\endcsname{\color{black}}%
+      \expandafter\def\csname LT7\endcsname{\color{black}}%
+      \expandafter\def\csname LT8\endcsname{\color{black}}%
+    \fi
+  \fi
+    \setlength{\unitlength}{0.0500bp}%
+    \ifx\gptboxheight\undefined%
+      \newlength{\gptboxheight}%
+      \newlength{\gptboxwidth}%
+      \newsavebox{\gptboxtext}%
+    \fi%
+    \setlength{\fboxrule}{0.5pt}%
+    \setlength{\fboxsep}{1pt}%
+    \definecolor{tbcol}{rgb}{1,1,1}%
+\begin{picture}(8640.00,4320.00)%
+    \gplgaddtomacro\gplbacktext{%
+      \csname LTb\endcsname%%
+      \put(1181,655){\makebox(0,0)[r]{\strut{}$0$}}%
+      \csname LTb\endcsname%%
+      \put(1181,1228){\makebox(0,0)[r]{\strut{}$0.1$}}%
+      \csname LTb\endcsname%%
+      \put(1181,1801){\makebox(0,0)[r]{\strut{}$0.2$}}%
+      \csname LTb\endcsname%%
+      \put(1181,2375){\makebox(0,0)[r]{\strut{}$0.3$}}%
+      \csname LTb\endcsname%%
+      \put(1181,2948){\makebox(0,0)[r]{\strut{}$0.4$}}%
+      \csname LTb\endcsname%%
+      \put(1181,3521){\makebox(0,0)[r]{\strut{}$0.5$}}%
+      \csname LTb\endcsname%%
+      \put(1181,4095){\makebox(0,0)[r]{\strut{}$0.6$}}%
+      \csname LTb\endcsname%%
+      \put(1293,450){\makebox(0,0){\strut{}$-6$}}%
+      \csname LTb\endcsname%%
+      \put(2499,450){\makebox(0,0){\strut{}$-4$}}%
+      \csname LTb\endcsname%%
+      \put(3706,450){\makebox(0,0){\strut{}$-2$}}%
+      \csname LTb\endcsname%%
+      \put(4913,450){\makebox(0,0){\strut{}$0$}}%
+      \csname LTb\endcsname%%
+      \put(6120,450){\makebox(0,0){\strut{}$2$}}%
+      \csname LTb\endcsname%%
+      \put(7326,450){\makebox(0,0){\strut{}$4$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+      \csname LTb\endcsname%%
+      \put(6685,3910){\makebox(0,0)[r]{\strut{}$\beta=1$}}%
+      \csname LTb\endcsname%%
+      \put(6685,3706){\makebox(0,0)[r]{\strut{}$\beta=2$}}%
+      \csname LTb\endcsname%%
+      \put(6685,3501){\makebox(0,0)[r]{\strut{}$\beta=4$}}%
+      \csname LTb\endcsname%%
+      \put(658,2375){\rotatebox{-270.00}{\makebox(0,0){\strut{}p(x)}}}%
+      \csname LTb\endcsname%%
+      \put(4309,143){\makebox(0,0){\strut{}x}}%
+    }%
+    \gplbacktext
+    \put(0,0){\includegraphics[width={432.00bp},height={216.00bp}]{tracy_widom}}%
+    \gplfronttext
+  \end{picture}%
+\endgroup
diff --git a/report/figures/tracy-widom-approx/tracy_widom.txt b/report/figures/tracy-widom-approx/tracy_widom.txt
new file mode 100644
index 0000000..af0e3ea
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom.txt
@@ -0,0 +1,1000 @@
+ -6.00000000e+00 5.23065849e-06 2.29618752e-08 7.13915490e-09
+ -5.98998999e+00 5.57784813e-06 2.55499319e-08 8.06418410e-09
+ -5.97997998e+00 5.94626332e-06 2.84144167e-08 9.10380193e-09
+ -5.96996997e+00 6.33708317e-06 3.15831586e-08 1.02715245e-08
+ -5.95995996e+00 6.75154515e-06 3.50866094e-08 1.15823783e-08
+ -5.94994995e+00 7.19094755e-06 3.89580727e-08 1.30530592e-08
+ -5.93993994e+00 7.65665209e-06 4.32339517e-08 1.47021068e-08
+ -5.92992993e+00 8.15008651e-06 4.79540165e-08 1.65500962e-08
+ -5.91991992e+00 8.67274740e-06 5.31616925e-08 1.86198477e-08
+ -5.90990991e+00 9.22620298e-06 5.89043713e-08 2.09366574e-08
+ -5.89989990e+00 9.81209611e-06 6.52337458e-08 2.35285492e-08
+ -5.88988989e+00 1.04321472e-05 7.22061714e-08 2.64265509e-08
+ -5.87987988e+00 1.10881576e-05 7.98830541e-08 2.96649966e-08
+ -5.86986987e+00 1.17820123e-05 8.83312691e-08 3.32818566e-08
+ -5.85985986e+00 1.25156840e-05 9.76236100e-08 3.73190991e-08
+ -5.84984985e+00 1.32912360e-05 1.07839272e-07 4.18230839e-08
+ -5.83983984e+00 1.41108258e-05 1.19064371e-07 4.68449928e-08
+ -5.82982983e+00 1.49767090e-05 1.31392501e-07 5.24412993e-08
+ -5.81981982e+00 1.58912429e-05 1.44925332e-07 5.86742801e-08
+ -5.80980981e+00 1.68568902e-05 1.59773249e-07 6.56125725e-08
+ -5.79979980e+00 1.78762235e-05 1.76056043e-07 7.33317817e-08
+ -5.78978979e+00 1.89519288e-05 1.93903646e-07 8.19151412e-08
+ -5.77977978e+00 2.00868101e-05 2.13456915e-07 9.14542308e-08
+ -5.76976977e+00 2.12837936e-05 2.34868483e-07 1.02049758e-07
+ -5.75975976e+00 2.25459323e-05 2.58303656e-07 1.13812406e-07
+ -5.74974975e+00 2.38764102e-05 2.83941379e-07 1.26863752e-07
+ -5.73973974e+00 2.52785477e-05 3.11975268e-07 1.41337270e-07
+ -5.72972973e+00 2.67558055e-05 3.42614708e-07 1.57379411e-07
+ -5.71971972e+00 2.83117905e-05 3.76086030e-07 1.75150777e-07
+ -5.70970971e+00 2.99502603e-05 4.12633763e-07 1.94827390e-07
+ -5.69969970e+00 3.16751286e-05 4.52521972e-07 2.16602072e-07
+ -5.68968969e+00 3.34904705e-05 4.96035679e-07 2.40685929e-07
+ -5.67967968e+00 3.54005280e-05 5.43482385e-07 2.67309959e-07
+ -5.66966967e+00 3.74097158e-05 5.95193678e-07 2.96726792e-07
+ -5.65965966e+00 3.95226266e-05 6.51526957e-07 3.29212566e-07
+ -5.64964965e+00 4.17440377e-05 7.12867258e-07 3.65068952e-07
+ -5.63963964e+00 4.40789163e-05 7.79629194e-07 4.04625336e-07
+ -5.62962963e+00 4.65324262e-05 8.52259021e-07 4.48241174e-07
+ -5.61961962e+00 4.91099338e-05 9.31236831e-07 4.96308528e-07
+ -5.60960961e+00 5.18170146e-05 1.01707887e-06 5.49254797e-07
+ -5.59959960e+00 5.46594601e-05 1.11034003e-06 6.07545654e-07
+ -5.58958959e+00 5.76432840e-05 1.21161641e-06 6.71688201e-07
+ -5.57957958e+00 6.07747297e-05 1.32154816e-06 7.42234373e-07
+ -5.56956957e+00 6.40602767e-05 1.44082237e-06 8.19784573e-07
+ -5.55955956e+00 6.75066484e-05 1.57017618e-06 9.04991597e-07
+ -5.54954955e+00 7.11208186e-05 1.71040010e-06 9.98564827e-07
+ -5.53953954e+00 7.49100199e-05 1.86234145e-06 1.10127474e-06
+ -5.52952953e+00 7.88817506e-05 2.02690806e-06 1.21395772e-06
+ -5.51951952e+00 8.30437826e-05 2.20507216e-06 1.33752125e-06
+ -5.50950951e+00 8.74041696e-05 2.39787448e-06 1.47294942e-06
+ -5.49949950e+00 9.19712545e-05 2.60642854e-06 1.62130885e-06
+ -5.48948949e+00 9.67536784e-05 2.83192530e-06 1.78375505e-06
+ -5.47947948e+00 1.01760388e-04 3.07563790e-06 1.96153911e-06
+ -5.46946947e+00 1.07000645e-04 3.33892678e-06 2.15601499e-06
+ -5.45945946e+00 1.12484033e-04 3.62324501e-06 2.36864718e-06
+ -5.44944945e+00 1.18220469e-04 3.93014393e-06 2.60101895e-06
+ -5.43943944e+00 1.24220210e-04 4.26127909e-06 2.85484109e-06
+ -5.42942943e+00 1.30493863e-04 4.61841644e-06 3.13196123e-06
+ -5.41941942e+00 1.37052391e-04 5.00343891e-06 3.43437382e-06
+ -5.40940941e+00 1.43907130e-04 5.41835332e-06 3.76423067e-06
+ -5.39939940e+00 1.51069790e-04 5.86529756e-06 4.12385224e-06
+ -5.38938939e+00 1.58552468e-04 6.34654823e-06 4.51573954e-06
+ -5.37937938e+00 1.66367658e-04 6.86452855e-06 4.94258688e-06
+ -5.36936937e+00 1.74528261e-04 7.42181677e-06 5.40729535e-06
+ -5.35935936e+00 1.83047594e-04 8.02115490e-06 5.91298710e-06
+ -5.34934935e+00 1.91939400e-04 8.66545787e-06 6.46302056e-06
+ -5.33933934e+00 2.01217857e-04 9.35782316e-06 7.06100649e-06
+ -5.32932933e+00 2.10897591e-04 1.01015408e-05 7.71082505e-06
+ -5.31931932e+00 2.20993684e-04 1.09001041e-05 8.41664380e-06
+ -5.30930931e+00 2.31521686e-04 1.17572201e-05 9.18293681e-06
+ -5.29929930e+00 2.42497624e-04 1.26768219e-05 1.00145048e-05
+ -5.28928929e+00 2.53938013e-04 1.36630799e-05 1.09164966e-05
+ -5.27927928e+00 2.65859868e-04 1.47204147e-05 1.18944315e-05
+ -5.26926927e+00 2.78280713e-04 1.58535102e-05 1.29542230e-05
+ -5.25925926e+00 2.91218591e-04 1.70673270e-05 1.41022041e-05
+ -5.24924925e+00 3.04692080e-04 1.83671169e-05 1.53451536e-05
+ -5.23923924e+00 3.18720297e-04 1.97584376e-05 1.66903239e-05
+ -5.22922923e+00 3.33322915e-04 2.12471680e-05 1.81454706e-05
+ -5.21921922e+00 3.48520170e-04 2.28395245e-05 1.97188830e-05
+ -5.20920921e+00 3.64332875e-04 2.45420776e-05 2.14194169e-05
+ -5.19919920e+00 3.80782428e-04 2.63617692e-05 2.32565284e-05
+ -5.18918919e+00 3.97890827e-04 2.83059308e-05 2.52403101e-05
+ -5.17917918e+00 4.15680679e-04 3.03823022e-05 2.73815287e-05
+ -5.16916917e+00 4.34175211e-04 3.25990510e-05 2.96916642e-05
+ -5.15915916e+00 4.53398282e-04 3.49647928e-05 3.21829517e-05
+ -5.14914915e+00 4.73374395e-04 3.74886121e-05 3.48684245e-05
+ -5.13913914e+00 4.94128707e-04 4.01800842e-05 3.77619599e-05
+ -5.12912913e+00 5.15687040e-04 4.30492977e-05 4.08783266e-05
+ -5.11911912e+00 5.38075895e-04 4.61068777e-05 4.42332343e-05
+ -5.10910911e+00 5.61322459e-04 4.93640099e-05 4.78433861e-05
+ -5.09909910e+00 5.85454622e-04 5.28324659e-05 5.17265328e-05
+ -5.08908909e+00 6.10500981e-04 5.65246289e-05 5.59015295e-05
+ -5.07907908e+00 6.36490856e-04 6.04535201e-05 6.03883950e-05
+ -5.06906907e+00 6.63454301e-04 6.46328267e-05 6.52083737e-05
+ -5.05905906e+00 6.91422113e-04 6.90769302e-05 7.03839995e-05
+ -5.04904905e+00 7.20425844e-04 7.38009358e-05 7.59391635e-05
+ -5.03903904e+00 7.50497811e-04 7.88207025e-05 8.18991834e-05
+ -5.02902903e+00 7.81671107e-04 8.41528748e-05 8.82908764e-05
+ -5.01901902e+00 8.13979615e-04 8.98149143e-05 9.51426340e-05
+ -5.00900901e+00 8.47458011e-04 9.58251333e-05 1.02484501e-04
+ -4.99899900e+00 8.82141782e-04 1.02202729e-04 1.10348258e-04
+ -4.98898899e+00 9.18067232e-04 1.08967817e-04 1.18767503e-04
+ -4.97897898e+00 9.55271491e-04 1.16141470e-04 1.27777740e-04
+ -4.96896897e+00 9.93792531e-04 1.23745754e-04 1.37416473e-04
+ -4.95895896e+00 1.03366917e-03 1.31803763e-04 1.47723294e-04
+ -4.94894895e+00 1.07494108e-03 1.40339664e-04 1.58739985e-04
+ -4.93893894e+00 1.11764880e-03 1.49378731e-04 1.70510617e-04
+ -4.92892893e+00 1.16183376e-03 1.58947390e-04 1.83081652e-04
+ -4.91891892e+00 1.20753824e-03 1.69073261e-04 1.96502053e-04
+ -4.90890891e+00 1.25480545e-03 1.79785198e-04 2.10823391e-04
+ -4.89889890e+00 1.30367949e-03 1.91113335e-04 2.26099963e-04
+ -4.88888889e+00 1.35420536e-03 2.03089131e-04 2.42388907e-04
+ -4.87887888e+00 1.40642898e-03 2.15745416e-04 2.59750322e-04
+ -4.86886887e+00 1.46039720e-03 2.29116438e-04 2.78247396e-04
+ -4.85885886e+00 1.51615781e-03 2.43237910e-04 2.97946527e-04
+ -4.84884885e+00 1.57375953e-03 2.58147060e-04 3.18917464e-04
+ -4.83883884e+00 1.63325202e-03 2.73882679e-04 3.41233431e-04
+ -4.82882883e+00 1.69468592e-03 2.90485174e-04 3.64971272e-04
+ -4.81881882e+00 1.75811279e-03 3.07996621e-04 3.90211593e-04
+ -4.80880881e+00 1.82358519e-03 3.26460810e-04 4.17038900e-04
+ -4.79879880e+00 1.89115662e-03 3.45923309e-04 4.45541754e-04
+ -4.78878879e+00 1.96088158e-03 3.66431511e-04 4.75812921e-04
+ -4.77877878e+00 2.03281554e-03 3.88034689e-04 5.07949524e-04
+ -4.76876877e+00 2.10701495e-03 4.10784057e-04 5.42053201e-04
+ -4.75875876e+00 2.18353725e-03 4.34732823e-04 5.78230270e-04
+ -4.74874875e+00 2.26244087e-03 4.59936245e-04 6.16591887e-04
+ -4.73873874e+00 2.34378522e-03 4.86451694e-04 6.57254218e-04
+ -4.72872873e+00 2.42763074e-03 5.14338708e-04 7.00338601e-04
+ -4.71871872e+00 2.51403884e-03 5.43659052e-04 7.45971727e-04
+ -4.70870871e+00 2.60307192e-03 5.74476782e-04 7.94285806e-04
+ -4.69869870e+00 2.69479341e-03 6.06858300e-04 8.45418750e-04
+ -4.68868869e+00 2.78926772e-03 6.40872419e-04 8.99514347e-04
+ -4.67867868e+00 2.88656026e-03 6.76590421e-04 9.56722443e-04
+ -4.66866867e+00 2.98673745e-03 7.14086122e-04 1.01719913e-03
+ -4.65865866e+00 3.08986671e-03 7.53435931e-04 1.08110691e-03
+ -4.64864865e+00 3.19601643e-03 7.94718916e-04 1.14861492e-03
+ -4.63863864e+00 3.30525602e-03 8.38016861e-04 1.21989907e-03
+ -4.62862863e+00 3.41765588e-03 8.83414335e-04 1.29514227e-03
+ -4.61861862e+00 3.53328738e-03 9.30998749e-04 1.37453460e-03
+ -4.60860861e+00 3.65222290e-03 9.80860422e-04 1.45827348e-03
+ -4.59859860e+00 3.77453577e-03 1.03309264e-03 1.54656391e-03
+ -4.58858859e+00 3.90030031e-03 1.08779173e-03 1.63961861e-03
+ -4.57857858e+00 4.02959181e-03 1.14505710e-03 1.73765821e-03
+ -4.56856857e+00 4.16248651e-03 1.20499133e-03 1.84091149e-03
+ -4.55855856e+00 4.29906161e-03 1.26770019e-03 1.94961549e-03
+ -4.54854855e+00 4.43939527e-03 1.33329276e-03 2.06401574e-03
+ -4.53853854e+00 4.58356655e-03 1.40188145e-03 2.18436644e-03
+ -4.52852853e+00 4.73165547e-03 1.47358205e-03 2.31093061e-03
+ -4.51851852e+00 4.88374296e-03 1.54851382e-03 2.44398032e-03
+ -4.50850851e+00 5.03991086e-03 1.62679955e-03 2.58379679e-03
+ -4.49849850e+00 5.20024189e-03 1.70856557e-03 2.73067064e-03
+ -4.48848849e+00 5.36481967e-03 1.79394187e-03 2.88490198e-03
+ -4.47847848e+00 5.53372868e-03 1.88306209e-03 3.04680062e-03
+ -4.46846847e+00 5.70705428e-03 1.97606364e-03 3.21668623e-03
+ -4.45845846e+00 5.88488265e-03 2.07308770e-03 3.39488845e-03
+ -4.44844845e+00 6.06730080e-03 2.17427928e-03 3.58174707e-03
+ -4.43843844e+00 6.25439656e-03 2.27978730e-03 3.77761213e-03
+ -4.42842843e+00 6.44625856e-03 2.38976460e-03 3.98284412e-03
+ -4.41841842e+00 6.64297620e-03 2.50436800e-03 4.19781403e-03
+ -4.40840841e+00 6.84463964e-03 2.62375835e-03 4.42290349e-03
+ -4.39839840e+00 7.05133978e-03 2.74810056e-03 4.65850490e-03
+ -4.38838839e+00 7.26316826e-03 2.87756364e-03 4.90502151e-03
+ -4.37837838e+00 7.48021741e-03 3.01232075e-03 5.16286749e-03
+ -4.36836837e+00 7.70258024e-03 3.15254922e-03 5.43246805e-03
+ -4.35835836e+00 7.93035042e-03 3.29843058e-03 5.71425945e-03
+ -4.34834835e+00 8.16362225e-03 3.45015060e-03 6.00868911e-03
+ -4.33833834e+00 8.40249067e-03 3.60789930e-03 6.31621563e-03
+ -4.32832833e+00 8.64705117e-03 3.77187100e-03 6.63730882e-03
+ -4.31831832e+00 8.89739983e-03 3.94226432e-03 6.97244971e-03
+ -4.30830831e+00 9.15363327e-03 4.11928219e-03 7.32213058e-03
+ -4.29829830e+00 9.41584862e-03 4.30313187e-03 7.68685491e-03
+ -4.28828829e+00 9.68414347e-03 4.49402497e-03 8.06713739e-03
+ -4.27827828e+00 9.95861590e-03 4.69217746e-03 8.46350388e-03
+ -4.26826827e+00 1.02393644e-02 4.89780964e-03 8.87649131e-03
+ -4.25825826e+00 1.05264879e-02 5.11114617e-03 9.30664767e-03
+ -4.24824825e+00 1.08200856e-02 5.33241605e-03 9.75453187e-03
+ -4.23823824e+00 1.11202571e-02 5.56185261e-03 1.02207136e-02
+ -4.22822823e+00 1.14271024e-02 5.79969351e-03 1.07057734e-02
+ -4.21821822e+00 1.17407215e-02 6.04618071e-03 1.12103023e-02
+ -4.20820821e+00 1.20612150e-02 6.30156043e-03 1.17349015e-02
+ -4.19819820e+00 1.23886834e-02 6.56608317e-03 1.22801828e-02
+ -4.18818819e+00 1.27232276e-02 6.84000363e-03 1.28467677e-02
+ -4.17817818e+00 1.30649484e-02 7.12358069e-03 1.34352877e-02
+ -4.16816817e+00 1.34139469e-02 7.41707737e-03 1.40463837e-02
+ -4.15815816e+00 1.37703242e-02 7.72076080e-03 1.46807059e-02
+ -4.14814815e+00 1.41341813e-02 8.03490213e-03 1.53389134e-02
+ -4.13813814e+00 1.45056195e-02 8.35977650e-03 1.60216742e-02
+ -4.12812813e+00 1.48847397e-02 8.69566297e-03 1.67296645e-02
+ -4.11811812e+00 1.52716428e-02 9.04284444e-03 1.74635684e-02
+ -4.10810811e+00 1.56664298e-02 9.40160761e-03 1.82240778e-02
+ -4.09809810e+00 1.60692013e-02 9.77224285e-03 1.90118916e-02
+ -4.08808809e+00 1.64800576e-02 1.01550442e-02 1.98277156e-02
+ -4.07807808e+00 1.68990991e-02 1.05503091e-02 2.06722619e-02
+ -4.06806807e+00 1.73264255e-02 1.09583385e-02 2.15462486e-02
+ -4.05805806e+00 1.77621364e-02 1.13794368e-02 2.24503988e-02
+ -4.04804805e+00 1.82063309e-02 1.18139113e-02 2.33854408e-02
+ -4.03803804e+00 1.86591079e-02 1.22620726e-02 2.43521070e-02
+ -4.02802803e+00 1.91205654e-02 1.27242344e-02 2.53511336e-02
+ -4.01801802e+00 1.95908013e-02 1.32007129e-02 2.63832599e-02
+ -4.00800801e+00 2.00699127e-02 1.36918274e-02 2.74492278e-02
+ -3.99799800e+00 2.05579962e-02 1.41978994e-02 2.85497808e-02
+ -3.98798799e+00 2.10551477e-02 1.47192533e-02 2.96856640e-02
+ -3.97797798e+00 2.15614623e-02 1.52562152e-02 3.08576227e-02
+ -3.96796797e+00 2.20770345e-02 1.58091138e-02 3.20664022e-02
+ -3.95795796e+00 2.26019580e-02 1.63782796e-02 3.33127468e-02
+ -3.94794795e+00 2.31363254e-02 1.69640449e-02 3.45973992e-02
+ -3.93793794e+00 2.36802288e-02 1.75667434e-02 3.59210996e-02
+ -3.92792793e+00 2.42337589e-02 1.81867106e-02 3.72845848e-02
+ -3.91791792e+00 2.47970059e-02 1.88242830e-02 3.86885879e-02
+ -3.90790791e+00 2.53700586e-02 1.94797982e-02 4.01338368e-02
+ -3.89789790e+00 2.59530047e-02 2.01535946e-02 4.16210536e-02
+ -3.88788789e+00 2.65459310e-02 2.08460113e-02 4.31509540e-02
+ -3.87787788e+00 2.71489230e-02 2.15573879e-02 4.47242459e-02
+ -3.86786787e+00 2.77620648e-02 2.22880640e-02 4.63416289e-02
+ -3.85785786e+00 2.83854394e-02 2.30383794e-02 4.80037933e-02
+ -3.84784785e+00 2.90191283e-02 2.38086734e-02 4.97114187e-02
+ -3.83783784e+00 2.96632118e-02 2.45992850e-02 5.14651739e-02
+ -3.82782783e+00 3.03177686e-02 2.54105525e-02 5.32657150e-02
+ -3.81781782e+00 3.09828759e-02 2.62428132e-02 5.51136851e-02
+ -3.80780781e+00 3.16586095e-02 2.70964030e-02 5.70097129e-02
+ -3.79779780e+00 3.23450433e-02 2.79716565e-02 5.89544121e-02
+ -3.78778779e+00 3.30422500e-02 2.88689065e-02 6.09483796e-02
+ -3.77777778e+00 3.37503001e-02 2.97884839e-02 6.29921956e-02
+ -3.76776777e+00 3.44692627e-02 3.07307172e-02 6.50864214e-02
