(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1140475, 42674]*) (*NotebookOutlinePosition[ 1141191, 42699]*) (* CellTagsIndexPosition[ 1141147, 42695]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "The package VQM`FastFourier", StyleBox["`", "MB"] }], "Title"], Cell["\<\ Bernd Thaller Institute of Mathematics University of Graz Austria 04-10-2004\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Abstract", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " has a very efficient algorithm for calculating the Fourier transformation \ of a list. We use it for an approximate calculation of the Fourier \ transformation of a function. " }], "Text"], Cell[TextData[{ "This package VQM`FastFourier` provides commands for the numerical Fourier \ transform of complex-valued functions that are given as a list of complex \ values on a suitable grid of space points. This package is part of the VQM \ packages which can be obtained here: ", ButtonBox["http://www.uni-graz.at/imawww/vqm/software.html", ButtonData:>{ URL[ "http://www.uni-graz.at/imawww/vqm/software.html"], None}, ButtonStyle->"Hyperlink"], " (free download). The VQM packages are part of the Visual Quantum \ Mechanics project, see ", ButtonBox["http://www.uni-graz.at/imawww/vqm/", ButtonData:>{ URL[ "http://www.uni-graz.at/imawww/vqm/"], None}, ButtonStyle->"Hyperlink"], ". 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Since ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox[" ", "InlineFormula", FontFamily->"Times New Roman"], RowBox[{ StyleBox[\(\[Psi]\&\[Wedge]\), FontFamily->"Times New Roman"], RowBox[{ StyleBox["(", FontFamily->"Times New Roman"], StyleBox[ SubscriptBox[ StyleBox["k", FontWeight->"Plain", FontSlant->"Italic"], "s"], FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[")", FontFamily->"Times New Roman"]}]}], " "}], InputForm]]], "is periodic, we obtain the values of ", Cell[BoxData[ FormBox[ StyleBox[\(\[Psi]\&\[Wedge]\), FontFamily->"Times New Roman"], InputForm]]], " at the ", StyleBox["n", FontFamily->"Times New Roman", FontSlant->"Italic"], " points:" }], "Text"], Cell[TextData[{ StyleBox["{", FontFamily->"Times New Roman"], Cell[BoxData[ FormBox[ RowBox[{"-", FractionBox["\[Pi]", StyleBox[ RowBox[{"d", StyleBox["x", FontSlant->"Italic"]}]]]}], TraditionalForm]], FontFamily->"Times New Roman"], Cell[BoxData[ FormBox[ RowBox[{"+", " ", StyleBox[ RowBox[{"d", StyleBox["k", 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FontSlant->"Italic"], StyleBox["/2 + 1", "InlineFormula", FontFamily->"Times New Roman"], " places towards the left) by performing the cyclic permutation" }], "Text"], Cell[TextData[{ StyleBox["RotateLeft", FontFamily->"Courier", FontWeight->"Bold"], "[", StyleBox["{", FontFamily->"Times New Roman"], Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{\(\[Psi]\&\[Wedge]\), RowBox[{"(", StyleBox[ SubscriptBox[ StyleBox["k", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["1", FontSlant->"Plain"]], FontSlant->"Italic"], ")"}]}]}], InputForm]], FontFamily->"Times New Roman"], StyleBox[",", FontFamily->"Times New Roman"], Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{\(\[Psi]\&\[Wedge]\), RowBox[{"(", StyleBox[ SubscriptBox[ StyleBox["k", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["2", FontSlant->"Plain"]], FontSlant->"Italic"], ")"}]}]}], InputForm]], FontFamily->"Times New Roman"], StyleBox[", ... , ", FontFamily->"Times New Roman"], Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{\(\[Psi]\&\[Wedge]\), RowBox[{"(", StyleBox[ SubscriptBox[ StyleBox["k", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["n", FontSlant->"Italic"]], FontSlant->"Italic"], ")"}]}]}], InputForm]], FontFamily->"Times New Roman"], StyleBox["}, ", FontFamily->"Times New Roman"], StyleBox["n", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["/2+1", FontFamily->"Times New Roman"], "] ." }], "DisplayFormula"] }, Open ]], Cell[CellGroupData[{ Cell["Practical implementation", "Section"], Cell[TextData[{ "Assume that we are given a function ", StyleBox["f", "InlineFormula", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["[", "InlineFormula", FontFamily->"Times New Roman"], StyleBox["x", "InlineFormula", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["]", "InlineFormula", FontFamily->"Times New Roman"], " which vanishes outside an interval ", StyleBox["[", FontFamily->"Times New Roman"], StyleBox["a", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[", ", FontFamily->"Times New Roman"], StyleBox["b", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["]", FontFamily->"Times New Roman"], ". We want to determine a discrete approximation for the Fourier transform, \ suitable for plotting it quickly.\nWe first choose a grid of points on the \ x-axis. We assume that the grid points are equally spaced by ", StyleBox["d", FontFamily->"Times New Roman"], StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic"], " and given by the numbers ", StyleBox["n", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" d", FontFamily->"Times New Roman"], StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic"], ". Since it is best to choose ", StyleBox["n", FontSlant->"Italic"], " as a power of 2, we calculate d", StyleBox["x", FontSlant->"Italic"], ":" }], "Text"], Cell[BoxData[ \(dx = \(b - a\)\/n\)], "Input"], Cell[BoxData[ \(xgrid = Table[Floor[a\/dx]\ dx + k\ dx, {k, 1, n}]\)], "Input"], Cell[TextData[{ "Of course, the size of d", StyleBox["x", FontSlant->"Italic"], " depends on the variation of the given function. d", StyleBox["x", FontSlant->"Italic"], " determines the size of the interval in ", StyleBox["k", FontSlant->"Italic"], "-space, where the values of the Fourier transform are calculated. The \ spacing of the points in ", StyleBox["k", FontSlant->"Italic"], "-space depends on the size of the interval ", StyleBox["[", FontFamily->"Times New Roman"], StyleBox["a", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[",", FontFamily->"Times New Roman"], StyleBox["b", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["]", FontFamily->"Times New Roman"], ". If we want to evaluate the ", StyleBox["k", FontSlant->"Italic"], "-values at points which are closer together, we have to choose the \ interval in ", StyleBox["x", FontSlant->"Italic"], "-space larger. The points in xgrid are inside the significant interval ", StyleBox["[", FontFamily->"Times New Roman"], StyleBox["a", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[",", FontFamily->"Times New Roman"], StyleBox["b", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox["]", FontFamily->"Times New Roman"], ". We determine the function values at these points:" }], "Text"], Cell[BoxData[ \(fvals = f /@ xgrid\)], "Input"], Cell["Next we rotate the list of function values", "Text"], Cell[BoxData[ \(ind[x_] := Floor[\(x - a\)\/dx] + 1\)], "Input"], Cell[BoxData[ \(RotateLeft[fvals, ind[0] - 1]\)], "Input"], Cell["From this, we calculate the discrete Fourier transform", "Text"], Cell[BoxData[ \(\@\(n\/\(2\ \[Pi]\)\)\ dx\ InverseFourier[ RotateLeft[fvals, ind[0] - 1]]\)], "Input"], Cell[TextData[{ "The result has been multiplied by the appropriate factor. Finally, the \ result is rotated by ", StyleBox["n", FontSlant->"Italic"], "/2" }], "Text"], Cell[BoxData[ \(RotateLeft[\@\(n\/\(2\ \[Pi]\)\)\ dx\ InverseFourier[ RotateLeft[fvals, ind[0] - 1]], Round[n\/2 + 1]]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Explicit example", "Section"], Cell["This is the function we want to transform:", "Text"], Cell[BoxData[ \(\(f[ x_] = \((1\/\[Pi])\)\^\(1/4\)\ Exp[\(-\(x\^2\/2\)\) + I\ 2\ x];\)\)], "Input"], Cell["We choose an interval and grid points in x-space:", "Text"], Cell[BoxData[{ \(\(n = 512;\)\), "\n", \(a = \(-10\); b = 14;\)}], "Input"], Cell[BoxData[ \(\(dx = \(b - a\)\/n;\)\)], "Input"], Cell[BoxData[ \(\(xgrid = Table[Floor[a\/dx]\ dx + k\ dx, {k, 1, n}];\)\)], "Input"], Cell["\<\ Note that 0 is an element of xgrid. Now we evaluate the function on \ the grid points. This gives the discretization of the function f:\ \>", "Text"], Cell[BoxData[ \(\(fvals = f /@ xgrid;\)\)], "Input"], Cell["\<\ The following definition is useful for identifying the value of f \ at a particular point:\ \>", "Text"], Cell[BoxData[ \(ind[x_] := Floor[\(x - a\)\/dx] + 1\)], "Input"], Cell["\<\ Next, we compute the Fourier transform of this list, as described \ above:\ \>", "Text"], Cell[BoxData[ \(\(kvals = Chop[RotateLeft[\@\(n\/\(2\ \[Pi]\)\)\ dx\ InverseFourier[ RotateLeft[fvals, ind[0] - 1]], Round[n\/2]]];\)\)], "Input"], Cell["\<\ This list may be interpreted as a discretization of the Fourier \ transform of the function f. 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o`<30olm?CgofMWIomWIfOlR8R;o20P8=ooIfMT00onRXZ;o3`l?o`00000fomWIf@03o`000?oIfMWo fMWI01[ofMWI000homWIf@03ohZ:R_lH61So000003?ofMWI00CoM7Ado`000?l0003oRXZ:=ooIfMT0 0on:RX[o61PHo`00000gomWIf@06oemOGol820So0000o`000?lH61So_;bl=?oIfMT01_mdM7Co3`l? o`000?l0003o3`l?okbl_3SofMWI00?o?Cdmo`000?oIfMT0=OoIfMT5o`0001SofMWI0000\ \>"], ImageRangeCache->{{{0, 431}, {265.875, 0}} -> {-0.000937647, -5.00002*^-6, \ 0.00348681, 0.00564177}, {{0.375, 430.562}, {265.875, 0}} -> {-2.53016, \ -0.0807486, 0.0975153, 0.00512992}, {{0.375, 430.562}, {265.875, 0}} -> \ {-2.53016, -0.0807486, 0.0975153, 0.00512992}}] }, Open ]], Cell["\<\ We can easily combine the computation above in a single function. \ The following computes the Fourier transform of a numerically given function \ xlist and returns the list of Fourier-transformed values together with the \ information about the grid in k-space:\ \>", "Text"], Cell[BoxData[ \(\(fourierList[xlist_, {xleft_, xright_}] := Module[{n, dx, a, b, klist, kleft, kright, dk}, n = Length[xlist] - 1; dx = \(xright - xleft\)\/n; a = \(-\(xleft\/dx\)\); b = xright\/dx; klist = \@\(n\/\(2\ \[Pi]\)\)\ dx\ RotateLeft[ InverseFourier[RotateLeft[xlist, Round[a]]], Round[n\/2 + 1]]; kleft = \(-\(\[Pi]\/dx\)\); kright = \[Pi]\/dx; {klist, {kleft, kright}}];\)\)], "Input"], Cell[TextData[{ "This function is implemented as ", StyleBox["QFourierList", "InlineInput"], " in the package ", StyleBox["VQM`FastFourier`", "InlineInput"] }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The package VQM`FastFourier`", "Section"], Cell["\<\ The results described above form the theoretical background of the \ package VQM`FastFourier`. Here we show how to obtain the Fourier transform of \ a function f with the help of this package. The package VQM`ArgColorPlot` \ will be useful for the visualization of the function and its Fourier \ transform.\ \>", "Text"], Cell["This loads all declarations of the VQM packages:", "Text"], Cell["<", "Text"], Cell["\<\ The first argument of QFourierList is a list flist of complex \ numbers. You may interpret this list as the discretization of a function \ defined in some interval [a,b]. The second argument of QFourierList specifies \ this interval. Hence the function is called like this: \ QFourierList[flist,{a,b}]. In order to have an example, we generate a list of \ complex values from a function f. The package VQM`FastFourier` provides some \ auxiliary functions for this.