Intrepid: http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/src/Discretization/Integration/Intrepid_CubatureDirectLineGaussDef.hpp Source File

00001 // @HEADER
00002 // ************************************************************************
00003 //
00004 //                           Intrepid Package
00005 //                 Copyright (2007) Sandia Corporation
00006 //
00007 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
00008 // license for use of this work by or on behalf of the U.S. Government.
00009 //
00010 // This library is free software; you can redistribute it and/or modify
00011 // it under the terms of the GNU Lesser General Public License as
00012 // published by the Free Software Foundation; either version 2.1 of the
00013 // License, or (at your option) any later version.
00014 //
00015 // This library is distributed in the hope that it will be useful, but
00016 // WITHOUT ANY WARRANTY; without even the implied warranty of
00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00018 // Lesser General Public License for more details.
00019 //
00020 // You should have received a copy of the GNU Lesser General Public
00021 // License along with this library; if not, write to the Free Software
00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
00023 // USA
00024 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) or
00025 //                    Denis Ridzal (dridzal@sandia.gov).
00026 //
00027 // ************************************************************************
00028 // @HEADER
00029 
00035 namespace Intrepid {
00036 
00037 template <class Scalar, class ArrayType>
00038 CubatureDirectLineGauss<Scalar,ArrayType>::CubatureDirectLineGauss(const int degree) {
00039   this->degree_    = degree;
00040   this->dimension_ = 1;
00041   TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_LINE_GAUSS_MAX),
00042                      std::out_of_range,
00043                      ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree.");
00044 } // end constructor
00045 
00046 
00047 
00048 template <class Scalar, class ArrayType>
00049 const CubatureTemplate *  CubatureDirectLineGauss<Scalar,ArrayType>::exposeCubatureData() const {
00050   return cubature_data_;
00051 }
00052 
00053 
00054 
00055 template <class Scalar, class ArrayType>
00056 int CubatureDirectLineGauss<Scalar,ArrayType>::getMaxAccuracy() const {
00057   return INTREPID_CUBATURE_LINE_GAUSS_MAX;
00058 }
00059 
00060 
00061 
00062 template <class Scalar, class ArrayType>
00063 const char* CubatureDirectLineGauss<Scalar,ArrayType>::getName() const {
00064   return cubature_name_;
00065 } // end getName
00066 
00067 
00068 
00069 template <class Scalar, class ArrayType>
00070 const char* CubatureDirectLineGauss<Scalar,ArrayType>::cubature_name_ = "INTREPID_CUBATURE_LINE_GAUSS";
00071 
00072 
00073 //-------------------------------------------------------------------------------------//
00074 //                          Definition of cubature templates                           //
00075 //-------------------------------------------------------------------------------------//