+ -3.75775776e+00 3.51992050e-02 3.16959322e-02 6.72315994e-02
+ -3.74774775e+00 3.59401924e-02 3.26844522e-02 6.94282511e-02
+ -3.73773774e+00 3.66922882e-02 3.36965972e-02 7.16768768e-02
+ -3.72772773e+00 3.74555539e-02 3.47326838e-02 7.39779542e-02
+ -3.71771772e+00 3.82300491e-02 3.57930248e-02 7.63319374e-02
+ -3.70770771e+00 3.90158312e-02 3.68779292e-02 7.87392559e-02
+ -3.69769770e+00 3.98129554e-02 3.79877017e-02 8.12003135e-02
+ -3.68768769e+00 4.06214750e-02 3.91226421e-02 8.37154872e-02
+ -3.67767768e+00 4.14414410e-02 4.02830457e-02 8.62851263e-02
+ -3.66766767e+00 4.22729021e-02 4.14692024e-02 8.89095514e-02
+ -3.65765766e+00 4.31159047e-02 4.26813965e-02 9.15890530e-02
+ -3.64764765e+00 4.39704929e-02 4.39199068e-02 9.43238912e-02
+ -3.63763764e+00 4.48367086e-02 4.51850055e-02 9.71142939e-02
+ -3.62762763e+00 4.57145909e-02 4.64769587e-02 9.99604564e-02
+ -3.61761762e+00 4.66041766e-02 4.77960256e-02 1.02862540e-01
+ -3.60760761e+00 4.75055001e-02 4.91424584e-02 1.05820672e-01
+ -3.59759760e+00 4.84185931e-02 5.05165018e-02 1.08834943e-01
+ -3.58758759e+00 4.93434846e-02 5.19183928e-02 1.11905407e-01
+ -3.57757758e+00 5.02802012e-02 5.33483603e-02 1.15032083e-01
+ -3.56756757e+00 5.12287664e-02 5.48066251e-02 1.18214948e-01
+ -3.55755756e+00 5.21892015e-02 5.62933990e-02 1.21453942e-01
+ -3.54754755e+00 5.31615245e-02 5.78088851e-02 1.24748964e-01
+ -3.53753754e+00 5.41457510e-02 5.93532769e-02 1.28099875e-01
+ -3.52752753e+00 5.51418933e-02 6.09267586e-02 1.31506491e-01
+ -3.51751752e+00 5.61499613e-02 6.25295043e-02 1.34968587e-01
+ -3.50750751e+00 5.71699615e-02 6.41616777e-02 1.38485895e-01
+ -3.49749750e+00 5.82018977e-02 6.58234324e-02 1.42058105e-01
+ -3.48748749e+00 5.92457706e-02 6.75149106e-02 1.45684861e-01
+ -3.47747748e+00 6.03015779e-02 6.92362439e-02 1.49365762e-01
+ -3.46746747e+00 6.13693142e-02 7.09875521e-02 1.53100363e-01
+ -3.45745746e+00 6.24489710e-02 7.27689433e-02 1.56888173e-01
+ -3.44744745e+00 6.35405364e-02 7.45805137e-02 1.60728654e-01
+ -3.43743744e+00 6.46439958e-02 7.64223471e-02 1.64621223e-01
+ -3.42742743e+00 6.57593311e-02 7.82945146e-02 1.68565247e-01
+ -3.41741742e+00 6.68865208e-02 8.01970747e-02 1.72560049e-01
+ -3.40740741e+00 6.80255406e-02 8.21300725e-02 1.76604902e-01
+ -3.39739740e+00 6.91763624e-02 8.40935398e-02 1.80699033e-01
+ -3.38738739e+00 7.03389552e-02 8.60874948e-02 1.84841619e-01
+ -3.37737738e+00 7.15132844e-02 8.81119417e-02 1.89031791e-01
+ -3.36736737e+00 7.26993120e-02 9.01668706e-02 1.93268630e-01
+ -3.35735736e+00 7.38969969e-02 9.22522571e-02 1.97551171e-01
+ -3.34734735e+00 7.51062943e-02 9.43680624e-02 2.01878398e-01
+ -3.33733734e+00 7.63271560e-02 9.65142325e-02 2.06249250e-01
+ -3.32732733e+00 7.75595306e-02 9.86906988e-02 2.10662615e-01
+ -3.31731732e+00 7.88033629e-02 1.00897377e-01 2.15117336e-01
+ -3.30730731e+00 8.00585945e-02 1.03134168e-01 2.19612206e-01
+ -3.29729730e+00 8.13251632e-02 1.05400956e-01 2.24145974e-01
+ -3.28728729e+00 8.26030036e-02 1.07697610e-01 2.28717340e-01
+ -3.27727728e+00 8.38920466e-02 1.10023983e-01 2.33324957e-01
+ -3.26726727e+00 8.51922196e-02 1.12379913e-01 2.37967435e-01
+ -3.25725726e+00 8.65034464e-02 1.14765219e-01 2.42643335e-01
+ -3.24724725e+00 8.78256473e-02 1.17179705e-01 2.47351177e-01
+ -3.23723724e+00 8.91587391e-02 1.19623160e-01 2.52089434e-01
+ -3.22722723e+00 9.05026350e-02 1.22095354e-01 2.56856538e-01
+ -3.21721722e+00 9.18572446e-02 1.24596041e-01 2.61650876e-01
+ -3.20720721e+00 9.32224739e-02 1.27124958e-01 2.66470796e-01
+ -3.19719720e+00 9.45982253e-02 1.29681826e-01 2.71314602e-01
+ -3.18718719e+00 9.59843979e-02 1.32266348e-01 2.76180560e-01
+ -3.17717718e+00 9.73808868e-02 1.34878209e-01 2.81066898e-01
+ -3.16716717e+00 9.87875840e-02 1.37517079e-01 2.85971803e-01
+ -3.15715716e+00 1.00204377e-01 1.40182610e-01 2.90893427e-01
+ -3.14714715e+00 1.01631152e-01 1.42874436e-01 2.95829888e-01
+ -3.13713714e+00 1.03067789e-01 1.45592175e-01 3.00779266e-01
+ -3.12712713e+00 1.04514165e-01 1.48335427e-01 3.05739611e-01
+ -3.11711712e+00 1.05970155e-01 1.51103774e-01 3.10708938e-01
+ -3.10710711e+00 1.07435629e-01 1.53896783e-01 3.15685234e-01
+ -3.09709710e+00 1.08910455e-01 1.56714003e-01 3.20666456e-01
+ -3.08708709e+00 1.10394496e-01 1.59554965e-01 3.25650532e-01
+ -3.07707708e+00 1.11887611e-01 1.62419184e-01 3.30635366e-01
+ -3.06706707e+00 1.13389658e-01 1.65306158e-01 3.35618835e-01
+ -3.05705706e+00 1.14900490e-01 1.68215367e-01 3.40598795e-01
+ -3.04704705e+00 1.16419956e-01 1.71146277e-01 3.45573078e-01
+ -3.03703704e+00 1.17947903e-01 1.74098334e-01 3.50539497e-01
+ -3.02702703e+00 1.19484174e-01 1.77070971e-01 3.55495847e-01
+ -3.01701702e+00 1.21028609e-01 1.80063602e-01 3.60439908e-01
+ -3.00700701e+00 1.22581044e-01 1.83075626e-01 3.65369441e-01
+ -2.99699700e+00 1.24141312e-01 1.86106426e-01 3.70282198e-01
+ -2.98698699e+00 1.25709243e-01 1.89155369e-01 3.75175916e-01
+ -2.97697698e+00 1.27284663e-01 1.92221808e-01 3.80048327e-01
+ -2.96696697e+00 1.28867397e-01 1.95305077e-01 3.84897151e-01
+ -2.95695696e+00 1.30457264e-01 1.98404499e-01 3.89720105e-01
+ -2.94694695e+00 1.32054082e-01 2.01519380e-01 3.94514901e-01
+ -2.93693694e+00 1.33657665e-01 2.04649011e-01 3.99279248e-01
+ -2.92692693e+00 1.35267824e-01 2.07792670e-01 4.04010857e-01
+ -2.91691692e+00 1.36884367e-01 2.10949621e-01 4.08707440e-01
+ -2.90690691e+00 1.38507098e-01 2.14119112e-01 4.13366711e-01
+ -2.89689690e+00 1.40135821e-01 2.17300379e-01 4.17986392e-01
+ -2.88688689e+00 1.41770335e-01 2.20492647e-01 4.22564212e-01
+ -2.87687688e+00 1.43410436e-01 2.23695124e-01 4.27097909e-01
+ -2.86686687e+00 1.45055917e-01 2.26907009e-01 4.31585232e-01
+ -2.85685686e+00 1.46706571e-01 2.30127487e-01 4.36023945e-01
+ -2.84684685e+00 1.48362185e-01 2.33355731e-01 4.40411826e-01
+ -2.83683684e+00 1.50022544e-01 2.36590905e-01 4.44746670e-01
+ -2.82682683e+00 1.51687433e-01 2.39832159e-01 4.49026294e-01
+ -2.81681682e+00 1.53356631e-01 2.43078634e-01 4.53248532e-01
+ -2.80680681e+00 1.55029917e-01 2.46329461e-01 4.57411243e-01
+ -2.79679680e+00 1.56707066e-01 2.49583760e-01 4.61512312e-01
+ -2.78678679e+00 1.58387852e-01 2.52840643e-01 4.65549648e-01
+ -2.77677678e+00 1.60072046e-01 2.56099213e-01 4.69521191e-01
+ -2.76676677e+00 1.61759416e-01 2.59358563e-01 4.73424909e-01
+ -2.75675676e+00 1.63449729e-01 2.62617779e-01 4.77258805e-01
+ -2.74674675e+00 1.65142750e-01 2.65875940e-01 4.81020912e-01
+ -2.73673674e+00 1.66838241e-01 2.69132117e-01 4.84709303e-01
+ -2.72672673e+00 1.68535962e-01 2.72385375e-01 4.88322084e-01
+ -2.71671672e+00 1.70235672e-01 2.75634772e-01 4.91857403e-01
+ -2.70670671e+00 1.71937128e-01 2.78879361e-01 4.95313447e-01
+ -2.69669670e+00 1.73640084e-01 2.82118189e-01 4.98688445e-01
+ -2.68668669e+00 1.75344293e-01 2.85350301e-01 5.01980671e-01
+ -2.67667668e+00 1.77049506e-01 2.88574734e-01 5.05188441e-01
+ -2.66666667e+00 1.78755475e-01 2.91790525e-01 5.08310121e-01
+ -2.65665666e+00 1.80461945e-01 2.94996704e-01 5.11344123e-01
+ -2.64664665e+00 1.82168666e-01 2.98192302e-01 5.14288909e-01
+ -2.63663664e+00 1.83875381e-01 3.01376347e-01 5.17142991e-01
+ -2.62662663e+00 1.85581835e-01 3.04547863e-01 5.19904933e-01
+ -2.61661662e+00 1.87287770e-01 3.07705876e-01 5.22573352e-01
+ -2.60660661e+00 1.88992929e-01 3.10849411e-01 5.25146920e-01
+ -2.59659660e+00 1.90697052e-01 3.13977492e-01 5.27624363e-01
+ -2.58658659e+00 1.92399877e-01 3.17089144e-01 5.30004463e-01
+ -2.57657658e+00 1.94101145e-01 3.20183392e-01 5.32286061e-01
+ -2.56656657e+00 1.95800591e-01 3.23259266e-01 5.34468055e-01
+ -2.55655656e+00 1.97497954e-01 3.26315796e-01 5.36549401e-01
+ -2.54654655e+00 1.99192969e-01 3.29352013e-01 5.38529118e-01
+ -2.53653654e+00 2.00885372e-01 3.32366955e-01 5.40406281e-01
+ -2.52652653e+00 2.02574896e-01 3.35359660e-01 5.42180031e-01
+ -2.51651652e+00 2.04261278e-01 3.38329175e-01 5.43849566e-01
+ -2.50650651e+00 2.05944250e-01 3.41274547e-01 5.45414151e-01
+ -2.49649650e+00 2.07623546e-01 3.44194832e-01 5.46873110e-01
+ -2.48648649e+00 2.09298899e-01 3.47089091e-01 5.48225833e-01
+ -2.47647648e+00 2.10970043e-01 3.49956389e-01 5.49471772e-01
+ -2.46646647e+00 2.12636710e-01 3.52795803e-01 5.50610444e-01
+ -2.45645646e+00 2.14298633e-01 3.55606414e-01 5.51641428e-01
+ -2.44644645e+00 2.15955545e-01 3.58387310e-01 5.52564370e-01
+ -2.43643644e+00 2.17607179e-01 3.61137592e-01 5.53378979e-01
+ -2.42642643e+00 2.19253269e-01 3.63856366e-01 5.54085029e-01
+ -2.41641642e+00 2.20893547e-01 3.66542750e-01 5.54682357e-01
+ -2.40640641e+00 2.22527748e-01 3.69195870e-01 5.55170866e-01
+ -2.39639640e+00 2.24155606e-01 3.71814865e-01 5.55550523e-01
+ -2.38638639e+00 2.25776855e-01 3.74398883e-01 5.55821357e-01
+ -2.37637638e+00 2.27391232e-01 3.76947085e-01 5.55983462e-01
+ -2.36636637e+00 2.28998471e-01 3.79458643e-01 5.56036997e-01
+ -2.35635636e+00 2.30598310e-01 3.81932741e-01 5.55982181e-01
+ -2.34634635e+00 2.32190486e-01 3.84368578e-01 5.55819297e-01
+ -2.33633634e+00 2.33774738e-01 3.86765364e-01 5.55548689e-01
+ -2.32632633e+00 2.35350805e-01 3.89122324e-01 5.55170764e-01
+ -2.31631632e+00 2.36918428e-01 3.91438696e-01 5.54685989e-01
+ -2.30630631e+00 2.38477347e-01 3.93713736e-01 5.54094890e-01
+ -2.29629630e+00 2.40027307e-01 3.95946711e-01 5.53398054e-01
+ -2.28628629e+00 2.41568050e-01 3.98136904e-01 5.52596124e-01
+ -2.27627628e+00 2.43099322e-01 4.00283617e-01 5.51689805e-01
+ -2.26626627e+00 2.44620871e-01 4.02386164e-01 5.50679855e-01
+ -2.25625626e+00 2.46132443e-01 4.04443879e-01 5.49567088e-01
+ -2.24624625e+00 2.47633790e-01 4.06456110e-01 5.48352376e-01
+ -2.23623624e+00 2.49124662e-01 4.08422225e-01 5.47036642e-01
+ -2.22622623e+00 2.50604813e-01 4.10341606e-01 5.45620862e-01
+ -2.21621622e+00 2.52073998e-01 4.12213657e-01 5.44106065e-01
+ -2.20620621e+00 2.53531973e-01 4.14037796e-01 5.42493330e-01
+ -2.19619620e+00 2.54978497e-01 4.15813464e-01 5.40783786e-01
+ -2.18618619e+00 2.56413332e-01 4.17540116e-01 5.38978607e-01
+ -2.17617618e+00 2.57836239e-01 4.19217229e-01 5.37079018e-01
+ -2.16616617e+00 2.59246984e-01 4.20844299e-01 5.35086287e-01
+ -2.15615616e+00 2.60645333e-01 4.22420840e-01 5.33001727e-01
+ -2.14614615e+00 2.62031057e-01 4.23946387e-01 5.30826694e-01
+ -2.13613614e+00 2.63403926e-01 4.25420494e-01 5.28562585e-01
+ -2.12612613e+00 2.64763715e-01 4.26842737e-01 5.26210837e-01
+ -2.11611612e+00 2.66110200e-01 4.28212710e-01 5.23772926e-01
+ -2.10610611e+00 2.67443161e-01 4.29530028e-01 5.21250364e-01
+ -2.09609610e+00 2.68762378e-01 4.30794328e-01 5.18644702e-01
+ -2.08608609e+00 2.70067637e-01 4.32005266e-01 5.15957520e-01
+ -2.07607608e+00 2.71358723e-01 4.33162519e-01 5.13190435e-01
+ -2.06606607e+00 2.72635428e-01 4.34265787e-01 5.10345094e-01
+ -2.05605606e+00 2.73897542e-01 4.35314789e-01 5.07423172e-01
+ -2.04604605e+00 2.75144862e-01 4.36309267e-01 5.04426373e-01
+ -2.03603604e+00 2.76377186e-01 4.37248981e-01 5.01356430e-01
+ -2.02602603e+00 2.77594315e-01 4.38133717e-01 4.98215096e-01
+ -2.01601602e+00 2.78796053e-01 4.38963279e-01 4.95004150e-01
+ -2.00600601e+00 2.79982208e-01 4.39737493e-01 4.91725395e-01
+ -1.99599600e+00 2.81152590e-01 4.40456206e-01 4.88380649e-01
+ -1.98598599e+00 2.82307013e-01 4.41119289e-01 4.84971753e-01
+ -1.97597598e+00 2.83445293e-01 4.41726632e-01 4.81500563e-01
+ -1.96596597e+00 2.84567251e-01 4.42278147e-01 4.77968952e-01
+ -1.95595596e+00 2.85672710e-01 4.42773767e-01 4.74378804e-01
+ -1.94594595e+00 2.86761497e-01 4.43213448e-01 4.70732017e-01
+ -1.93593594e+00 2.87833443e-01 4.43597164e-01 4.67030502e-01
+ -1.92592593e+00 2.88888380e-01 4.43924913e-01 4.63276175e-01
+ -1.91591592e+00 2.89926147e-01 4.44196715e-01 4.59470962e-01
+ -1.90590591e+00 2.90946583e-01 4.44412606e-01 4.55616796e-01
+ -1.89589590e+00 2.91949534e-01 4.44572649e-01 4.51715613e-01
+ -1.88588589e+00 2.92934847e-01 4.44676924e-01 4.47769353e-01
+ -1.87587588e+00 2.93902373e-01 4.44725531e-01 4.43779957e-01
+ -1.86586587e+00 2.94851968e-01 4.44718595e-01 4.39749368e-01
+ -1.85585586e+00 2.95783490e-01 4.44656255e-01 4.35679525e-01
+ -1.84584585e+00 2.96696803e-01 4.44538676e-01 4.31572368e-01
+ -1.83583584e+00 2.97591772e-01 4.44366040e-01 4.27429830e-01
+ -1.82582583e+00 2.98468268e-01 4.44138548e-01 4.23253840e-01
+ -1.81581582e+00 2.99326165e-01 4.43856422e-01 4.19046321e-01
+ -1.80580581e+00 3.00165341e-01 4.43519904e-01 4.14809186e-01
+ -1.79579580e+00 3.00985677e-01 4.43129253e-01 4.10544342e-01
+ -1.78578579e+00 3.01787059e-01 4.42684749e-01 4.06253682e-01
+ -1.77577578e+00 3.02569377e-01 4.42186689e-01 4.01939091e-01
+ -1.76576577e+00 3.03332524e-01 4.41635389e-01 3.97602437e-01
+ -1.75575576e+00 3.04076397e-01 4.41031183e-01 3.93245577e-01
+ -1.74574575e+00 3.04800899e-01 4.40374422e-01 3.88870352e-01
+ -1.73573574e+00 3.05505934e-01 4.39665478e-01 3.84478587e-01
+ -1.72572573e+00 3.06191412e-01 4.38904735e-01 3.80072089e-01
+ -1.71571572e+00 3.06857246e-01 4.38092598e-01 3.75652646e-01
+ -1.70570571e+00 3.07503354e-01 4.37229486e-01 3.71222029e-01
+ -1.69569570e+00 3.08129657e-01 4.36315837e-01 3.66781986e-01
+ -1.68568569e+00 3.08736082e-01 4.35352103e-01 3.62334246e-01
+ -1.67567568e+00 3.09322557e-01 4.34338752e-01 3.57880513e-01
+ -1.66566567e+00 3.09889016e-01 4.33276267e-01 3.53422472e-01
+ -1.65565566e+00 3.10435397e-01 4.32165146e-01 3.48961781e-01
+ -1.64564565e+00 3.10961643e-01 4.31005904e-01 3.44500074e-01
+ -1.63563564e+00 3.11467698e-01 4.29799067e-01 3.40038960e-01
+ -1.62562563e+00 3.11953513e-01 4.28545176e-01 3.35580021e-01
+ -1.61561562e+00 3.12419043e-01 4.27244785e-01 3.31124815e-01
+ -1.60560561e+00 3.12864244e-01 4.25898464e-01 3.26674868e-01
+ -1.59559560e+00 3.13289080e-01 4.24506792e-01 3.22231682e-01
+ -1.58558559e+00 3.13693517e-01 4.23070363e-01 3.17796729e-01
+ -1.57557558e+00 3.14077525e-01 4.21589781e-01 3.13371452e-01
+ -1.56556557e+00 3.14441079e-01 4.20065663e-01 3.08957263e-01
+ -1.55555556e+00 3.14784157e-01 4.18498637e-01 3.04555545e-01
+ -1.54554555e+00 3.15106741e-01 4.16889342e-01 3.00167651e-01
+ -1.53553554e+00 3.15408819e-01 4.15238426e-01 2.95794903e-01
+ -1.52552553e+00 3.15690381e-01 4.13546550e-01 2.91438590e-01
+ -1.51551552e+00 3.15951422e-01 4.11814382e-01 2.87099972e-01
+ -1.50550551e+00 3.16191940e-01 4.10042599e-01 2.82780275e-01
+ -1.49549550e+00 3.16411937e-01 4.08231889e-01 2.78480693e-01
+ -1.48548549e+00 3.16611421e-01 4.06382947e-01 2.74202389e-01
+ -1.47547548e+00 3.16790402e-01 4.04496476e-01 2.69946493e-01
+ -1.46546547e+00 3.16948894e-01 4.02573187e-01 2.65714101e-01
+ -1.45545546e+00 3.17086916e-01 4.00613799e-01 2.61506277e-01
+ -1.44544545e+00 3.17204489e-01 3.98619035e-01 2.57324053e-01
+ -1.43543544e+00 3.17301640e-01 3.96589628e-01 2.53168426e-01
+ -1.42542543e+00 3.17378399e-01 3.94526314e-01 2.49040362e-01
+ -1.41541542e+00 3.17434799e-01 3.92429836e-01 2.44940793e-01
+ -1.40540541e+00 3.17470878e-01 3.90300943e-01 2.40870617e-01
+ -1.39539540e+00 3.17486677e-01 3.88140386e-01 2.36830702e-01
+ -1.38538539e+00 3.17482242e-01 3.85948922e-01 2.32821879e-01
+ -1.37537538e+00 3.17457620e-01 3.83727314e-01 2.28844950e-01
+ -1.36536537e+00 3.17412865e-01 3.81476325e-01 2.24900682e-01
+ -1.35535536e+00 3.17348031e-01 3.79196722e-01 2.20989810e-01
+ -1.34534535e+00 3.17263180e-01 3.76889277e-01 2.17113038e-01
+ -1.33533534e+00 3.17158373e-01 3.74554762e-01 2.13271037e-01
+ -1.32532533e+00 3.17033679e-01 3.72193953e-01 2.09464445e-01
+ -1.31531532e+00 3.16889166e-01 3.69807624e-01 2.05693870e-01
+ -1.30530531e+00 3.16724909e-01 3.67396555e-01 2.01959888e-01
+ -1.29529530e+00 3.16540984e-01 3.64961524e-01 1.98263044e-01
+ -1.28528529e+00 3.16337473e-01 3.62503309e-01 1.94603853e-01
+ -1.27527528e+00 3.16114460e-01 3.60022690e-01 1.90982799e-01
+ -1.26526527e+00 3.15872030e-01 3.57520447e-01 1.87400335e-01
+ -1.25525526e+00 3.15610276e-01 3.54997356e-01 1.83856886e-01
+ -1.24524525e+00 3.15329290e-01 3.52454196e-01 1.80352847e-01
+ -1.23523524e+00 3.15029171e-01 3.49891742e-01 1.76888584e-01
+ -1.22522523e+00 3.14710017e-01 3.47310769e-01 1.73464435e-01
+ -1.21521522e+00 3.14371932e-01 3.44712050e-01 1.70080710e-01
+ -1.20520521e+00 3.14015022e-01 3.42096355e-01 1.66737689e-01
+ -1.19519520e+00 3.13639397e-01 3.39464451e-01 1.63435630e-01
+ -1.18518519e+00 3.13245169e-01 3.36817102e-01 1.60174759e-01
+ -1.17517518e+00 3.12832453e-01 3.34155071e-01 1.56955278e-01
+ -1.16516517e+00 3.12401368e-01 3.31479115e-01 1.53777365e-01
+ -1.15515516e+00 3.11952034e-01 3.28789987e-01 1.50641171e-01
+ -1.14514515e+00 3.11484575e-01 3.26088438e-01 1.47546822e-01
+ -1.13513514e+00 3.10999118e-01 3.23375213e-01 1.44494420e-01
+ -1.12512513e+00 3.10495792e-01 3.20651052e-01 1.41484044e-01