\ \>", "Text"], Cell["\<\ We repeat the example above with the help of this package and \ consider the function\ \>", "Text"], Cell[BoxData[ \(\(f[ x_] = \((1\/\[Pi])\)\^\(1/4\)\ Exp[\(-\(x\^2\/2\)\) + I\ 2\ x];\)\)], "Input"], Cell["in the interval [-10,14]:", "Text"], Cell[CellGroupData[{ Cell["QArgColorPlot[f[x],{x,-10,14},PlotRange->All]", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0 1 0 0.618034 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of sub-graphic p 0 0 1 0.618034 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.01472 L .05743 .01472 L F 1 .519 0 r .05743 .01472 m .05743 .01472 L .05847 .01472 L .05847 .01472 L F 1 .569 0 r .05847 .01472 m .05847 .01472 L .05848 .01472 L .05848 .01472 L F 1 .57 0 r .05848 .01472 m .05848 .01472 L .05866 .01472 L .05866 .01472 L F 1 .579 0 r .05866 .01472 m .05866 .01472 L .05936 .01472 L .05936 .01472 L F 1 .612 0 r .05936 .01472 m .05936 .01472 L .05969 .01472 L .05969 .01472 L F 1 .628 0 r .05969 .01472 m .05969 .01472 L .0599 .01472 L .0599 .01472 L F 1 .638 0 r .0599 .01472 m .0599 .01472 L .06 .01472 L .06 .01472 L F 1 .643 0 r .06 .01472 m .06 .01472 L .06111 .01472 L .06111 .01472 L F 1 .697 0 r .06111 .01472 m .06111 .01472 L .06113 .01472 L .06113 .01472 L F .06113 .01472 m .06113 .01472 L .06119 .01472 L .06119 .01472 L F 1 .7 0 r .06119 .01472 m .06119 .01472 L .06244 .01472 L .06244 .01472 L F 1 .761 0 r .06244 .01472 m .06244 .01472 L .06371 .01472 L .06371 .01472 L F 1 .822 0 r .06371 .01472 m .06371 .01472 L .06371 .01472 L .06371 .01472 L F .06371 .01472 m .06371 .01472 L .06486 .01472 L .06486 .01472 L F 1 .877 0 r .06486 .01472 m .06486 .01472 L .06504 .01472 L .06504 .01472 L F 1 .886 0 r .06504 .01472 m .06504 .01472 L .0651 .01472 L .0651 .01472 L F 1 .889 0 r .0651 .01472 m .0651 .01472 L .06617 .01472 L .06617 .01472 L F 1 .94 0 r .06617 .01472 m .06617 .01472 L .06655 .01472 L .06655 .01472 L F 1 .959 0 r .06655 .01472 m .06655 .01472 L .06742 .01472 L .06742 .01472 L F 1 1 0 r .06742 .01472 m .06742 .01472 L .06745 .01472 L .06745 .01472 L F .998 1 0 r .06745 .01472 m .06745 .01472 L .0679 .01472 L .0679 .01472 L F .977 1 0 r .0679 .01472 m .0679 .01472 L .06876 .01472 L .06876 .01472 L F .935 1 0 r .06876 .01472 m .06876 .01472 L .06917 .01472 L .06917 .01472 L F .916 1 0 r .06917 .01472 m .06917 .01472 L .06989 .01472 L .06989 .01472 L F .881 1 0 r .06989 .01472 m .06989 .01472 L .07019 .01472 L .07019 .01472 L F .866 1 0 r .07019 .01472 m .07019 .01472 L .07032 .01472 L .07032 .01472 L F .86 1 0 r .07032 .01472 m .07032 .01472 L .07108 .01472 L .07108 .01472 L F .824 1 0 r .07108 .01472 m .07108 .01472 L .07155 .01472 L .07155 .01472 L F .801 1 0 r .07155 .01472 m .07155 .01472 L .07165 .01472 L .07165 .01472 L F .796 1 0 r .07165 .01472 m .07165 .01472 L .07216 .01472 L .07216 .01472 L F .772 1 0 r .07216 .01472 m .07216 .01472 L .07277 .01472 L .07277 .01472 L F .742 1 0 r .07277 .01472 m .07277 .01472 L .0729 .01472 L .0729 .01472 L F .736 1 0 r .0729 .01472 m .0729 .01472 L .07336 .01472 L .07336 .01472 L F .714 1 0 r .07336 .01472 m .07336 .01472 L .07402 .01472 L .07402 .01472 L F .682 1 0 r .07402 .01472 m .07402 .01472 L .07427 .01472 L .07427 .01472 L F .67 1 0 r .07427 .01472 m .07427 .01472 L .07465 .01472 L .07465 .01472 L F .652 1 0 r .07465 .01472 m .07465 .01472 L .07517 .01472 L .07517 .01472 L F .627 1 0 r .07517 .01472 m .07517 .01472 L .07532 .01472 L .07532 .01472 L F .619 1 0 r .07532 .01472 m .07532 .01472 L .07572 .01472 L .07572 .01472 L F .6 1 0 r .07572 .01472 m .07572 .01472 L .07605 .01472 L .07605 .01472 L F .584 1 0 r .07605 .01472 m .07605 .01472 L .07643 .01472 L .07643 .01472 L F .566 1 0 r .07643 .01472 m .07643 .01472 L .07674 .01472 L .07674 .01472 L F .551 1 0 r .07674 .01472 m .07674 .01472 L .07695 .01472 L .07695 .01472 L F .541 1 0 r .07695 .01472 m .07695 .01472 L .07738 .01472 L .07738 .01472 L F .52 1 0 r .07738 .01472 m .07738 .01472 L .07776 .01472 L .07776 .01472 L F .502 1 0 r .07776 .01472 m .07776 .01472 L .07831 .01472 L .07831 .01472 L F .475 1 0 r .07831 .01472 m .07831 .01472 L .07865 .01472 L .07865 .01472 L F .459 1 0 r .07865 .01472 m .07865 .01472 L .07892 .01472 L .07892 .01472 L F .446 1 0 r .07892 .01472 m .07892 .01472 L .07937 .01472 L .07937 .01472 L F .424 1 0 r .07937 .01472 m .07937 .01472 L .07977 .01472 L .07977 .01472 L F .405 1 0 r .07977 .01472 m .07977 .01472 L .08001 .01472 L .08001 .01472 L F .394 1 0 r .08001 .01472 m .08001 .01472 L .08005 .01472 L .08005 .01472 L F .392 1 0 r .08005 .01472 m .08005 .01472 L .08076 .01472 L .08076 .01472 L F .358 1 0 r .08076 .01472 m .08076 .01472 L .08129 .01472 L .08129 .01472 L F .332 1 0 r .08129 .01472 m .08129 .01472 L .08134 .01472 L .08134 .01472 L F .33 1 0 r .08134 .01472 m .08134 .01472 L .08141 .01472 L .08141 .01472 L F .326 1 0 r .08141 .01472 m .08141 .01472 L .08218 .01472 L .08218 .01472 L F .289 1 0 r .08218 .01472 m .08218 .01472 L .08247 .01472 L .08247 .01472 L F .275 1 0 r .08247 .01472 m .08247 .01472 L .08282 .01472 L .08282 .01472 L F .258 1 0 r .08282 .01472 m .08282 .01472 L .08288 .01472 L .08288 .01472 L F .256 1 0 r .08288 .01472 m .08288 .01472 L .08384 .01472 L .08384 .01472 L F .209 1 0 r .08384 .01472 m .08384 .01472 L .08418 .01472 L .08418 .01472 L F .193 1 0 r .08418 .01472 m .08418 .01472 L .08421 .01472 L .08421 .01472 L F .191 1 0 r .08421 .01472 m .08421 .01472 L .08495 .01472 L .08495 .01472 L F .156 1 0 r .08495 .01472 m .08495 .01472 L .08533 .01472 L .08533 .01472 L F .138 1 0 r .08533 .01472 m .08533 .01472 L .08544 .01472 L .08544 .01472 L F .133 1 0 r .08544 .01472 m .08544 .01472 L .08564 .01472 L .08564 .01472 L F .123 1 0 r .08564 .01472 m .08564 .01472 L .08664 .01472 L .08664 .01472 L F .075 1 0 r .08664 .01472 m .08664 .01472 L .08678 .01472 L .08678 .01472 L F .068 1 0 r .08678 .01472 m .08678 .01472 L .08687 .01472 L .08687 .01472 L F .064 1 0 r .08687 .01472 m .08687 .01472 L .08804 .01472 L .08804 .01472 L F .007 1 0 r .08804 .01472 m .08804 .01472 L .08804 .01472 L .08804 .01472 L F .08804 .01472 m .08804 .01472 L .0882 .01472 L .0882 .01472 L F 0 1 .001 r .0882 .01472 m .0882 .01472 L .0889 .01472 L .0889 .01472 L F 0 1 .034 r .0889 .01472 m .0889 .01472 L .08918 .01472 L .08918 .01472 L F 0 1 .048 r .08918 .01472 m .08918 .01472 L .08942 .01472 L .08942 .01472 L F 0 1 .059 r .08942 .01472 m .08942 .01472 L .08967 .01472 L .08967 .01472 L F 0 1 .071 r .08967 .01472 m .08967 .01472 L .09043 .01472 L .09043 .01472 L F 0 1 .108 r .09043 .01472 m .09043 .01472 L .09054 .01472 L .09054 .01472 L F 0 1 .113 r .09054 .01472 m .09054 .01472 L .09071 .01472 L .09071 .01472 L F 0 1 .121 r .09071 .01472 m .09071 .01472 L .09123 .01472 L .09123 .01472 L F 0 1 .146 r .09123 .01472 m .09123 .01472 L .092 .01472 L .092 .01472 L F 0 1 .183 r .092 .01472 m .092 .01472 L .09267 .01472 L .09267 .01472 L F 0 1 .215 r .09267 .01472 m .09267 .01472 L .09313 .01472 L .09313 .01472 L F 0 1 .238 r .09313 .01472 m .09313 .01472 L .09338 .01472 L .09338 .01472 L F 0 1 .25 r .09338 .01472 m .09338 .01472 L .09401 .01472 L .09401 .01472 L F 0 1 .28 r .09401 .01472 m .09401 .01472 L .09464 .01472 L .09464 .01472 L F 0 1 .311 r .09464 .01472 m .09464 .01472 L .09537 .01472 L .09537 .01472 L F 0 1 .346 r .09537 .01472 m .09537 .01472 L .09584 .01472 L .09584 .01472 L F 0 1 .368 r .09584 .01472 m .09584 .01472 L .09685 .01472 L .09685 .01472 L F 0 1 .417 r .09685 .01472 m .09685 .01472 L .09695 .01472 L .09695 .01472 L F 0 1 .422 r .09695 .01472 m .09695 .01472 L .09817 .01472 L .09817 .01472 L F 0 1 .48 r .09817 .01472 m .09817 .01472 L .09825 .01472 L .09825 .01472 L F 0 1 .484 r .09825 .01472 m .09825 .01472 L .09859 .01472 L .09859 .01472 L F 0 1 .501 r .09859 .01472 m .09859 .01472 L .09948 .01472 L .09948 .01472 L F 0 1 .543 r .09948 .01472 m .09948 .01472 L .09954 .01472 L .09954 .01472 L F 0 1 .546 r .09954 .01472 m .09954 .01472 L .10008 .01472 L .10008 .01472 L F 0 1 .572 r .10008 .01472 m .10008 .01472 L .1007 .01472 L .1007 .01472 L F 0 1 .602 r .1007 .01472 m .1007 .01472 L .10085 .01472 L .10085 .01472 L F 0 1 .609 r .10085 .01472 m .10085 .01472 L .10148 .01472 L .10148 .01472 L F 0 1 .64 r .10148 .01472 m .10148 .01472 L .10199 .01472 L .10199 .01472 L F 0 1 .664 r .10199 .01472 m .10199 .01472 L .10215 .01472 L .10215 .01472 L F 0 1 .672 r .10215 .01472 m .10215 .01472 L .10226 .01472 L .10226 .01472 L F 0 1 .677 r .10226 .01472 m .10226 .01472 L .1031 .01472 L .1031 .01472 L F 0 1 .718 r .1031 .01472 m .1031 .01472 L .10331 .01472 L .10331 .01472 L F 0 1 .728 r .10331 .01472 m .10331 .01472 L .10332 .01472 L .10332 .01472 L F .10332 .01472 m .10332 .01472 L .10387 .01472 L .10387 .01472 L F 0 1 .755 r .10387 .01472 m .10387 .01472 L .10458 .01472 L .10458 .01472 L F 0 1 .789 r .10458 .01472 m .10458 .01472 L .10575 .01472 L .10575 .01472 L F 0 1 .845 r .10575 .01472 m .10575 .01472 L .10576 .01472 L .10576 .01472 L F 0 1 .846 r .10576 .01472 m .10576 .01472 L .1058 .01472 L .1058 .01472 L F 0 1 .848 r .1058 .01472 m .1058 .01472 L .10692 .01472 L .10692 .01472 L F 0 1 .901 r .10692 .01472 m .10692 .01472 L .10702 .01472 L .10702 .01472 L F 0 1 .906 r .10702 .01472 m .10702 .01472 L .10704 .01472 L .10704 .01472 L F 0 1 .907 r .10704 .01472 m .10704 .01472 L .10769 .01472 L .10769 .01472 L F 0 1 .938 r .10769 .01472 m .10769 .01472 L .10815 .01472 L .10815 .01472 L F 0 1 .961 r .10815 .01472 m .10815 .01472 L .10838 .01472 L .10838 .01472 L F 0 1 .972 r .10838 .01472 m .10838 .01472 L .10929 .01472 L .10929 .01472 L F 0 .985 1 r .10929 .01472 m .10929 .01472 L .10944 .01472 L .10944 .01472 L F 0 .977 1 r .10944 .01472 m .10944 .01472 L .10965 .01472 L .10965 .01472 L F 0 .967 1 r .10965 .01472 m .10965 .01472 L .11068 .01472 L .11068 .01472 L F 0 .918 1 r .11068 .01472 m .11068 .01472 L .11085 .01472 L .11085 .01472 L F 0 .91 1 r .11085 .01472 m .11085 .01472 L .11162 .01472 L .11162 .01472 L F 0 .872 1 r .11162 .01472 m .11162 .01472 L .11199 .01472 L .11199 .01472 L F 0 .855 1 r .11199 .01472 m .11199 .01472 L .11211 .01472 L .11211 .01472 L F 0 .849 1 r .11211 .01472 m .11211 .01472 L .11286 .01472 L .11286 .01472 L F 0 .813 1 r .11286 .01472 m .11286 .01472 L .11319 .01472 L .11319 .01472 L F 0 .797 1 r .11319 .01472 m .11319 .01472 L .114 .01472 L .114 .01472 L F 0 .758 1 r .114 .01472 m .114 .01472 L .11437 .01472 L .11437 .01472 L F 0 .74 1 r .11437 .01472 m .11437 .01472 L .11444 .01472 L .11444 .01472 L F 0 .737 1 r .11444 .01472 m .11444 .01472 L .11507 .01472 L .11507 .01472 L F 0 .706 1 r .11507 .01472 m .11507 .01472 L .11536 .01472 L .11536 .01472 L F 0 .692 1 r .11536 .01472 m .11536 .01472 L .1157 .01472 L .1157 .01472 L F 0 .676 1 r .1157 .01472 m .1157 .01472 L .11573 .01472 L .11573 .01472 L F 0 .675 1 r .11573 .01472 m .11573 .01472 L .11664 .01472 L .11664 .01472 L F 0 .631 1 r .11664 .01472 m .11664 .01472 L .11696 .01472 L .11696 .01472 L F 0 .615 1 r .11696 .01472 m .11696 .01472 L .11703 .01472 L .11703 .01472 L F 0 .612 1 r .11703 .01472 m .11703 .01472 L .11779 .01472 L .11779 .01472 L F 0 .576 1 r .11779 .01472 m .11779 .01472 L .11829 .01472 L .11829 .01472 L F 0 .552 1 r .11829 .01472 m .11829 .01472 L .11903 .01472 L .11903 .01472 L F 0 .516 1 r .11903 .01472 m .11903 .01472 L .11941 .01472 L .11941 .01472 L F 0 .497 1 r .11941 .01472 m .11941 .01472 L .11972 .01472 L .11972 .01472 L F 0 .482 1 r .11972 .01472 m .11972 .01472 L .12039 .01472 L .12039 .01472 L F 0 .45 1 r .12039 .01472 m .12039 .01472 L .12098 .01472 L .12098 .01472 L F 0 .422 1 r .12098 .01472 m .12098 .01472 L .12182 .01472 L .12182 .01472 L F 0 .381 1 r .12182 .01472 m .12182 .01472 L .12198 .01472 L .12198 .01472 L F 0 .374 1 r .12198 .01472 m .12198 .01472 L .12231 .01472 L .12231 .01472 L F 0 .358 1 r .12231 .01472 m .12231 .01472 L .12305 .01472 L .12305 .01472 L F 0 .322 1 r .12305 .01472 m .12305 .01472 L .12345 .01472 L .12345 .01472 L F 0 .303 1 r .12345 .01472 m .12345 .01472 L .12439 .01472 L .12439 .01472 L F 0 .258 1 r .12439 .01472 m .12439 .01472 L .1247 .01472 L .1247 .01472 L F 0 .243 1 r .1247 .01472 m .1247 .01472 L .1248 .01472 L .1248 .01472 L F 0 .238 1 r .1248 .01472 m .1248 .01472 L .1258 .01472 L .1258 .01472 L F 0 .19 1 r .1258 .01472 m .1258 .01472 L .12594 .01472 L .12594 .01472 L F 0 .183 1 r .12594 .01472 m .12594 .01472 L .12711 .01472 L .12711 .01472 L F 0 .127 1 r .12711 .01472 m .12711 .01472 L .12713 .01472 L .12713 .01472 L F 0 .126 1 r .12713 .01472 m .12713 .01472 L .12833 .01472 L .12833 .01472 L F 0 .068 1 r .12833 .01472 m .12833 .01472 L .12931 .01472 L .12931 .01472 L F 0 .021 1 r .12931 .01472 m .12931 .01472 L .12942 .01472 L .12942 .01472 L F 0 .016 1 r .12942 .01472 m .12942 .01472 L .12964 .01472 L .12964 .01472 L F 0 .005 1 r .12964 .01472 m .12964 .01472 L .13054 .01472 L .13054 .01472 L F .038 0 1 r .13054 .01472 m .13054 .01472 L .13064 .01472 L .13064 .01472 L F .043 0 1 r .13064 .01472 m .13064 .01472 L .13105 .01472 L .13105 .01472 L F .063 0 1 r .13105 .01472 m .13105 .01472 L .13168 .01472 L .13168 .01472 L F .093 0 1 r .13168 .01472 m .13168 .01472 L .13196 .01472 L .13196 .01472 L F .107 0 1 r .13196 .01472 m .13196 .01472 L .13256 .01472 L .13256 .01472 L F .135 0 1 r .13256 .01472 m .13256 .01472 L .13293 .01472 L .13293 .01472 L F .153 0 1 r .13293 .01472 m .13293 .01472 L .13322 .01472 L .13322 .01472 L F .167 0 1 r .13322 .01472 m .13322 .01472 L .13384 .01472 L .13384 .01472 L F .197 0 1 r .13384 .01472 m .13384 .01472 L .13425 .01472 L .13425 .01472 L F .217 0 1 r .13425 .01472 m .13425 .01472 L .13438 .01472 L .13438 .01472 L F .223 0 1 r .13438 .01472 m .13438 .01472 L .13526 .01472 L .13526 .01472 L F .265 0 1 r .13526 .01472 m .13526 .01472 L .13531 .01472 L .13531 .01472 L F .268 0 1 r .13531 .01472 m .13531 .01472 L .13545 .01472 L .13545 .01472 L F .275 0 1 r .13545 .01472 m .13545 .01472 L .13644 .01472 L .13644 .01472 L F .322 0 1 r .13644 .01472 m .13644 .01472 L .13657 .01472 L .13657 .01472 L F .329 0 1 r .13657 .01472 m .13657 .01472 L .13664 .01472 L .13664 .01472 L F .332 0 1 r .13664 .01472 m .13664 .01472 L .13778 .01472 L .13778 .01472 L F .387 0 1 r .13778 .01472 m .13778 .01472 L .13788 .01472 L .13788 .01472 L F .392 0 1 r .13788 .01472 m .13788 .01472 L .1385 .01472 L .1385 .01472 L F .421 0 1 r .1385 .01472 m .1385 .01472 L .13905 .01472 L .13905 .01472 L F .448 0 1 r .13905 .01472 m .13905 .01472 L .1391 .01472 L .1391 .01472 L F .45 0 1 r .1391 .01472 m .1391 .01472 L .13969 .01472 L .13969 .01472 L F .478 0 1 r .13969 .01472 m 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.65441 .01472 L .65558 .01472 L .65558 .01472 L F 1 0 .692 r .65558 .01472 m .65558 .01472 L .6557 .01472 L .6557 .01472 L F 1 0 .687 r .6557 .01472 m .6557 .01472 L .65622 .01472 L .65622 .01472 L F 1 0 .662 r .65622 .01472 m .65622 .01472 L .65677 .01472 L .65677 .01472 L F 1 0 .635 r .65677 .01472 m .65677 .01472 L .6572 .01472 L .6572 .01472 L F 1 0 .615 r .6572 .01472 m .6572 .01472 L .65861 .01472 L .65861 .01472 L F 1 0 .547 r .65861 .01472 m .65861 .01472 L .65869 .01472 L .65869 .01472 L F 1 0 .543 r .65869 .01472 m .65869 .01472 L .659 .01472 L .659 .01472 L F 1 0 .528 r .659 .01472 m .659 .01472 L .66024 .01472 L .66024 .01472 L F 1 0 .468 r .66024 .01472 m .66024 .01472 L .66107 .01472 L .66107 .01472 L F 1 0 .428 r .66107 .01472 m .66107 .01472 L .66135 .01472 L .66135 .01472 L F 1 0 .415 r .66135 .01472 m .66135 .01472 L .6614 .01472 L .6614 .01472 L F 1 0 .412 r .6614 .01472 m .6614 .01472 L .66266 .01472 L .66266 .01472 L F 1 0 .351 r .66266 .01472 m .66266 .01472 L 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.68999 .01472 L F 1 .964 0 r .68999 .01472 m .68999 .01472 L .69069 .01472 L .69069 .01472 L F 1 .997 0 r .69069 .01472 m .69069 .01472 L .69107 .01472 L .69107 .01472 L F .985 1 0 r .69107 .01472 m .69107 .01472 L .69107 .01472 L .69107 .01472 L F .984 1 0 r .69107 .01472 m .69107 .01472 L .69222 .01472 L .69222 .01472 L F .929 1 0 r .69222 .01472 m .69222 .01472 L .69297 .01472 L .69297 .01472 L F .893 1 0 r .69297 .01472 m .69297 .01472 L .69349 .01472 L .69349 .01472 L F .868 1 0 r .69349 .01472 m .69349 .01472 L .69371 .01472 L .69371 .01472 L F .857 1 0 r .69371 .01472 m .69371 .01472 L .69423 .01472 L .69423 .01472 L F .832 1 0 r .69423 .01472 m .69423 .01472 L .69466 .01472 L .69466 .01472 L F .812 1 0 r .69466 .01472 m .69466 .01472 L .69495 .01472 L .69495 .01472 L F .798 1 0 r .69495 .01472 m .69495 .01472 L .69541 .01472 L .69541 .01472 L F .775 1 0 r .69541 .01472 m .69541 .01472 L .69599 .01472 L .69599 .01472 L F .748 1 0 r .69599 .01472 m .69599 .01472 L .69629 .01472 L .69629 .01472 L F .733 1 0 r .69629 .01472 m .69629 .01472 L .69672 .01472 L .69672 .01472 L F .713 1 0 r .69672 .01472 m .69672 .01472 L .69724 .01472 L .69724 .01472 L F .688 1 0 r .69724 .01472 m .69724 .01472 L .69747 .01472 L .69747 .01472 L F .676 1 0 r .69747 .01472 m .69747 .01472 L .69811 .01472 L .69811 .01472 L F .646 1 0 r .69811 .01472 m .69811 .01472 L .69836 .01472 L .69836 .01472 L F .634 1 0 r .69836 .01472 m .69836 .01472 L .69872 .01472 L .69872 .01472 L F .616 1 0 r .69872 .01472 m .69872 .01472 L .69946 .01472 L .69946 .01472 L F .58 1 0 r .69946 .01472 m .69946 .01472 L .69957 .01472 L .69957 .01472 L F .575 1 0 r .69957 .01472 m .69957 .01472 L .69985 .01472 L .69985 .01472 L F .562 1 0 r .69985 .01472 m .69985 .01472 L .70069 .01472 L .70069 .01472 L F .521 1 0 r .70069 .01472 m .70069 .01472 L .70081 .01472 L .70081 .01472 L F .516 1 0 r .70081 .01472 m .70081 .01472 L .70109 .01472 L .70109 .01472 L F .502 1 0 r .70109 .01472 m .70109 .01472 L .70194 .01472 L .70194 .01472 L F .461 1 0 r .70194 .01472 m .70194 .01472 L .70309 .01472 L .70309 .01472 L F .406 1 0 r .70309 .01472 m .70309 .01472 L .70324 .01472 L .70324 .01472 L F .399 1 0 r .70324 .01472 m .70324 .01472 L .70327 .01472 L .70327 .01472 L F .397 1 0 r .70327 .01472 m .70327 .01472 L .70443 .01472 L .70443 .01472 L F .341 1 0 r .70443 .01472 m .70443 .01472 L .70447 .01472 L .70447 .01472 L F .339 1 0 r .70447 .01472 m .70447 .01472 L .7046 .01472 L .7046 .01472 L F .333 1 0 r .7046 .01472 m .7046 .01472 L .70561 .01472 L .70561 .01472 L F .285 1 0 r .70561 .01472 m .70561 .01472 L .70581 .01472 L .70581 .01472 L F .275 1 0 r .70581 .01472 m .70581 .01472 L .70589 .01472 L .70589 .01472 L F .271 1 0 r .70589 .01472 m .70589 .01472 L .70666 .01472 L .70666 .01472 L F .234 1 0 r .70666 .01472 m .70666 .01472 L .70712 .01472 L .70712 .01472 L F .212 1 0 r .70712 .01472 m .70712 .01472 L .70726 .01472 L .70726 .01472 L F .205 1 0 r .70726 .01472 m .70726 .01472 L .70782 .01472 L .70782 .01472 L F .178 1 0 r .70782 .01472 m .70782 .01472 L .70852 .01472 L .70852 .01472 L F .145 1 0 r .70852 .01472 m .70852 .01472 L .70854 .01472 L .70854 .01472 L F .143 1 0 r .70854 .01472 m .70854 .01472 L .70905 .01472 L .70905 .01472 L F .119 1 0 r .70905 .01472 m .70905 .01472 L .70986 .01472 L .70986 .01472 L F .08 1 0 r .70986 .01472 m .70986 .01472 L .71081 .01472 L .71081 .01472 L F .034 1 0 r .71081 .01472 m .71081 .01472 L .71107 .01472 L .71107 .01472 L F .022 1 0 r .71107 .01472 m .71107 .01472 L .71211 .01472 L .71211 .01472 L F 0 1 .028 r .71211 .01472 m .71211 .01472 L .71232 .01472 L .71232 .01472 L F 0 1 .039 r .71232 .01472 m .71232 .01472 L .71333 .01472 L .71333 .01472 L F 0 1 .087 r .71333 .01472 m .71333 .01472 L .71347 .01472 L .71347 .01472 L F 0 1 .094 r .71347 .01472 m .71347 .01472 L .71406 .01472 L .71406 .01472 L F 0 1 .122 r .71406 .01472 m .71406 .01472 L .71459 .01472 L .71459 .01472 L F 0 1 .147 r .71459 .01472 m .71459 .01472 L .71463 .01472 L .71463 .01472 L F 0 1 .15 r .71463 .01472 m .71463 .01472 L .71578 .01472 L .71578 .01472 L F 0 1 .205 r .71578 .01472 m .71578 .01472 L .71588 .01472 L .71588 .01472 L F 0 1 .21 r .71588 .01472 m .71588 .01472 L .71669 .01472 L .71669 .01472 L F 0 1 .249 r .71669 .01472 m .71669 .01472 L .71698 .01472 L .71698 .01472 L F 0 1 .263 r .71698 .01472 m .71698 .01472 L .71715 .01472 L .71715 .01472 L F 0 1 .271 r .71715 .01472 m .71715 .01472 L .71815 .01472 L .71815 .01472 L F 0 1 .319 r .71815 .01472 m .71815 .01472 L .7184 .01472 L .7184 .01472 L F 0 1 .331 r .7184 .01472 m .7184 .01472 L .71912 .01472 L .71912 .01472 L F 0 1 .366 r .71912 .01472 m .71912 .01472 L .71947 .01472 L .71947 .01472 L F 0 1 .382 r .71947 .01472 m .71947 .01472 L .72017 .01472 L .72017 .01472 L F 0 1 .416 r .72017 .01472 m .72017 .01472 L .72064 .01472 L .72064 .01472 L F 0 1 .439 r .72064 .01472 m .72064 .01472 L .72089 .01472 L .72089 .01472 L F 0 1 .451 r .72089 .01472 m .72089 .01472 L .72131 .01472 L .72131 .01472 L F 0 1 .471 r .72131 .01472 m .72131 .01472 L .72177 .01472 L .72177 .01472 L F 0 1 .493 r .72177 .01472 m .72177 .01472 L .72238 .01472 L .72238 .01472 L F 0 1 .522 r .72238 .01472 m .72238 .01472 L .72244 .01472 L .72244 .01472 L F 0 1 .525 r .72244 .01472 m .72244 .01472 L .72302 .01472 L .72302 .01472 L F 0 1 .553 r .72302 .01472 m .72302 .01472 L .7236 .01472 L .7236 .01472 L F 0 1 .581 r .7236 .01472 m .7236 .01472 L .72408 .01472 L .72408 .01472 L F 0 1 .604 r .72408 .01472 m .72408 .01472 L .72492 .01472 L .72492 .01472 L F 0 1 .645 r .72492 .01472 m .72492 .01472 L .72516 .01472 L .72516 .01472 L F 0 1 .657 r .72516 .01472 m .72516 .01472 L .72522 .01472 L .72522 .01472 L F 0 1 .659 r .72522 .01472 m .72522 .01472 L .72618 .01472 L .72618 .01472 L F 0 1 .705 r .72618 .01472 m .72618 .01472 L .7265 .01472 L .7265 .01472 L F 0 1 .721 r .7265 .01472 m .7265 .01472 L .72729 .01472 L .72729 .01472 L F 0 1 .759 r .72729 .01472 m .72729 .01472 L .72733 .01472 L .72733 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.01472 L F 0 .722 1 r .73807 .01472 m .73807 .01472 L .73816 .01472 L .73816 .01472 L F 0 .718 1 r .73816 .01472 m .73816 .01472 L .73923 .01472 L .73923 .01472 L F 0 .666 1 r .73923 .01472 m .73923 .01472 L .73926 .01472 L .73926 .01472 L F 0 .665 1 r .73926 .01472 m .73926 .01472 L .73941 .01472 L .73941 .01472 L F 0 .658 1 r .73941 .01472 m .73941 .01472 L .74052 .01472 L .74052 .01472 L F 0 .604 1 r .74052 .01472 m .74052 .01472 L .74057 .01472 L .74057 .01472 L F 0 .602 1 r .74057 .01472 m .74057 .01472 L .74075 .01472 L .74075 .01472 L F 0 .593 1 r .74075 .01472 m .74075 .01472 L .74176 .01472 L .74176 .01472 L F 0 .545 1 r .74176 .01472 m .74176 .01472 L .7418 .01472 L .7418 .01472 L F 0 .543 1 r .7418 .01472 m .7418 .01472 L .74222 .01472 L .74222 .01472 L F 0 .522 1 r .74222 .01472 m .74222 .01472 L .74309 .01472 L .74309 .01472 L F 0 .481 1 r .74309 .01472 m .74309 .01472 L .74319 .01472 L .74319 .01472 L F 0 .476 1 r .74319 .01472 m .74319 .01472 L .74434 .01472 L .74434 .01472 L F 0 .42 1 r .74434 .01472 m .74434 .01472 L .7445 .01472 L .7445 .01472 L F 0 .413 1 r .7445 .01472 m .7445 .01472 L .74467 .01472 L .74467 .01472 L F 0 .405 1 r .74467 .01472 m .74467 .01472 L .74548 .01472 L .74548 .01472 L F 0 .366 1 r .74548 .01472 m .74548 .01472 L .74567 .01472 L .74567 .01472 L F 0 .357 1 r .74567 .01472 m .74567 .01472 L .74682 .01472 L .74682 .01472 L F 0 .301 1 r .74682 .01472 m .74682 .01472 L .74695 .01472 L .74695 .01472 L F 0 .295 1 r .74695 .01472 m .74695 .01472 L .74699 .01472 L .74699 .01472 L F 0 .293 1 r .74699 .01472 m .74699 .01472 L .74805 .01472 L .74805 .01472 L F 0 .242 1 r .74805 .01472 m .74805 .01472 L .74827 .01472 L .74827 .01472 L F 0 .231 1 r .74827 .01472 m .74827 .01472 L .74927 .01472 L .74927 .01472 L F 0 .183 1 r .74927 .01472 m .74927 .01472 L .74964 .01472 L .74964 .01472 L F 0 .166 1 r .74964 .01472 m .74964 .01472 L .74966 .01472 L .74966 .01472 L F 0 .165 1 r .74966 .01472 m .74966 .01472 L .75054 .01472 L .75054 .01472 L F 0 .122 1 r .75054 .01472 m .75054 .01472 L .75084 .01472 L .75084 .01472 L F 0 .108 1 r .75084 .01472 m .75084 .01472 L .7509 .01472 L .7509 .01472 L F 0 .105 1 r .7509 .01472 m .7509 .01472 L .75174 .01472 L .75174 .01472 L F 0 .065 1 r .75174 .01472 m .75174 .01472 L .75208 .01472 L .75208 .01472 L F 0 .048 1 r .75208 .01472 m .75208 .01472 L .75209 .01472 L .75209 .01472 L F .75209 .01472 m .75209 .01472 L .75277 .01472 L .75277 .01472 L F 0 .015 1 r .75277 .01472 m .75277 .01472 L .75318 .01472 L .75318 .01472 L F .005 