00076 
00077 /*
00078    Cubature templates for lines are defined the reference cell:
00079 
00080    Line -> (-1,0,0),(1,0,0)
00081 */
00082 
00083 /*
00084    This static const member contains templates for Gauss(-Legendre) rules.
00085 */
00086 
00087 template <class Scalar, class ArrayType>
00088 const CubatureTemplate CubatureDirectLineGauss<Scalar,ArrayType>::cubature_data_[INTREPID_CUBATURE_LINE_GAUSS_MAX+1] =
00089 {
00090 
00091   // Collection of Gauss rules on [-1,1]
00092   // The rule with array index i is exact for polynomials up to order i
00093   {
00094     1,
00095     {{0e0, 0.0, 0.0}},
00096     {2e0}
00097   },
00098   {
00099     1,
00100     {{0e0, 0.0, 0.0}},
00101     {2e0}
00102   },
00103   {
00104     2,
00105     {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
00106      {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
00107     {1e0,
00108      1e0}
00109   },
00110   {
00111     2,
00112     {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
00113      {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
00114     {1e0,
00115      1e0}
00116   },
00117   {
00118     3,
00119     {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
00120      {0e0, 0.0, 0.0},
00121      {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
00122     {5.555555555555555555555555555555555555556e-1,
00123      8.888888888888888888888888888888888888889e-1,
00124      5.555555555555555555555555555555555555556e-1}
00125   },
00126   {
00127     3,
00128     {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
00129      {0e0, 0.0, 0.0},
00130      {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
00131     {5.555555555555555555555555555555555555556e-1,
00132      8.888888888888888888888888888888888888889e-1,
00133      5.555555555555555555555555555555555555556e-1}
00134   },
00135   {
00136     4,
00137     {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
00138      {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00139      {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00140      {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
00141     {3.478548451374538573730639492219994072353e-1,
00142      6.521451548625461426269360507780005927647e-1,
00143      6.521451548625461426269360507780005927647e-1,
00144      3.478548451374538573730639492219994072353e-1}
00145   },
00146   {
00147     4,
00148     {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
00149      {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00150      {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00151      {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
00152     {3.478548451374538573730639492219994072353e-1,
00153      6.521451548625461426269360507780005927647e-1,
00154      6.521451548625461426269360507780005927647e-1,
00155      3.478548451374538573730639492219994072353e-1}
00156   },
00157   {
00158     5,
00159     {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
00160      {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00161      {0e0, 0.0, 0.0},
00162      {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00163      {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
00164     {2.369268850561890875142640407199173626433e-1,
00165      4.786286704993664680412915148356381929123e-1,
00166      5.688888888888888888888888888888888888889e-1,
00167      4.786286704993664680412915148356381929123e-1,
00168      2.369268850561890875142640407199173626433e-1}
00169   },
00170   {
00171     5,
00172     {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
00173      {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00174      {0e0, 0.0, 0.0},
00175      {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00176      {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
00177     {2.369268850561890875142640407199173626433e-1,
00178      4.786286704993664680412915148356381929123e-1,
00179      5.688888888888888888888888888888888888889e-1,
00180      4.786286704993664680412915148356381929123e-1,
00181      2.369268850561890875142640407199173626433e-1}
00182   },
00183   {
00184     6,
00185     {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
00186      {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00187      {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00188      {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00189      {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00190      {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
00191     {1.713244923791703450402961421727328935268e-1,
00192      3.607615730481386075698335138377161116615e-1,
00193      4.679139345726910473898703439895509948117e-1,
00194      4.679139345726910473898703439895509948117e-1,
00195      3.607615730481386075698335138377161116615e-1,
00196      1.713244923791703450402961421727328935268e-1}
00197   },
00198   {
00199     6,
00200     {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
00201      {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00202      {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00203      {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00204      {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00205      {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
00206     {1.713244923791703450402961421727328935268e-1,
00207      3.607615730481386075698335138377161116615e-1,