+ -1.11511512e+00 3.09974728e-01 3.17916691e-01 1.38515750e-01
+ -1.10510511e+00 3.09436062e-01 3.15172860e-01 1.35589570e-01
+ -1.09509510e+00 3.08879931e-01 3.12420284e-01 1.32705517e-01
+ -1.08508509e+00 3.08306473e-01 3.09659681e-01 1.29863578e-01
+ -1.07507508e+00 3.07715831e-01 3.06891766e-01 1.27063724e-01
+ -1.06506507e+00 3.07108150e-01 3.04117243e-01 1.24305902e-01
+ -1.05505506e+00 3.06483577e-01 3.01336813e-01 1.21590040e-01
+ -1.04504505e+00 3.05842259e-01 2.98551170e-01 1.18916047e-01
+ -1.03503504e+00 3.05184350e-01 2.95761000e-01 1.16283815e-01
+ -1.02502503e+00 3.04510001e-01 2.92966982e-01 1.13693214e-01
+ -1.01501502e+00 3.03819370e-01 2.90169788e-01 1.11144099e-01
+ -1.00500501e+00 3.03112613e-01 2.87370082e-01 1.08636309e-01
+ -9.94994995e-01 3.02389891e-01 2.84568521e-01 1.06169664e-01
+ -9.84984985e-01 3.01651366e-01 2.81765752e-01 1.03743969e-01
+ -9.74974975e-01 3.00897200e-01 2.78962417e-01 1.01359014e-01
+ -9.64964965e-01 3.00127561e-01 2.76159147e-01 9.90145740e-02
+ -9.54954955e-01 2.99342615e-01 2.73356566e-01 9.67104091e-02
+ -9.44944945e-01 2.98542532e-01 2.70555290e-01 9.44462665e-02
+ -9.34934935e-01 2.97727482e-01 2.67755923e-01 9.22218798e-02
+ -9.24924925e-01 2.96897639e-01 2.64959064e-01 9.00369700e-02
+ -9.14914915e-01 2.96053176e-01 2.62165301e-01 8.78912460e-02
+ -9.04904905e-01 2.95194270e-01 2.59375212e-01 8.57844051e-02
+ -8.94894895e-01 2.94321097e-01 2.56589368e-01 8.37161335e-02
+ -8.84884885e-01 2.93433838e-01 2.53808329e-01 8.16861068e-02
+ -8.74874875e-01 2.92532671e-01 2.51032647e-01 7.96939905e-02
+ -8.64864865e-01 2.91617778e-01 2.48262861e-01 7.77394406e-02
+ -8.54854855e-01 2.90689343e-01 2.45499505e-01 7.58221042e-02
+ -8.44844845e-01 2.89747549e-01 2.42743100e-01 7.39416194e-02
+ -8.34834835e-01 2.88792582e-01 2.39994157e-01 7.20976168e-02
+ -8.24824825e-01 2.87824629e-01 2.37253180e-01 7.02897188e-02
+ -8.14814815e-01 2.86843875e-01 2.34520659e-01 6.85175410e-02
+ -8.04804805e-01 2.85850511e-01 2.31797078e-01 6.67806921e-02
+ -7.94794795e-01 2.84844726e-01 2.29082908e-01 6.50787748e-02
+ -7.84784785e-01 2.83826710e-01 2.26378611e-01 6.34113858e-02
+ -7.74774775e-01 2.82796654e-01 2.23684638e-01 6.17781165e-02
+ -7.64764765e-01 2.81754751e-01 2.21001432e-01 6.01785533e-02
+ -7.54754755e-01 2.80701193e-01 2.18329423e-01 5.86122780e-02
+ -7.44744745e-01 2.79636175e-01 2.15669033e-01 5.70788685e-02
+ -7.34734735e-01 2.78559890e-01 2.13020671e-01 5.55778987e-02
+ -7.24724725e-01 2.77472533e-01 2.10384739e-01 5.41089394e-02
+ -7.14714715e-01 2.76374300e-01 2.07761627e-01 5.26715582e-02
+ -7.04704705e-01 2.75265387e-01 2.05151714e-01 5.12653202e-02
+ -6.94694695e-01 2.74145990e-01 2.02555370e-01 4.98897884e-02
+ -6.84684685e-01 2.73016306e-01 1.99972954e-01 4.85445237e-02
+ -6.74674675e-01 2.71876532e-01 1.97404817e-01 4.72290855e-02
+ -6.64664665e-01 2.70726866e-01 1.94851295e-01 4.59430320e-02
+ -6.54654655e-01 2.69567505e-01 1.92312719e-01 4.46859206e-02
+ -6.44644645e-01 2.68398648e-01 1.89789406e-01 4.34573079e-02
+ -6.34634635e-01 2.67220492e-01 1.87281666e-01 4.22567504e-02
+ -6.24624625e-01 2.66033237e-01 1.84789796e-01 4.10838045e-02
+ -6.14614615e-01 2.64837079e-01 1.82314086e-01 3.99380270e-02
+ -6.04604605e-01 2.63632218e-01 1.79854813e-01 3.88189752e-02
+ -5.94594595e-01 2.62418853e-01 1.77412245e-01 3.77262072e-02
+ -5.84584585e-01 2.61197180e-01 1.74986643e-01 3.66592822e-02
+ -5.74574575e-01 2.59967399e-01 1.72578253e-01 3.56177607e-02
+ -5.64564565e-01 2.58729707e-01 1.70187317e-01 3.46012049e-02
+ -5.54554555e-01 2.57484303e-01 1.67814063e-01 3.36091787e-02
+ -5.44544545e-01 2.56231383e-01 1.65458711e-01 3.26412479e-02
+ -5.34534535e-01 2.54971145e-01 1.63121472e-01 3.16969809e-02
+ -5.24524525e-01 2.53703787e-01 1.60802546e-01 3.07759480e-02
+ -5.14514515e-01 2.52429504e-01 1.58502127e-01 2.98777226e-02
+ -5.04504505e-01 2.51148493e-01 1.56220395e-01 2.90018806e-02
+ -4.94494494e-01 2.49860949e-01 1.53957526e-01 2.81480010e-02
+ -4.84484484e-01 2.48567068e-01 1.51713682e-01 2.73156658e-02
+ -4.74474474e-01 2.47267044e-01 1.49489021e-01 2.65044606e-02
+ -4.64464464e-01 2.45961071e-01 1.47283687e-01 2.57139743e-02
+ -4.54454454e-01 2.44649344e-01 1.45097821e-01 2.49437991e-02
+ -4.44444444e-01 2.43332054e-01 1.42931550e-01 2.41935315e-02
+ -4.34434434e-01 2.42009394e-01 1.40784995e-01 2.34627715e-02
+ -4.24424424e-01 2.40681555e-01 1.38658270e-01 2.27511230e-02
+ -4.14414414e-01 2.39348728e-01 1.36551478e-01 2.20581944e-02
+ -4.04404404e-01 2.38011102e-01 1.34464715e-01 2.13835978e-02
+ -3.94394394e-01 2.36668867e-01 1.32398070e-01 2.07269501e-02
+ -3.84384384e-01 2.35322211e-01 1.30351622e-01 2.00878722e-02
+ -3.74374374e-01 2.33971320e-01 1.28325443e-01 1.94659896e-02
+ -3.64364364e-01 2.32616382e-01 1.26319599e-01 1.88609324e-02
+ -3.54354354e-01 2.31257581e-01 1.24334147e-01 1.82723354e-02
+ -3.44344344e-01 2.29895102e-01 1.22369135e-01 1.76998379e-02
+ -3.34334334e-01 2.28529128e-01 1.20424606e-01 1.71430841e-02
+ -3.24324324e-01 2.27159841e-01 1.18500596e-01 1.66017230e-02
+ -3.14314314e-01 2.25787423e-01 1.16597133e-01 1.60754084e-02
+ -3.04304304e-01 2.24412052e-01 1.14714236e-01 1.55637991e-02
+ -2.94294294e-01 2.23033909e-01 1.12851922e-01 1.50665587e-02
+ -2.84284284e-01 2.21653170e-01 1.11010198e-01 1.45833559e-02
+ -2.74274274e-01 2.20270012e-01 1.09189065e-01 1.41138643e-02
+ -2.64264264e-01 2.18884611e-01 1.07388518e-01 1.36577627e-02
+ -2.54254254e-01 2.17497139e-01 1.05608545e-01 1.32147347e-02
+ -2.44244244e-01 2.16107770e-01 1.03849129e-01 1.27844691e-02
+ -2.34234234e-01 2.14716675e-01 1.02110247e-01 1.23666597e-02
+ -2.24224224e-01 2.13324024e-01 1.00391869e-01 1.19610056e-02
+ -2.14214214e-01 2.11929986e-01 9.86939592e-02 1.15672106e-02
+ -2.04204204e-01 2.10534727e-01 9.70164783e-02 1.11849839e-02
+ -1.94194194e-01 2.09138414e-01 9.53593796e-02 1.08140394e-02
+ -1.84184184e-01 2.07741210e-01 9.37226116e-02 1.04540966e-02
+ -1.74174174e-01 2.06343279e-01 9.21061179e-02 1.01048794e-02
+ -1.64164164e-01 2.04944783e-01 9.05098368e-02 9.76611714e-03
+ -1.54154154e-01 2.03545881e-01 8.89337016e-02 9.43754409e-03
+ -1.44144144e-01 2.02146731e-01 8.73776410e-02 9.11889942e-03
+ -1.34134134e-01 2.00747490e-01 8.58415790e-02 8.80992729e-03
+ -1.24124124e-01 1.99348315e-01 8.43254350e-02 8.51037677e-03
+ -1.14114114e-01 1.97949358e-01 8.28291242e-02 8.22000183e-03
+ -1.04104104e-01 1.96550771e-01 8.13525574e-02 7.93856129e-03
+ -9.40940941e-02 1.95152706e-01 7.98956412e-02 7.66581880e-03
+ -8.40840841e-02 1.93755312e-01 7.84582783e-02 7.40154278e-03
+ -7.40740741e-02 1.92358735e-01 7.70403676e-02 7.14550638e-03
+ -6.40640641e-02 1.90963121e-01 7.56418040e-02 6.89748746e-03
+ -5.40540541e-02 1.89568615e-01 7.42624791e-02 6.65726854e-03
+ -4.40440440e-02 1.88175359e-01 7.29022807e-02 6.42463672e-03
+ -3.40340340e-02 1.86783493e-01 7.15610933e-02 6.19938368e-03
+ -2.40240240e-02 1.85393157e-01 7.02387983e-02 5.98130560e-03
+ -1.40140140e-02 1.84004488e-01 6.89352739e-02 5.77020310e-03
+ -4.00400400e-03 1.82617621e-01 6.76503951e-02 5.56588123e-03
+ 6.00600601e-03 1.81232691e-01 6.63840342e-02 5.36814936e-03
+ 1.60160160e-02 1.79849829e-01 6.51360607e-02 5.17682119e-03
+ 2.60260260e-02 1.78469166e-01 6.39063413e-02 4.99171464e-03
+ 3.60360360e-02 1.77090831e-01 6.26947402e-02 4.81265180e-03
+ 4.60460460e-02 1.75714950e-01 6.15011194e-02 4.63945891e-03
+ 5.60560561e-02 1.74341648e-01 6.03253382e-02 4.47196625e-03
+ 6.60660661e-02 1.72971050e-01 5.91672539e-02 4.31000814e-03
+ 7.60760761e-02 1.71603276e-01 5.80267216e-02 4.15342280e-03
+ 8.60860861e-02 1.70238446e-01 5.69035945e-02 4.00205239e-03
+ 9.60960961e-02 1.68876679e-01 5.57977237e-02 3.85574286e-03
+ 1.06106106e-01 1.67518090e-01 5.47089588e-02 3.71434394e-03
+ 1.16116116e-01 1.66162794e-01 5.36371474e-02 3.57770905e-03
+ 1.26126126e-01 1.64810904e-01 5.25821357e-02 3.44569528e-03
+ 1.36136136e-01 1.63462530e-01 5.15437683e-02 3.31816326e-03
+ 1.46146146e-01 1.62117782e-01 5.05218885e-02 3.19497718e-03
+ 1.56156156e-01 1.60776766e-01 4.95163382e-02 3.07600465e-03
+ 1.66166166e-01 1.59439589e-01 4.85269581e-02 2.96111671e-03
+ 1.76176176e-01 1.58106353e-01 4.75535878e-02 2.85018771e-03
+ 1.86186186e-01 1.56777161e-01 4.65960659e-02 2.74309527e-03
+ 1.96196196e-01 1.55452113e-01 4.56542300e-02 2.63972023e-03
+ 2.06206206e-01 1.54131306e-01 4.47279168e-02 2.53994657e-03
+ 2.16216216e-01 1.52814838e-01 4.38169625e-02 2.44366136e-03
+ 2.26226226e-01 1.51502803e-01 4.29212022e-02 2.35075470e-03
+ 2.36236236e-01 1.50195293e-01 4.20404707e-02 2.26111966e-03
+ 2.46246246e-01 1.48892400e-01 4.11746021e-02 2.17465219e-03
+ 2.56256256e-01 1.47594213e-01 4.03234301e-02 2.09125112e-03
+ 2.66266266e-01 1.46300819e-01 3.94867882e-02 2.01081804e-03
+ 2.76276276e-01 1.45012304e-01 3.86645092e-02 1.93325727e-03
+ 2.86286286e-01 1.43728752e-01 3.78564261e-02 1.85847583e-03
+ 2.96296296e-01 1.42450245e-01 3.70623714e-02 1.78638331e-03
+ 3.06306306e-01 1.41176864e-01 3.62821778e-02 1.71689189e-03
+ 3.16316316e-01 1.39908686e-01 3.55156777e-02 1.64991621e-03
+ 3.26326326e-01 1.38645789e-01 3.47627038e-02 1.58537339e-03
+ 3.36336336e-01 1.37388248e-01 3.40230887e-02 1.52318292e-03
+ 3.46346346e-01 1.36136136e-01 3.32966652e-02 1.46326661e-03
+ 3.56356356e-01 1.34889525e-01 3.25832665e-02 1.40554858e-03
+ 3.66366366e-01 1.33648485e-01 3.18827259e-02 1.34995515e-03
+ 3.76376376e-01 1.32413083e-01 3.11948771e-02 1.29641481e-03
+ 3.86386386e-01 1.31183386e-01 3.05195542e-02 1.24485819e-03
+ 3.96396396e-01 1.29959459e-01 2.98565918e-02 1.19521798e-03
+ 4.06406406e-01 1.28741365e-01 2.92058249e-02 1.14742888e-03
+ 4.16416416e-01 1.27529165e-01 2.85670892e-02 1.10142758e-03
+ 4.26426426e-01 1.26322919e-01 2.79402209e-02 1.05715266e-03
+ 4.36436436e-01 1.25122685e-01 2.73250569e-02 1.01454461e-03
+ 4.46446446e-01 1.23928519e-01 2.67214346e-02 9.73545720e-04
+ 4.56456456e-01 1.22740476e-01 2.61291925e-02 9.34100067e-04
+ 4.66466466e-01 1.21558609e-01 2.55481697e-02 8.96153460e-04
+ 4.76476476e-01 1.20382969e-01 2.49782059e-02 8.59653397e-04
+ 4.86486486e-01 1.19213606e-01 2.44191421e-02 8.24549022e-04
+ 4.96496496e-01 1.18050569e-01 2.38708199e-02 7.90791078e-04
+ 5.06506507e-01 1.16893904e-01 2.33330820e-02 7.58331867e-04
+ 5.16516517e-01 1.15743656e-01 2.28057718e-02 7.27125207e-04
+ 5.26526527e-01 1.14599868e-01 2.22887341e-02 6.97126394e-04
+ 5.36536537e-01 1.13462583e-01 2.17818144e-02 6.68292160e-04
+ 5.46546547e-01 1.12331840e-01 2.12848595e-02 6.40580630e-04
+ 5.56556557e-01 1.11207680e-01 2.07977171e-02 6.13951291e-04
+ 5.66566567e-01 1.10090138e-01 2.03202363e-02 5.88364949e-04
+ 5.76576577e-01 1.08979252e-01 1.98522671e-02 5.63783693e-04
+ 5.86586587e-01 1.07875054e-01 1.93936608e-02 5.40170860e-04
+ 5.96596597e-01 1.06777579e-01 1.89442698e-02 5.17490997e-04
+ 6.06606607e-01 1.05686857e-01 1.85039478e-02 4.95709830e-04
+ 6.16616617e-01 1.04602918e-01 1.80725499e-02 4.74794228e-04
+ 6.26626627e-01 1.03525792e-01 1.76499322e-02 4.54712170e-04
+ 6.36636637e-01 1.02455504e-01 1.72359523e-02 4.35432713e-04
+ 6.46646647e-01 1.01392082e-01 1.68304690e-02 4.16925960e-04
+ 6.56656657e-01 1.00335548e-01 1.64333424e-02 3.99163029e-04
+ 6.66666667e-01 9.92859271e-02 1.60444340e-02 3.82116024e-04
+ 6.76676677e-01 9.82432393e-02 1.56636067e-02 3.65758004e-04
+ 6.86686687e-01 9.72075055e-02 1.52907247e-02 3.50062955e-04
+ 6.96696697e-01 9.61787445e-02 1.49256536e-02 3.35005762e-04
+ 7.06706707e-01 9.51569739e-02 1.45682604e-02 3.20562182e-04
+ 7.16716717e-01 9.41422099e-02 1.42184135e-02 3.06708814e-04
+ 7.26726727e-01 9.31344676e-02 1.38759828e-02 2.93423081e-04
+ 7.36736737e-01 9.21337608e-02 1.35408394e-02 2.80683194e-04
+ 7.46746747e-01 9.11401018e-02 1.32128561e-02 2.68468135e-04
+ 7.56756757e-01 9.01535020e-02 1.28919071e-02 2.56757631e-04
+ 7.66766767e-01 8.91739714e-02 1.25778678e-02 2.45532129e-04
+ 7.76776777e-01 8.82015188e-02 1.22706154e-02 2.34772774e-04
+ 7.86786787e-01 8.72361518e-02 1.19700283e-02 2.24461388e-04
+ 7.96796797e-01 8.62778768e-02 1.16759864e-02 2.14580447e-04
+ 8.06806807e-01 8.53266993e-02 1.13883712e-02 2.05113059e-04
+ 8.16816817e-01 8.43826232e-02 1.11070655e-02 1.96042945e-04
+ 8.26826827e-01 8.34456517e-02 1.08319538e-02 1.87354420e-04
+ 8.36836837e-01 8.25157867e-02 1.05629218e-02 1.79032371e-04
+ 8.46846847e-01 8.15930289e-02 1.02998568e-02 1.71062240e-04
+ 8.56856857e-01 8.06773781e-02 1.00426476e-02 1.63430004e-04
+ 8.66866867e-01 7.97688330e-02 9.79118438e-03 1.56122160e-04
+ 8.76876877e-01 7.88673913e-02 9.54535891e-03 1.49125706e-04
+ 8.86886887e-01 7.79730495e-02 9.30506431e-03 1.42428121e-04
+ 8.96896897e-01 7.70858032e-02 9.07019520e-03 1.36017355e-04
+ 9.06906907e-01 7.62056470e-02 8.84064767e-03 1.29881810e-04
+ 9.16916917e-01 7.53325745e-02 8.61631925e-03 1.24010323e-04
+ 9.26926927e-01 7.44665783e-02 8.39710892e-03 1.18392153e-04
+ 9.36936937e-01 7.36076502e-02 8.18291711e-03 1.13016967e-04
+ 9.46946947e-01 7.27557809e-02 7.97364568e-03 1.07874823e-04
+ 9.56956957e-01 7.19109602e-02 7.76919792e-03 1.02956162e-04
+ 9.66966967e-01 7.10731771e-02 7.56947855e-03 9.82517885e-05
+ 9.76976977e-01 7.02424197e-02 7.37439371e-03 9.37528607e-05
+ 9.86986987e-01 6.94186751e-02 7.18385096e-03 8.94508785e-05
+ 9.96996997e-01 6.86019296e-02 6.99775923e-03 8.53376706e-05
+ 1.00700701e+00 6.77921687e-02 6.81602887e-03 8.14053828e-05
+ 1.01701702e+00 6.69893771e-02 6.63857161e-03 7.76464670e-05
+ 1.02702703e+00 6.61935387e-02 6.46530055e-03 7.40536701e-05
+ 1.03703704e+00 6.54046366e-02 6.29613018e-03 7.06200236e-05
+ 1.04704705e+00 6.46226530e-02 6.13097630e-03 6.73388330e-05
+ 1.05705706e+00 6.38475694e-02 5.96975611e-03 6.42036682e-05
+ 1.06706707e+00 6.30793667e-02 5.81238810e-03 6.12083536e-05
+ 1.07707708e+00 6.23180249e-02 5.65879213e-03 5.83469591e-05
+ 1.08708709e+00 6.15635234e-02 5.50888934e-03 5.56137909e-05
+ 1.09709710e+00 6.08158409e-02 5.36260219e-03 5.30033829e-05
+ 1.10710711e+00 6.00749552e-02 5.21985442e-03 5.05104881e-05
+ 1.11711712e+00 5.93408437e-02 5.08057107e-03 4.81300707e-05
+ 1.12712713e+00 5.86134830e-02 4.94467843e-03 4.58572983e-05
+ 1.13713714e+00 5.78928492e-02 4.81210407e-03 4.36875339e-05
+ 1.14714715e+00 5.71789176e-02 4.68277677e-03 4.16163288e-05
+ 1.15715716e+00 5.64716630e-02 4.55662658e-03 3.96394157e-05
+ 1.16716717e+00 5.57710596e-02 4.43358475e-03 3.77527015e-05
+ 1.17717718e+00 5.50770809e-02 4.31358372e-03 3.59522610e-05
+ 1.18718719e+00 5.43897001e-02 4.19655717e-03 3.42343300e-05
+ 1.19719720e+00 5.37088896e-02 4.08243991e-03 3.25952998e-05
+ 1.20720721e+00 5.30346214e-02 3.97116796e-03 3.10317108e-05
+ 1.21721722e+00 5.23668668e-02 3.86267847e-03 2.95402469e-05
+ 1.22722723e+00 5.17055968e-02 3.75690974e-03 2.81177298e-05
+ 1.23723724e+00 5.10507818e-02 3.65380120e-03 2.67611138e-05
+ 1.24724725e+00 5.04023918e-02 3.55329339e-03 2.54674807e-05
+ 1.25725726e+00 4.97603962e-02 3.45532795e-03 2.42340346e-05
+ 1.26726727e+00 4.91247641e-02 3.35984762e-03 2.30580974e-05
+ 1.27727728e+00 4.84954640e-02 3.26679619e-03 2.19371037e-05
+ 1.28728729e+00 4.78724640e-02 3.17611854e-03 2.08685970e-05
+ 1.29729730e+00 4.72557320e-02 3.08776058e-03 1.98502247e-05
+ 1.30730731e+00 4.66452352e-02 3.00166926e-03 1.88797345e-05
+ 1.31731732e+00 4.60409406e-02 2.91779253e-03 1.79549700e-05
+ 1.32732733e+00 4.54428147e-02 2.83607937e-03 1.70738672e-05
+ 1.33733734e+00 4.48508238e-02 2.75647975e-03 1.62344507e-05
+ 1.34734735e+00 4.42649338e-02 2.67894459e-03 1.54348299e-05
+ 1.35735736e+00 4.36851100e-02 2.60342582e-03 1.46731958e-05
+ 1.36736737e+00 4.31113178e-02 2.52987629e-03 1.39478177e-05
+ 1.37737738e+00 4.25435220e-02 2.45824978e-03 1.32570399e-05
+ 1.38738739e+00 4.19816871e-02 2.38850102e-03 1.25992787e-05
+ 1.39739740e+00 4.14257776e-02 2.32058563e-03 1.19730194e-05
+ 1.40740741e+00 4.08757572e-02 2.25446015e-03 1.13768135e-05
+ 1.41741742e+00 4.03315899e-02 2.19008197e-03 1.08092760e-05
+ 1.42742743e+00 3.97932391e-02 2.12740937e-03 1.02690829e-05
+ 1.43743744e+00 3.92606679e-02 2.06640149e-03 9.75496822e-06
+ 1.44744745e+00 3.87338395e-02 2.00701830e-03 9.26572216e-06
+ 1.45745746e+00 3.82127166e-02 1.94922061e-03 8.80018836e-06
+ 1.46746747e+00 3.76972618e-02 1.89297004e-03 8.35726181e-06
+ 1.47747748e+00 3.71874374e-02 1.83822902e-03 7.93588668e-06
+ 1.48748749e+00 3.66832056e-02 1.78496077e-03 7.53505424e-06
+ 1.49749750e+00 3.61845284e-02 1.73312928e-03 7.15380090e-06
+ 1.50750751e+00 3.56913676e-02 1.68269931e-03 6.79120625e-06
+ 1.51751752e+00 3.52036849e-02 1.63363638e-03 6.44639127e-06
+ 1.52752753e+00 3.47214418e-02 1.58590673e-03 6.11851652e-06
+ 1.53753754e+00 3.42445998e-02 1.53947736e-03 5.80678052e-06
+ 1.54754755e+00 3.37731199e-02 1.49431594e-03 5.51041806e-06