0 1 r .75318 .01472 m .75318 .01472 L .75322 .01472 L .75322 .01472 L F .007 0 1 r .75322 .01472 m .75322 .01472 L .75387 .01472 L .75387 .01472 L F .038 0 1 r .75387 .01472 m .75387 .01472 L .7544 .01472 L .7544 .01472 L F .063 0 1 r .7544 .01472 m .7544 .01472 L .75447 .01472 L .75447 .01472 L F .067 0 1 r .75447 .01472 m .75447 .01472 L .75507 .01472 L .75507 .01472 L F .096 0 1 r .75507 .01472 m .75507 .01472 L .75569 .01472 L .75569 .01472 L F .126 0 1 r .75569 .01472 m .75569 .01472 L .75617 .01472 L .75617 .01472 L F .149 0 1 r .75617 .01472 m .75617 .01472 L .75635 .01472 L .75635 .01472 L F .157 0 1 r .75635 .01472 m .75635 .01472 L .75668 .01472 L .75668 .01472 L F .173 0 1 r .75668 .01472 m .75668 .01472 L .75706 .01472 L .75706 .01472 L F .191 0 1 r .75706 .01472 m .75706 .01472 L .75747 .01472 L .75747 .01472 L F .211 0 1 r .75747 .01472 m .75747 .01472 L .75792 .01472 L .75792 .01472 L F .233 0 1 r .75792 .01472 m .75792 .01472 L .75835 .01472 L .75835 .01472 L F .253 0 1 r .75835 .01472 m .75835 .01472 L .75865 .01472 L .75865 .01472 L F .268 0 1 r .75865 .01472 m .75865 .01472 L .75925 .01472 L .75925 .01472 L F .297 0 1 r .75925 .01472 m .75925 .01472 L .7596 .01472 L .7596 .01472 L F .314 0 1 r .7596 .01472 m .7596 .01472 L .76002 .01472 L .76002 .01472 L F .334 0 1 r .76002 .01472 m .76002 .01472 L .76041 .01472 L .76041 .01472 L F .353 0 1 r .76041 .01472 m .76041 .01472 L .76076 .01472 L .76076 .01472 L F .37 0 1 r 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.77698 .01472 L .77768 .01472 L .77768 .01472 L F 1 0 .816 r .77768 .01472 m .77768 .01472 L .77827 .01472 L .77827 .01472 L F 1 0 .788 r .77827 .01472 m .77827 .01472 L .77896 .01472 L .77896 .01472 L F 1 0 .754 r .77896 .01472 m .77896 .01472 L .77929 .01472 L .77929 .01472 L F 1 0 .739 r .77929 .01472 m .77929 .01472 L .77963 .01472 L .77963 .01472 L F 1 0 .722 r .77963 .01472 m .77963 .01472 L .77968 .01472 L .77968 .01472 L F 1 0 .72 r .77968 .01472 m .77968 .01472 L .78033 .01472 L .78033 .01472 L F 1 0 .688 r .78033 .01472 m .78033 .01472 L .78079 .01472 L .78079 .01472 L F 1 0 .666 r .78079 .01472 m .78079 .01472 L .78152 .01472 L .78152 .01472 L F 1 0 .631 r .78152 .01472 m .78152 .01472 L .78167 .01472 L .78167 .01472 L F 1 0 .624 r .78167 .01472 m .78167 .01472 L .78206 .01472 L .78206 .01472 L F 1 0 .605 r .78206 .01472 m .78206 .01472 L .78237 .01472 L .78237 .01472 L F 1 0 .59 r .78237 .01472 m .78237 .01472 L .78277 .01472 L .78277 .01472 L F 1 0 .571 r .78277 .01472 m .78277 .01472 L .78312 .01472 L .78312 .01472 L F 1 0 .554 r .78312 .01472 m .78312 .01472 L .78344 .01472 L .78344 .01472 L F 1 0 .539 r .78344 .01472 m .78344 .01472 L .78391 .01472 L .78391 .01472 L F 1 0 .516 r .78391 .01472 m .78391 .01472 L .78436 .01472 L .78436 .01472 L F 1 0 .494 r .78436 .01472 m .78436 .01472 L .78491 .01472 L .78491 .01472 L F 1 0 .468 r .78491 .01472 m .78491 .01472 L .78507 .01472 L .78507 .01472 L F 1 0 .46 r .78507 .01472 m .78507 .01472 L .78516 .01472 L .78516 .01472 L F 1 0 .456 r .78516 .01472 m .78516 .01472 L .78573 .01472 L .78573 .01472 L F 1 0 .428 r .78573 .01472 m .78573 .01472 L .7863 .01472 L .7863 .01472 L F 1 0 .401 r .7863 .01472 m .7863 .01472 L .78653 .01472 L .78653 .01472 L F 1 0 .39 r .78653 .01472 m .78653 .01472 L .78697 .01472 L .78697 .01472 L F 1 0 .369 r .78697 .01472 m .78697 .01472 L .78756 .01472 L .78756 .01472 L F 1 0 .34 r .78756 .01472 m .78756 .01472 L .78781 .01472 L .78781 .01472 L F 1 0 .328 r .78781 .01472 m .78781 .01472 L .7881 .01472 L .7881 .01472 L F 1 0 .315 r .7881 .01472 m .7881 .01472 L .78884 .01472 L .78884 .01472 L F 1 0 .279 r .78884 .01472 m .78884 .01472 L .78901 .01472 L .78901 .01472 L F 1 0 .271 r .78901 .01472 m .78901 .01472 L .78939 .01472 L .78939 .01472 L F 1 0 .252 r .78939 .01472 m .78939 .01472 L .79001 .01472 L .79001 .01472 L F 1 0 .222 r .79001 .01472 m .79001 .01472 L .79035 .01472 L .79035 .01472 L F 1 0 .206 r .79035 .01472 m .79035 .01472 L .79062 .01472 L .79062 .01472 L F 1 0 .193 r .79062 .01472 m .79062 .01472 L .79131 .01472 L .79131 .01472 L F 1 0 .16 r .79131 .01472 m .79131 .01472 L .79162 .01472 L .79162 .01472 L F 1 0 .145 r .79162 .01472 m .79162 .01472 L .79168 .01472 L .79168 .01472 L F 1 0 .142 r .79168 .01472 m .79168 .01472 L .79268 .01472 L .79268 .01472 L F 1 0 .094 r .79268 .01472 m .79268 .01472 L .79276 .01472 L .79276 .01472 L F 1 0 .09 r .79276 .01472 m .79276 .01472 L .79285 .01472 L .79285 .01472 L F 1 0 .086 r .79285 .01472 m .79285 .01472 L .79387 .01472 L .79387 .01472 L F 1 0 .037 r .79387 .01472 m .79387 .01472 L .79399 .01472 L .79399 .01472 L F 1 0 .031 r .79399 .01472 m .79399 .01472 L .79408 .01472 L .79408 .01472 L F 1 0 .027 r .79408 .01472 m .79408 .01472 L .79498 .01472 L .79498 .01472 L F 1 .017 0 r .79498 .01472 m .79498 .01472 L .79522 .01472 L .79522 .01472 L F 1 .028 0 r .79522 .01472 m .79522 .01472 L .79534 .01472 L .79534 .01472 L F 1 .034 0 r .79534 .01472 m .79534 .01472 L .79621 .01472 L .79621 .01472 L F 1 .076 0 r .79621 .01472 m .79621 .01472 L .79629 .01472 L .79629 .01472 L F 1 .08 0 r .79629 .01472 m .79629 .01472 L .79675 .01472 L .79675 .01472 L F 1 .102 0 r .79675 .01472 m .79675 .01472 L .79727 .01472 L .79727 .01472 L F 1 .127 0 r .79727 .01472 m .79727 .01472 L .79752 .01472 L .79752 .01472 L F 1 .139 0 r .79752 .01472 m .79752 .01472 L .79797 .01472 L .79797 .01472 L F 1 .16 0 r .79797 .01472 m .79797 .01472 L .79834 .01472 L .79834 .01472 L F 1 .178 0 r .79834 .01472 m .79834 .01472 L .7987 .01472 L .7987 .01472 L F 1 .195 0 r .7987 .01472 m .7987 .01472 L .7993 .01472 L .7993 .01472 L F 1 .224 0 r .7993 .01472 m .7993 .01472 L .79947 .01472 L .79947 .01472 L F 1 .233 0 r .79947 .01472 m .79947 .01472 L .79978 .01472 L .79978 .01472 L F 1 .248 0 r .79978 .01472 m .79978 .01472 L .80054 .01472 L .80054 .01472 L F 1 .284 0 r .80054 .01472 m .80054 .01472 L .80062 .01472 L .80062 .01472 L F 1 .288 0 r .80062 .01472 m .80062 .01472 L .80098 .01472 L .80098 .01472 L F 1 .305 0 r .80098 .01472 m .80098 .01472 L .80171 .01472 L .80171 .01472 L F 1 .341 0 r .80171 .01472 m .80171 .01472 L .80185 .01472 L .80185 .01472 L F 1 .347 0 r .80185 .01472 m .80185 .01472 L .80226 .01472 L .80226 .01472 L F 1 .367 0 r .80226 .01472 m .80226 .01472 L .80276 .01472 L .80276 .01472 L F 1 .391 0 r .80276 .01472 m .80276 .01472 L .8036 .01472 L .8036 .01472 L F 1 .432 0 r .8036 .01472 m .8036 .01472 L .80391 .01472 L .80391 .01472 L F 1 .446 0 r .80391 .01472 m .80391 .01472 L .80406 .01472 L .80406 .01472 L F 1 .454 0 r .80406 .01472 m .80406 .01472 L .80487 .01472 L .80487 .01472 L F 1 .493 0 r .80487 .01472 m .80487 .01472 L .80515 .01472 L .80515 .01472 L F 1 .506 0 r .80515 .01472 m .80515 .01472 L .806 .01472 L .806 .01472 L F 1 .547 0 r .806 .01472 m .806 .01472 L .80645 .01472 L .80645 .01472 L F 1 .569 0 r .80645 .01472 m .80645 .01472 L .80647 .01472 L .80647 .01472 L F 1 .57 0 r .80647 .01472 m .80647 .01472 L .80724 .01472 L .80724 .01472 L F 1 .607 0 r .80724 .01472 m .80724 .01472 L .8076 .01472 L .8076 .01472 L F 1 .624 0 r .8076 .01472 m .8076 .01472 L .80781 .01472 L .80781 .01472 L F 1 .634 0 r .80781 .01472 m .80781 .01472 L .80831 .01472 L .80831 .01472 L F 1 .658 0 r .80831 .01472 m .80831 .01472 L .80884 .01472 L .80884 .01472 L F 1 .684 0 r .80884 .01472 m .80884 .01472 L .80908 .01472 L .80908 .01472 L F 1 .695 0 r .80908 .01472 m .80908 .01472 L .80949 .01472 L .80949 .01472 L F 1 .715 0 r .80949 .01472 m .80949 .01472 L .81 .01472 L .81 .01472 L F 1 .74 0 r .81 .01472 m .81 .01472 L .81072 .01472 L .81072 .01472 L F 1 .774 0 r .81072 .01472 m .81072 .01472 L .81106 .01472 L .81106 .01472 L F 1 .79 0 r .81106 .01472 m .81106 .01472 L .81167 .01472 L .81167 .01472 L F 1 .82 0 r .81167 .01472 m .81167 .01472 L .81187 .01472 L .81187 .01472 L F 1 .83 0 r .81187 .01472 m .81187 .01472 L .81222 .01472 L .81222 .01472 L F 1 .846 0 r .81222 .01472 m .81222 .01472 L .81295 .01472 L .81295 .01472 L F 1 .881 0 r .81295 .01472 m .81295 .01472 L .813 .01472 L .813 .01472 L F 1 .884 0 r .813 .01472 m .813 .01472 L .81344 .01472 L .81344 .01472 L F 1 .905 0 r .81344 .01472 m .81344 .01472 L .81393 .01472 L .81393 .01472 L F 1 .929 0 r .81393 .01472 m .81393 .01472 L .81442 .01472 L .81442 .01472 L F 1 .952 0 r .81442 .01472 m .81442 .01472 L .81451 .01472 L .81451 .01472 L F 1 .956 0 r .81451 .01472 m .81451 .01472 L .81506 .01472 L .81506 .01472 L F 1 .983 0 r .81506 .01472 m .81506 .01472 L .8155 .01472 L .8155 .01472 L F .996 1 0 r .8155 .01472 m .8155 .01472 L .81574 .01472 L .81574 .01472 L F .984 1 0 r .81574 .01472 m .81574 .01472 L .81614 .01472 L .81614 .01472 L F .965 1 0 r .81614 .01472 m .81614 .01472 L .81659 .01472 L .81659 .01472 L F .943 1 0 r .81659 .01472 m .81659 .01472 L .81699 .01472 L .81699 .01472 L F .924 1 0 r .81699 .01472 m .81699 .01472 L .81739 .01472 L .81739 .01472 L F .905 1 0 r .81739 .01472 m .81739 .01472 L .81775 .01472 L .81775 .01472 L F .888 1 0 r .81775 .01472 m .81775 .01472 L .81812 .01472 L .81812 .01472 L F .87 1 0 r .81812 .01472 m .81812 .01472 L .81874 .01472 L .81874 .01472 L F .84 1 0 r .81874 .01472 m .81874 .01472 L .81899 .01472 L .81899 .01472 L F .828 1 0 r .81899 .01472 m .81899 .01472 L .81934 .01472 L .81934 .01472 L F .811 1 0 r .81934 .01472 m .81934 .01472 L .81969 .01472 L .81969 .01472 L F .794 1 0 r .81969 .01472 m .81969 .01472 L .82002 .01472 L .82002 .01472 L F .778 1 0 r .82002 .01472 m .82002 .01472 L .82035 .01472 L .82035 .01472 L F .763 1 0 r .82035 .01472 m .82035 .01472 L .82067 .01472 L .82067 .01472 L F .747 1 0 r .82067 .01472 m .82067 .01472 L .82103 .01472 L .82103 .01472 L F .73 1 0 r .82103 .01472 m .82103 .01472 L .82119 .01472 L .82119 .01472 L F .722 1 0 r .82119 .01472 m .82119 .01472 L .82167 .01472 L .82167 .01472 L F .699 1 0 r .82167 .01472 m .82167 .01472 L .82214 .01472 L .82214 .01472 L F .676 1 0 r .82214 .01472 m .82214 .01472 L .82225 .01472 L .82225 .01472 L F .671 1 0 r .82225 .01472 m .82225 .01472 L .82241 .01472 L .82241 .01472 L F .663 1 0 r .82241 .01472 m .82241 .01472 L .82288 .01472 L .82288 .01472 L F .641 1 0 r .82288 .01472 m .82288 .01472 L .82309 .01472 L .82309 .01472 L F .63 1 0 r .82309 .01472 m .82309 .01472 L .82342 .01472 L .82342 .01472 L F .615 1 0 r .82342 .01472 m .82342 .01472 L .82367 .01472 L .82367 .01472 L F .602 1 0 r .82367 .01472 m .82367 .01472 L .82432 .01472 L .82432 .01472 L F .571 1 0 r .82432 .01472 m .82432 .01472 L .82463 .01472 L .82463 .01472 L F .556 1 0 r .82463 .01472 m .82463 .01472 L .82511 .01472 L .82511 .01472 L F .533 1 0 r .82511 .01472 m .82511 .01472 L .82545 .01472 L .82545 .01472 L F .517 1 0 r .82545 .01472 m .82545 .01472 L .82576 .01472 L .82576 .01472 L F .502 1 0 r .82576 .01472 m .82576 .01472 L .82647 .01472 L .82647 .01472 L F .468 1 0 r .82647 .01472 m .82647 .01472 L .82669 .01472 L .82669 .01472 L F .457 1 0 r .82669 .01472 m .82669 .01472 L .82709 .01472 L .82709 .01472 L F .438 1 0 r .82709 .01472 m .82709 .01472 L .8279 .01472 L .8279 .01472 L F .399 1 0 r .8279 .01472 m .8279 .01472 L .82801 .01472 L .82801 .01472 L F .393 1 0 r .82801 .01472 m .82801 .01472 L .82835 .01472 L .82835 .01472 L F .377 1 0 r .82835 .01472 m .82835 .01472 L .82912 .01472 L .82912 .01472 L F .34 1 0 r .82912 .01472 m .82912 .01472 L .82932 .01472 L .82932 .01472 L F .33 1 0 r .82932 .01472 m .82932 .01472 L .82948 .01472 L .82948 .01472 L F .323 1 0 r .82948 .01472 m .82948 .01472 L .83006 .01472 L .83006 .01472 L F .295 1 0 r .83006 .01472 m .83006 .01472 L .83046 .01472 L .83046 .01472 L F .276 1 0 r .83046 .01472 m .83046 .01472 L .83071 .01472 L .83071 .01472 L F .264 1 0 r .83071 .01472 m .83071 .01472 L .83074 .01472 L .83074 .01472 L F .262 1 0 r .83074 .01472 m .83074 .01472 L .83182 .01472 L .83182 .01472 