00208      4.679139345726910473898703439895509948117e-1,
00209      4.679139345726910473898703439895509948117e-1,
00210      3.607615730481386075698335138377161116615e-1,
00211      1.713244923791703450402961421727328935268e-1}
00212   },
00213   {
00214     7,
00215     {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
00216      {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00217      {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00218      {0e0, 0.0, 0.0},
00219      {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00220      {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00221      {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
00222     {1.294849661688696932706114326790820183286e-1,
00223      2.797053914892766679014677714237795824869e-1,
00224      3.818300505051189449503697754889751338784e-1,
00225      4.179591836734693877551020408163265306122e-1,
00226      3.818300505051189449503697754889751338784e-1,
00227      2.797053914892766679014677714237795824869e-1,
00228      1.294849661688696932706114326790820183286e-1}
00229   },
00230   {
00231     7,
00232     {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
00233      {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00234      {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00235      {0e0, 0.0, 0.0},
00236      {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00237      {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00238      {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
00239     {1.294849661688696932706114326790820183286e-1,
00240      2.797053914892766679014677714237795824869e-1,
00241      3.818300505051189449503697754889751338784e-1,
00242      4.179591836734693877551020408163265306122e-1,
00243      3.818300505051189449503697754889751338784e-1,
00244      2.797053914892766679014677714237795824869e-1,
00245      1.294849661688696932706114326790820183286e-1}
00246   },
00247   {
00248     8,
00249     {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
00250      {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00251      {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00252      {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00253      {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00254      {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00255      {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00256      {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
00257     {1.012285362903762591525313543099621901154e-1,
00258      2.223810344533744705443559944262408844301e-1,
00259      3.137066458778872873379622019866013132603e-1,
00260      3.626837833783619829651504492771956121941e-1,
00261      3.626837833783619829651504492771956121941e-1,
00262      3.137066458778872873379622019866013132603e-1,
00263      2.223810344533744705443559944262408844301e-1,
00264      1.012285362903762591525313543099621901154e-1}
00265   },
00266   {
00267     8,
00268     {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
00269      {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00270      {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00271      {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00272      {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00273      {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00274      {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00275      {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
00276     {1.012285362903762591525313543099621901154e-1,
00277      2.223810344533744705443559944262408844301e-1,
00278      3.137066458778872873379622019866013132603e-1,
00279      3.626837833783619829651504492771956121941e-1,
00280      3.626837833783619829651504492771956121941e-1,
00281      3.137066458778872873379622019866013132603e-1,
00282      2.223810344533744705443559944262408844301e-1,
00283      1.012285362903762591525313543099621901154e-1}
00284   },
00285   {
00286     9,
00287     {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
00288      {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00289      {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00290      {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00291      {0e0, 0.0, 0.0},
00292      {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00293      {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00294      {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00295      {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
00296     {8.127438836157441197189215811052365067566e-2,
00297      1.806481606948574040584720312429128095143e-1,
00298      2.606106964029354623187428694186328497718e-1,
00299      3.123470770400028400686304065844436655988e-1,
00300      3.302393550012597631645250692869740488788e-1,
00301      3.123470770400028400686304065844436655988e-1,
00302      2.606106964029354623187428694186328497718e-1,
00303      1.806481606948574040584720312429128095143e-1,
00304      8.127438836157441197189215811052365067566e-2}
00305   },
00306   {
00307     9,
00308     {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
00309      {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00310      {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00311      {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00312      {0e0, 0.0, 0.0},