+ 1.55755756e+00 3.33069634e-02 1.45039089e-03 5.22869865e-06
+ 1.56756757e+00 3.28460913e-02 1.40767129e-03 4.96092506e-06
+ 1.57757758e+00 3.23904644e-02 1.36612690e-03 4.70643187e-06
+ 1.58758759e+00 3.19400436e-02 1.32572816e-03 4.46458404e-06
+ 1.59759760e+00 3.14947897e-02 1.28644616e-03 4.23477569e-06
+ 1.60760761e+00 3.10546632e-02 1.24825263e-03 4.01642872e-06
+ 1.61761762e+00 3.06196248e-02 1.21111993e-03 3.80899168e-06
+ 1.62762763e+00 3.01896350e-02 1.17502104e-03 3.61193857e-06
+ 1.63763764e+00 2.97646543e-02 1.13992956e-03 3.42476771e-06
+ 1.64764765e+00 2.93446430e-02 1.10581967e-03 3.24700069e-06
+ 1.65765766e+00 2.89295617e-02 1.07266615e-03 3.07818133e-06
+ 1.66766767e+00 2.85193707e-02 1.04044434e-03 2.91787471e-06
+ 1.67767768e+00 2.81140304e-02 1.00913017e-03 2.76566620e-06
+ 1.68768769e+00 2.77135011e-02 9.78700108e-04 2.62116060e-06
+ 1.69769770e+00 2.73177431e-02 9.49131158e-04 2.48398121e-06
+ 1.70770771e+00 2.69267168e-02 9.20400869e-04 2.35376906e-06
+ 1.71771772e+00 2.65403826e-02 8.92487309e-04 2.23018210e-06
+ 1.72772773e+00 2.61587009e-02 8.65369059e-04 2.11289440e-06
+ 1.73773774e+00 2.57816320e-02 8.39025202e-04 2.00159548e-06
+ 1.74774775e+00 2.54091364e-02 8.13435313e-04 1.89598958e-06
+ 1.75775776e+00 2.50411747e-02 7.88579452e-04 1.79579499e-06
+ 1.76776777e+00 2.46777072e-02 7.64438150e-04 1.70074343e-06
+ 1.77777778e+00 2.43186946e-02 7.40992403e-04 1.61057942e-06
+ 1.78778779e+00 2.39640976e-02 7.18223661e-04 1.52505970e-06
+ 1.79779780e+00 2.36138768e-02 6.96113819e-04 1.44395269e-06
+ 1.80780781e+00 2.32679930e-02 6.74645208e-04 1.36703792e-06
+ 1.81781782e+00 2.29264071e-02 6.53800587e-04 1.29410555e-06
+ 1.82782783e+00 2.25890799e-02 6.33563132e-04 1.22495584e-06
+ 1.83783784e+00 2.22559726e-02 6.13916431e-04 1.15939875e-06
+ 1.84784785e+00 2.19270462e-02 5.94844470e-04 1.09725341e-06
+ 1.85785786e+00 2.16022620e-02 5.76331629e-04 1.03834776e-06
+ 1.86786787e+00 2.12815813e-02 5.58362675e-04 9.82518094e-07
+ 1.87787788e+00 2.09649654e-02 5.40922746e-04 9.29608704e-07
+ 1.88788789e+00 2.06523760e-02 5.23997354e-04 8.79471483e-07
+ 1.89789790e+00 2.03437747e-02 5.07572366e-04 8.31965577e-07
+ 1.90790791e+00 2.00391233e-02 4.91634006e-04 7.86957044e-07
+ 1.91791792e+00 1.97383837e-02 4.76168840e-04 7.44318527e-07
+ 1.92792793e+00 1.94415180e-02 4.61163773e-04 7.03928945e-07
+ 1.93793794e+00 1.91484884e-02 4.46606039e-04 6.65673192e-07
+ 1.94794795e+00 1.88592572e-02 4.32483197e-04 6.29441857e-07
+ 1.95795796e+00 1.85737868e-02 4.18783118e-04 5.95130953e-07
+ 1.96796797e+00 1.82920399e-02 4.05493986e-04 5.62641656e-07
+ 1.97797798e+00 1.80139793e-02 3.92604283e-04 5.31880060e-07
+ 1.98798799e+00 1.77395680e-02 3.80102788e-04 5.02756942e-07
+ 1.99799800e+00 1.74687690e-02 3.67978568e-04 4.75187536e-07
+ 2.00800801e+00 1.72015455e-02 3.56220973e-04 4.49091321e-07
+ 2.01801802e+00 1.69378612e-02 3.44819627e-04 4.24391813e-07
+ 2.02802803e+00 1.66776795e-02 3.33764423e-04 4.01016371e-07
+ 2.03803804e+00 1.64209643e-02 3.23045518e-04 3.78896013e-07
+ 2.04804805e+00 1.61676794e-02 3.12653326e-04 3.57965237e-07
+ 2.05805806e+00 1.59177892e-02 3.02578512e-04 3.38161851e-07
+ 2.06806807e+00 1.56712579e-02 2.92811986e-04 3.19426815e-07
+ 2.07807808e+00 1.54280500e-02 2.83344896e-04 3.01704080e-07
+ 2.08808809e+00 1.51881302e-02 2.74168627e-04 2.84940452e-07
+ 2.09809810e+00 1.49514636e-02 2.65274791e-04 2.69085442e-07
+ 2.10810811e+00 1.47180151e-02 2.56655221e-04 2.54091139e-07
+ 2.11811812e+00 1.44877501e-02 2.48301970e-04 2.39912081e-07
+ 2.12812813e+00 1.42606341e-02 2.40207304e-04 2.26505135e-07
+ 2.13813814e+00 1.40366328e-02 2.32363695e-04 2.13829382e-07
+ 2.14814815e+00 1.38157121e-02 2.24763817e-04 2.01846004e-07
+ 2.15815816e+00 1.35978382e-02 2.17400544e-04 1.90518185e-07
+ 2.16816817e+00 1.33829773e-02 2.10266939e-04 1.79811007e-07
+ 2.17817818e+00 1.31710961e-02 2.03356258e-04 1.69691359e-07
+ 2.18818819e+00 1.29621614e-02 1.96661936e-04 1.60127842e-07
+ 2.19819820e+00 1.27561400e-02 1.90177590e-04 1.51090688e-07
+ 2.20820821e+00 1.25529992e-02 1.83897010e-04 1.42551676e-07
+ 2.21821822e+00 1.23527064e-02 1.77814157e-04 1.34484053e-07
+ 2.22822823e+00 1.21552292e-02 1.71923158e-04 1.26862464e-07
+ 2.23823824e+00 1.19605356e-02 1.66218303e-04 1.19662877e-07
+ 2.24824825e+00 1.17685935e-02 1.60694039e-04 1.12862518e-07
+ 2.25825826e+00 1.15793713e-02 1.55344965e-04 1.06439809e-07
+ 2.26826827e+00 1.13928376e-02 1.50165834e-04 1.00374303e-07
+ 2.27827828e+00 1.12089611e-02 1.45151543e-04 9.46466314e-08
+ 2.28828829e+00 1.10277108e-02 1.40297133e-04 8.92384452e-08
+ 2.29829830e+00 1.08490559e-02 1.35597781e-04 8.41323652e-08
+ 2.30830831e+00 1.06729658e-02 1.31048804e-04 7.93119313e-08
+ 2.31831832e+00 1.04994104e-02 1.26645647e-04 7.47615555e-08
+ 2.32832833e+00 1.03283594e-02 1.22383886e-04 7.04664775e-08
+ 2.33833834e+00 1.01597830e-02 1.18259222e-04 6.64127219e-08
+ 2.34834835e+00 9.99365163e-03 1.14267477e-04 6.25870577e-08
+ 2.35835836e+00 9.82993589e-03 1.10404592e-04 5.89769596e-08
+ 2.36836837e+00 9.66860664e-03 1.06666626e-04 5.55705721e-08
+ 2.37837838e+00 9.50963496e-03 1.03049748e-04 5.23566743e-08
+ 2.38838839e+00 9.35299218e-03 9.95502390e-05 4.93246470e-08
+ 2.39839840e+00 9.19864986e-03 9.61644852e-05 4.64644415e-08
+ 2.40840841e+00 9.04657979e-03 9.28889781e-05 4.37665497e-08
+ 2.41841842e+00 8.89675402e-03 8.97203102e-05 4.12219761e-08
+ 2.42842843e+00 8.74914481e-03 8.66551729e-05 3.88222107e-08
+ 2.43843844e+00 8.60372467e-03 8.36903534e-05 3.65592038e-08
+ 2.44844845e+00 8.46046635e-03 8.08227327e-05 3.44253416e-08
+ 2.45845846e+00 8.31934283e-03 7.80492826e-05 3.24134235e-08
+ 2.46846847e+00 8.18032734e-03 7.53670635e-05 3.05166401e-08
+ 2.47847848e+00 8.04339332e-03 7.27732221e-05 2.87285527e-08
+ 2.48848849e+00 7.90851449e-03 7.02649888e-05 2.70430735e-08
+ 2.49849850e+00 7.77566476e-03 6.78396757e-05 2.54544474e-08
+ 2.50850851e+00 7.64481830e-03 6.54946742e-05 2.39572337e-08
+ 2.51851852e+00 7.51594953e-03 6.32274529e-05 2.25462902e-08
+ 2.52852853e+00 7.38903307e-03 6.10355555e-05 2.12167564e-08
+ 2.53853854e+00 7.26404382e-03 5.89165988e-05 1.99640393e-08
+ 2.54854855e+00 7.14095687e-03 5.68682704e-05 1.87837984e-08
+ 2.55855856e+00 7.01974758e-03 5.48883273e-05 1.76719328e-08
+ 2.56856857e+00 6.90039153e-03 5.29745934e-05 1.66245678e-08
+ 2.57857858e+00 6.78286453e-03 5.11249579e-05 1.56380431e-08
+ 2.58858859e+00 6.66714264e-03 4.93373736e-05 1.47089011e-08
+ 2.59859860e+00 6.55320212e-03 4.76098548e-05 1.38338761e-08
+ 2.60860861e+00 6.44101950e-03 4.59404760e-05 1.30098838e-08
+ 2.61861862e+00 6.33057152e-03 4.43273699e-05 1.22340115e-08
+ 2.62862863e+00 6.22183515e-03 4.27687258e-05 1.15035089e-08
+ 2.63863864e+00 6.11478760e-03 4.12627881e-05 1.08157792e-08
+ 2.64864865e+00 6.00940631e-03 3.98078548e-05 1.01683708e-08
+ 2.65865866e+00 5.90566893e-03 3.84022755e-05 9.55896926e-09
+ 2.66866867e+00 5.80355336e-03 3.70444509e-05 8.98539013e-09
+ 2.67867868e+00 5.70303772e-03 3.57328301e-05 8.44557146e-09
+ 2.68868869e+00 5.60410034e-03 3.44659104e-05 7.93756736e-09
+ 2.69869870e+00 5.50671979e-03 3.32422352e-05 7.45954152e-09
+ 2.70870871e+00 5.41087487e-03 3.20603927e-05 7.00976124e-09
+ 2.71871872e+00 5.31654459e-03 3.09190149e-05 6.58659170e-09
+ 2.72872873e+00 5.22370819e-03 2.98167762e-05 6.18849060e-09
+ 2.73873874e+00 5.13234511e-03 2.87523923e-05 5.81400303e-09
+ 2.74874875e+00 5.04243505e-03 2.77246186e-05 5.46175665e-09
+ 2.75875876e+00 4.95395789e-03 2.67322495e-05 5.13045710e-09
+ 2.76876877e+00 4.86689374e-03 2.57741171e-05 4.81888371e-09
+ 2.77877878e+00 4.78122294e-03 2.48490899e-05 4.52588537e-09
+ 2.78878879e+00 4.69692604e-03 2.39560721e-05 4.25037671e-09
+ 2.79879880e+00 4.61398378e-03 2.30940022e-05 3.99133437e-09
+ 2.80880881e+00 4.53237714e-03 2.22618523e-05 3.74779359e-09
+ 2.81881882e+00 4.45208730e-03 2.14586268e-05 3.51884493e-09
+ 2.82882883e+00 4.37309567e-03 2.06833618e-05 3.30363116e-09
+ 2.83883884e+00 4.29538383e-03 1.99351236e-05 3.10134432e-09
+ 2.84884885e+00 4.21893360e-03 1.92130085e-05 2.91122300e-09
+ 2.85885886e+00 4.14372701e-03 1.85161414e-05 2.73254967e-09
+ 2.86886887e+00 4.06974626e-03 1.78436752e-05 2.56464824e-09
+ 2.87887888e+00 3.99697380e-03 1.71947896e-05 2.40688171e-09
+ 2.88888889e+00 3.92539224e-03 1.65686910e-05 2.25864997e-09
+ 2.89889890e+00 3.85498442e-03 1.59646107e-05 2.11938770e-09
+ 2.90890891e+00 3.78573338e-03 1.53818053e-05 1.98856241e-09
+ 2.91891892e+00 3.71762233e-03 1.48195548e-05 1.86567259e-09
+ 2.92892893e+00 3.65063472e-03 1.42771628e-05 1.75024589e-09
+ 2.93893894e+00 3.58475415e-03 1.37539552e-05 1.64183755e-09
+ 2.94894895e+00 3.51996445e-03 1.32492797e-05 1.54002875e-09
+ 2.95895896e+00 3.45624964e-03 1.27625054e-05 1.44442517e-09
+ 2.96896897e+00 3.39359390e-03 1.22930216e-05 1.35465557e-09
+ 2.97897898e+00 3.33198164e-03 1.18402377e-05 1.27037047e-09
+ 2.98898899e+00 3.27139743e-03 1.14035823e-05 1.19124093e-09
+ 2.99899900e+00 3.21182605e-03 1.09825027e-05 1.11695733e-09
+ 3.00900901e+00 3.15325245e-03 1.05764642e-05 1.04722829e-09
+ 3.01901902e+00 3.09566177e-03 1.01849497e-05 9.81779584e-10
+ 3.02902903e+00 3.03903933e-03 9.80745913e-06 9.20353197e-10
+ 3.03903904e+00 2.98337063e-03 9.44350885e-06 8.62706354e-10
+ 3.04904905e+00 2.92864136e-03 9.09263115e-06 8.08610649e-10
+ 3.05905906e+00 2.87483738e-03 8.75437380e-06 7.57851213e-10
+ 3.06906907e+00 2.82194474e-03 8.42829952e-06 7.10225928e-10
+ 3.07907908e+00 2.76994964e-03 8.11398555e-06 6.65544687e-10
+ 3.08908909e+00 2.71883847e-03 7.81102315e-06 6.23628693e-10
+ 3.09909910e+00 2.66859780e-03 7.51901720e-06 5.84309803e-10
+ 3.10910911e+00 2.61921436e-03 7.23758574e-06 5.47429902e-10
+ 3.11911912e+00 2.57067506e-03 6.96635956e-06 5.12840323e-10
+ 3.12912913e+00 2.52296695e-03 6.70498182e-06 4.80401290e-10
+ 3.13913914e+00 2.47607729e-03 6.45310762e-06 4.49981397e-10
+ 3.14914915e+00 2.42999347e-03 6.21040364e-06 4.21457119e-10
+ 3.15915916e+00 2.38470307e-03 5.97654778e-06 3.94712349e-10
+ 3.16916917e+00 2.34019379e-03 5.75122877e-06 3.69637958e-10
+ 3.17917918e+00 2.29645355e-03 5.53414585e-06 3.46131388e-10
+ 3.18918919e+00 2.25347038e-03 5.32500844e-06 3.24096263e-10
+ 3.19919920e+00 2.21123250e-03 5.12353578e-06 3.03442023e-10
+ 3.20920921e+00 2.16972825e-03 4.92945663e-06 2.84083581e-10
+ 3.21921922e+00 2.12894617e-03 4.74250898e-06 2.65940997e-10
+ 3.22922923e+00 2.08887492e-03 4.56243973e-06 2.48939175e-10
+ 3.23923924e+00 2.04950332e-03 4.38900439e-06 2.33007573e-10
+ 3.24924925e+00 2.01082034e-03 4.22196684e-06 2.18079935e-10
+ 3.25925926e+00 1.97281510e-03 4.06109903e-06 2.04094034e-10
+ 3.26926927e+00 1.93547687e-03 3.90618071e-06 1.90991429e-10
+ 3.27927928e+00 1.89879507e-03 3.75699919e-06 1.78717244e-10
+ 3.28928929e+00 1.86275925e-03 3.61334909e-06 1.67219953e-10
+ 3.29929930e+00 1.82735912e-03 3.47503212e-06 1.56451176e-10
+ 3.30930931e+00 1.79258450e-03 3.34185680e-06 1.46365498e-10
+ 3.31931932e+00 1.75842539e-03 3.21363827e-06 1.36920280e-10
+ 3.32932933e+00 1.72487191e-03 3.09019807e-06 1.28075504e-10
+ 3.33933934e+00 1.69191431e-03 2.97136391e-06 1.19793607e-10
+ 3.34934935e+00 1.65954298e-03 2.85696950e-06 1.12039335e-10
+ 3.35935936e+00 1.62774845e-03 2.74685431e-06 1.04779607e-10
+ 3.36936937e+00 1.59652139e-03 2.64086342e-06 9.79833771e-11
+ 3.37937938e+00 1.56585257e-03 2.53884727e-06 9.16215189e-11
+ 3.38938939e+00 1.53573293e-03 2.44066158e-06 8.56667037e-11
+ 3.39939940e+00 1.50615350e-03 2.34616706e-06 8.00932936e-11
+ 3.40940941e+00 1.47710547e-03 2.25522934e-06 7.48772387e-11
+ 3.41941942e+00 1.44858013e-03 2.16771875e-06 6.99959803e-11
+ 3.42942943e+00 1.42056892e-03 2.08351018e-06 6.54283600e-11
+ 3.43943944e+00 1.39306337e-03 2.00248291e-06 6.11545347e-11
+ 3.44944945e+00 1.36605516e-03 1.92452049e-06 5.71558959e-11
+ 3.45945946e+00 1.33953609e-03 1.84951058e-06 5.34149945e-11
+ 3.46946947e+00 1.31349804e-03 1.77734480e-06 4.99154696e-11
+ 3.47947948e+00 1.28793306e-03 1.70791862e-06 4.66419822e-11
+ 3.48948949e+00 1.26283328e-03 1.64113121e-06 4.35801523e-11
+ 3.49949950e+00 1.23819096e-03 1.57688532e-06 4.07164996e-11
+ 3.50950951e+00 1.21399846e-03 1.51508718e-06 3.80383890e-11
+ 3.51951952e+00 1.19024828e-03 1.45564632e-06 3.55339778e-11
+ 3.52952953e+00 1.16693300e-03 1.39847554e-06 3.31921671e-11
+ 3.53953954e+00 1.14404532e-03 1.34349073e-06 3.10025563e-11
+ 3.54954955e+00 1.12157805e-03 1.29061080e-06 2.89553990e-11
+ 3.55955956e+00 1.09952411e-03 1.23975755e-06 2.70415635e-11
+ 3.56956957e+00 1.07787651e-03 1.19085561e-06 2.52524942e-11
+ 3.57957958e+00 1.05662839e-03 1.14383231e-06 2.35801757e-11
+ 3.58958959e+00 1.03577298e-03 1.09861758e-06 2.20170999e-11
+ 3.59959960e+00 1.01530359e-03 1.05514390e-06 2.05562337e-11
+ 3.60960961e+00 9.95213674e-04 1.01334618e-06 1.91909900e-11
+ 3.61961962e+00 9.75496748e-04 9.73161665e-07 1.79151996e-11
+ 3.62962963e+00 9.56146443e-04 9.34529899e-07 1.67230853e-11
+ 3.63963964e+00 9.37156484e-04 8.97392601e-07 1.56092371e-11
+ 3.64964965e+00 9.18520691e-04 8.61693611e-07 1.45685897e-11
+ 3.65965966e+00 9.00232977e-04 8.27378809e-07 1.35964004e-11
+ 3.66966967e+00 8.82287352e-04 7.94396047e-07 1.26882294e-11
+ 3.67967968e+00 8.64677913e-04 7.62695078e-07 1.18399203e-11
+ 3.68968969e+00 8.47398852e-04 7.32227489e-07 1.10475826e-11
+ 3.69969970e+00 8.30444447e-04 7.02946639e-07 1.03075748e-11
+ 3.70970971e+00 8.13809068e-04 6.74807592e-07 9.61648895e-12
+ 3.71971972e+00 7.97487171e-04 6.47767062e-07 8.97113553e-12
+ 3.72972973e+00 7.81473296e-04 6.21783351e-07 8.36853002e-12
+ 3.73973974e+00 7.65762072e-04 5.96816295e-07 7.80587979e-12
+ 3.74974975e+00 7.50348209e-04 5.72827207e-07 7.28057196e-12
+ 3.75975976e+00 7.35226501e-04 5.49778829e-07 6.79016202e-12
+ 3.76976977e+00 7.20391823e-04 5.27635277e-07 6.33236315e-12
+ 3.77977978e+00 7.05839132e-04 5.06361993e-07 5.90503623e-12
+ 3.78978979e+00 6.91563464e-04 4.85925699e-07 5.50618040e-12
+ 3.79979980e+00 6.77559934e-04 4.66294352e-07 5.13392431e-12
+ 3.80980981e+00 6.63823733e-04 4.47437097e-07 4.78651783e-12
+ 3.81981982e+00 6.50350130e-04 4.29324225e-07 4.46232435e-12
+ 3.82982983e+00 6.37134470e-04 4.11927135e-07 4.15981349e-12
+ 3.83983984e+00 6.24172169e-04 3.95218290e-07 3.87755436e-12
+ 3.84984985e+00 6.11458721e-04 3.79171183e-07 3.61420915e-12
+ 3.85985986e+00 5.98989690e-04 3.63760294e-07 3.36852717e-12
+ 3.86986987e+00 5.86760710e-04 3.48961061e-07 3.13933929e-12
+ 3.87987988e+00 5.74767489e-04 3.34749841e-07 2.92555267e-12
+ 3.88988989e+00 5.63005802e-04 3.21103879e-07 2.72614587e-12
+ 3.89989990e+00 5.51471492e-04 3.08001274e-07 2.54016427e-12
+ 3.90990991e+00 5.40160471e-04 2.95420948e-07 2.36671571e-12
+ 3.91991992e+00 5.29068718e-04 2.83342618e-07 2.20496654e-12
+ 3.92992993e+00 5.18192277e-04 2.71746767e-07 2.05413778e-12
+ 3.93993994e+00 5.07527255e-04 2.60614612e-07 1.91350160e-12
+ 3.94994995e+00 4.97069826e-04 2.49928084e-07 1.78237804e-12
+ 3.95995996e+00 4.86816224e-04 2.39669794e-07 1.66013187e-12
+ 3.96996997e+00 4.76762748e-04 2.29823015e-07 1.54616969e-12
+ 3.97997998e+00 4.66905755e-04 2.20371655e-07 1.43993727e-12
+ 3.98998999e+00 4.57241665e-04 2.11300231e-07 1.34091692e-12
+ 4.00000000e+00 4.47766955e-04 2.02593852e-07 1.24862519e-12
diff --git a/report/figures/tracy-widom-approx/tracy_widom_compare.pdf b/report/figures/tracy-widom-approx/tracy_widom_compare.pdf
new file mode 100644
index 0000000..a68386f
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom_compare.pdf
diff --git a/report/figures/tracy-widom-approx/tracy_widom_compare.tex b/report/figures/tracy-widom-approx/tracy_widom_compare.tex
new file mode 100644
index 0000000..ed97668
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom_compare.tex
@@ -0,0 +1,128 @@
+% GNUPLOT: LaTeX picture with Postscript
+\begingroup
+  \makeatletter
+  \providecommand\color[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package color not loaded in conjunction with
+      terminal option `colourtext'%
+    }{See the gnuplot documentation for explanation.%
+    }{Either use 'blacktext' in gnuplot or load the package
+      color.sty in LaTeX.}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \@ifundefined{ifGPcolor}{%
+    \newif\ifGPcolor
+    \GPcolortrue
+  }{}%
+  \@ifundefined{ifGPblacktext}{%
+    \newif\ifGPblacktext
+    \GPblacktexttrue
+  }{}%
+  % define a \g@addto@macro without @ in the name:
+  \let\gplgaddtomacro\g@addto@macro
+  % define empty templates for all commands taking text:
+  \gdef\gplbacktext{}%
+  \gdef\gplfronttext{}%
+  \makeatother
+  \ifGPblacktext
+    % no textcolor at all
+    \def\colorrgb#1{}%
+    \def\colorgray#1{}%
+  \else
+    % gray or color?