L F .21 1 0 r .83182 .01472 m .83182 .01472 L .83198 .01472 L .83198 .01472 L F .202 1 0 r .83198 .01472 m .83198 .01472 L .83205 .01472 L .83205 .01472 L F .199 1 0 r .83205 .01472 m .83205 .01472 L .83272 .01472 L .83272 .01472 L F .167 1 0 r .83272 .01472 m .83272 .01472 L .8331 .01472 L .8331 .01472 L F .149 1 0 r .8331 .01472 m .8331 .01472 L .8333 .01472 L .8333 .01472 L F .139 1 0 r .8333 .01472 m .8333 .01472 L .83346 .01472 L .83346 .01472 L F .131 1 0 r .83346 .01472 m .83346 .01472 L .83425 .01472 L .83425 .01472 L F .093 1 0 r .83425 .01472 m .83425 .01472 L .83477 .01472 L .83477 .01472 L F .068 1 0 r .83477 .01472 m .83477 .01472 L .8355 .01472 L .8355 .01472 L F .033 1 0 r .8355 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.83965 .01472 L .84038 .01472 L .84038 .01472 L F 0 1 .202 r .84038 .01472 m .84038 .01472 L .84063 .01472 L .84063 .01472 L F 0 1 .214 r .84063 .01472 m .84063 .01472 L .8409 .01472 L .8409 .01472 L F 0 1 .227 r .8409 .01472 m .8409 .01472 L .84171 .01472 L .84171 .01472 L F 0 1 .266 r .84171 .01472 m .84171 .01472 L .84174 .01472 L .84174 .01472 L F 0 1 .267 r .84174 .01472 m .84174 .01472 L .84214 .01472 L .84214 .01472 L F 0 1 .286 r .84214 .01472 m .84214 .01472 L .84268 .01472 L .84268 .01472 L F 0 1 .313 r .84268 .01472 m .84268 .01472 L .84298 .01472 L .84298 .01472 L F 0 1 .327 r .84298 .01472 m .84298 .01472 L .84328 .01472 L .84328 .01472 L F 0 1 .341 r .84328 .01472 m .84328 .01472 L .84381 .01472 L .84381 .01472 L F 0 1 .367 r .84381 .01472 m .84381 .01472 L .84411 .01472 L .84411 .01472 L F 0 1 .381 r .84411 .01472 m .84411 .01472 L .84454 .01472 L .84454 .01472 L F 0 1 .402 r .84454 .01472 m .84454 .01472 L .84487 .01472 L .84487 .01472 L F 0 1 .418 r .84487 .01472 m .84487 .01472 L .84519 .01472 L .84519 .01472 L F 0 1 .433 r .84519 .01472 m .84519 .01472 L .84525 .01472 L .84525 .01472 L F 0 1 .436 r .84525 .01472 m .84525 .01472 L .84588 .01472 L .84588 .01472 L F 0 1 .467 r .84588 .01472 m .84588 .01472 L .84603 .01472 L .84603 .01472 L F 0 1 .474 r .84603 .01472 m .84603 .01472 L .84637 .01472 L .84637 .01472 L F 0 1 .49 r .84637 .01472 m .84637 .01472 L .84706 .01472 L .84706 .01472 L F 0 1 .523 r .84706 .01472 m .84706 .01472 L .84726 .01472 L .84726 .01472 L F 0 1 .533 r .84726 .01472 m .84726 .01472 L .8476 .01472 L .8476 .01472 L F 0 1 .549 r .8476 .01472 m .8476 .01472 L .8483 .01472 L .8483 .01472 L F 0 1 .583 r .8483 .01472 m .8483 .01472 L .84832 .01472 L .84832 .01472 L F 0 1 .584 r .84832 .01472 m .84832 .01472 L .84876 .01472 L .84876 .01472 L F 0 1 .605 r .84876 .01472 m .84876 .01472 L .84945 .01472 L .84945 .01472 L F 0 1 .638 r .84945 .01472 m .84945 .01472 L .84952 .01472 L .84952 .01472 L F 0 1 .642 r .84952 .01472 m .84952 .01472 L .85012 .01472 L .85012 .01472 L F 0 1 .67 r .85012 .01472 m .85012 .01472 L .85062 .01472 L .85062 .01472 L F 0 1 .695 r .85062 .01472 m .85062 .01472 L .85069 .01472 L .85069 .01472 L F 0 1 .698 r .85069 .01472 m .85069 .01472 L .85141 .01472 L .85141 .01472 L F 0 1 .732 r .85141 .01472 m .85141 .01472 L .85188 .01472 L .85188 .01472 L F 0 1 .755 r .85188 .01472 m .85188 .01472 L .85202 .01472 L .85202 .01472 L F 0 1 .762 r .85202 .01472 m .85202 .01472 L .85257 .01472 L .85257 .01472 L F 0 1 .788 r .85257 .01472 m .85257 .01472 L .85308 .01472 L .85308 .01472 L F 0 1 .813 r .85308 .01472 m .85308 .01472 L .85327 .01472 L .85327 .01472 L F 0 1 .822 r .85327 .01472 m .85327 .01472 L .85383 .01472 L .85383 .01472 L F 0 1 .849 r .85383 .01472 m .85383 .01472 L .85416 .01472 L .85416 .01472 L F 0 1 .865 r .85416 .01472 m .85416 .01472 L .85441 .01472 L .85441 .01472 L F 0 1 .877 r .85441 .01472 m .85441 .01472 L .8552 .01472 L .8552 .01472 L F 0 1 .915 r .8552 .01472 m .8552 .01472 L .85532 .01472 L .85532 .01472 L F 0 1 .921 r .85532 .01472 m .85532 .01472 L .85559 .01472 L .85559 .01472 L F 0 1 .934 r .85559 .01472 m .85559 .01472 L .85597 .01472 L .85597 .01472 L F 0 1 .952 r .85597 .01472 m .85597 .01472 L .85659 .01472 L .85659 .01472 L F 0 1 .982 r .85659 .01472 m .85659 .01472 L .85666 .01472 L .85666 .01472 L F 0 1 .985 r .85666 .01472 m .85666 .01472 L .85669 .01472 L .85669 .01472 L F 0 1 .987 r .85669 .01472 m .85669 .01472 L .85724 .01472 L .85724 .01472 L F 0 .987 1 r .85724 .01472 m .85724 .01472 L .85732 .01472 L .85732 .01472 L F 0 .983 1 r .85732 .01472 m .85732 .01472 L .85791 .01472 L .85791 .01472 L F 0 .955 1 r .85791 .01472 m .85791 .01472 L .85794 .01472 L .85794 .01472 L F 0 .953 1 r .85794 .01472 m .85794 .01472 L .85802 .01472 L .85802 .01472 L F 0 .949 1 r .85802 .01472 m .85802 .01472 L .85919 .01472 L .85919 .01472 L F 0 .893 1 r .85919 .01472 m .85919 .01472 L .85922 .01472 L .85922 .01472 L F 0 .892 1 r .85922 .01472 m .85922 .01472 L .85929 .01472 L .85929 .01472 L F 0 .888 1 r .85929 .01472 m .85929 .01472 L .86036 .01472 L .86036 .01472 L F 0 .837 1 r .86036 .01472 m .86036 .01472 L .86051 .01472 L .86051 .01472 L F 0 .829 1 r .86051 .01472 m .86051 .01472 L .86054 .01472 L .86054 .01472 L F 0 .828 1 r .86054 .01472 m .86054 .01472 L .86116 .01472 L .86116 .01472 L F 0 .798 1 r .86116 .01472 m .86116 .01472 L .86148 .01472 L .86148 .01472 L F 0 .783 1 r .86148 .01472 m .86148 .01472 L .86167 .01472 L .86167 .01472 L F 0 .774 1 r .86167 .01472 m .86167 .01472 L .86188 .01472 L .86188 .01472 L F 0 .764 1 r .86188 .01472 m .86188 .01472 L .86265 .01472 L .86265 .01472 L F 0 .727 1 r .86265 .01472 m .86265 .01472 L .86298 .01472 L .86298 .01472 L F 0 .711 1 r .86298 .01472 m .86298 .01472 L .86314 .01472 L .86314 .01472 L F 0 .703 1 r .86314 .01472 m .86314 .01472 L .86421 .01472 L .86421 .01472 L F 0 .651 1 r .86421 .01472 m .86421 .01472 L .86432 .01472 L .86432 .01472 L F 0 .646 1 r .86432 .01472 m .86432 .01472 L .86474 .01472 L .86474 .01472 L F 0 .626 1 r .86474 .01472 m .86474 .01472 L .86536 .01472 L .86536 .01472 L F 0 .596 1 r .86536 .01472 m .86536 .01472 L .86552 .01472 L .86552 .01472 L F 0 .589 1 r .86552 .01472 m .86552 .01472 L .86641 .01472 L .86641 .01472 L F 0 .545 1 r .86641 .01472 m .86641 .01472 L .86664 .01472 L .86664 .01472 L F 0 .534 1 r .86664 .01472 m .86664 .01472 L .86721 .01472 L .86721 .01472 L F 0 .507 1 r .86721 .01472 m .86721 .01472 L .86757 .01472 L .86757 .01472 L F 0 .49 1 r .86757 .01472 m .86757 .01472 L .86766 .01472 L .86766 .01472 L F 0 .486 1 r .86766 .01472 m .86766 .01472 L .86875 .01472 L .86875 .01472 L F 0 .433 1 r .86875 .01472 m .86875 .01472 L .86881 .01472 L .86881 .01472 L F 0 .43 1 r .86881 .01472 m .86881 .01472 L .86946 .01472 L .86946 .01472 L F 0 .399 1 r .86946 .01472 m .86946 .01472 L .86995 .01472 L .86995 .01472 L F 0 .375 1 r .86995 .01472 m .86995 .01472 L .87004 .01472 L .87004 .01472 L F 0 .371 1 r .87004 .01472 m .87004 .01472 L .87073 .01472 L .87073 .01472 L F 0 .338 1 r .87073 .01472 m .87073 .01472 L .87073 .01472 L .87073 .01472 L F .87073 .01472 m .87073 .01472 L .87122 .01472 L .87122 .01472 L F 0 .314 1 r .87122 .01472 m .87122 .01472 L .87137 .01472 L .87137 .01472 L F 0 .307 1 r .87137 .01472 m .87137 .01472 L .87193 .01472 L .87193 .01472 L F 0 .28 1 r .87193 .01472 m .87193 .01472 L .8723 .01472 L .8723 .01472 L F 0 .262 1 r .8723 .01472 m .8723 .01472 L .87254 .01472 L .87254 .01472 L F 0 .251 1 r .87254 .01472 m .87254 .01472 L .8732 .01472 L .8732 .01472 L F 0 .219 1 r .8732 .01472 m .8732 .01472 L .87349 .01472 L .87349 .01472 L F 0 .205 1 r .87349 .01472 m .87349 .01472 L .87377 .01472 L .87377 .01472 L F 0 .191 1 r .87377 .01472 m .87377 .01472 L .87415 .01472 L .87415 .01472 L F 0 .173 1 r .87415 .01472 m .87415 .01472 L .87442 .01472 L .87442 .01472 L F 0 .16 1 r .87442 .01472 m .87442 .01472 L .87457 .01472 L .87457 .01472 L F 0 .153 1 r .87457 .01472 m .87457 .01472 L .87488 .01472 L .87488 .01472 L F 0 .138 1 r .87488 .01472 m .87488 .01472 L .87512 .01472 L .87512 .01472 L F 0 .126 1 r .87512 .01472 m .87512 .01472 L .87577 .01472 L .87577 .01472 L F 0 .095 1 r .87577 .01472 m .87577 .01472 L .87619 .01472 L .87619 .01472 L F 0 .075 1 r .87619 .01472 m .87619 .01472 L .87638 .01472 L .87638 .01472 L F 0 .066 1 r .87638 .01472 m .87638 .01472 L .87705 .01472 L .87705 .01472 L F 0 .034 1 r .87705 .01472 m .87705 .01472 L .87715 .01472 L .87715 .01472 L F 0 .028 1 r .87715 .01472 m .87715 .01472 L .87747 .01472 L .87747 .01472 L F 0 .013 1 r .87747 .01472 m .87747 .01472 L .87788 .01472 L .87788 .01472 L F .007 0 1 r .87788 .01472 m .87788 .01472 L .87813 .01472 L .87813 .01472 L F .019 0 1 r .87813 .01472 m .87813 .01472 L .87854 .01472 L .87854 .01472 L F .038 0 1 r .87854 .01472 m .87854 .01472 L .87866 .01472 L .87866 .01472 L F .044 0 1 r .87866 .01472 m .87866 .01472 L .87924 .01472 L .87924 .01472 L F .072 0 1 r .87924 .01472 m .87924 .01472 L .87933 .01472 L .87933 .01472 L F .076 0 1 r .87933 .01472 m .87933 .01472 L .87939 .01472 L .87939 .01472 L F .079 0 1 r .87939 .01472 m .87939 .01472 L .88007 .01472 L .88007 .01472 L F .112 0 1 r .88007 .01472 m .88007 .01472 L .88055 .01472 L .88055 .01472 L F .135 0 1 r .88055 .01472 m .88055 .01472 L .88073 .01472 L .88073 .01472 L F .144 0 1 r .88073 .01472 m .88073 .01472 L .88135 .01472 L .88135 .01472 L F .174 0 1 r .88135 .01472 m .88135 .01472 L .88178 .01472 L .88178 .01472 L F .194 0 1 r .88178 .01472 m .88178 .01472 L .88202 .01472 L .88202 .01472 L F .206 0 1 r .88202 .01472 m .88202 .01472 L .88207 .01472 L .88207 .01472 L F .208 0 1 r .88207 .01472 m .88207 .01472 L .88248 .01472 L .88248 .01472 L F .228 0 1 r .88248 .01472 m .88248 .01472 L .88273 .01472 L .88273 .01472 L F .24 0 1 r .88273 .01472 m .88273 .01472 L .88273 .01472 L .88273 .01472 L F .88273 .01472 m .88273 .01472 L .88313 .01472 L .88313 .01472 L F .259 0 1 r .88313 .01472 m .88313 .01472 L .88345 .01472 L .88345 .01472 L F .274 0 1 r .88345 .01472 m .88345 .01472 L .8835 .01472 L .8835 .01472 L F .277 0 1 r .8835 .01472 m .8835 .01472 L .88387 .01472 L .88387 .01472 L F .295 0 1 r .88387 .01472 m .88387 .01472 L .88422 .01472 L .88422 .01472 L F .311 0 1 r .88422 .01472 m .88422 .01472 L .88424 .01472 L .88424 .01472 L F .313 0 1 r .88424 .01472 m .88424 .01472 L .88457 .01472 L .88457 .01472 L F .328 0 1 r .88457 .01472 m .88457 .01472 L .88491 .01472 L .88491 .01472 L F .345 0 1 r .88491 .01472 m .88491 .01472 L .88525 .01472 L .88525 .01472 L F .361 0 1 r .88525 .01472 m .88525 .01472 L .88542 .01472 L .88542 .01472 L F .369 0 1 r .88542 .01472 m .88542 .01472 L .88597 .01472 L .88597 .01472 L F .396 0 1 r .88597 .01472 m .88597 .01472 L .88622 .01472 L .88622 .01472 L F .408 0 1 r .88622 .01472 m .88622 .01472 L .88654 .01472 L .88654 .01472 L F .424 0 1 r .88654 .01472 m .88654 .01472 L .88694 .01472 L .88694 .01472 L F .442 0 1 r .88694 .01472 m .88694 .01472 L .88723 .01472 L .88723 .01472 L F .457 0 1 r .88723 .01472 m .88723 .01472 L .88727 .01472 L .88727 .01472 L F .458 0 1 r .88727 .01472 m .88727 .01472 L .88761 .01472 L .88761 .01472 L F .475 0 1 r .88761 .01472 m .88761 .01472 L .88788 .01472 L .88788 .01472 L F .488 0 1 r .88788 .01472 m .88788 .01472 L .88806 .01472 L .88806 .01472 L F .497 0 1 r .88806 .01472 m .88806 .01472 L .88881 .01472 L .88881 .01472 L F .533 0 1 r .88881 .01472 m .88881 .01472 L .88882 .01472 L .88882 .01472 L F .88882 .01472 m .88882 .01472 L .8891 .01472 L .8891 .01472 L F .546 0 1 r .8891 .01472 m .8891 .01472 L .88948 .01472 L .88948 .01472 L F .565 0 1 r .88948 .01472 m .88948 .01472 L .89012 .01472 L .89012 .01472 L F .596 0 1 r .89012 .01472 m .89012 .01472 L .89021 .01472 L .89021 .01472 L F .6 0 1 r .89021 .01472 m .89021 .01472 L .89038 .01472 L .89038 .01472 L F .608 0 1 r .89038 .01472 m .89038 .01472 L .89137 .01472 L .89137 .01472 L F .656 0 1 r .89137 .01472 m .89137 .01472 L .89143 .01472 L .89143 .01472 L F .659 0 1 r .89143 .01472 m .89143 .01472 L .89157 .01472 L .89157 .01472 L F .665 0 1 r .89157 .01472 m .89157 .01472 L .89212 .01472 L .89212 .01472 L F .692 0 1 r .89212 .01472 m .89212 .01472 L .89251 .01472 L .89251 .01472 L F .711 0 1 r .89251 .01472 m .89251 .01472 L .89277 .01472 L .89277 .01472 L F .723 0 1 r .89277 .01472 m .89277 .01472 L .89287 .01472 L .89287 .01472 L F .728 0 1 r .89287 .01472 m .89287 .01472 L .89353 .01472 L .89353 .01472 L F .76 0 1 r .89353 .01472 m .89353 .01472 L .89382 .01472 L .89382 .01472 L F .774 0 1 r .89382 .01472 m .89382 .01472 L .89408 .01472 L .89408 .01472 L F .786 0 1 r .89408 .01472 m .89408 .01472 L .89425 .01472 L .89425 .01472 L F .794 0 1 r .89425 .01472 m .89425 .01472 L .89506 .01472 L .89506 .01472 L F .833 0 1 r .89506 .01472 m .89506 .01472 L .89547 .01472 L .89547 .01472 L F .853 0 1 r .89547 .01472 m .89547 .01472 L .89547 .01472 L .89547 .01472 L F .89547 .01472 m .89547 .01472 L .89621 .01472 L .89621 .01472 L F .889 0 1 r .89621 .01472 m .89621 .01472 L .89661 .01472 L .89661 .01472 L F .908 0 1 r .89661 .01472 m .89661 .01472 L .89727 .01472 L .89727 .01472 L F .94 0 1 r .89727 .01472 m .89727 .01472 L .89778 .01472 L .89778 .01472 L F .964 0 1 r .89778 .01472 m .89778 .01472 L .89785 .01472 L .89785 .01472 L F .968 0 1 r .89785 .01472 m .89785 .01472 L .89843 .01472 L .89843 .01472 L F .995 0 1 r .89843 .01472 m .89843 .01472 L .89855 .01472 L .89855 .01472 L F 1 0 .999 r .89855 .01472 m .89855 .01472 L .899 .01472 L .899 .01472 L F 1 0 .977 r .899 .01472 m .899 .01472 L .89918 .01472 L .89918 .01472 L F 1 0 .968 r .89918 .01472 m .89918 .01472 L .89966 .01472 L .89966 .01472 L F 1 0 .945 r .89966 .01472 m .89966 .01472 L .90031 .01472 L .90031 .01472 L F 1 0 .914 r .90031 .01472 m .90031 .01472 L .90046 .01472 L .90046 .01472 L F 1 0 .907 r .90046 .01472 m .90046 .01472 L .9009 .01472 L .9009 .01472 L F 1 0 .886 r .9009 .01472 m .9009 .01472 L .90119 .01472 L .90119 .01472 L F 1 0 .872 r .90119 .01472 m .90119 .01472 L .90159 .01472 L .90159 .01472 L F 1 0 .852 r .90159 .01472 m .90159 .01472 L .90164 .01472 L .90164 .01472 L F 1 0 .85 r .90164 .01472 m .90164 .01472 L .90185 .01472 L .90185 .01472 L F 1 0 .84 r .90185 .01472 m .90185 .01472 L .90223 .01472 L .90223 .01472 L F 1 0 .822 r .90223 .01472 m .90223 .01472 L .90289 .01472 L .90289 .01472 L F 1 0 .79 r .90289 .01472 m .90289 .01472 L .90307 .01472 L .90307 .01472 L F 1 0 .781 r .90307 .01472 m .90307 .01472 L .90346 .01472 L .90346 .01472 L F 1 0 .762 r .90346 .01472 m .90346 .01472 L .90431 .01472 L .90431 .01472 L F 1 0 .721 r .90431 .01472 m .90431 .01472 L .90437 .01472 L .90437 .01472 L F 1 0 .719 r .90437 .01472 m .90437 .01472 L .90463 .01472 L .90463 .01472 L F 1 0 .706 r .90463 .01472 m .90463 .01472 L .90529 .01472 L .90529 .01472 L F 1 0 .674 r .90529 .01472 m .90529 .01472 L .90547 .01472 L .90547 .01472 L F 1 0 .666 r .90547 .01472 m .90547 .01472 L .90562 .01472 L .90562 .01472 L F 1 0 .659 r .90562 .01472 m .90562 .01472 L .90599 .01472 L .90599 .01472 L F 1 0 .641 r .90599 .01472 m .90599 .01472 L .90665 .01472 L .90665 .01472 L F 1 0 .609 r .90665 .01472 m .90665 .01472 L .90682 .01472 L .90682 .01472 L F 1 0 .601 r .90682 .01472 m .90682 .01472 L .90725 .01472 L .90725 .01472 L F 1 0 .58 r .90725 .01472 m .90725 .01472 L .90776 .01472 L .90776 .01472 L F 1 0 .555 r .90776 .01472 m .90776 .01472 L .90802 .01472 L .90802 .01472 L F 1 0 .543 r .90802 .01472 m .90802 .01472 L .90813 .01472 L .90813 .01472 L F 1 0 .538 r .90813 .01472 m .90813 .01472 L .90875 .01472 L .90875 .01472 L F 1 0 .508 r .90875 .01472 m .90875 .01472 L .90878 .01472 L .90878 .01472 L F 1 0 .506 r .90878 .01472 m .90878 .01472 L .90937 .01472 L .90937 .01472 L F 1 0 .478 r .90937 .01472 m .90937 .01472 L .90941 .01472 L .90941 .01472 L F 1 0 .476 r .90941 .01472 m .90941 .01472 L .90997 .01472 L .90997 .01472 L F 1 0 .449 r .90997 .01472 m .90997 .01472 L .91011 .01472 L .91011 .01472 L F 1 0 .442 r .91011 .01472 m .91011 .01472 L .91052 .01472 L .91052 .01472 L F 1 0 .423 r .91052 .01472 m .91052 .01472 L .91121 .01472 L .91121 .01472 L F 1 0 .389 r .91121 .01472 m .91121 .01472 L .91127 .01472 L .91127 .01472 L F 1 0 .386 r .91127 .01472 m .91127 .01472 L .91143 .01472 L .91143 .01472 L F 1 0 .379 r .91143 .01472 m .91143 .01472 L .91197 .01472 L .91197 .01472 L F 1 0 .353 r .91197 .01472 m .91197 .01472 L .9125 .01472 L .9125 .01472 L F 1 0 .327 r .9125 .01472 m .9125 .01472 L .91263 .01472 L .91263 .01472 L F 1 0 .321 r .91263 .01472 m .91263 .01472 L .91266 .01472 L .91266 .01472 L F 1 0 .32 r .91266 .01472 m .91266 .01472 L .91333 .01472 L .91333 .01472 L F 1 0 .287 r .91333 .01472 m .91333 .01472 L .91336 .01472 L .91336 .01472 L F 1 0 .286 r .91336 .01472 m .91336 .01472 L .91363 .01472 L .91363 .01472 L F 1 0 .273 r .91363 .01472 m .91363 .01472 L .91396 .01472 L .91396 .01472 L F 1 0 .257 r .91396 .01472 m .91396 .01472 L .914 .01472 L .914 .01472 L F 1 0 .255 r .914 .01472 m .914 .01472 L .91466 .01472 L .91466 .01472 L F 1 0 .223 r .91466 .01472 m .91466 .01472 L .91475 .01472 L .91475 .01472 L F 1 0 .219 r .91475 .01472 m .91475 .01472 L .91482 .01472 L .91482 .01472 L F 1 0 .215 r .91482 .01472 m .91482 .01472 L .91545 .01472 L .91545 .01472 L F 1 0 .185 r .91545 .01472 m .91545 .01472 L .91588 .01472 L .91588 .01472 L F 1 0 .164 r .91588 .01472 m .91588 .01472 L .91611 .01472 L .91611 .01472 L F 1 0 .154 r .91611 .01472 m .91611 .01472 L .91613 .01472 L .91613 .01472 L F 1 0 .153 r .91613 .01472 m .91613 .01472 L .91663 .01472 L .91663 .01472 L F 1 0 .129 r .91663 .01472 m .91663 .01472 L .91685 .01472 L .91685 .01472 L F 1 0 .118 r .91685 .01472 m .91685 .01472 L .91731 .01472 L .91731 .01472 L F 1 0 .096 r .91731 .01472 m .91731 .01472 L .91732 .01472 L .91732 .01472 L F 1 0 .095 r .91732 .01472 m .91732 .01472 L .91804 .01472 L .91804 .01472 L F 1 0 .06 r .91804 .01472 m .91804 .01472 L .91815 .01472 L .91815 .01472 L F 1 0 .055 r .91815 .01472 m .91815 .01472 L .91844 .01472 L .91844 .01472 L F 1 0 .042 r .91844 .01472 m .91844 .01472 L .91884 .01472 L .91884 .01472 L F 1 0 .022 r .91884 .01472 m .91884 .01472 L .91887 .01472 L .91887 .01472 L F 1 0 .021 r .91887 .01472 m .91887 .01472 L .91955 .01472 L .91955 .01472 L F 1 .012 0 r .91955 .01472 m .91955 .01472 L .91958 .01472 L .91958 .01472 L F 1 .013 0 r .91958 .01472 m .91958 .01472 L .91967 .01472 L .91967 .01472 L F 1 .018 0 r .91967 .01472 m .91967 .01472 L .92026 .01472 L .92026 .01472 L F 1 .046 0 r .92026 .01472 m .92026 .01472 L .92029 .01472 L .92029 .01472 L F 1 .048 0 r .92029 .01472 m .92029 .01472 L .92037 .01472 L .92037 .01472 L F 1 .052 0 r .92037 .01472 m .92037 .01472 L .92096 .01472 L .92096 .01472 L F 1 .08 0 r .92096 .01472 m .92096 .01472 L .92102 .01472 L .92102 .01472 L F 1 .083 0 r .92102 .01472 m .92102 .01472 L .92109 .01472 L .92109 .01472 L F 1 .086 0 r .92109 .01472 m .92109 .01472 L .9216 .01472 L .9216 .01472 L F 1 .111 0 r .9216 .01472 m .9216 .01472 L .92232 .01472 L .92232 .01472 L F 1 .145 0 r .92232 .01472 m .92232 .01472 L .92234 .01472 L .92234 .01472 L F 1 .146 0 r .92234 .01472 m .92234 .01472 L .92275 .01472 L .92275 .01472 L F 1 .166 0 r .92275 .01472 m .92275 .01472 L .92301 .01472 L .92301 .01472 L F 1 .179 0 r .92301 .01472 m .92301 .01472 L .92308 .01472 L .92308 .01472 L F 1 .182 0 r .92308 .01472 m .92308 .01472 L .92366 .01472 L .92366 .01472 L F 1 .21 0 r .92366 .01472 m .92366 .01472 L .92375 .01472 L .92375 .01472 L F 1 .214 0 r .92375 .01472 m .92375 .01472 L .924 .01472 L .924 .01472 L F 1 .226 0 r .924 .01472 m .924 .01472 L .92442 .01472 L .92442 .01472 L F 1 .246 0 r .92442 .01472 m .92442 .01472 L .92496 .01472 L .92496 .01472 L F 1 .273 0 r .92496 .01472 m .92496 .01472 L .92509 .01472 L .92509 .01472 L F 1 .279 0 r .92509 .01472 m .92509 .01472 L .92513 .01472 L .92513 .01472 L F 1 .28 0 r .92513 .01472 m .92513 .01472 L .92624 .01472 L .92624 .01472 L F 1 .334 0 r .92624 .01472 m .92624 .01472 L .92636 .01472 L .92636 .01472 L F 1 .34 0 r .92636 .01472 m .92636 .01472 L .9264 .01472 L .9264 .01472 L F 1 .342 0 r .9264 .01472 m .9264 .01472 L .92711 .01472 L .92711 .01472 L F 1 .376 0 r .92711 .01472 m .92711 .01472 L .92751 .01472 L .92751 .01472 L F 1 .395 0 r .92751 .01472 m .92751 .01472 L .92777 .01472 L .92777 .01472 L F 1 .408 0 r .92777 .01472 m .92777 .01472 L .92854 .01472 L .92854 .01472 L F 1 .445 0 r .92854 .01472 m .92854 .01472 L .92866 .01472 L .92866 .01472 L F 1 .451 0 r .92866 .01472 m .92866 .01472 L .92869 .01472 L .92869 .01472 L F 1 .452 0 r .92869 .01472 m .92869 .01472 L .92928 .01472 L .92928 .01472 L F 1 .48 0 r .92928 .01472 m .92928 .01472 L .92997 .01472 L .92997 .01472 L F 1 .514 0 r .92997 .01472 m .92997 .01472 L .92998 .01472 L .92998 .01472 L F .92998 .01472 m .92998 .01472 L .93059 .01472 L .93059 .01472 L F 1 .543 0 r .93059 .01472 m .93059 .01472 L .93071 .01472 L .93071 .01472 L F 1 .549 0 r .93071 .01472 m .93071 .01472 L .93119 .01472 L .93119 .01472 L F 1 .572 0 r .93119 .01472 m .93119 .01472 L .93137 .01472 L .93137 .01472 L F 1 .581 0 r .93137 .01472 m .93137 .01472 L .93179 .01472 L .93179 .01472 L F 1 .601 0 r .93179 .01472 m .93179 .01472 L .93201 .01472 L .93201 .01472 L F 1 .612 0 r .93201 .01472 m .93201 .01472 L .93244 .01472 L .93244 .01472 L F 1 .632 0 r .93244 .01472 m .93244 .01472 L .9327 .01472 L .9327 .01472 L F 1 .645 0 r .9327 .01472 m .9327 .01472 L .93309 .01472 L .93309 .01472 L F 1 .664 0 r .93309 .01472 m .93309 .01472 L .93378 .01472 L .93378 .01472 L F 1 .697 0 r .93378 .01472 m .93378 .01472 L .93382 .01472 L .93382 .01472 L F 1 .699 0 r .93382 .01472 m .93382 .01472 L .93392 .01472 L .93392 .01472 L F 1 .704 0 r .93392 .01472 m .93392 .01472 L .9345 .01472 L .9345 .01472 L F 1 .732 0 r .9345 .01472 m .9345 .01472 L .93451 .01472 L .93451 .01472 L F .93451 .01472 m .93451 .01472 L .93521 .01472 L .93521 .01472 L F 1 .766 0 r .93521 .01472 m .93521 .01472 L .93525 .01472 L .93525 .01472 L F 1 .767 0 r .93525 .01472 m .93525 .01472 L .93579 .01472 L .93579 .01472 L F 1 .794 0 r .93579 .01472 m .93579 .01472 L .936 .01472 L .936 .01472 L F 1 .804 0 r .936 .01472 m .936 .01472 L .93644 .01472 L .93644 .01472 L F 1 .825 0 r .93644 .01472 m .93644 .01472 L .93652 .01472 L .93652 .01472 L F 1 .829 0 r .93652 .01472 m .93652 .01472 L .9367 .01472 L .9367 .01472 L F 1 .837 0 r .9367 .01472 m .9367 .01472 L .93715 .01472 L .93715 .01472 L F 1 .859 0 r .93715 .01472 m .93715 .01472 L .93774 .01472 L .93774 .01472 L F 1 .887 0 r .93774 .01472 m .93774 .01472 L .93797 .01472 L .93797 .01472 L F 1 .899 0 r .93797 .01472 m .93797 .01472 L .93841 .01472 L .93841 .01472 L F 1 .92 0 r .93841 .01472 m .93841 .01472 L .93887 .01472 L .93887 .01472 L F 1 .942 0 r .93887 .01472 m .93887 .01472 L .93913 .01472 L .93913 .01472 L F 1 .954 0 r .93913 .01472 m .93913 .01472 L .93958 .01472 L .93958 .01472 L F 1 .976 0 r .93958 .01472 m .93958 .01472 L .93977 .01472 L .93977 .01472 L F 1 .985 0 r .93977 .01472 m .93977 .01472 L .94011 .01472 L .94011 .01472 L F .999 1 0 r .94011 .01472 m .94011 .01472 L .94029 .01472 L .94029 .01472 L F .99 1 0 r .94029 .01472 m .94029 .01472 L .94047 .01472 L .94047 .01472 L F .981 1 0 r .94047 .01472 m .94047 .01472 L .94097 .01472 L .94097 .01472 L F .957 1 0 r .94097 .01472 m .94097 .01472 L .94143 .01472 L .94143 .01472 L F .935 1 0 r .94143 .01472 m .94143 .01472 L .94174 .01472 L .94174 .01472 L F .92 1 0 r .94174 .01472 m .94174 .01472 L .94218 .01472 L .94218 .01472 L F .899 1 0 r .94218 .01472 m .94218 .01472 L .94223 .01472 L .94223 .01472 L F .896 1 0 r .94223 .01472 m .94223 .01472 L .94287 .01472 L .94287 .01472 L F .866 1 0 r .94287 .01472 m .94287 .01472 L .94287 .01472 L .94287 .01472 L F .94287 .01472 m .94287 .01472 L .94294 .01472 L .94294 .01472 L F .862 1 0 r .94294 .01472 m .94294 .01472 L .9436 .01472 L .9436 .01472 L F .831 1 0 r .9436 .01472 m .9436 .01472 L .94361 .01472 L .94361 .01472 L F .83 1 0 r .94361 .01472 m .94361 .01472 L .94391 .01472 L .94391 .01472 L F .816 1 0 r .94391 .01472 m .94391 .01472 L .94431 .01472 L .94431 .01472 L F .796 1 0 r .94431 .01472 m .94431 .01472 L .94443 .01472 L .94443 .01472 L F .791 1 0 r .94443 .01472 m .94443 .01472 L .94505 .01472 L .94505 .01472 L F .761 1 0 r .94505 .01472 m .94505 .01472 L .94508 .01472 L .94508 .01472 L F .759 1 0 r .94508 .01472 m .94508 .01472 L .9458 .01472 L .9458 .01472 L F .725 1 0 r .9458 .01472 m .9458 .01472 L .94625 .01472 L .94625 .01472 L F .703 1 0 r .94625 .01472 m .94625 .01472 L .94626 .01472 L .94626 .01472 L F .702 1 0 r .94626 .01472 m .94626 .01472 L .94655 .01472 L .94655 .01472 L F .688 1 0 r .94655 .01472 m .94655 .01472 L .94725 .01472 L .94725 .01472 L F .655 1 0 r .94725 .01472 m .94725 .01472 L .9473 .01472 L .9473 .01472 L F .653 1 0 r .9473 .01472 m .9473 .01472 L .94737 .01472 L .94737 .01472 L F .649 1 0 r .94737 .01472 m .94737 .01472 L .94794 .01472 L .94794 .01472 L F .622 1 0 r .94794 .01472 m .94794 .01472 L .94827 .01472 L .94827 .01472 L F .606 1 0 r .94827 .01472 m .94827 .01472 L .94858 .01472 L .94858 .01472 L F .591 1 0 r .94858 .01472 m .94858 .01472 L .94869 .01472 L .94869 .01472 L F .585 1 0 r .94869 .01472 m .94869 .01472 L .94935 .01472 L .94935 .01472 L F .554 1 0 r .94935 .01472 m .94935 .01472 L .9498 .01472 L .9498 .01472 L F .532 1 0 r .9498 .01472 m .9498 .01472 L .94991 .01472 L .94991 .01472 L F .527 1 0 r .94991 .01472 m .94991 .01472 L .95049 .01472 L .95049 .01472 L F .499 1 0 r .95049 .01472 m .95049 .01472 L .9511 .01472 L .9511 .01472 L F .47 1 0 r .9511 .01472 m .9511 .01472 L .95111 .01472 L .95111 .01472 L F .469 1 0 r .95111 .01472 m .95111 .01472 L .95151 .01472 L .95151 .01472 L F .45 1 0 r .95151 .01472 m .95151 .01472 L .95184 .01472 L .95184 .01472 L F .434 1 0 r .95184 .01472 m .95184 .01472 L .95241 .01472 L .95241 .01472 L F .407 1 0 r .95241 .01472 m .95241 .01472 L .95253 .01472 L .95253 .01472 L F .401 1 0 r .95253 .01472 m .95253 .01472 L .95262 .01472 L .95262 .01472 L F .396 1 0 r .95262 .01472 m .95262 .01472 L .95306 .01472 L .95306 .01472 L F .375 1 0 r .95306 .01472 m .95306 .01472 L .95367 .01472 L .95367 .01472 L F .346 1 0 r .95367 .01472 m .95367 .01472 L .95368 .01472 L .95368 .01472 L F .345 1 0 r .95368 .01472 m .95368 .01472 L .95377 .01472 L .95377 .01472 L F .341 1 0 r .95377 .01472 m .95377 .01472 L .95464 .01472 L .95464 .01472 L F .299 1 0 r .95464 .01472 m .95464 .01472 L .95493 .01472 L .95493 .01472 L F .285 1 0 r .95493 .01472 m .95493 .01472 L .95504 .01472 L .95504 .01472 L F .28 1 0 r .95504 .01472 m .95504 .01472 L .95551 .01472 L .95551 .01472 L F .257 1 0 r .95551 .01472 m .95551 .01472 L .9561 .01472 L .9561 .01472 L F .229 1 0 r .9561 .01472 m .9561 .01472 L .95629 .01472 L .95629 .01472 L F .22 1 0 r .95629 .01472 m .95629 .01472 L .95648 .01472 L .95648 .01472 L F .211 1 0 r .95648 .01472 m .95648 .01472 L .95718 .01472 L .95718 .01472 L F .177 1 0 r .95718 .01472 m .95718 .01472 L .95744 .01472 L .95744 .01472 L F .164 1 0 r .95744 .01472 m .95744 .01472 L .95837 .01472 L .95837 .01472 L F .12 1 0 r .95837 .01472 m .95837 .01472 L .95842 .01472 L .95842 .01472 L F .117 1 0 r .95842 .01472 m .95842 .01472 L .95871 .01472 L .95871 .01472 L F .103 1 0 r .95871 .01472 m .95871 .01472 L .95935 .01472 L .95935 .01472 L F .072 1 0 r .95935 .01472 m .95935 .01472 L .95955 .01472 L .95955 .01472 L F .063 1 0 r .95955 .01472 m .95955 .01472 L .95967 .01472 L .95967 .01472 L F .057 1 0 r .95967 .01472 m .95967 .01472 L .96005 .01472 L .96005 .01472 L F .039 1 0 r .96005 .01472 m .96005 .01472 L .96033 .01472 L .96033 .01472 L F .025 1 0 r .96033 .01472 m .96033 .01472 L .96073 .01472 L .96073 .01472 L F .006 1 0 r .96073 .01472 m .96073 .01472 L .96104 .01472 L .96104 .01472 L F 0 1 .009 r .96104 .01472 m .96104 .01472 L .96123 .01472 L .96123 .01472 L F 0 1 .018 r .96123 .01472 m .96123 .01472 L .96175 .01472 L .96175 .01472 L F 0 1 .043 r .96175 .01472 m .96175 .01472 L .9623 .01472 L .9623 .01472 L F 0 1 .07 r .9623 .01472 m .9623 .01472 L .9625 .01472 L .9625 .01472 L F 0 1 .079 r .9625 .01472 m .9625 .01472 L .96284 .01472 L .96284 .01472 L F 0 1 .095 r .96284 .01472 m .96284 .01472 L .963 .01472 L .963 .01472 L F 0 1 .103 r .963 .01472 m .963 .01472 L .96364 .01472 L .96364 .01472 L F 0 1 .134 r .96364 .01472 m .96364 .01472 L .9637 .01472 L .9637 .01472 L F 0 1 .137 r .9637 .01472 m .9637 .01472 L .96401 .01472 L .96401 .01472 L F 0 1 .152 r .96401 .01472 m .96401 .01472 L .96435 .01472 L .96435 .01472 L F 0 1 .168 r .96435 .01472 m .96435 .01472 L .96479 .01472 L .96479 .01472 L F 0 1 .189 r .96479 .01472 m .96479 .01472 L .9651 .01472 L .9651 .01472 L F 0 1 .204 r .9651 .01472 m .9651 .01472 L .96511 .01472 L .96511 .01472 L F 0 1 .205 r .96511 .01472 m .96511 .01472 L .96592 .01472 L .96592 .01472 L F 0 1 .244 r .96592 .01472 m .96592 .01472 L .96636 .01472 L .96636 .01472 L F 0 1 .265 r .96636 .01472 m .96636 .01472 L .96641 .01472 L .96641 .01472 L F 0 1 .267 r .96641 .01472 m .96641 .01472 L .96696 .01472 L .96696 .01472 L F 0 1 .294 r .96696 .01472 m .96696 .01472 L .96707 .01472 L .96707 .01472 L F 0 1 .299 r .96707 .01472 m .96707 .01472 L .96759 .01472 L .96759 .01472 L F 0 1 .324 r .96759 .01472 m .96759 .01472 L .96774 .01472 L .96774 .01472 L F 0 1 .331 r .96774 .01472 m .96774 .01472 L .96811 .01472 L .96811 .01472 L F 0 1 .349 r .96811 .01472 m .96811 .01472 L .9687 .01472 L .9687 .01472 L F 0 1 .377 r .9687 .01472 m .9687 .01472 L .96898 .01472 L .96898 .01472 L F 0 1 .391 r .96898 .01472 m .96898 .01472 L .96933 .01472 L .96933 .01472 L F 0 1 .408 r .96933 .01472 m .96933 .01472 L .96972 .01472 L .96972 .01472 L F 0 1 .426 r .96972 .01472 m .96972 .01472 L .97012 .01472 L .97012 .01472 L F 0 1 .446 r .97012 .01472 m .97012 .01472 L .9705 .01472 L .9705 .01472 L F 0 1 .464 r .9705 .01472 m .9705 .01472 L .97083 .01472 L .97083 .01472 L F 0 1 .48 r .97083 .01472 m .97083 .01472 L .97143 .01472 L .97143 .01472 L F 0 1 .509 r .97143 .01472 m .97143 .01472 L .9716 .01472 L .9716 .01472 L F 0 1 .517 r .9716 .01472 m .9716 .01472 L .97202 .01472 L .97202 .01472 L F 0 1 .537 r .97202 .01472 m .97202 .01472 L .97258 .01472 L .97258 .01472 L F 0 1 .564 r .97258 .01472 m .97258 .01472 L .97268 .01472 L .97268 .01472 L F 0 1 .569 r .97268 .01472 m .97268 .01472 L .97304 .01472 L .97304 .01472 L F 0 1 .587 r .97304 .01472 m .97304 .01472 L .97356 .01472 L .97356 .01472 L F 0 1 .611 r .97356 .01472 m .97356 .01472 L .97365 .01472 L .97365 .01472 L F 0 1 .616 r .97365 .01472 m .97365 .01472 L .974 .01472 L .974 .01472 L F 0 1 .633 r .974 .01472 m .974 .01472 L .9745 .01472 L .9745 .01472 L F 0 1 .657 r .9745 .01472 m .9745 .01472 L .97488 .01472 L .97488 .01472 L F 0 1 .675 r .97488 .01472 m .97488 .01472 L .97506 .01472 L .97506 .01472 L F 0 1 .684 r .97506 .01472 m .97506 .01472 L .9753 .01472 L .9753 .01472 L F 0 1 .695 r .9753 .01472 m .9753 .01472 L .97619 .01472 L .97619 .01472 L F 0 g .5 Mabswid .02381 .01472 m .02499 .01472 L .02605 .01472 L .02729 .01472 L .02846 .01472 L .02954 .01472 L .03053 .01472 L .03163 .01472 L .0317 .01472 L .03279 .01472 L .03395 .01472 L .03506 .01472 L .0352 .01472 L .03638 .01472 L .03746 .01472 L .03756 .01472 L .03873 .01472 L .03891 .01472 L .04011 .01472 L .0402 .01472 L .04136 .01472 L .04141 .01472 L .04262 .01472 L .04386 .01472 L .04386 .01472 L .04517 .01472 L .04521 .01472 L .04642 .01472 L .04648 .01472 L .04755 .01472 L .04765 .01472 L .04871 .01472 L .04886 .01472 L .0496 .01472 L .04987 .01472 L .05028 .01472 L .05108 .01472 L .05153 .01472 L .05221 .01472 L .05285 .01472 L .05354 .01472 L .054 .01472 L .0548 .01472 L .05522 .01472 L .05592 .01472 L .05637 .01472 L .05715 .01472 L .05743 .01472 L .05847 .01472 L .05848 .01472 L Mistroke .05866 .01472 L .05936 .01472 L .05969 .01472 L .0599 .01472 L .06 .01472 L .06111 .01472 L .06113 .01472 L .06119 .01472 L .06244 .01472 L .06371 .01472 L .06371 .01472 L .06486 .01472 L .06504 .01472 L .0651 .01472 L .06617 .01472 L .06655 .01472 L .06742 .01472 L .06745 .01472 L .0679 .01472 L .06876 .01472 L .06917 .01472 L .06989 .01472 L .07019 .01472 L .07032 .01472 L .07108 .01472 L .07155 .01472 L .07165 .01472 L .07216 .01472 L .07277 .01472 L .0729 .01472 L .07336 .01472 L .07402 .01472 L .07427 .01472 L .07465 .01472 L .07517 .01472 L .07532 .01472 L .07572 .01472 L .07605 .01472 L .07643 .01472 L .07674 .01472 L .07695 .01472 L .07738 .01472 L .07776 .01472 L .07831 .01472 L .07865 .01472 L .07892 .01472 L .07937 .01472 L .07977 .01472 L .08001 .01472 L .08005 .01472 L Mistroke .08076 .01472 L .08129 .01472 L .08134 .01472 L .08141 .01472 L .08218 .01472 L .08247 .01472 L .08282 .01472 L .08288 .01472 L .08384 .01472 L .08418 .01472 L .08421 .01472 L .08495 .01472 L .08533 .01472 L .08544 .01472 L .08564 .01472 L .08664 .01472 L .08678 .01472 L .08687 .01472 L .08804 .01472 L .08804 .01472 L .0882 .01472 L .0889 .01472 L .08918 .01472 L .08942 .01472 L .08967 .01472 L .09043 .01472 L .09054 .01472 L .09071 .01472 L .09123 .01472 L .092 .01472 L .09267 .01472 L .09313 .01472 L .09338 .01472 L .09401 .01472 L .09464 .01472 L .09537 .01472 L .09584 .01472 L .09685 .01472 L .09695 .01472 L .09817 .01472 L .09825 .01472 L .09859 .01472 L .09948 .01472 L .09954 .01472 L .10008 .01472 L .1007 .01472 L .10085 .01472 L .10148 .01472 L .10199 .01472 L .10215 .01472 L Mistroke .10226 .01472 L .1031 .01472 L .10331 .01472 L .10332 .01472 L .10387 .01472 L .10458 .01472 L .10575 .01472 L .10576 .01472 L .1058 .01472 L .10692 .01472 L .10702 .01472 L .10704 .01472 L .10769 .01472 L .10815 .01472 L .10838 .01472 L .10929 .01472 L .10944 .01472 L .10965 .01472 L .11068 .01472 L .11085 .01472 L .11162 .01472 L .11199 .01472 L .11211 .01472 L .11286 .01472 L .11319 .01472 L .114 .01472 L .11437 .01472 L .11444 .01472 L .11507 .01472 L .11536 .01472 L .1157 .01472 L .11573 .01472 L .11664 .01472 L .11696 .01472 L .11703 .01472 L .11779 .01472 L .11829 .01472 L .11903 .01472 L .11941 .01472 L .11972 .01472 L .12039 .01472 L .12098 .01472 L .12182 .01472 L .12198 .01472 L .12231 .01472 L .12305 .01472 L .12345 .01472 L .12439 .01472 L .1247 .01472 L .1248 .01472 L Mistroke .1258 .01472 L .12594 .01472 L .12711 .01472 L .12713 .01472 L .12833 .01472 L .12931 .01472 L .12942 .01472 L .12964 .01472 L .13054 .01472 L .13064 .01472 L .13105 .01472 L .13168 .01472 L .13196 .01472 L .13256 .01472 L .13293 .01472 L .13322 .01472 L .13384 .01472 L .13425 .01472 L .13438 .01472 L .13526 .01472 L .13531 .01472 L .13545 .01472 L .13644 .01472 L .13657 .01472 L .13664 .01472 L .13778 .01472 L .13788 .01472 L .1385 .01472 L .13905 .01472 L .1391 .01472 L .13969 .01472 L .14012 .01472 L .1405 .01472 L .14094 .01472 L .1411 .01472 L .14218 .01472 L .14284 .01472 L .14318 .01472 L .14332 .01472 L .14417 .01472 L .14441 .01472 L .14455 .01472 L .14541 .01472 L .14575 .01472 L .14589 .01472 L .14669 .01472 L .14715 .01472 L .14803 .01472 L .14817 .01472 L .14831 .01472 L Mistroke .14936 .01472 L .15045 .01472 L .15051 .01472 L .15053 .01472 L .15172 .01472 L .1518 .01472 L .15271 .01472 L .15285 .01472 L .15306 .01472 L .15416 .01472 L .15452 .01472 L .15541 .01472 L .15592 .01472 L .15711 .01472 L .15766 .01472 L .15776 .01472 L .15842 .01472 L .15907 .01472 L .16018 .01472 L .16028 .01472 L .1607 .01472 L .16158 .01472 L .16162 .01472 L .16199 .01472 L .1629 .01472 L .16304 .01472 L .16337 .01472 L .16403 .01472 L .16466 .01472 L .16526 .01472 L .16542 .01472 L .16585 .01472 L .16638 .01472 L .16676 .01472 L .16741 .01472 L .168 .01472 L .16826 .01472 L .16849 .01472 L .16946 .01472 L .16953 .01472 L .17027 .01472 