00313      {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00314      {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00315      {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00316      {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
00317     {8.127438836157441197189215811052365067566e-2,
00318      1.806481606948574040584720312429128095143e-1,
00319      2.606106964029354623187428694186328497718e-1,
00320      3.123470770400028400686304065844436655988e-1,
00321      3.302393550012597631645250692869740488788e-1,
00322      3.123470770400028400686304065844436655988e-1,
00323      2.606106964029354623187428694186328497718e-1,
00324      1.806481606948574040584720312429128095143e-1,
00325      8.127438836157441197189215811052365067566e-2}
00326   },
00327   {
00328     10,
00329     {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
00330      {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00331      {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00332      {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00333      {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00334      {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00335      {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00336      {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00337      {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00338      {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
00339     {6.667134430868813759356880989333179285786e-2,
00340      1.494513491505805931457763396576973324026e-1,
00341      2.190863625159820439955349342281631924588e-1,
00342      2.692667193099963550912269215694693528598e-1,
00343      2.95524224714752870173892994651338329421e-1,
00344      2.95524224714752870173892994651338329421e-1,
00345      2.692667193099963550912269215694693528598e-1,
00346      2.190863625159820439955349342281631924588e-1,
00347      1.494513491505805931457763396576973324026e-1,
00348      6.667134430868813759356880989333179285786e-2}
00349   },
00350   {
00351     10,
00352     {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
00353      {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00354      {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00355      {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00356      {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00357      {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00358      {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00359      {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00360      {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00361      {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
00362     {6.667134430868813759356880989333179285786e-2,
00363      1.494513491505805931457763396576973324026e-1,
00364      2.190863625159820439955349342281631924588e-1,
00365      2.692667193099963550912269215694693528598e-1,
00366      2.95524224714752870173892994651338329421e-1,
00367      2.95524224714752870173892994651338329421e-1,
00368      2.692667193099963550912269215694693528598e-1,
00369      2.190863625159820439955349342281631924588e-1,
00370      1.494513491505805931457763396576973324026e-1,
00371      6.667134430868813759356880989333179285786e-2}
00372   },
00373   {
00374     11,
00375     {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
00376      {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00377      {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00378      {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00379      {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00380      {0e0, 0.0, 0.0},
00381      {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00382      {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00383      {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00384      {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00385      {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
00386     {5.566856711617366648275372044254857872852e-2,
00387      1.255803694649046246346942992239401001976e-1,
00388      1.862902109277342514260976414316558916913e-1,
00389      2.331937645919904799185237048431751394318e-1,
00390      2.628045445102466621806888698905091953728e-1,
00391      2.72925086777900630714483528336342189156e-1,
00392      2.628045445102466621806888698905091953728e-1,
00393      2.331937645919904799185237048431751394318e-1,
00394      1.862902109277342514260976414316558916913e-1,
00395      1.255803694649046246346942992239401001976e-1,
00396      5.566856711617366648275372044254857872852e-2}
00397   },
00398   {
00399     11,
00400     {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
00401      {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00402      {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00403      {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00404      {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00405      {0e0, 0.0, 0.0},
00406      {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00407      {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00408      {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00409      {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00410      {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
00411     {5.566856711617366648275372044254857872852e-2,
00412      1.255803694649046246346942992239401001976e-1,