+    \ifGPcolor
+      \def\colorrgb#1{\color[rgb]{#1}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
+      \expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
+      \expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
+      \expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
+      \expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
+      \expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
+      \expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
+      \expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
+      \expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
+    \else
+      % gray
+      \def\colorrgb#1{\color{black}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color{black}}%
+      \expandafter\def\csname LT1\endcsname{\color{black}}%
+      \expandafter\def\csname LT2\endcsname{\color{black}}%
+      \expandafter\def\csname LT3\endcsname{\color{black}}%
+      \expandafter\def\csname LT4\endcsname{\color{black}}%
+      \expandafter\def\csname LT5\endcsname{\color{black}}%
+      \expandafter\def\csname LT6\endcsname{\color{black}}%
+      \expandafter\def\csname LT7\endcsname{\color{black}}%
+      \expandafter\def\csname LT8\endcsname{\color{black}}%
+    \fi
+  \fi
+    \setlength{\unitlength}{0.0500bp}%
+    \ifx\gptboxheight\undefined%
+      \newlength{\gptboxheight}%
+      \newlength{\gptboxwidth}%
+      \newsavebox{\gptboxtext}%
+    \fi%
+    \setlength{\fboxrule}{0.5pt}%
+    \setlength{\fboxsep}{1pt}%
+    \definecolor{tbcol}{rgb}{1,1,1}%
+\begin{picture}(8640.00,4320.00)%
+    \gplgaddtomacro\gplbacktext{%
+      \csname LTb\endcsname%%
+      \put(1181,655){\makebox(0,0)[r]{\strut{}$0$}}%
+      \csname LTb\endcsname%%
+      \put(1181,1146){\makebox(0,0)[r]{\strut{}$0.05$}}%
+      \csname LTb\endcsname%%
+      \put(1181,1638){\makebox(0,0)[r]{\strut{}$0.1$}}%
+      \csname LTb\endcsname%%
+      \put(1181,2129){\makebox(0,0)[r]{\strut{}$0.15$}}%
+      \csname LTb\endcsname%%
+      \put(1181,2620){\makebox(0,0)[r]{\strut{}$0.2$}}%
+      \csname LTb\endcsname%%
+      \put(1181,3112){\makebox(0,0)[r]{\strut{}$0.25$}}%
+      \csname LTb\endcsname%%
+      \put(1181,3603){\makebox(0,0)[r]{\strut{}$0.3$}}%
+      \csname LTb\endcsname%%
+      \put(1181,4095){\makebox(0,0)[r]{\strut{}$0.35$}}%
+      \csname LTb\endcsname%%
+      \put(1293,450){\makebox(0,0){\strut{}$-6$}}%
+      \csname LTb\endcsname%%
+      \put(2499,450){\makebox(0,0){\strut{}$-4$}}%
+      \csname LTb\endcsname%%
+      \put(3706,450){\makebox(0,0){\strut{}$-2$}}%
+      \csname LTb\endcsname%%
+      \put(4913,450){\makebox(0,0){\strut{}$0$}}%
+      \csname LTb\endcsname%%
+      \put(6120,450){\makebox(0,0){\strut{}$2$}}%
+      \csname LTb\endcsname%%
+      \put(7326,450){\makebox(0,0){\strut{}$4$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+      \csname LTb\endcsname%%
+      \put(6685,3910){\makebox(0,0)[r]{\strut{}TW\textsubscript{1}}}%
+      \csname LTb\endcsname%%
+      \put(6685,3706){\makebox(0,0)[r]{\strut{}Normal}}%
+      \csname LTb\endcsname%%
+      \put(546,2375){\rotatebox{-270.00}{\makebox(0,0){\strut{}p(x)}}}%
+      \csname LTb\endcsname%%
+      \put(4309,143){\makebox(0,0){\strut{}x}}%
+    }%
+    \gplbacktext
+    \put(0,0){\includegraphics[width={432.00bp},height={216.00bp}]{tracy_widom_compare}}%
+    \gplfronttext
+  \end{picture}%
+\endgroup
diff --git a/report/figures/tracy-widom-approx/tracy_widom_normal.txt b/report/figures/tracy-widom-approx/tracy_widom_normal.txt
new file mode 100644
index 0000000..8e23a1a
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracy_widom_normal.txt
@@ -0,0 +1,1000 @@
+ -6.00000000e+00 5.23065849e-06 4.12181736e-04
+ -5.98998999e+00 5.57784813e-06 4.24196356e-04
+ -5.97997998e+00 5.94626332e-06 4.36533981e-04
+ -5.96996997e+00 6.33708317e-06 4.49202448e-04
+ -5.95995996e+00 6.75154515e-06 4.62209755e-04
+ -5.94994995e+00 7.19094755e-06 4.75564068e-04
+ -5.93993994e+00 7.65665209e-06 4.89273727e-04
+ -5.92992993e+00 8.15008651e-06 5.03347240e-04
+ -5.91991992e+00 8.67274740e-06 5.17793295e-04
+ -5.90990991e+00 9.22620298e-06 5.32620757e-04
+ -5.89989990e+00 9.81209611e-06 5.47838674e-04
+ -5.88988989e+00 1.04321472e-05 5.63456278e-04
+ -5.87987988e+00 1.10881576e-05 5.79482989e-04
+ -5.86986987e+00 1.17820123e-05 5.95928416e-04
+ -5.85985986e+00 1.25156840e-05 6.12802366e-04
+ -5.84984985e+00 1.32912360e-05 6.30114837e-04
+ -5.83983984e+00 1.41108258e-05 6.47876032e-04
+ -5.82982983e+00 1.49767090e-05 6.66096352e-04
+ -5.81981982e+00 1.58912429e-05 6.84786408e-04
+ -5.80980981e+00 1.68568902e-05 7.03957018e-04
+ -5.79979980e+00 1.78762235e-05 7.23619212e-04
+ -5.78978979e+00 1.89519288e-05 7.43784235e-04
+ -5.77977978e+00 2.00868101e-05 7.64463552e-04
+ -5.76976977e+00 2.12837936e-05 7.85668847e-04
+ -5.75975976e+00 2.25459323e-05 8.07412032e-04
+ -5.74974975e+00 2.38764102e-05 8.29705245e-04
+ -5.73973974e+00 2.52785477e-05 8.52560856e-04
+ -5.72972973e+00 2.67558055e-05 8.75991469e-04
+ -5.71971972e+00 2.83117905e-05 9.00009925e-04
+ -5.70970971e+00 2.99502603e-05 9.24629309e-04
+ -5.69969970e+00 3.16751286e-05 9.49862948e-04
+ -5.68968969e+00 3.34904705e-05 9.75724417e-04
+ -5.67967968e+00 3.54005280e-05 1.00222754e-03
+ -5.66966967e+00 3.74097158e-05 1.02938641e-03
+ -5.65965966e+00 3.95226266e-05 1.05721535e-03
+ -5.64964965e+00 4.17440377e-05 1.08572896e-03
+ -5.63963964e+00 4.40789163e-05 1.11494212e-03
+ -5.62962963e+00 4.65324262e-05 1.14486995e-03
+ -5.61961962e+00 4.91099338e-05 1.17552785e-03
+ -5.60960961e+00 5.18170146e-05 1.20693151e-03
+ -5.59959960e+00 5.46594601e-05 1.23909688e-03
+ -5.58958959e+00 5.76432840e-05 1.27204020e-03
+ -5.57957958e+00 6.07747297e-05 1.30577798e-03
+ -5.56956957e+00 6.40602767e-05 1.34032705e-03
+ -5.55955956e+00 6.75066484e-05 1.37570450e-03
+ -5.54954955e+00 7.11208186e-05 1.41192773e-03
+ -5.53953954e+00 7.49100199e-05 1.44901444e-03
+ -5.52952953e+00 7.88817506e-05 1.48698262e-03
+ -5.51951952e+00 8.30437826e-05 1.52585058e-03
+ -5.50950951e+00 8.74041696e-05 1.56563692e-03
+ -5.49949950e+00 9.19712545e-05 1.60636058e-03
+ -5.48948949e+00 9.67536784e-05 1.64804078e-03
+ -5.47947948e+00 1.01760388e-04 1.69069710e-03
+ -5.46946947e+00 1.07000645e-04 1.73434940e-03
+ -5.45945946e+00 1.12484033e-04 1.77901789e-03
+ -5.44944945e+00 1.18220469e-04 1.82472310e-03
+ -5.43943944e+00 1.24220210e-04 1.87148591e-03
+ -5.42942943e+00 1.30493863e-04 1.91932750e-03
+ -5.41941942e+00 1.37052391e-04 1.96826942e-03
+ -5.40940941e+00 1.43907130e-04 2.01833355e-03
+ -5.39939940e+00 1.51069790e-04 2.06954212e-03
+ -5.38938939e+00 1.58552468e-04 2.12191768e-03
+ -5.37937938e+00 1.66367658e-04 2.17548318e-03
+ -5.36936937e+00 1.74528261e-04 2.23026189e-03
+ -5.35935936e+00 1.83047594e-04 2.28627743e-03
+ -5.34934935e+00 1.91939400e-04 2.34355382e-03
+ -5.33933934e+00 2.01217857e-04 2.40211540e-03
+ -5.32932933e+00 2.10897591e-04 2.46198690e-03
+ -5.31931932e+00 2.20993684e-04 2.52319342e-03
+ -5.30930931e+00 2.31521686e-04 2.58576042e-03
+ -5.29929930e+00 2.42497624e-04 2.64971374e-03
+ -5.28928929e+00 2.53938013e-04 2.71507960e-03
+ -5.27927928e+00 2.65859868e-04 2.78188460e-03
+ -5.26926927e+00 2.78280713e-04 2.85015572e-03
+ -5.25925926e+00 2.91218591e-04 2.91992033e-03
+ -5.24924925e+00 3.04692080e-04 2.99120618e-03
+ -5.23923924e+00 3.18720297e-04 3.06404142e-03
+ -5.22922923e+00 3.33322915e-04 3.13845458e-03
+ -5.21921922e+00 3.48520170e-04 3.21447461e-03
+ -5.20920921e+00 3.64332875e-04 3.29213082e-03
+ -5.19919920e+00 3.80782428e-04 3.37145296e-03
+ -5.18918919e+00 3.97890827e-04 3.45247116e-03
+ -5.17917918e+00 4.15680679e-04 3.53521596e-03
+ -5.16916917e+00 4.34175211e-04 3.61971830e-03
+ -5.15915916e+00 4.53398282e-04 3.70600953e-03
+ -5.14914915e+00 4.73374395e-04 3.79412142e-03
+ -5.13913914e+00 4.94128707e-04 3.88408614e-03
+ -5.12912913e+00 5.15687040e-04 3.97593628e-03
+ -5.11911912e+00 5.38075895e-04 4.06970484e-03
+ -5.10910911e+00 5.61322459e-04 4.16542523e-03
+ -5.09909910e+00 5.85454622e-04 4.26313131e-03
+ -5.08908909e+00 6.10500981e-04 4.36285732e-03
+ -5.07907908e+00 6.36490856e-04 4.46463794e-03
+ -5.06906907e+00 6.63454301e-04 4.56850827e-03
+ -5.05905906e+00 6.91422113e-04 4.67450383e-03
+ -5.04904905e+00 7.20425844e-04 4.78266056e-03
+ -5.03903904e+00 7.50497811e-04 4.89301483e-03
+ -5.02902903e+00 7.81671107e-04 5.00560344e-03
+ -5.01901902e+00 8.13979615e-04 5.12046360e-03
+ -5.00900901e+00 8.47458011e-04 5.23763295e-03
+ -4.99899900e+00 8.82141782e-04 5.35714957e-03
+ -4.98898899e+00 9.18067232e-04 5.47905195e-03
+ -4.97897898e+00 9.55271491e-04 5.60337901e-03
+ -4.96896897e+00 9.93792531e-04 5.73017011e-03
+ -4.95895896e+00 1.03366917e-03 5.85946501e-03
+ -4.94894895e+00 1.07494108e-03 5.99130391e-03
+ -4.93893894e+00 1.11764880e-03 6.12572743e-03
+ -4.92892893e+00 1.16183376e-03 6.26277664e-03
+ -4.91891892e+00 1.20753824e-03 6.40249298e-03
+ -4.90890891e+00 1.25480545e-03 6.54491837e-03
+ -4.89889890e+00 1.30367949e-03 6.69009511e-03
+ -4.88888889e+00 1.35420536e-03 6.83806593e-03
+ -4.87887888e+00 1.40642898e-03 6.98887400e-03
+ -4.86886887e+00 1.46039720e-03 7.14256287e-03
+ -4.85885886e+00 1.51615781e-03 7.29917654e-03
+ -4.84884885e+00 1.57375953e-03 7.45875940e-03
+ -4.83883884e+00 1.63325202e-03 7.62135626e-03
+ -4.82882883e+00 1.69468592e-03 7.78701234e-03
+ -4.81881882e+00 1.75811279e-03 7.95577326e-03
+ -4.80880881e+00 1.82358519e-03 8.12768504e-03
+ -4.79879880e+00 1.89115662e-03 8.30279412e-03
+ -4.78878879e+00 1.96088158e-03 8.48114732e-03
+ -4.77877878e+00 2.03281554e-03 8.66279185e-03
+ -4.76876877e+00 2.10701495e-03 8.84777534e-03
+ -4.75875876e+00 2.18353725e-03 9.03614577e-03
+ -4.74874875e+00 2.26244087e-03 9.22795152e-03
+ -4.73873874e+00 2.34378522e-03 9.42324137e-03
+ -4.72872873e+00 2.42763074e-03 9.62206443e-03
+ -4.71871872e+00 2.51403884e-03 9.82447022e-03
+ -4.70870871e+00 2.60307192e-03 1.00305086e-02
+ -4.69869870e+00 2.69479341e-03 1.02402298e-02
+ -4.68868869e+00 2.78926772e-03 1.04536845e-02
+ -4.67867868e+00 2.88656026e-03 1.06709235e-02
+ -4.66866867e+00 2.98673745e-03 1.08919982e-02
+ -4.65865866e+00 3.08986671e-03 1.11169601e-02
+ -4.64864865e+00 3.19601643e-03 1.13458613e-02
+ -4.63863864e+00 3.30525602e-03 1.15787539e-02
+ -4.62862863e+00 3.41765588e-03 1.18156908e-02
+ -4.61861862e+00 3.53328738e-03 1.20567246e-02
+ -4.60860861e+00 3.65222290e-03 1.23019088e-02
+ -4.59859860e+00 3.77453577e-03 1.25512967e-02
+ -4.58858859e+00 3.90030031e-03 1.28049423e-02
+ -4.57857858e+00 4.02959181e-03 1.30628996e-02
+ -4.56856857e+00 4.16248651e-03 1.33252231e-02
+ -4.55855856e+00 4.29906161e-03 1.35919673e-02
+ -4.54854855e+00 4.43939527e-03 1.38631873e-02
+ -4.53853854e+00 4.58356655e-03 1.41389381e-02
+ -4.52852853e+00 4.73165547e-03 1.44192752e-02
+ -4.51851852e+00 4.88374296e-03 1.47042542e-02
+ -4.50850851e+00 5.03991086e-03 1.49939310e-02
+ -4.49849850e+00 5.20024189e-03 1.52883616e-02
+ -4.48848849e+00 5.36481967e-03 1.55876025e-02
+ -4.47847848e+00 5.53372868e-03 1.58917100e-02
+ -4.46846847e+00 5.70705428e-03 1.62007409e-02
+ -4.45845846e+00 5.88488265e-03 1.65147520e-02
+ -4.44844845e+00 6.06730080e-03 1.68338002e-02
+ -4.43843844e+00 6.25439656e-03 1.71579429e-02
+ -4.42842843e+00 6.44625856e-03 1.74872372e-02
+ -4.41841842e+00 6.64297620e-03 1.78217406e-02
+ -4.40840841e+00 6.84463964e-03 1.81615106e-02
+ -4.39839840e+00 7.05133978e-03 1.85066050e-02
+ -4.38838839e+00 7.26316826e-03 1.88570814e-02
+ -4.37837838e+00 7.48021741e-03 1.92129977e-02
+ -4.36836837e+00 7.70258024e-03 1.95744119e-02
+ -4.35835836e+00 7.93035042e-03 1.99413817e-02
+ -4.34834835e+00 8.16362225e-03 2.03139653e-02
+ -4.33833834e+00 8.40249067e-03 2.06922206e-02
+ -4.32832833e+00 8.64705117e-03 2.10762057e-02
+ -4.31831832e+00 8.89739983e-03 2.14659786e-02
+ -4.30830831e+00 9.15363327e-03 2.18615972e-02
+ -4.29829830e+00 9.41584862e-03 2.22631197e-02
+ -4.28828829e+00 9.68414347e-03 2.26706038e-02
+ -4.27827828e+00 9.95861590e-03 2.30841076e-02
+ -4.26826827e+00 1.02393644e-02 2.35036886e-02
+ -4.25825826e+00 1.05264879e-02 2.39294047e-02
+ -4.24824825e+00 1.08200856e-02 2.43613135e-02
+ -4.23823824e+00 1.11202571e-02 2.47994723e-02
+ -4.22822823e+00 1.14271024e-02 2.52439385e-02
+ -4.21821822e+00 1.17407215e-02 2.56947693e-02
+ -4.20820821e+00 1.20612150e-02 2.61520216e-02
+ -4.19819820e+00 1.23886834e-02 2.66157522e-02
+ -4.18818819e+00 1.27232276e-02 2.70860176e-02
+ -4.17817818e+00 1.30649484e-02 2.75628743e-02
+ -4.16816817e+00 1.34139469e-02 2.80463782e-02
+ -4.15815816e+00 1.37703242e-02 2.85365852e-02
+ -4.14814815e+00 1.41341813e-02 2.90335508e-02
+ -4.13813814e+00 1.45056195e-02 2.95373302e-02
+ -4.12812813e+00 1.48847397e-02 3.00479784e-02
+ -4.11811812e+00 1.52716428e-02 3.05655498e-02
+ -4.10810811e+00 1.56664298e-02 3.10900988e-02
+ -4.09809810e+00 1.60692013e-02 3.16216790e-02
+ -4.08808809e+00 1.64800576e-02 3.21603439e-02
+ -4.07807808e+00 1.68990991e-02 3.27061464e-02
+ -4.06806807e+00 1.73264255e-02 3.32591391e-02
+ -4.05805806e+00 1.77621364e-02 3.38193741e-02
+ -4.04804805e+00 1.82063309e-02 3.43869029e-02
+ -4.03803804e+00 1.86591079e-02 3.49617766e-02
+ -4.02802803e+00 1.91205654e-02 3.55440458e-02
+ -4.01801802e+00 1.95908013e-02 3.61337603e-02
+ -4.00800801e+00 2.00699127e-02 3.67309698e-02
+ -3.99799800e+00 2.05579962e-02 3.73357228e-02
+ -3.98798799e+00 2.10551477e-02 3.79480678e-02
+ -3.97797798e+00 2.15614623e-02 3.85680522e-02
+ -3.96796797e+00 2.20770345e-02 3.91957230e-02
+ -3.95795796e+00 2.26019580e-02 3.98311263e-02
+ -3.94794795e+00 2.31363254e-02 4.04743078e-02
+ -3.93793794e+00 2.36802288e-02 4.11253121e-02
+ -3.92792793e+00 2.42337589e-02 4.17841833e-02
+ -3.91791792e+00 2.47970059e-02 4.24509647e-02
+ -3.90790791e+00 2.53700586e-02 4.31256988e-02
+ -3.89789790e+00 2.59530047e-02 4.38084271e-02
+ -3.88788789e+00 2.65459310e-02 4.44991904e-02
+ -3.87787788e+00 2.71489230e-02 4.51980288e-02
+ -3.86786787e+00 2.77620648e-02 4.59049811e-02
+ -3.85785786e+00 2.83854394e-02 4.66200856e-02
+ -3.84784785e+00 2.90191283e-02 4.73433794e-02
+ -3.83783784e+00 2.96632118e-02 4.80748987e-02
+ -3.82782783e+00 3.03177686e-02 4.88146787e-02
+ -3.81781782e+00 3.09828759e-02 4.95627536e-02
+ -3.80780781e+00 3.16586095e-02 5.03191566e-02
+ -3.79779780e+00 3.23450433e-02 5.10839198e-02
+ -3.78778779e+00 3.30422500e-02 5.18570742e-02
+ -3.77777778e+00 3.37503001e-02 5.26386497e-02
+ -3.76776777e+00 3.44692627e-02 5.34286751e-02
+ -3.75775776e+00 3.51992050e-02 5.42271780e-02
+ -3.74774775e+00 3.59401924e-02 5.50341848e-02
+ -3.73773774e+00 3.66922882e-02 5.58497208e-02
+ -3.72772773e+00 3.74555539e-02 5.66738099e-02
+ -3.71771772e+00 3.82300491e-02 5.75064749e-02
+ -3.70770771e+00 3.90158312e-02 5.83477373e-02
+ -3.69769770e+00 3.98129554e-02 5.91976172e-02
+ -3.68768769e+00 4.06214750e-02 6.00561333e-02
+ -3.67767768e+00 4.14414410e-02 6.09233033e-02
+ -3.66766767e+00 4.22729021e-02 6.17991431e-02
+ -3.65765766e+00 4.31159047e-02 6.26836675e-02
+ -3.64764765e+00 4.39704929e-02 6.35768898e-02
+ -3.63763764e+00 4.48367086e-02 6.44788217e-02
+ -3.62762763e+00 4.57145909e-02 6.53894736e-02
+ -3.61761762e+00 4.66041766e-02 6.63088543e-02
+ -3.60760761e+00 4.75055001e-02 6.72369713e-02
+ -3.59759760e+00 4.84185931e-02 6.81738302e-02
+ -3.58758759e+00 4.93434846e-02 6.91194354e-02
+ -3.57757758e+00 5.02802012e-02 7.00737894e-02
+ -3.56756757e+00 5.12287664e-02 7.10368933e-02
+ -3.55755756e+00 5.21892015e-02 7.20087465e-02
+ -3.54754755e+00 5.31615245e-02 7.29893466e-02
+ -3.53753754e+00 5.41457510e-02 7.39786899e-02
+ -3.52752753e+00 5.51418933e-02 7.49767706e-02
+ -3.51751752e+00 5.61499613e-02 7.59835814e-02
+ -3.50750751e+00 5.71699615e-02 7.69991132e-02
+ -3.49749750e+00 5.82018977e-02 7.80233551e-02
+ -3.48748749e+00 5.92457706e-02 7.90562945e-02
+ -3.47747748e+00 6.03015779e-02 8.00979170e-02
+ -3.46746747e+00 6.13693142e-02 8.11482062e-02
+ -3.45745746e+00 6.24489710e-02 8.22071440e-02
+ -3.44744745e+00 6.35405364e-02 8.32747105e-02
+ -3.43743744e+00 6.46439958e-02 8.43508838e-02
+ -3.42742743e+00 6.57593311e-02 8.54356401e-02
+ -3.41741742e+00 6.68865208e-02 8.65289538e-02
+ -3.40740741e+00 6.80255406e-02 8.76307971e-02
+ -3.39739740e+00 6.91763624e-02 8.87411405e-02
+ -3.38738739e+00 7.03389552e-02 8.98599525e-02
+ -3.37737738e+00 7.15132844e-02 9.09871995e-02
+ -3.36736737e+00 7.26993120e-02 9.21228459e-02
+ -3.35735736e+00 7.38969969e-02 9.32668541e-02
+ -3.34734735e+00 7.51062943e-02 9.44191845e-02
+ -3.33733734e+00 7.63271560e-02 9.55797954e-02
+ -3.32732733e+00 7.75595306e-02 9.67486431e-02
+ -3.31731732e+00 7.88033629e-02 9.79256816e-02
+ -3.30730731e+00 8.00585945e-02 9.91108632e-02
+ -3.29729730e+00 8.13251632e-02 1.00304138e-01
+ -3.28728729e+00 8.26030036e-02 1.01505453e-01