L .17058 .01472 L .17087 .01472 L .17164 .01472 L .17267 .01472 L .17281 .01472 L .17312 .01472 L .17405 .01472 L .1744 .01472 L .17482 .01472 L Mistroke .1751 .01472 L .17559 .01472 L .17626 .01472 L .17683 .01472 L .17751 .01472 L .17782 .01472 L .17885 .01472 L .17903 .01472 L .17986 .01472 L .18011 .01472 L .18126 .01472 L .1814 .01472 L .1822 .01472 L .18355 .01472 L .18443 .01472 L .18485 .01472 L .18607 .01472 L .18669 .01472 L .1868 .01472 L .18853 .01472 L .18902 .01472 L .18991 .01472 L .19118 .01472 L .19146 .01472 L .19158 .01472 L .19281 .01472 L .19283 .01472 L .19332 .01472 L .19345 .01472 L .19409 .01472 L .19413 .01472 L .19489 .01472 L .19559 .01472 L .19565 .01472 L .19624 .01472 L .19648 .01472 L .19695 .01472 L .1977 .01472 L .19809 .01472 L .19838 .01472 L .19909 .01472 L .19916 .01472 L .1999 .01472 L .20036 .01472 L .20041 .01472 L .20122 .01472 L .20182 .01472 L .20197 .01472 L .20265 .01472 L .20307 .01472 L Mistroke .20381 .01472 L .20435 .01472 L .20506 .01472 L .20562 .01472 L .20623 .01472 L .20674 .01472 L .20731 .01472 L .20792 .01472 L .20857 .01472 L .20932 .01472 L .20994 .01472 L .2104 .01472 L .21123 .01472 L .21176 .01472 L .21243 .01472 L .21379 .01472 L .21401 .01472 L .21506 .01472 L .21598 .01472 L .21604 .01472 L .21744 .01472 L .21827 .01472 L .21867 .01472 L .21878 .01472 L .22001 .01472 L .2206 .01472 L .22112 .01472 L .22227 .01472 L .22278 .01472 L .22278 .01472 L .22353 .01472 L .22471 .01472 L .22525 .01472 L .22536 .01472 L .2258 .01472 L .22708 .01472 L .2275 .01472 L .22776 .01472 L .22824 .01472 L .22888 .01472 L .22957 .01472 L .23009 .01472 L .23039 .01472 L .23083 .01472 L .23193 .01472 L .23255 .01472 L .23313 .01472 L .23319 .01472 L .23439 .01472 L .23556 .01473 L Mistroke .23587 .01473 L .23691 .01473 L .23766 .01473 L .23838 .01473 L .23883 .01473 L .2399 .01473 L .24064 .01474 L .24119 .01474 L .24165 .01474 L .24255 .01474 L .24308 .01474 L .24499 .01475 L .24532 .01475 L .24635 .01475 L .24687 .01476 L .24762 .01476 L .24778 .01476 L .24973 .01477 L .25035 .01477 L .25051 .01478 L .25113 .01478 L .25241 .01479 L .25274 .01479 L .25304 .01479 L .25357 .0148 L .25468 .01481 L .25535 .01482 L .25585 .01482 L .25703 .01484 L .25713 .01484 L .25801 .01485 L .25844 .01485 L .25917 .01486 L .25943 .01487 L .25983 .01488 L .26055 .01489 L .26112 .0149 L .26162 .01491 L .26234 .01492 L .2635 .01495 L .26474 .01498 L .26557 .015 L .26645 .01503 L .26699 .01504 L .26836 .01509 L .26889 .01511 L .26966 .01514 L .27013 .01516 L .27157 .01522 L .27209 .01525 L Mistroke .27385 .01534 L .27466 .01539 L .27503 .01542 L .27631 .01551 L .27703 .01556 L .27762 .0156 L .27964 .01578 L .28034 .01585 L .28076 .01589 L .28148 .01597 L .2824 .01608 L .28269 .01611 L .28339 .0162 L .28342 .01621 L .28403 .01629 L .28527 .01647 L .28632 .01663 L .28639 .01664 L .28693 .01673 L .2876 .01685 L .28875 .01707 L .28888 .01709 L .28981 .01728 L .29087 .01752 L .29118 .01759 L .29161 .01769 L .29186 .01776 L .29296 .01804 L .29413 .01837 L .2953 .01873 L .29585 .01891 L .29653 .01914 L .29676 .01922 L .29873 .01997 L .30087 .02091 L .3013 .02111 L .30154 .02123 L .30372 .02239 L .3055 .02346 L .3059 .02372 L .30689 .02439 L .30804 .02523 L .30827 .0254 L .31044 .02717 L .3118 .02841 L .31182 .02842 L .31257 .02915 L .31328 .02987 L .31357 .03017 L .31453 .03121 L Mistroke .31517 .03193 L .31586 .03275 L .31712 .03431 L .31722 .03445 L .31782 .03524 L .31846 .03611 L .31847 .03612 L .31972 .03791 L .32091 .03974 L .32224 .04192 L .32294 .04314 L .32344 .04404 L .32614 .04927 L .32731 .05177 L .32791 .0531 L .32864 .05479 L .331 .06062 L .33219 .06382 L .33255 .06483 L .33459 .07082 L .33629 .0762 L .33682 .07798 L .33761 .08067 L .33809 .08238 L .33925 .08655 L .33926 .08663 L .34052 .09142 L .34123 .0942 L .34189 .09687 L .342 .09736 L .34304 .10174 L .34311 .10201 L .34411 .10639 L .34528 .11171 L .34651 .11756 L .34759 .12289 L .34875 .1288 L .35084 .14003 L .35111 .14154 L .35332 .15433 L .35355 .15574 L .35558 .16824 L .35612 .17167 L .36066 .20256 L .36086 .20397 L .36345 .22311 L .36354 .22378 L .36505 .23542 L .36578 .24109 L .36618 .24429 L Mistroke .36645 .24646 L .36763 .25593 L .36893 .26656 L .37019 .2771 L .3709 .2831 L .37155 .28864 L .37276 .29898 L .37388 .3087 L .3751 .31948 L .37621 .32929 L .37642 .33108 L .3791 .35503 L .38075 .3699 L .38153 .37692 L .382 .38118 L .38563 .41363 L .38639 .42033 L .38843 .43817 L .38965 .4487 L .39099 .46002 L .39153 .46452 L .3922 .47002 L .39226 .47056 L .39344 .48015 L .39469 .49004 L .39539 .49546 L .39602 .5003 L .39733 .5101 L .39799 .51491 L .39872 .52008 L .40001 .52894 L .40074 .53383 L .40121 .53687 L .40177 .54042 L .40392 .55338 L .40553 .56216 L .40657 .5675 L .40684 .56878 L .40905 .57875 L .41066 .58501 L .41175 .58876 L .41217 .59007 L .41217 .59008 L .4136 .59415 L .41455 .59645 L .415 .59741 L .41608 .59946 L .41629 .5998 L .41681 .60059 L .41704 .60091 L Mistroke .4175 .60149 L .41751 .6015 L .41814 .60216 L .41881 .6027 L .41884 .60272 L .42005 .60326 L .42011 .60327 L .42074 .60332 L .42085 .60331 L .42147 .60319 L .42155 .60316 L .42272 .60251 L .42277 .60247 L .42398 .60124 L .42398 .60123 L .42516 .59951 L .4253 .59927 L .42623 .59749 L .42627 .59742 L .42655 .59683 L .4277 .59406 L .42887 .59078 L .43133 .58232 L .43136 .58221 L .4322 .57883 L .43478 .56709 L .43609 .56034 L .43711 .5547 L .43855 .54629 L .43993 .53767 L .44121 .52932 L .4417 .52597 L .44234 .52155 L .44252 .52028 L .44326 .51499 L .44396 .50995 L .44469 .50451 L .44536 .49947 L .44613 .49354 L .44686 .48785 L .44807 .47821 L .44935 .46775 L .45044 .45865 L .4505 .45814 L .45164 .44845 L .45433 .4252 L .45517 .41775 L .45684 .40295 L .45779 .39439 L .46019 .37283 L Mistroke .46065 .36874 L .46276 .34976 L .46403 .33844 L .4652 .32799 L .46581 .32258 L .46638 .3176 L .46745 .30825 L .46863 .29796 L .46989 .28713 L .47054 .28166 L .47082 .27931 L .47122 .27593 L .47244 .26578 L .47375 .25505 L .47449 .24905 L .47519 .24351 L .47538 .24198 L .47759 .22482 L .48017 .2057 L .48088 .2006 L .48155 .19593 L .48588 .16708 L .48829 .15235 L .48955 .14499 L .48975 .14385 L .49071 .13851 L .49089 .1375 L .49207 .13119 L .49335 .12452 L .49452 .1187 L .49562 .11346 L .49597 .11183 L .49693 .10743 L .49767 .10414 L .49836 .10117 L .49862 .10008 L .49962 .09592 L .50025 .09336 L .50076 .09139 L .50095 .09061 L .50216 .08604 L .50346 .08136 L .50355 .08105 L .50582 .07349 L .50879 .06462 L .5104 .06029 L .51151 .05748 L .51405 .05156 L .5157 .0481 L .51676 .04603 L Mistroke .51685 .04585 L .51842 .04298 L .51986 .04054 L .52072 .03917 L .52103 .03869 L .52186 .03745 L .52229 .03684 L .52347 .03521 L .52454 .03381 L .52536 .0328 L .52581 .03227 L .52652 .03145 L .52718 .03073 L .52724 .03066 L .52839 .02946 L .52965 .02824 L .52967 .02822 L .53089 .02712 L .53183 .02633 L .5322 .02602 L .53435 .02441 L .53443 .02436 L .53458 .02425 L .53685 .0228 L .53935 .02142 L .53948 .02136 L .53998 .02111 L .5419 .02024 L .54425 .01932 L .54456 .0192 L .54489 .01909 L .5459 .01875 L .54738 .0183 L .54867 .01795 L .54874 .01793 L .54985 .01765 L .55012 .01758 L .5505 .0175 L .55121 .01734 L .55251 .01707 L .55313 .01695 L .55366 .01685 L .55372 .01684 L .555 .01662 L .55585 .01649 L .55614 .01644 L .55621 .01643 L .55731 .01628 L .55848 .01613 L .55862 .01611 L Mistroke .55885 .01608 L .55971 .01598 L .56117 .01583 L .56192 .01576 L .56343 .01562 L .56359 .01561 L .566 .01543 L .56615 .01542 L .56689 .01538 L .56833 .01529 L .56871 .01527 L .57017 .0152 L .5705 .01519 L .57152 .01514 L .57152 .01514 L .57279 .01509 L .57286 .01509 L .57399 .01505 L .5759 .01499 L .57623 .01499 L .57714 .01496 L .57749 .01495 L .57829 .01494 L .57865 .01493 L .5795 .01491 L .57992 .0149 L .58056 .01489 L .58088 .01488 L .58127 .01488 L .58204 .01487 L .58255 .01486 L .58375 .01484 L .58423 .01484 L .58506 .01483 L .58541 .01482 L .58579 .01482 L .58646 .01481 L .58662 .01481 L .58768 .0148 L .58798 .0148 L .589 .01479 L .58942 .01478 L .5907 .01478 L .59139 .01477 L .59207 .01477 L .59302 .01476 L .59465 .01475 L .59558 .01475 L .59704 .01475 L .59797 .01474 L Mistroke .59954 .01474 L .60015 .01474 L .60066 .01474 L .60135 .01473 L .60189 .01473 L .60266 .01473 L .60392 .01473 L .60446 .01473 L .60506 .01473 L 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\[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["Let us first generate a suitable grid in x-space:", "Text"], Cell["a = -10.; b = 14.; n = 512;", "Input"], Cell["xgrid = QGrid[a,b,n];", "Input"], Cell[TextData[{ "This command divides the interval [-10,10] by equally spaced points ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ SubscriptBox[ StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic"], "0"], " ", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"a", "<", " ", SubscriptBox[ StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic"], \(\(1\)\(\ \)\)], "<", " ", SubscriptBox[ StyleBox["x", FontSlant->"Italic"], \(\(2\)\(\ \)\)], "<"}], " ", "..."}], " ", "<", " ", SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "n"]}], "=", " ", "b"}]}], FontFamily->"Times New Roman"], InputForm]], FontFamily->"Times New Roman"], " and returns the list {", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ SubscriptBox[ StyleBox["x", FontFamily->"Times New Roman", FontSlant->"Italic"], "1"], ",", " ", SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "2"], ",", " ", "...", " ", ",", " ", SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "n"]}]}], InputForm]], FontFamily->"Times New Roman"], "}. The number n should be even. You can obtain information about the space \ grid via the following functions." }], "Text"], Cell[CellGroupData[{ Cell["{QLeftBorder[a,b,n],QRightBorder[a,b,n],QSpaceStep[a,b,n]}", "Input"], Cell[BoxData[ \({\(-9.984375`\), 13.96875`, 0.046875`}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["QIndexPosition[", "InlineInput"], StyleBox["x", FontSlant->"Italic"], StyleBox[",", "InlineInput"], StyleBox["a", FontSlant->"Italic"], StyleBox[",", "InlineInput"], StyleBox["b", FontSlant->"Italic"], StyleBox[",", "InlineInput"], StyleBox["n", FontSlant->"Italic"], StyleBox["]", "InlineInput"], " lets you access the element of xgrid corresponding to a special value of \ ", StyleBox["x", FontSlant->"Italic"] }], "Text"], Cell[CellGroupData[{ Cell["QIndexPosition[5.,a,b,n]", "Input"], Cell[BoxData[ \(321\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["xgrid[[321]]", "Input"], Cell[BoxData[ \(5.015625`\)], "Output"] }, Open ]], Cell["We can now define a discretization of the function f 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You can obtain a list of the points in k-space \ by QFourierGrid[-10.,10,100]. Information about the grid in Fourier space can \ be obtained by\ \>", "Text"], Cell[CellGroupData[{ Cell["\<\ {kleft,kright,dk}={QFourierLeftBorder[a,b,n],QFourierRightBorder[a,\ b,n],QFourierStep[a,b,n]}\ \>", "Input"], Cell[BoxData[ \({\(-66.7588438887831`\), 67.02064327658225`, 0.2617993877991494`}\)], "Output"] }, Open ]], Cell["Hence ", "Text"], Cell[CellGroupData[{ Cell["QFourierGrid[a,b,n]==Table[n,{n,kleft,kright,dk}]", "Input"], Cell[BoxData[ \(False\)], "Output"] }, Open ]], Cell["\<\ If the function in x-space is given on the points of QGrid, then \ QFourierList returns the values of the Fourier transform on the points \ QFourierGrid in k-space.\ \>", "Text"], Cell["Ff = QFourierList[fvals,{a,b}];", "Input"], Cell["\<\ QFourierList returns the list of Fourier values and the interval in \ k-space: {Fflist,{kleft,kright}}.\ \>", "Text"], Cell["Ffvals = Ff[[1]]; kinterval = Ff[[2]];", "Input"], Cell[CellGroupData[{ Cell["\<\ QListArgColorPlot[Ffvals,PlotRange->All, \ 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