00413      1.862902109277342514260976414316558916913e-1,
00414      2.331937645919904799185237048431751394318e-1,
00415      2.628045445102466621806888698905091953728e-1,
00416      2.72925086777900630714483528336342189156e-1,
00417      2.628045445102466621806888698905091953728e-1,
00418      2.331937645919904799185237048431751394318e-1,
00419      1.862902109277342514260976414316558916913e-1,
00420      1.255803694649046246346942992239401001976e-1,
00421      5.566856711617366648275372044254857872852e-2}
00422   },
00423   {
00424     12,
00425     { // points
00426      {.9815606342467192506905490901492808229602    ,0.0, 0.0},
00427      {.9041172563704748566784658661190961925376    ,0.0, 0.0},
00428      {.7699026741943046870368938332128180759849    ,0.0, 0.0},
00429      {.5873179542866174472967024189405342803691    ,0.0, 0.0},
00430      {.3678314989981801937526915366437175612564    ,0.0, 0.0},
00431      {.1252334085114689154724413694638531299834    ,0.0, 0.0},
00432      {-.1252334085114689154724413694638531299834   ,0.0, 0.0},
00433      {-.3678314989981801937526915366437175612564   ,0.0, 0.0},
00434      {-.5873179542866174472967024189405342803691   ,0.0, 0.0},
00435      {-.7699026741943046870368938332128180759849   ,0.0, 0.0},
00436      {-.9041172563704748566784658661190961925376   ,0.0, 0.0},
00437      {-.9815606342467192506905490901492808229602   ,0.0, 0.0}
00438     },
00439     { // weights
00440      .04717533638651182719461596148501706031703,
00441      .1069393259953184309602547181939962242146,
00442      .160078328543346226334652529543359071872,
00443      .2031674267230659217490644558097983765065,
00444      .2334925365383548087608498989248780562594,
00445      .2491470458134027850005624360429512108305,
00446       .2491470458134027850005624360429512108305,
00447       .2334925365383548087608498989248780562594,
00448       .2031674267230659217490644558097983765065,
00449       .160078328543346226334652529543359071872,
00450       .1069393259953184309602547181939962242146,
00451       .04717533638651182719461596148501706031703
00452     }
00453   },
00454   {
00455     12,
00456     { // points
00457      {.9815606342467192506905490901492808229602    ,0.0, 0.0},
00458      {.9041172563704748566784658661190961925376    ,0.0, 0.0},
00459      {.7699026741943046870368938332128180759849    ,0.0, 0.0},
00460      {.5873179542866174472967024189405342803691    ,0.0, 0.0},
00461      {.3678314989981801937526915366437175612564    ,0.0, 0.0},
00462      {.1252334085114689154724413694638531299834    ,0.0, 0.0},
00463      {-.1252334085114689154724413694638531299834   ,0.0, 0.0},
00464      {-.3678314989981801937526915366437175612564   ,0.0, 0.0},
00465      {-.5873179542866174472967024189405342803691   ,0.0, 0.0},
00466      {-.7699026741943046870368938332128180759849   ,0.0, 0.0},
00467      {-.9041172563704748566784658661190961925376   ,0.0, 0.0},
00468      {-.9815606342467192506905490901492808229602   ,0.0, 0.0}
00469     },
00470     { // weights
00471      .04717533638651182719461596148501706031703,
00472      .1069393259953184309602547181939962242146,
00473      .160078328543346226334652529543359071872,
00474      .2031674267230659217490644558097983765065,
00475      .2334925365383548087608498989248780562594,
00476      .2491470458134027850005624360429512108305,
00477       .2491470458134027850005624360429512108305,
00478       .2334925365383548087608498989248780562594,
00479       .2031674267230659217490644558097983765065,
00480       .160078328543346226334652529543359071872,
00481       .1069393259953184309602547181939962242146,
00482       .04717533638651182719461596148501706031703
00483     }
00484   },
00485   {
00486     13,
00487     { // points
00488      {.984183054718588149472829448807109611065     ,0.0, 0.0},
00489      {.9175983992229779652065478365007195123905    ,0.0, 0.0},
00490      {.8015780907333099127942064895828598903056    ,0.0, 0.0},
00491      {.6423493394403402206439846069955156500717    ,0.0, 0.0},
00492      {.4484927510364468528779128521276398678019    ,0.0, 0.0},
00493      {.2304583159551347940655281210979888352115    ,0.0, 0.0},
00494      { 0                                           ,0.0, 0.0},
00495      {-.2304583159551347940655281210979888352115   ,0.0, 0.0},
00496      {-.4484927510364468528779128521276398678019   ,0.0, 0.0},
00497      {-.6423493394403402206439846069955156500717   ,0.0, 0.0},
00498      {-.8015780907333099127942064895828598903056   ,0.0, 0.0},
00499      {-.9175983992229779652065478365007195123905   ,0.0, 0.0},
00500      {-.984183054718588149472829448807109611065    ,0.0, 0.0}
00501     },
00502     { // weights
00503      .04048400476531587952002159220098606004199,
00504      .09212149983772844791442177595379712092368,
00505      .1388735102197872384636017768688714676219,
00506      .1781459807619457382800466919960979955128,
00507      .2078160475368885023125232193060527633866,
00508      .2262831802628972384120901860397766184348,
00509      .2325515532308739101945895152688359481566,
00510      .2262831802628972384120901860397766184348,
00511      .2078160475368885023125232193060527633866,
00512      .1781459807619457382800466919960979955128,
00513      .1388735102197872384636017768688714676219,
00514      .09212149983772844791442177595379712092368,
00515      .04048400476531587952002159220098606004199
00516     }