+ -3.27727728e+00 8.38920466e-02 1.02714754e-01
+ -3.26726727e+00 8.51922196e-02 1.03931986e-01
+ -3.25725726e+00 8.65034464e-02 1.05157089e-01
+ -3.24724725e+00 8.78256473e-02 1.06390002e-01
+ -3.23723724e+00 8.91587391e-02 1.07630662e-01
+ -3.22722723e+00 9.05026350e-02 1.08879005e-01
+ -3.21721722e+00 9.18572446e-02 1.10134963e-01
+ -3.20720721e+00 9.32224739e-02 1.11398467e-01
+ -3.19719720e+00 9.45982253e-02 1.12669443e-01
+ -3.18718719e+00 9.59843979e-02 1.13947819e-01
+ -3.17717718e+00 9.73808868e-02 1.15233519e-01
+ -3.16716717e+00 9.87875840e-02 1.16526462e-01
+ -3.15715716e+00 1.00204377e-01 1.17826570e-01
+ -3.14714715e+00 1.01631152e-01 1.19133759e-01
+ -3.13713714e+00 1.03067789e-01 1.20447943e-01
+ -3.12712713e+00 1.04514165e-01 1.21769035e-01
+ -3.11711712e+00 1.05970155e-01 1.23096946e-01
+ -3.10710711e+00 1.07435629e-01 1.24431582e-01
+ -3.09709710e+00 1.08910455e-01 1.25772851e-01
+ -3.08708709e+00 1.10394496e-01 1.27120655e-01
+ -3.07707708e+00 1.11887611e-01 1.28474895e-01
+ -3.06706707e+00 1.13389658e-01 1.29835471e-01
+ -3.05705706e+00 1.14900490e-01 1.31202278e-01
+ -3.04704705e+00 1.16419956e-01 1.32575212e-01
+ -3.03703704e+00 1.17947903e-01 1.33954164e-01
+ -3.02702703e+00 1.19484174e-01 1.35339025e-01
+ -3.01701702e+00 1.21028609e-01 1.36729681e-01
+ -3.00700701e+00 1.22581044e-01 1.38126019e-01
+ -2.99699700e+00 1.24141312e-01 1.39527920e-01
+ -2.98698699e+00 1.25709243e-01 1.40935267e-01
+ -2.97697698e+00 1.27284663e-01 1.42347937e-01
+ -2.96696697e+00 1.28867397e-01 1.43765808e-01
+ -2.95695696e+00 1.30457264e-01 1.45188753e-01
+ -2.94694695e+00 1.32054082e-01 1.46616644e-01
+ -2.93693694e+00 1.33657665e-01 1.48049351e-01
+ -2.92692693e+00 1.35267824e-01 1.49486743e-01
+ -2.91691692e+00 1.36884367e-01 1.50928683e-01
+ -2.90690691e+00 1.38507098e-01 1.52375036e-01
+ -2.89689690e+00 1.40135821e-01 1.53825662e-01
+ -2.88688689e+00 1.41770335e-01 1.55280421e-01
+ -2.87687688e+00 1.43410436e-01 1.56739170e-01
+ -2.86686687e+00 1.45055917e-01 1.58201763e-01
+ -2.85685686e+00 1.46706571e-01 1.59668053e-01
+ -2.84684685e+00 1.48362185e-01 1.61137891e-01
+ -2.83683684e+00 1.50022544e-01 1.62611126e-01
+ -2.82682683e+00 1.51687433e-01 1.64087603e-01
+ -2.81681682e+00 1.53356631e-01 1.65567168e-01
+ -2.80680681e+00 1.55029917e-01 1.67049663e-01
+ -2.79679680e+00 1.56707066e-01 1.68534929e-01
+ -2.78678679e+00 1.58387852e-01 1.70022805e-01
+ -2.77677678e+00 1.60072046e-01 1.71513127e-01
+ -2.76676677e+00 1.61759416e-01 1.73005730e-01
+ -2.75675676e+00 1.63449729e-01 1.74500447e-01
+ -2.74674675e+00 1.65142750e-01 1.75997110e-01
+ -2.73673674e+00 1.66838241e-01 1.77495547e-01
+ -2.72672673e+00 1.68535962e-01 1.78995586e-01
+ -2.71671672e+00 1.70235672e-01 1.80497054e-01
+ -2.70670671e+00 1.71937128e-01 1.81999773e-01
+ -2.69669670e+00 1.73640084e-01 1.83503567e-01
+ -2.68668669e+00 1.75344293e-01 1.85008257e-01
+ -2.67667668e+00 1.77049506e-01 1.86513660e-01
+ -2.66666667e+00 1.78755475e-01 1.88019595e-01
+ -2.65665666e+00 1.80461945e-01 1.89525877e-01
+ -2.64664665e+00 1.82168666e-01 1.91032321e-01
+ -2.63663664e+00 1.83875381e-01 1.92538739e-01
+ -2.62662663e+00 1.85581835e-01 1.94044944e-01
+ -2.61661662e+00 1.87287770e-01 1.95550744e-01
+ -2.60660661e+00 1.88992929e-01 1.97055947e-01
+ -2.59659660e+00 1.90697052e-01 1.98560363e-01
+ -2.58658659e+00 1.92399877e-01 2.00063795e-01
+ -2.57657658e+00 1.94101145e-01 2.01566048e-01
+ -2.56656657e+00 1.95800591e-01 2.03066926e-01
+ -2.55655656e+00 1.97497954e-01 2.04566231e-01
+ -2.54654655e+00 1.99192969e-01 2.06063763e-01
+ -2.53653654e+00 2.00885372e-01 2.07559322e-01
+ -2.52652653e+00 2.02574896e-01 2.09052707e-01
+ -2.51651652e+00 2.04261278e-01 2.10543716e-01
+ -2.50650651e+00 2.05944250e-01 2.12032144e-01
+ -2.49649650e+00 2.07623546e-01 2.13517788e-01
+ -2.48648649e+00 2.09298899e-01 2.15000441e-01
+ -2.47647648e+00 2.10970043e-01 2.16479899e-01
+ -2.46646647e+00 2.12636710e-01 2.17955953e-01
+ -2.45645646e+00 2.14298633e-01 2.19428397e-01
+ -2.44644645e+00 2.15955545e-01 2.20897021e-01
+ -2.43643644e+00 2.17607179e-01 2.22361616e-01
+ -2.42642643e+00 2.19253269e-01 2.23821973e-01
+ -2.41641642e+00 2.20893547e-01 2.25277881e-01
+ -2.40640641e+00 2.22527748e-01 2.26729129e-01
+ -2.39639640e+00 2.24155606e-01 2.28175506e-01
+ -2.38638639e+00 2.25776855e-01 2.29616799e-01
+ -2.37637638e+00 2.27391232e-01 2.31052796e-01
+ -2.36636637e+00 2.28998471e-01 2.32483285e-01
+ -2.35635636e+00 2.30598310e-01 2.33908053e-01
+ -2.34634635e+00 2.32190486e-01 2.35326886e-01
+ -2.33633634e+00 2.33774738e-01 2.36739572e-01
+ -2.32632633e+00 2.35350805e-01 2.38145896e-01
+ -2.31631632e+00 2.36918428e-01 2.39545645e-01
+ -2.30630631e+00 2.38477347e-01 2.40938606e-01
+ -2.29629630e+00 2.40027307e-01 2.42324564e-01
+ -2.28628629e+00 2.41568050e-01 2.43703307e-01
+ -2.27627628e+00 2.43099322e-01 2.45074620e-01
+ -2.26626627e+00 2.44620871e-01 2.46438292e-01
+ -2.25625626e+00 2.46132443e-01 2.47794108e-01
+ -2.24624625e+00 2.47633790e-01 2.49141856e-01
+ -2.23623624e+00 2.49124662e-01 2.50481324e-01
+ -2.22622623e+00 2.50604813e-01 2.51812300e-01
+ -2.21621622e+00 2.52073998e-01 2.53134573e-01
+ -2.20620621e+00 2.53531973e-01 2.54447931e-01
+ -2.19619620e+00 2.54978497e-01 2.55752164e-01
+ -2.18618619e+00 2.56413332e-01 2.57047062e-01
+ -2.17617618e+00 2.57836239e-01 2.58332417e-01
+ -2.16616617e+00 2.59246984e-01 2.59608019e-01
+ -2.15615616e+00 2.60645333e-01 2.60873662e-01
+ -2.14614615e+00 2.62031057e-01 2.62129139e-01
+ -2.13613614e+00 2.63403926e-01 2.63374244e-01
+ -2.12612613e+00 2.64763715e-01 2.64608772e-01
+ -2.11611612e+00 2.66110200e-01 2.65832519e-01
+ -2.10610611e+00 2.67443161e-01 2.67045283e-01
+ -2.09609610e+00 2.68762378e-01 2.68246862e-01
+ -2.08608609e+00 2.70067637e-01 2.69437056e-01
+ -2.07607608e+00 2.71358723e-01 2.70615664e-01
+ -2.06606607e+00 2.72635428e-01 2.71782491e-01
+ -2.05605606e+00 2.73897542e-01 2.72937338e-01
+ -2.04604605e+00 2.75144862e-01 2.74080011e-01
+ -2.03603604e+00 2.76377186e-01 2.75210317e-01
+ -2.02602603e+00 2.77594315e-01 2.76328062e-01
+ -2.01601602e+00 2.78796053e-01 2.77433057e-01
+ -2.00600601e+00 2.79982208e-01 2.78525112e-01
+ -1.99599600e+00 2.81152590e-01 2.79604040e-01
+ -1.98598599e+00 2.82307013e-01 2.80669655e-01
+ -1.97597598e+00 2.83445293e-01 2.81721774e-01
+ -1.96596597e+00 2.84567251e-01 2.82760215e-01
+ -1.95595596e+00 2.85672710e-01 2.83784798e-01
+ -1.94594595e+00 2.86761497e-01 2.84795343e-01
+ -1.93593594e+00 2.87833443e-01 2.85791677e-01
+ -1.92592593e+00 2.88888380e-01 2.86773623e-01
+ -1.91591592e+00 2.89926147e-01 2.87741011e-01
+ -1.90590591e+00 2.90946583e-01 2.88693669e-01
+ -1.89589590e+00 2.91949534e-01 2.89631432e-01
+ -1.88588589e+00 2.92934847e-01 2.90554132e-01
+ -1.87587588e+00 2.93902373e-01 2.91461607e-01
+ -1.86586587e+00 2.94851968e-01 2.92353697e-01
+ -1.85585586e+00 2.95783490e-01 2.93230242e-01
+ -1.84584585e+00 2.96696803e-01 2.94091087e-01
+ -1.83583584e+00 2.97591772e-01 2.94936078e-01
+ -1.82582583e+00 2.98468268e-01 2.95765063e-01
+ -1.81581582e+00 2.99326165e-01 2.96577896e-01
+ -1.80580581e+00 3.00165341e-01 2.97374429e-01
+ -1.79579580e+00 3.00985677e-01 2.98154520e-01
+ -1.78578579e+00 3.01787059e-01 2.98918028e-01
+ -1.77577578e+00 3.02569377e-01 2.99664815e-01
+ -1.76576577e+00 3.03332524e-01 3.00394747e-01
+ -1.75575576e+00 3.04076397e-01 3.01107691e-01
+ -1.74574575e+00 3.04800899e-01 3.01803518e-01
+ -1.73573574e+00 3.05505934e-01 3.02482101e-01
+ -1.72572573e+00 3.06191412e-01 3.03143318e-01
+ -1.71571572e+00 3.06857246e-01 3.03787047e-01
+ -1.70570571e+00 3.07503354e-01 3.04413172e-01
+ -1.69569570e+00 3.08129657e-01 3.05021577e-01
+ -1.68568569e+00 3.08736082e-01 3.05612152e-01
+ -1.67567568e+00 3.09322557e-01 3.06184788e-01
+ -1.66566567e+00 3.09889016e-01 3.06739380e-01
+ -1.65565566e+00 3.10435397e-01 3.07275827e-01
+ -1.64564565e+00 3.10961643e-01 3.07794029e-01
+ -1.63563564e+00 3.11467698e-01 3.08293892e-01
+ -1.62562563e+00 3.11953513e-01 3.08775323e-01
+ -1.61561562e+00 3.12419043e-01 3.09238233e-01
+ -1.60560561e+00 3.12864244e-01 3.09682537e-01
+ -1.59559560e+00 3.13289080e-01 3.10108153e-01
+ -1.58558559e+00 3.13693517e-01 3.10515002e-01
+ -1.57557558e+00 3.14077525e-01 3.10903008e-01
+ -1.56556557e+00 3.14441079e-01 3.11272100e-01
+ -1.55555556e+00 3.14784157e-01 3.11622209e-01
+ -1.54554555e+00 3.15106741e-01 3.11953270e-01
+ -1.53553554e+00 3.15408819e-01 3.12265221e-01
+ -1.52552553e+00 3.15690381e-01 3.12558006e-01
+ -1.51551552e+00 3.15951422e-01 3.12831568e-01
+ -1.50550551e+00 3.16191940e-01 3.13085858e-01
+ -1.49549550e+00 3.16411937e-01 3.13320827e-01
+ -1.48548549e+00 3.16611421e-01 3.13536432e-01
+ -1.47547548e+00 3.16790402e-01 3.13732633e-01
+ -1.46546547e+00 3.16948894e-01 3.13909394e-01
+ -1.45545546e+00 3.17086916e-01 3.14066680e-01
+ -1.44544545e+00 3.17204489e-01 3.14204464e-01
+ -1.43543544e+00 3.17301640e-01 3.14322718e-01
+ -1.42542543e+00 3.17378399e-01 3.14421422e-01
+ -1.41541542e+00 3.17434799e-01 3.14500556e-01
+ -1.40540541e+00 3.17470878e-01 3.14560106e-01
+ -1.39539540e+00 3.17486677e-01 3.14600060e-01
+ -1.38538539e+00 3.17482242e-01 3.14620412e-01
+ -1.37537538e+00 3.17457620e-01 3.14621157e-01
+ -1.36536537e+00 3.17412865e-01 3.14602295e-01
+ -1.35535536e+00 3.17348031e-01 3.14563830e-01
+ -1.34534535e+00 3.17263180e-01 3.14505769e-01
+ -1.33533534e+00 3.17158373e-01 3.14428123e-01
+ -1.32532533e+00 3.17033679e-01 3.14330906e-01
+ -1.31531532e+00 3.16889166e-01 3.14214137e-01
+ -1.30530531e+00 3.16724909e-01 3.14077837e-01
+ -1.29529530e+00 3.16540984e-01 3.13922032e-01
+ -1.28528529e+00 3.16337473e-01 3.13746750e-01
+ -1.27527528e+00 3.16114460e-01 3.13552025e-01
+ -1.26526527e+00 3.15872030e-01 3.13337893e-01
+ -1.25525526e+00 3.15610276e-01 3.13104394e-01
+ -1.24524525e+00 3.15329290e-01 3.12851571e-01
+ -1.23523524e+00 3.15029171e-01 3.12579472e-01
+ -1.22522523e+00 3.14710017e-01 3.12288147e-01
+ -1.21521522e+00 3.14371932e-01 3.11977650e-01
+ -1.20520521e+00 3.14015022e-01 3.11648039e-01
+ -1.19519520e+00 3.13639397e-01 3.11299375e-01
+ -1.18518519e+00 3.13245169e-01 3.10931724e-01
+ -1.17517518e+00 3.12832453e-01 3.10545153e-01
+ -1.16516517e+00 3.12401368e-01 3.10139733e-01
+ -1.15515516e+00 3.11952034e-01 3.09715541e-01
+ -1.14514515e+00 3.11484575e-01 3.09272655e-01
+ -1.13513514e+00 3.10999118e-01 3.08811155e-01
+ -1.12512513e+00 3.10495792e-01 3.08331129e-01
+ -1.11511512e+00 3.09974728e-01 3.07832664e-01
+ -1.10510511e+00 3.09436062e-01 3.07315852e-01
+ -1.09509510e+00 3.08879931e-01 3.06780789e-01
+ -1.08508509e+00 3.08306473e-01 3.06227572e-01
+ -1.07507508e+00 3.07715831e-01 3.05656303e-01
+ -1.06506507e+00 3.07108150e-01 3.05067088e-01
+ -1.05505506e+00 3.06483577e-01 3.04460034e-01
+ -1.04504505e+00 3.05842259e-01 3.03835252e-01
+ -1.03503504e+00 3.05184350e-01 3.03192857e-01
+ -1.02502503e+00 3.04510001e-01 3.02532965e-01
+ -1.01501502e+00 3.03819370e-01 3.01855697e-01
+ -1.00500501e+00 3.03112613e-01 3.01161176e-01
+ -9.94994995e-01 3.02389891e-01 3.00449529e-01
+ -9.84984985e-01 3.01651366e-01 2.99720884e-01
+ -9.74974975e-01 3.00897200e-01 2.98975373e-01
+ -9.64964965e-01 3.00127561e-01 2.98213131e-01
+ -9.54954955e-01 2.99342615e-01 2.97434295e-01
+ -9.44944945e-01 2.98542532e-01 2.96639007e-01
+ -9.34934935e-01 2.97727482e-01 2.95827408e-01
+ -9.24924925e-01 2.96897639e-01 2.94999644e-01
+ -9.14914915e-01 2.96053176e-01 2.94155865e-01
+ -9.04904905e-01 2.95194270e-01 2.93296219e-01
+ -8.94894895e-01 2.94321097e-01 2.92420862e-01
+ -8.84884885e-01 2.93433838e-01 2.91529948e-01
+ -8.74874875e-01 2.92532671e-01 2.90623637e-01
+ -8.64864865e-01 2.91617778e-01 2.89702088e-01
+ -8.54854855e-01 2.90689343e-01 2.88765464e-01
+ -8.44844845e-01 2.89747549e-01 2.87813932e-01
+ -8.34834835e-01 2.88792582e-01 2.86847658e-01
+ -8.24824825e-01 2.87824629e-01 2.85866812e-01
+ -8.14814815e-01 2.86843875e-01 2.84871566e-01
+ -8.04804805e-01 2.85850511e-01 2.83862094e-01
+ -7.94794795e-01 2.84844726e-01 2.82838572e-01
+ -7.84784785e-01 2.83826710e-01 2.81801178e-01
+ -7.74774775e-01 2.82796654e-01 2.80750092e-01
+ -7.64764765e-01 2.81754751e-01 2.79685496e-01
+ -7.54754755e-01 2.80701193e-01 2.78607573e-01
+ -7.44744745e-01 2.79636175e-01 2.77516510e-01
+ -7.34734735e-01 2.78559890e-01 2.76412492e-01
+ -7.24724725e-01 2.77472533e-01 2.75295709e-01
+ -7.14714715e-01 2.76374300e-01 2.74166351e-01
+ -7.04704705e-01 2.75265387e-01 2.73024611e-01
+ -6.94694695e-01 2.74145990e-01 2.71870682e-01
+ -6.84684685e-01 2.73016306e-01 2.70704759e-01
+ -6.74674675e-01 2.71876532e-01 2.69527039e-01
+ -6.64664665e-01 2.70726866e-01 2.68337719e-01
+ -6.54654655e-01 2.69567505e-01 2.67136998e-01
+ -6.44644645e-01 2.68398648e-01 2.65925077e-01
+ -6.34634635e-01 2.67220492e-01 2.64702158e-01
+ -6.24624625e-01 2.66033237e-01 2.63468442e-01
+ -6.14614615e-01 2.64837079e-01 2.62224134e-01
+ -6.04604605e-01 2.63632218e-01 2.60969438e-01
+ -5.94594595e-01 2.62418853e-01 2.59704560e-01
+ -5.84584585e-01 2.61197180e-01 2.58429707e-01
+ -5.74574575e-01 2.59967399e-01 2.57145087e-01
+ -5.64564565e-01 2.58729707e-01 2.55850906e-01
+ -5.54554555e-01 2.57484303e-01 2.54547375e-01
+ -5.44544545e-01 2.56231383e-01 2.53234704e-01
+ -5.34534535e-01 2.54971145e-01 2.51913101e-01
+ -5.24524525e-01 2.53703787e-01 2.50582779e-01
+ -5.14514515e-01 2.52429504e-01 2.49243949e-01
+ -5.04504505e-01 2.51148493e-01 2.47896823e-01
+ -4.94494494e-01 2.49860949e-01 2.46541612e-01
+ -4.84484484e-01 2.48567068e-01 2.45178531e-01
+ -4.74474474e-01 2.47267044e-01 2.43807790e-01
+ -4.64464464e-01 2.45961071e-01 2.42429605e-01
+ -4.54454454e-01 2.44649344e-01 2.41044187e-01
+ -4.44444444e-01 2.43332054e-01 2.39651751e-01
+ -4.34434434e-01 2.42009394e-01 2.38252510e-01
+ -4.24424424e-01 2.40681555e-01 2.36846678e-01
+ -4.14414414e-01 2.39348728e-01 2.35434469e-01
+ -4.04404404e-01 2.38011102e-01 2.34016095e-01
+ -3.94394394e-01 2.36668867e-01 2.32591771e-01
+ -3.84384384e-01 2.35322211e-01 2.31161709e-01
+ -3.74374374e-01 2.33971320e-01 2.29726123e-01
+ -3.64364364e-01 2.32616382e-01 2.28285225e-01
+ -3.54354354e-01 2.31257581e-01 2.26839227e-01
+ -3.44344344e-01 2.29895102e-01 2.25388342e-01
+ -3.34334334e-01 2.28529128e-01 2.23932781e-01
+ -3.24324324e-01 2.27159841e-01 2.22472755e-01
+ -3.14314314e-01 2.25787423e-01 2.21008474e-01
+ -3.04304304e-01 2.24412052e-01 2.19540149e-01
+ -2.94294294e-01 2.23033909e-01 2.18067988e-01
+ -2.84284284e-01 2.21653170e-01 2.16592201e-01
+ -2.74274274e-01 2.20270012e-01 2.15112995e-01
+ -2.64264264e-01 2.18884611e-01 2.13630577e-01
+ -2.54254254e-01 2.17497139e-01 2.12145153e-01
+ -2.44244244e-01 2.16107770e-01 2.10656929e-01
+ -2.34234234e-01 2.14716675e-01 2.09166110e-01
+ -2.24224224e-01 2.13324024e-01 2.07672899e-01
+ -2.14214214e-01 2.11929986e-01 2.06177497e-01
+ -2.04204204e-01 2.10534727e-01 2.04680108e-01
+ -1.94194194e-01 2.09138414e-01 2.03180931e-01
+ -1.84184184e-01 2.07741210e-01 2.01680166e-01
+ -1.74174174e-01 2.06343279e-01 2.00178010e-01
+ -1.64164164e-01 2.04944783e-01 1.98674660e-01
+ -1.54154154e-01 2.03545881e-01 1.97170313e-01
+ -1.44144144e-01 2.02146731e-01 1.95665162e-01
+ -1.34134134e-01 2.00747490e-01 1.94159401e-01
+ -1.24124124e-01 1.99348315e-01 1.92653221e-01
+ -1.14114114e-01 1.97949358e-01 1.91146812e-01
+ -1.04104104e-01 1.96550771e-01 1.89640363e-01
+ -9.40940941e-02 1.95152706e-01 1.88134062e-01
+ -8.40840841e-02 1.93755312e-01 1.86628095e-01
+ -7.40740741e-02 1.92358735e-01 1.85122644e-01
+ -6.40640641e-02 1.90963121e-01 1.83617895e-01
+ -5.40540541e-02 1.89568615e-01 1.82114026e-01
+ -4.40440440e-02 1.88175359e-01 1.80611219e-01
+ -3.40340340e-02 1.86783493e-01 1.79109650e-01
+ -2.40240240e-02 1.85393157e-01 1.77609496e-01
+ -1.40140140e-02 1.84004488e-01 1.76110931e-01
+ -4.00400400e-03 1.82617621e-01 1.74614127e-01
+ 6.00600601e-03 1.81232691e-01 1.73119256e-01
+ 1.60160160e-02 1.79849829e-01 1.71626487e-01
+ 2.60260260e-02 1.78469166e-01 1.70135986e-01
+ 3.60360360e-02 1.77090831e-01 1.68647918e-01
+ 4.60460460e-02 1.75714950e-01 1.67162448e-01
+ 5.60560561e-02 1.74341648e-01 1.65679737e-01
+ 6.60660661e-02 1.72971050e-01 1.64199944e-01
+ 7.60760761e-02 1.71603276e-01 1.62723226e-01
+ 8.60860861e-02 1.70238446e-01 1.61249740e-01
+ 9.60960961e-02 1.68876679e-01 1.59779638e-01
+ 1.06106106e-01 1.67518090e-01 1.58313073e-01
+ 1.16116116e-01 1.66162794e-01 1.56850194e-01
+ 1.26126126e-01 1.64810904e-01 1.55391148e-01
+ 1.36136136e-01 1.63462530e-01 1.53936081e-01
+ 1.46146146e-01 1.62117782e-01 1.52485135e-01
+ 1.56156156e-01 1.60776766e-01 1.51038453e-01
+ 1.66166166e-01 1.59439589e-01 1.49596172e-01
+ 1.76176176e-01 1.58106353e-01 1.48158430e-01
+ 1.86186186e-01 1.56777161e-01 1.46725362e-01
+ 1.96196196e-01 1.55452113e-01 1.45297101e-01
+ 2.06206206e-01 1.54131306e-01 1.43873775e-01
+ 2.16216216e-01 1.52814838e-01 1.42455514e-01
+ 2.26226226e-01 1.51502803e-01 1.41042444e-01
+ 2.36236236e-01 1.50195293e-01 1.39634689e-01
+ 2.46246246e-01 1.48892400e-01 1.38232369e-01
+ 2.56256256e-01 1.47594213e-01 1.36835605e-01
+ 2.66266266e-01 1.46300819e-01 1.35444513e-01
+ 2.76276276e-01 1.45012304e-01 1.34059208e-01
+ 2.86286286e-01 1.43728752e-01 1.32679803e-01
+ 2.96296296e-01 1.42450245e-01 1.31306408e-01
+ 3.06306306e-01 1.41176864e-01 1.29939131e-01
+ 3.16316316e-01 1.39908686e-01 1.28578078e-01
+ 3.26326326e-01 1.38645789e-01 1.27223352e-01
+ 3.36336336e-01 1.37388248e-01 1.25875056e-01
+ 3.46346346e-01 1.36136136e-01 1.24533287e-01
+ 3.56356356e-01 1.34889525e-01 1.23198143e-01
+ 3.66366366e-01 1.33648485e-01 1.21869718e-01
+ 3.76376376e-01 1.32413083e-01 1.20548105e-01
+ 3.86386386e-01 1.31183386e-01 1.19233392e-01
+ 3.96396396e-01 1.29959459e-01 1.17925669e-01
+ 4.06406406e-01 1.28741365e-01 1.16625020e-01
+ 4.16416416e-01 1.27529165e-01 1.15331529e-01
+ 4.26426426e-01 1.26322919e-01 1.14045276e-01
+ 4.36436436e-01 1.25122685e-01 1.12766341e-01
+ 4.46446446e-01 1.23928519e-01 1.11494799e-01
+ 4.56456456e-01 1.22740476e-01 1.10230726e-01
+ 4.66466466e-01 1.21558609e-01 1.08974192e-01
+ 4.76476476e-01 1.20382969e-01 1.07725268e-01
+ 4.86486486e-01 1.19213606e-01 1.06484021e-01
+ 4.96496496e-01 1.18050569e-01 1.05250516e-01
+ 5.06506507e-01 1.16893904e-01 1.04024818e-01
+ 5.16516517e-01 1.15743656e-01 1.02806986e-01
+ 5.26526527e-01 1.14599868e-01 1.01597080e-01
+ 5.36536537e-01 1.13462583e-01 1.00395156e-01
+ 5.46546547e-01 1.12331840e-01 9.92012685e-02
+ 5.56556557e-01 1.11207680e-01 9.80154701e-02
+ 5.66566567e-01 1.10090138e-01 9.68378110e-02
+ 5.76576577e-01 1.08979252e-01 9.56683392e-02
+ 5.86586587e-01 1.07875054e-01 9.45071007e-02
+ 5.96596597e-01 1.06777579e-01 9.33541395e-02
+ 6.06606607e-01 1.05686857e-01 9.22094974e-02
+ 6.16616617e-01 1.04602918e-01 9.10732142e-02
+ 6.26626627e-01 1.03525792e-01 8.99453276e-02
+ 6.36636637e-01 1.02455504e-01 8.88258733e-02
+ 6.46646647e-01 1.01392082e-01 8.77148851e-02
+ 6.56656657e-01 1.00335548e-01 8.66123947e-02
+ 6.66666667e-01 9.92859271e-02 8.55184318e-02
+ 6.76676677e-01 9.82432393e-02 8.44330242e-02
+ 6.86686687e-01 9.72075055e-02 8.33561978e-02
+ 6.96696697e-01 9.61787445e-02 8.22879764e-02
+ 7.06706707e-01 9.51569739e-02 8.12283820e-02
+ 7.16716717e-01 9.41422099e-02 8.01774349e-02
+ 7.26726727e-01 9.31344676e-02 7.91351532e-02
+ 7.36736737e-01 9.21337608e-02 7.81015533e-02
+ 7.46746747e-01 9.11401018e-02 7.70766499e-02
+ 7.56756757e-01 9.01535020e-02 7.60604557e-02
+ 7.66766767e-01 8.91739714e-02 7.50529818e-02
+ 7.76776777e-01 8.82015188e-02 7.40542373e-02
+ 7.86786787e-01 8.72361518e-02 7.30642298e-02
+ 7.96796797e-01 8.62778768e-02 7.20829650e-02
+ 8.06806807e-01 8.53266993e-02 7.11104469e-02
+ 8.16816817e-01 8.43826232e-02 7.01466781e-02
+ 8.26826827e-01 8.34456517e-02 6.91916591e-02
+ 8.36836837e-01 8.25157867e-02 6.82453891e-02
+ 8.46846847e-01 8.15930289e-02 6.73078656e-02
+ 8.56856857e-01 8.06773781e-02 6.63790844e-02
+ 8.66866867e-01 7.97688330e-02 6.54590399e-02
+ 8.76876877e-01 7.88673913e-02 6.45477249e-02
+ 8.86886887e-01 7.79730495e-02 6.36451306e-02
+ 8.96896897e-01 7.70858032e-02 6.27512469e-02
+ 9.06906907e-01 7.62056470e-02 6.18660619e-02
+ 9.16916917e-01 7.53325745e-02 6.09895625e-02
+ 9.26926927e-01 7.44665783e-02 6.01217342e-02
+ 9.36936937e-01 7.36076502e-02 5.92625609e-02
+ 9.46946947e-01 7.27557809e-02 5.84120253e-02
+ 9.56956957e-01 7.19109602e-02 5.75701087e-02
+ 9.66966967e-01 7.10731771e-02 5.67367911e-02
+ 9.76976977e-01 7.02424197e-02 5.59120509e-02
+ 9.86986987e-01 6.94186751e-02 5.50958657e-02
+ 9.96996997e-01 6.86019296e-02 5.42882116e-02
+ 1.00700701e+00 6.77921687e-02 5.34890633e-02
+ 1.01701702e+00 6.69893771e-02 5.26983945e-02
+ 1.02702703e+00 6.61935387e-02 5.19161778e-02
+ 1.03703704e+00 6.54046366e-02 5.11423845e-02
+ 1.04704705e+00 6.46226530e-02 5.03769846e-02
+ 1.05705706e+00 6.38475694e-02 4.96199474e-02
+ 1.06706707e+00 6.30793667e-02 4.88712407e-02
+ 1.07707708e+00 6.23180249e-02 4.81308315e-02
+ 1.08708709e+00 6.15635234e-02 4.73986856e-02
+ 1.09709710e+00 6.08158409e-02 4.66747679e-02
+ 1.10710711e+00 6.00749552e-02 4.59590424e-02
+ 1.11711712e+00 5.93408437e-02 4.52514718e-02
+ 1.12712713e+00 5.86134830e-02 4.45520181e-02
+ 1.13713714e+00 5.78928492e-02 4.38606424e-02
+ 1.14714715e+00 5.71789176e-02 4.31773049e-02
+ 1.15715716e+00 5.64716630e-02 4.25019648e-02
+ 1.16716717e+00 5.57710596e-02 4.18345804e-02
+ 1.17717718e+00 5.50770809e-02 4.11751095e-02
+ 1.18718719e+00 5.43897001e-02 4.05235089e-02
+ 1.19719720e+00 5.37088896e-02 3.98797345e-02
+ 1.20720721e+00 5.30346214e-02 3.92437416e-02
+ 1.21721722e+00 5.23668668e-02 3.86154847e-02
+ 1.22722723e+00 5.17055968e-02 3.79949178e-02
+ 1.23723724e+00 5.10507818e-02 3.73819939e-02
+ 1.24724725e+00 5.04023918e-02 3.67766655e-02
+ 1.25725726e+00 4.97603962e-02 3.61788845e-02
+ 1.26726727e+00 4.91247641e-02 3.55886020e-02
+ 1.27727728e+00 4.84954640e-02 3.50057688e-02
+ 1.28728729e+00 4.78724640e-02 3.44303348e-02
+ 1.29729730e+00 4.72557320e-02 3.38622495e-02
+ 1.30730731e+00 4.66452352e-02 3.33014620e-02
+ 1.31731732e+00 4.60409406e-02 3.27479207e-02
+ 1.32732733e+00 4.54428147e-02 3.22015736e-02
+ 1.33733734e+00 4.48508238e-02 3.16623681e-02
+ 1.34734735e+00 4.42649338e-02 3.11302513e-02
+ 1.35735736e+00 4.36851100e-02 3.06051699e-02
+ 1.36736737e+00 4.31113178e-02 3.00870700e-02
+ 1.37737738e+00 4.25435220e-02 2.95758976e-02
+ 1.38738739e+00 4.19816871e-02 2.90715981e-02
+ 1.39739740e+00 4.14257776e-02 2.85741165e-02
+ 1.40740741e+00 4.08757572e-02 2.80833978e-02
+ 1.41741742e+00 4.03315899e-02 2.75993865e-02
+ 1.42742743e+00 3.97932391e-02 2.71220266e-02
+ 1.43743744e+00 3.92606679e-02 2.66512622e-02
+ 1.44744745e+00 3.87338395e-02 2.61870370e-02
+ 1.45745746e+00 3.82127166e-02 2.57292943e-02
+ 1.46746747e+00 3.76972618e-02 2.52779775e-02
+ 1.47747748e+00 3.71874374e-02 2.48330296e-02
+ 1.48748749e+00 3.66832056e-02 2.43943934e-02
+ 1.49749750e+00 3.61845284e-02 2.39620116e-02
+ 1.50750751e+00 3.56913676e-02 2.35358269e-02
+ 1.51751752e+00 3.52036849e-02 2.31157816e-02
+ 1.52752753e+00 3.47214418e-02 2.27018180e-02
+ 1.53753754e+00 3.42445998e-02 2.22938784e-02
+ 1.54754755e+00 3.37731199e-02 2.18919049e-02
+ 1.55755756e+00 3.33069634e-02 2.14958396e-02
+ 1.56756757e+00 3.28460913e-02 2.11056245e-02
+ 1.57757758e+00 3.23904644e-02 2.07212016e-02
+ 1.58758759e+00 3.19400436e-02 2.03425128e-02
+ 1.59759760e+00 3.14947897e-02 1.99695002e-02
+ 1.60760761e+00 3.10546632e-02 1.96021058e-02
+ 1.61761762e+00 3.06196248e-02 1.92402715e-02
+ 1.62762763e+00 3.01896350e-02 1.88839393e-02
+ 1.63763764e+00 2.97646543e-02 1.85330515e-02
+ 1.64764765e+00 2.93446430e-02 1.81875501e-02
+ 1.65765766e+00 2.89295617e-02 1.78473774e-02
+ 1.66766767e+00 2.85193707e-02 1.75124758e-02
+ 1.67767768e+00 2.81140304e-02 1.71827876e-02
+ 1.68768769e+00 2.77135011e-02 1.68582555e-02
+ 1.69769770e+00 2.73177431e-02 1.65388221e-02
+ 1.70770771e+00 2.69267168e-02 1.62244302e-02
+ 1.71771772e+00 2.65403826e-02 1.59150228e-02
+ 1.72772773e+00 2.61587009e-02 1.56105431e-02
+ 1.73773774e+00 2.57816320e-02 1.53109343e-02
+ 1.74774775e+00 2.54091364e-02 1.50161401e-02
+ 1.75775776e+00 2.50411747e-02 1.47261039e-02
+ 1.76776777e+00 2.46777072e-02 1.44407699e-02
+ 1.77777778e+00 2.43186946e-02 1.41600820e-02
+ 1.78778779e+00 2.39640976e-02 1.38839845e-02
+ 1.79779780e+00 2.36138768e-02 1.36124222e-02
+ 1.80780781e+00 2.32679930e-02 1.33453397e-02
+ 1.81781782e+00 2.29264071e-02 1.30826822e-02
+ 1.82782783e+00 2.25890799e-02 1.28243950e-02
+ 1.83783784e+00 2.22559726e-02 1.25704236e-02
+ 1.84784785e+00 2.19270462e-02 1.23207140e-02
+ 1.85785786e+00 2.16022620e-02 1.20752122e-02
+ 1.86786787e+00 2.12815813e-02 1.18338648e-02
+ 1.87787788e+00 2.09649654e-02 1.15966185e-02
+ 1.88788789e+00 2.06523760e-02 1.13634203e-02
+ 1.89789790e+00 2.03437747e-02 1.11342176e-02
+ 1.90790791e+00 2.00391233e-02 1.09089581e-02
+ 1.91791792e+00 1.97383837e-02 1.06875898e-02
+ 1.92792793e+00 1.94415180e-02 1.04700611e-02
+ 1.93793794e+00 1.91484884e-02 1.02563207e-02
+ 1.94794795e+00 1.88592572e-02 1.00463175e-02
+ 1.95795796e+00 1.85737868e-02 9.84000096e-03
+ 1.96796797e+00 1.82920399e-02 9.63732085e-03
+ 1.97797798e+00 1.80139793e-02 9.43822724e-03
+ 1.98798799e+00 1.77395680e-02 9.24267060e-03
+ 1.99799800e+00 1.74687690e-02 9.05060177e-03
+ 2.00800801e+00 1.72015455e-02 8.86197196e-03
+ 2.01801802e+00 1.69378612e-02 8.67673276e-03
+ 2.02802803e+00 1.66776795e-02 8.49483614e-03
+ 2.03803804e+00 1.64209643e-02 8.31623446e-03
+ 2.04804805e+00 1.61676794e-02 8.14088048e-03
+ 2.05805806e+00 1.59177892e-02 7.96872734e-03
+ 2.06806807e+00 1.56712579e-02 7.79972857e-03
+ 2.07807808e+00 1.54280500e-02 7.63383814e-03
+ 2.08808809e+00 1.51881302e-02 7.47101037e-03
+ 2.09809810e+00 1.49514636e-02 7.31120002e-03
+ 2.10810811e+00 1.47180151e-02 7.15436226e-03
+ 2.11811812e+00 1.44877501e-02 7.00045265e-03
+ 2.12812813e+00 1.42606341e-02 6.84942718e-03
+ 2.13813814e+00 1.40366328e-02 6.70124224e-03
+ 2.14814815e+00 1.38157121e-02 6.55585466e-03
+ 2.15815816e+00 1.35978382e-02 6.41322166e-03
+ 2.16816817e+00 1.33829773e-02 6.27330090e-03
+ 2.17817818e+00 1.31710961e-02 6.13605046e-03
+ 2.18818819e+00 1.29621614e-02 6.00142883e-03
+ 2.19819820e+00 1.27561400e-02 5.86939493e-03
+ 2.20820821e+00 1.25529992e-02 5.73990810e-03
+ 2.21821822e+00 1.23527064e-02 5.61292812e-03
+ 2.22822823e+00 1.21552292e-02 5.48841518e-03
+ 2.23823824e+00 1.19605356e-02 5.36632989e-03
+ 2.24824825e+00 1.17685935e-02 5.24663331e-03
+ 2.25825826e+00 1.15793713e-02 5.12928691e-03
+ 2.26826827e+00 1.13928376e-02 5.01425258e-03
+ 2.27827828e+00 1.12089611e-02 4.90149265e-03
+ 2.28828829e+00 1.10277108e-02 4.79096986e-03
+ 2.29829830e+00 1.08490559e-02 4.68264740e-03
+ 2.30830831e+00 1.06729658e-02 4.57648886e-03
+ 2.31831832e+00 1.04994104e-02 4.47245827e-03
+ 2.32832833e+00 1.03283594e-02 4.37052007e-03
+ 2.33833834e+00 1.01597830e-02 4.27063913e-03
+ 2.34834835e+00 9.99365163e-03 4.17278075e-03
+ 2.35835836e+00 9.82993589e-03 4.07691063e-03
+ 2.36836837e+00 9.66860664e-03 3.98299491e-03
+ 2.37837838e+00 9.50963496e-03 3.89100014e-03
+ 2.38838839e+00 9.35299218e-03 3.80089328e-03
+ 2.39839840e+00 9.19864986e-03 3.71264171e-03
+ 2.40840841e+00 9.04657979e-03 3.62621322e-03
+ 2.41841842e+00 8.89675402e-03 3.54157604e-03
+ 2.42842843e+00 8.74914481e-03 3.45869876e-03
+ 2.43843844e+00 8.60372467e-03 3.37755041e-03
+ 2.44844845e+00 8.46046635e-03 3.29810043e-03
+ 2.45845846e+00 8.31934283e-03 3.22031866e-03
+ 2.46846847e+00 8.18032734e-03 3.14417532e-03
+ 2.47847848e+00 8.04339332e-03 3.06964105e-03
+ 2.48848849e+00 7.90851449e-03 2.99668690e-03
+ 2.49849850e+00 7.77566476e-03 2.92528429e-03
+ 2.50850851e+00 7.64481830e-03 2.85540505e-03
+ 2.51851852e+00 7.51594953e-03 2.78702139e-03
+ 2.52852853e+00 7.38903307e-03 2.72010592e-03
+ 2.53853854e+00 7.26404382e-03 2.65463162e-03
+ 2.54854855e+00 7.14095687e-03 2.59057187e-03
+ 2.55855856e+00 7.01974758e-03 2.52790042e-03
+ 2.56856857e+00 6.90039153e-03 2.46659141e-03
+ 2.57857858e+00 6.78286453e-03 2.40661933e-03
+ 2.58858859e+00 6.66714264e-03 2.34795906e-03
+ 2.59859860e+00 6.55320212e-03 2.29058586e-03
+ 2.60860861e+00 6.44101950e-03 2.23447534e-03
+ 2.61861862e+00 6.33057152e-03 2.17960347e-03
+ 2.62862863e+00 6.22183515e-03 2.12594659e-03
+ 2.63863864e+00 6.11478760e-03 2.07348140e-03
+ 2.64864865e+00 6.00940631e-03 2.02218494e-03
+ 2.65865866e+00 5.90566893e-03 1.97203462e-03
+ 2.66866867e+00 5.80355336e-03 1.92300818e-03
+ 2.67867868e+00 5.70303772e-03 1.87508372e-03
+ 2.68868869e+00 5.60410034e-03 1.82823968e-03
+ 2.69869870e+00 5.50671979e-03 1.78245482e-03
+ 2.70870871e+00 5.41087487e-03 1.73770827e-03
+ 2.71871872e+00 5.31654459e-03 1.69397945e-03
+ 2.72872873e+00 5.22370819e-03 1.65124814e-03
+ 2.73873874e+00 5.13234511e-03 1.60949444e-03
+ 2.74874875e+00 5.04243505e-03 1.56869877e-03
+ 2.75875876e+00 4.95395789e-03 1.52884186e-03
+ 2.76876877e+00 4.86689374e-03 1.48990476e-03
+ 2.77877878e+00 4.78122294e-03 1.45186884e-03
+ 2.78878879e+00 4.69692604e-03 1.41471578e-03
+ 2.79879880e+00 4.61398378e-03 1.37842755e-03
+ 2.80880881e+00 4.53237714e-03 1.34298643e-03
+ 2.81881882e+00 4.45208730e-03 1.30837501e-03
+ 2.82882883e+00 4.37309567e-03 1.27457616e-03
+ 2.83883884e+00 4.29538383e-03 1.24157305e-03
+ 2.84884885e+00 4.21893360e-03 1.20934913e-03
+ 2.85885886e+00 4.14372701e-03 1.17788815e-03
+ 2.86886887e+00 4.06974626e-03 1.14717412e-03
+ 2.87887888e+00 3.99697380e-03 1.11719135e-03
+ 2.88888889e+00 3.92539224e-03 1.08792441e-03
+ 2.89889890e+00 3.85498442e-03 1.05935816e-03
+ 2.90890891e+00 3.78573338e-03 1.03147770e-03
+ 2.91891892e+00 3.71762233e-03 1.00426841e-03
+ 2.92892893e+00 3.65063472e-03 9.77715949e-04
+ 2.93893894e+00 3.58475415e-03 9.51806203e-04
+ 2.94894895e+00 3.51996445e-03 9.26525329e-04
+ 2.95895896e+00 3.45624964e-03 9.01859733e-04
+ 2.96896897e+00 3.39359390e-03 8.77796068e-04
+ 2.97897898e+00 3.33198164e-03 8.54321233e-04
+ 2.98898899e+00 3.27139743e-03 8.31422368e-04
+ 2.99899900e+00 3.21182605e-03 8.09086850e-04
+ 3.00900901e+00 3.15325245e-03 7.87302291e-04
+ 3.01901902e+00 3.09566177e-03 7.66056537e-04
+ 3.02902903e+00 3.03903933e-03 7.45337659e-04
+ 3.03903904e+00 2.98337063e-03 7.25133955e-04
+ 3.04904905e+00 2.92864136e-03 7.05433944e-04
+ 3.05905906e+00 2.87483738e-03 6.86226364e-04
+ 3.06906907e+00 2.82194474e-03 6.67500168e-04
+ 3.07907908e+00 2.76994964e-03 6.49244523e-04
+ 3.08908909e+00 2.71883847e-03 6.31448803e-04
+ 3.09909910e+00 2.66859780e-03 6.14102589e-04
+ 3.10910911e+00 2.61921436e-03 5.97195665e-04
+ 3.11911912e+00 2.57067506e-03 5.80718017e-04
+ 3.12912913e+00 2.52296695e-03 5.64659824e-04
+ 3.13913914e+00 2.47607729e-03 5.49011461e-04
+ 3.14914915e+00 2.42999347e-03 5.33763494e-04
+ 3.15915916e+00 2.38470307e-03 5.18906677e-04
+ 3.16916917e+00 2.34019379e-03 5.04431949e-04
+ 3.17917918e+00 2.29645355e-03 4.90330430e-04
+ 3.18918919e+00 2.25347038e-03 4.76593419e-04
+ 3.19919920e+00 2.21123250e-03 4.63212394e-04
+ 3.20920921e+00 2.16972825e-03 4.50179004e-04
+ 3.21921922e+00 2.12894617e-03 4.37485069e-04
+ 3.22922923e+00 2.08887492e-03 4.25122576e-04
+ 3.23923924e+00 2.04950332e-03 4.13083680e-04
+ 3.24924925e+00 2.01082034e-03 4.01360695e-04
+ 3.25925926e+00 1.97281510e-03 3.89946096e-04
+ 3.26926927e+00 1.93547687e-03 3.78832517e-04
+ 3.27927928e+00 1.89879507e-03 3.68012742e-04
+ 3.28928929e+00 1.86275925e-03 3.57479710e-04
+ 3.29929930e+00 1.82735912e-03 3.47226508e-04
+ 3.30930931e+00 1.79258450e-03 3.37246369e-04
+ 3.31931932e+00 1.75842539e-03 3.27532672e-04
+ 3.32932933e+00 1.72487191e-03 3.18078934e-04
+ 3.33933934e+00 1.69191431e-03 3.08878814e-04
+ 3.34934935e+00 1.65954298e-03 2.99926106e-04
+ 3.35935936e+00 1.62774845e-03 2.91214740e-04
+ 3.36936937e+00 1.59652139e-03 2.82738774e-04
+ 3.37937938e+00 1.56585257e-03 2.74492399e-04
+ 3.38938939e+00 1.53573293e-03 2.66469931e-04
+ 3.39939940e+00 1.50615350e-03 2.58665812e-04
+ 3.40940941e+00 1.47710547e-03 2.51074604e-04
+ 3.41941942e+00 1.44858013e-03 2.43690993e-04
+ 3.42942943e+00 1.42056892e-03 2.36509779e-04
+ 3.43943944e+00 1.39306337e-03 2.29525881e-04
+ 3.44944945e+00 1.36605516e-03 2.22734328e-04
+ 3.45945946e+00 1.33953609e-03 2.16130265e-04
+ 3.46946947e+00 1.31349804e-03 2.09708942e-04
+ 3.47947948e+00 1.28793306e-03 2.03465719e-04
+ 3.48948949e+00 1.26283328e-03 1.97396060e-04
+ 3.49949950e+00 1.23819096e-03 1.91495533e-04
+ 3.50950951e+00 1.21399846e-03 1.85759806e-04
+ 3.51951952e+00 1.19024828e-03 1.80184648e-04
+ 3.52952953e+00 1.16693300e-03 1.74765924e-04
+ 3.53953954e+00 1.14404532e-03 1.69499594e-04
+ 3.54954955e+00 1.12157805e-03 1.64381713e-04
+ 3.55955956e+00 1.09952411e-03 1.59408427e-04
+ 3.56956957e+00 1.07787651e-03 1.54575972e-04
+ 3.57957958e+00 1.05662839e-03 1.49880671e-04
+ 3.58958959e+00 1.03577298e-03 1.45318936e-04
+ 3.59959960e+00 1.01530359e-03 1.40887259e-04
+ 3.60960961e+00 9.95213674e-04 1.36582220e-04
+ 3.61961962e+00 9.75496748e-04 1.32400477e-04
+ 3.62962963e+00 9.56146443e-04 1.28338768e-04
+ 3.63963964e+00 9.37156484e-04 1.24393910e-04
+ 3.64964965e+00 9.18520691e-04 1.20562794e-04
+ 3.65965966e+00 9.00232977e-04 1.16842388e-04
+ 3.66966967e+00 8.82287352e-04 1.13229732e-04
+ 3.67967968e+00 8.64677913e-04 1.09721938e-04
+ 3.68968969e+00 8.47398852e-04 1.06316187e-04
+ 3.69969970e+00 8.30444447e-04 1.03009731e-04
+ 3.70970971e+00 8.13809068e-04 9.97998862e-05
+ 3.71971972e+00 7.97487171e-04 9.66840366e-05
+ 3.72972973e+00 7.81473296e-04 9.36596297e-05
+ 3.73973974e+00 7.65762072e-04 9.07241762e-05
+ 3.74974975e+00 7.50348209e-04 8.78752483e-05
+ 3.75975976e+00 7.35226501e-04 8.51104783e-05
+ 3.76976977e+00 7.20391823e-04 8.24275577e-05
+ 3.77977978e+00 7.05839132e-04 7.98242354e-05
+ 3.78978979e+00 6.91563464e-04 7.72983169e-05
+ 3.79979980e+00 6.77559934e-04 7.48476625e-05
+ 3.80980981e+00 6.63823733e-04 7.24701868e-05
+ 3.81981982e+00 6.50350130e-04 7.01638570e-05
+ 3.82982983e+00 6.37134470e-04 6.79266916e-05
+ 3.83983984e+00 6.24172169e-04 6.57567599e-05
+ 3.84984985e+00 6.11458721e-04 6.36521801e-05
+ 3.85985986e+00 5.98989690e-04 6.16111188e-05
+ 3.86986987e+00 5.86760710e-04 5.96317894e-05
+ 3.87987988e+00 5.74767489e-04 5.77124515e-05
+ 3.88988989e+00 5.63005802e-04 5.58514096e-05
+ 3.89989990e+00 5.51471492e-04 5.40470120e-05
+ 3.90990991e+00 5.40160471e-04 5.22976499e-05
+ 3.91991992e+00 5.29068718e-04 5.06017566e-05
+ 3.92992993e+00 5.18192277e-04 4.89578060e-05
+ 3.93993994e+00 5.07527255e-04 4.73643123e-05
+ 3.94994995e+00 4.97069826e-04 4.58198284e-05
+ 3.95995996e+00 4.86816224e-04 4.43229458e-05
+ 3.96996997e+00 4.76762748e-04 4.28722927e-05
+ 3.97997998e+00 4.66905755e-04 4.14665340e-05
+ 3.98998999e+00 4.57241665e-04 4.01043699e-05
+ 4.00000000e+00 4.47766955e-04 3.87845354e-05
diff --git a/report/figures/tracy-widom-approx/tracywidom_appx.m b/report/figures/tracy-widom-approx/tracywidom_appx.m
new file mode 100644
index 0000000..bbab815
--- /dev/null
+++ b/report/figures/tracy-widom-approx/tracywidom_appx.m
@@ -0,0 +1,38 @@
+function [pdftwappx, cdftwappx] = tracywidom_appx(x, i) 
+% 
+%
+% [pdftwappx, cdftwappx]=tracywidom_appx(x, i)
+%
+% SHIFTED GAMMA APPROXIMATION FOR THE TRACY-WIDOM LAWS, by M. Chiani, 2012
+%
+% TW ~ Gamma[k,theta]-alpha   
+%
+% [pdf,cdf]=tracywidom_appx(x,2) gives the approximated pdf(x) and CDF(x) of the TW2   
+%
+% [pdf,cdf]=tracywidom_appx(x,i) for i=1,2,4 gives TW1, TW2, TW4     
+%
+% see paper M.Chiani, "Distribution of the largest eigenvalue for real 
+% Wishart and Gaussian random matrices and a simple approximation for the 
+% Tracy-Widom distribution", submitted 2012, ArXiv
+%
+kappx = [46.44604884387787, 79.6594870666346, 0, 146.0206131050228];   %  K, THETA, ALPHA 
+thetaappx = [0.18605402228279347, 0.10103655775856243, 0, 0.05954454047933292];  
+alphaappx = [9.848007781128567, 9.819607173436484, 0, 11.00161520109004]; 
+cdftwappx = cdfgamma(x+alphaappx(i), thetaappx(i), kappx(i));   % Chiani's appx: Tracy-Widom as a shifted Gamma
+pdftwappx = pdfgamma(x+alphaappx(i), thetaappx(i), kappx(i));   % Chiani's appx: Tracy-Widom as a shifted Gamma 
+end
+function [pdfgamma]=pdfgamma(x, ta, ka) % Utility: PDF of a Gamma 
+ if(x > 0)
+     pdfgamma=1/(gamma(ka)*ta^ka) * x.^(ka - 1) .* exp(-x/ta);
+ else
+     pdfgamma=0 ;
+ end
+end
+function[cdfgamma]=cdfgamma(x, ta, ka)  % Utility: CDF of a Gamma
+ if(x > 0) 
+     cdfgamma=gammainc(x/ta,ka); 
+ else
+     cdfgamma=0; 
+ end
+ 
+end
diff --git a/report/refs.bib b/report/refs.bib
index cf0a85f..196a83e 100644
--- a/report/refs.bib
+++ b/report/refs.bib
@@ -1,82 +1,90 @@
 @book{novak2022,
+    address = {Sharon, Vermont},
+    publisher = {Equal Share Press},
     year = {2022},
-    author = {Kyle A. Novak},
-    isbn = {9798985421804},
     title = {Numerical Methods for Scientific Computing},
-    note = {Chapter 4},
     month = {March},
-    publisher = {Equal Share Press},
-    address = {Sharon, Vermont},
+    note = {Chapter 4},
+    isbn = {9798985421804},
+    author = {Kyle A. Novak},
 }
 
 @book{watkins2002,
+    isbn = {0471213942},
+    author = {David S. Watkins},
     title = {Fundamenals of Matrix Computations (2nd Edition)},
+    publisher = {John Wiley and Sons},
     month = {January},
+    note = {Chapter 5},
     address = {New York},
     year = {2002},
-    author = {David S. Watkins},
-    isbn = {0471213942},
-    note = {Chapter 5},
-    publisher = {John Wiley and Sons},
 }
 
 @article{golub2009The_QR,
-    pages = {467-485},
     issn = {1464-3642},
-    number = {3},
-    doi = {10.1093/imanum/drp012},
-    publisher = {Oxford University Press (OUP)},
-    volume = {29},
     title = {{The QR Algorithm: 50 Years Later its Genesis by John Francis and Vera Kublanovskaya and Subsequent Developments}},
     journal = {IMA Journal of Numerical Analysis},
-    month = {June},
     author = {Golub, G. and Uhlig, F.},
     note = {},
     url = {http://dx.doi.org/10.1093/imanum/drp012},
     year = {2009},
+    volume = {29},
+    month = {June},
+    pages = {467-485},
+    publisher = {Oxford University Press (OUP)},
+    number = {3},
+    doi = {10.1093/imanum/drp012},
 }
 
 @article{wigner1955Charac,
-    number = {3},
-    publisher = {JSTOR},
-    pages = {548},
-    url = {http://dx.doi.org/10.2307/1970079},
-    title = {{Characteristic Vectors of Bordered Matrices With Infinite Dimensions}},
-    doi = {10.2307/1970079},
-    journal = {The Annals of Mathematics},
     issn = {0003-486X},
-    year = {1955},
+    title = {{Characteristic Vectors of Bordered Matrices With Infinite Dimensions}},
+    pages = {548},
     volume = {62},
+    number = {3},
     author = {Wigner, Eugene P.},
+    year = {1955},
+    journal = {The Annals of Mathematics},
+    url = {http://dx.doi.org/10.2307/1970079},
+    doi = {10.2307/1970079},
+    publisher = {JSTOR},
 }
 
 @book{anderson2009An_Int,
-    isbn = {9781107471580},
     author = {Anderson, Greg W. and Guionnet, Alice and Zeitouni, Ofer},
+    note = {Chapters 1 and 2},
+    year = {2009},
+    url = {http://dx.doi.org/10.1017/CBO9780511801334},
+    doi = {10.1017/cbo9780511801334},
+    isbn = {9781107471580},
     month = {February},
     publisher = {Cambridge University Press},
-    doi = {10.1017/cbo9780511801334},
-    url = {http://dx.doi.org/10.1017/CBO9780511801334},
-    note = {Chapters 1 and 2},
     title = {{An Introduction to Random Matrices}},
-    year = {2009},
 }
 
 @misc{marco2013,
-    author = {Marco},
-    title = {{Approximation for the Tracy-Widom Laws}},
-    year = {2013},
     howpublished = {Published to the MATLAB Central File Exchange},
     note = {Retrieved April 25th, 2026. \href{https://www.mathworks.com/matlabcentral/fileexchange/44711-approximation-for-the-tracy-widom-laws}{Available online.}},
+    year = {2013},
+    title = {{Approximation for the Tracy-Widom Laws}},
+    author = {Marco},
 }
 
 @article{chiani2012Distri,
-    doi = {10.48550/ARXIV.1209.3394},
     url = {https://arxiv.org/abs/1209.3394},
-    author = {Chiani, Marco},
+    copyright = {arXiv.org perpetual, non-exclusive license},
     keywords = {Information Theory (cs.IT), Statistics Theory (math.ST), FOS: Computer and information sciences, FOS: Computer and information sciences, FOS: Mathematics, FOS: Mathematics},
-    title = {{Distribution of the Largest Eigenvalue for Real Wishart and Gaussian Random Matrices and a Simple Approximation for the Tracy-Widom Distribution}},
     publisher = {arXiv},
-    copyright = {arXiv.org perpetual, non-exclusive license},
     year = {2012},
+    author = {Chiani, Marco},
+    doi = {10.48550/ARXIV.1209.3394},
+    title = {{Distribution of the Largest Eigenvalue for Real Wishart and Gaussian Random Matrices and a Simple Approximation for the Tracy-Widom Distribution}},
+}
+
+@book{siegrist2021,
+    year = {2021},
+    publisher = {Open Education Resource LibreTexts},
+    note = {Chapter 4. \href{https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)}{Available online.}},
+    author = {Kyle Siegrist},
+    title = {{Probability Theory Probability, Mathematical Statistics, and Stochastic Processes (2021 Edition)}},
 }
\ No newline at end of file
diff --git a/report/report.tex b/report/report.tex
index 7b66883..2d73bb4 100644
--- a/report/report.tex
+++ b/report/report.tex
@@ -6,10 +6,13 @@
 
 \usepackage{xcolor}
 \usepackage{graphicx}
-\graphicspath{{./figures/}}
+\graphicspath{{./figures/} {./figures/tracy-widom-approx/}}
 \usepackage{amsmath}
 \usepackage{booktabs}
 \usepackage{longtable}
+\usepackage{caption}
+\captionsetup{margin=0.5cm} % Sets a 1cm margin on both sides
+\captionsetup{labelfont=bf}
 
 \usepackage{hyperref}
 \hypersetup{colorlinks=true,
@@ -39,26 +42,62 @@ This work considers Gaussian orthogonal ensembles (GOEs) specifically and attemp
 \section{Relevant Theory}
 
 \subsection{Random Ensembles}
-The GOE-based random matrix has some properties that go beyond simply being normally distributed. Namely, the matrix is square, symmetric, and the standard deviation $\sigma$ is unity except for elements on the diagonal where $\sigma=2$. The mean $\mu$ is considered as zero for all elements. Consider the normal distribution with notation $N(\mu, \sigma$). Then, an example is provided below for a $5\times5$ matrix:
+The GOE-based random matrix has some properties that go beyond simply being normally distributed. Namely, the matrix is square, symmetric, and the standard deviation $\sigma$ is unity except for elements on the diagonal where $\sigma=2$. The mean $\mu$ is considered as zero for all elements. Consider the normal distribution with notation $N(\mu, \sigma$). Then, the matrix is constructed using:
 \begin{equation*}
-    \mathbf{A} = 
-    \begin{pmatrix}
-        N(0,2) & N(0,1) & N(0,1) & N(0,1) & N(0,1) \\
-        N(0,1) & N(0,2) & N(0,1) & N(0,1) & N(0,1) \\
-        N(0,1) & N(0,1) & N(0,2) & N(0,1) & N(0,1) \\
-        N(0,1) & N(0,1) & N(0,1) & N(0,2) & N(0,1) \\
-        N(0,1) & N(0,1) & N(0,1) & N(0,1) & N(0,2) \\
-    \end{pmatrix}
+    \mathbf{A}(i,j) \sim
+    \begin{cases}
+    N(0, 1) & \forall (i \neq j) \\
+    N(0, 2) & \forall (i = j)
+    \end{cases}
 \end{equation*}
 The diagonal standard deviation of 2 is what makes this ensemble orthogonal. Note that the representation above does not explicitly state the symmetry, but $\mathbf{A}(i,j) = \mathbf{A}(j,i)\, \forall(i,j)$.
 
 \subsection{The Tracy-Widom Distributions}
-Various distributions can be 
+Various distributions can be reconstructed from the eigenvalues of a GOE. For example, the case of the global eigenvalues yields a semicircle distribution \cite{anderson2009An_Int}. Consider the $N$ eigenvalues of a vector $|\lambda_1| \ge |\lambda_2| \ge |\lambda_3\| \ge ... \ge |\lambda_N|$. In this case, $\lambda_1$ is considered the \emph{dominant} eigenvalue so long as $|\lambda_1| > |\lambda_2|$. Taking the distribution of the dominant eigenvalues $\lambda_1$ yields an entirely different result that is known as the \emph{Tracy-Widom} distribution. This distribution can be parametrized in terms of which division algebra is used in its definition. Wigner's work considered real, complex, and Quaternion cases, shown below in Figure \ref{fig:tracy-widoms}:
+
+\begin{figure}[H]
+    \centering
+    \input{figures/tracy-widom-approx/tracy_widom.tex}
+    \caption{Various Tracy-Widom distributions for $\beta=1,2,4$. The different values of $\beta$ depend on which division algebra is used for the Gaussian ensemble (real/complex/quaternion). This work considers only the TW\textsubscript{1} distribution defined for real numbers, shown in red as the shallowest peak compared with the complex and quaternion versions.}
+    \label{fig:tracy-widoms}
+\end{figure}
+
+Compared with a normal distribution, it is also difficult to distinguish between the two visually. Figure \ref{fig:tracy-widom-vs-normal} shows a comparison between a Tracy-Widom and a normal distribution:
+
+\begin{figure}[H]
+    \centering
+    \input{figures/tracy-widom-approx/tracy_widom_compare.tex}
+    \caption{The TW\textsubscript{1} distribution compared with a normal distribution of arbitrary mean and standard deviation. Note that while the peaks are centered, the Tracy-Widom has a `fatter' tail on the $+x$ side and a slimmer one on the $-x$ side. Both distributions are quite similar visually, so this asymmetry will play an important role in quantifying their differences.}
+    \label{fig:tracy-widom-vs-normal}
+\end{figure}
+Because of their similarities, a smart approach to validating the generation of a Tracy-Widom distribution should include some type of quantifiable, statistical assurance that a normal distribution was not generated.
 
 \subsection{Statistical Differentiation}
-The Tracy-Widom and normal distributions are hard to differentiate based on shape alone. Because of this, it is necessary to consider quantifying the differences in some meaningful way. One way to do this is to consider the important differences between the two distributions. For example, while the normal distribution is symmetric, the Tray-Widom is not. The symmetry of a distribution is something that can be quantified
+There are various ways to go about discerning a Tracy-Widom distribution from a normal one. Perhaps the most elegant is to exploit some basic differences in properties between the two. As mentioned earlier, the Tracy-Widom has a fatter side and a slimmer side, which makes it asymmetric. This is not the case with the normal distribution which is identical on either side of the mean value $\mu$. It turns out that the symmetry of a distribution is readily quantifiable using existing statistical tools, and as such that will be the backbone of the statistical analysis. First consider the \emph{expected value} of a probability density function (PDF) $p(x)$, defined as \cite{siegrist2021}:
+\begin{equation}
+    E[x] = \int_s x p(x)\, dx \approx \left(\sum_i x_i\,p(i)\right) \Delta x
+    \label{eqn:expected}
+\end{equation}
+where the approximation applies for a discrete PDF with equi-distance bins along $x$. The expected value has \emph{moments} that give quantifiable insights into the behaviour and shape of a PDF. The general equation for the $n$th central moment of $E(x)$ is given as:
+\begin{equation}
+    E\left[(x-a_n)^n\right]
+\end{equation}
+where $a_n$ is some constant. The first moment (taken as a so-called \emph{raw moment} with $a=0$) simply reduces to \ref{eqn:expected}. The second moment is the variance of the function and is taken with $a=\mu$:
+\begin{equation}
+    \sigma^2 = E\left[(x - E[x])^2\right] = E\left[ (x - \mu)^2\right]
+\end{equation}
+The next two moments are of particular value for this project as they quantify the symmetry of the distribution. The third moment is the \emph{skewness} of the distribution, which deviates from the central moments above and is normalized by the standard deviation $\sigma$:
+\begin{equation}
+    \mathrm{Skewness} = E\left[\frac{(x-\mu)^3}{\sigma}\right]
+\end{equation}
+Lastly, the 4th moment is the kurtosis of the distribution. Kurtosis comes from the Greek word for \emph{bulging}, and as a parameter it quantifies the `sharpness' of the PDF. A larger value of kurtosis implies that the distribution has fatter tails \cite{siegrist2021}. Note that kurtosis is always a positive value and is equal to 3 for a standard normal distribution. Therefore, the  \emph{excess} kurtosis is considered by subtracting 3. The relation is given as:
+\begin{equation}
+    \mathrm{Excess\ Kurtosis} = E\left[ \frac{(x - \mu)^4}{\sigma} \right] - 3
+\end{equation}
+These tests, while perhaps simple, will do a fine job in the strict context of differentiating a Tracy-Widom distribution from a normal distribution. In the case of the normal distribution, the skewness and excess kurtosis are both zero. For comparison, the approximate Tracy-Widom has a skewness of $\approx 0.2935$ and an excess kurtosis of $\approx 0.1292$.This was calculated using an Octave script that sampled 50,000 bins in the range $[-9,9]$ for both distributions. This also verified the calculations as it properly reconstructed the exact mean and standard deviation for the normal distribution sampled from its the closed-form equation.
 
 \section{Numerical Methods}
+The natural extension of defining the prerequisite statistical tests to confirm a Tracy-Widom is to actually sample a Tracy-Widom. The issue with this, however, is that it can be quite computationally demanding. The Tracy-Widom is quite similar to the normal except for near the very tails, meaning that most samples (occurring near the peaks) will show agreement between the two. Additionally, it is theorized that the dimension of the matrix $N$ has to be on the order of thousands to get a very Tracy-Widom distribution. The combination of these two points motivates finding a convenient way to calculate the maximum eigenvalue of a large matrix repeated such that thousands of calculations can be performed in a meaningfully short amount of time.
 \subsection{The Power Method}
 One relatively cheap way to find the maximum eigenvalue is through the so-called power method. The power method is an iterative approach to finding the maximum eigenvalue of a matrix that exploits the spectral gap ($\lambda_1 - \lambda_2$). Consider an initial guess in the form of a vector of length $N$ given as $\mathbf{x_0}$. Then, perform the multiplication:
 \begin{equation}