00517   },
00518   {
00519     13,
00520     { // points
00521      {.984183054718588149472829448807109611065     ,0.0, 0.0},
00522      {.9175983992229779652065478365007195123905    ,0.0, 0.0},
00523      {.8015780907333099127942064895828598903056    ,0.0, 0.0},
00524      {.6423493394403402206439846069955156500717    ,0.0, 0.0},
00525      {.4484927510364468528779128521276398678019    ,0.0, 0.0},
00526      {.2304583159551347940655281210979888352115    ,0.0, 0.0},
00527      { 0                                           ,0.0, 0.0},
00528      {-.2304583159551347940655281210979888352115   ,0.0, 0.0},
00529      {-.4484927510364468528779128521276398678019   ,0.0, 0.0},
00530      {-.6423493394403402206439846069955156500717   ,0.0, 0.0},
00531      {-.8015780907333099127942064895828598903056   ,0.0, 0.0},
00532      {-.9175983992229779652065478365007195123905   ,0.0, 0.0},
00533      {-.984183054718588149472829448807109611065    ,0.0, 0.0}
00534     },
00535     { // weights
00536      .04048400476531587952002159220098606004199,
00537      .09212149983772844791442177595379712092368,
00538      .1388735102197872384636017768688714676219,
00539      .1781459807619457382800466919960979955128,
00540      .2078160475368885023125232193060527633866,
00541      .2262831802628972384120901860397766184348,
00542      .2325515532308739101945895152688359481566,
00543      .2262831802628972384120901860397766184348,
00544      .2078160475368885023125232193060527633866,
00545      .1781459807619457382800466919960979955128,
00546      .1388735102197872384636017768688714676219,
00547      .09212149983772844791442177595379712092368,
00548      .04048400476531587952002159220098606004199
00549     }
00550   },
00551   {
00552     14,
00553     { // points
00554      {.9862838086968123388415972667040528016761    ,0.0, 0.0},
00555      {.928434883663573517336391139377874264477     ,0.0, 0.0},
00556      {.8272013150697649931897947426503949610397    ,0.0, 0.0},
00557      {.6872929048116854701480198030193341375384    ,0.0, 0.0},
00558      {.5152486363581540919652907185511886623089    ,0.0, 0.0},
00559      {.3191123689278897604356718241684754668343    ,0.0, 0.0},
00560      {.108054948707343662066244650219834747612     ,0.0, 0.0},
00561      {-.108054948707343662066244650219834747612    ,0.0, 0.0},
00562      {-.3191123689278897604356718241684754668343   ,0.0, 0.0},
00563      {-.5152486363581540919652907185511886623089   ,0.0, 0.0},
00564      {-.6872929048116854701480198030193341375384   ,0.0, 0.0},
00565      {-.8272013150697649931897947426503949610397   ,0.0, 0.0},
00566      {-.928434883663573517336391139377874264477    ,0.0, 0.0},
00567      {-.9862838086968123388415972667040528016761   ,0.0, 0.0}
00568     },
00569     { // weights
00570      .03511946033175186303183287613819178061971,
00571      .0801580871597602098056332770628543095837,
00572      .1215185706879031846894148090724766259567,
00573      .1572031671581935345696019386238421566057,
00574      .1855383974779378137417165901251570362489,
00575      .2051984637212956039659240656612180557103,
00576      .215263853463157790195876443316260035275,
00577      .215263853463157790195876443316260035275,
00578      .2051984637212956039659240656612180557103,
00579      .1855383974779378137417165901251570362489,
00580      .1572031671581935345696019386238421566057,
00581      .1215185706879031846894148090724766259567,
00582      .0801580871597602098056332770628543095837,
00583      .03511946033175186303183287613819178061971
00584     }
00585   },
00586   {
00587     14,
00588     { // points
00589      {.9862838086968123388415972667040528016761    ,0.0, 0.0},
00590      {.928434883663573517336391139377874264477     ,0.0, 0.0},
00591      {.8272013150697649931897947426503949610397    ,0.0, 0.0},
00592      {.6872929048116854701480198030193341375384    ,0.0, 0.0},
00593      {.5152486363581540919652907185511886623089    ,0.0, 0.0},
00594      {.3191123689278897604356718241684754668343    ,0.0, 0.0},
00595      {.108054948707343662066244650219834747612     ,0.0, 0.0},
00596      {-.108054948707343662066244650219834747612    ,0.0, 0.0},
00597      {-.3191123689278897604356718241684754668343   ,0.0, 0.0},
00598      {-.5152486363581540919652907185511886623089   ,0.0, 0.0},
00599      {-.6872929048116854701480198030193341375384   ,0.0, 0.0},
00600      {-.8272013150697649931897947426503949610397   ,0.0, 0.0},
00601      {-.928434883663573517336391139377874264477    ,0.0, 0.0},
00602      {-.9862838086968123388415972667040528016761   ,0.0, 0.0}
00603     },
00604     { // weights
00605      .03511946033175186303183287613819178061971,
00606      .0801580871597602098056332770628543095837,
00607      .1215185706879031846894148090724766259567,
00608      .1572031671581935345696019386238421566057,
00609      .1855383974779378137417165901251570362489,
00610      .2051984637212956039659240656612180557103,
00611      .215263853463157790195876443316260035275,
00612      .215263853463157790195876443316260035275,
00613      .2051984637212956039659240656612180557103,
00614      .1855383974779378137417165901251570362489,
00615      .1572031671581935345696019386238421566057,
00616      .1215185706879031846894148090724766259567,
00617      .0801580871597602098056332770628543095837,
00618      .03511946033175186303183287613819178061971
00619     }
00620   },
00621   {
00622     15,
00623     { // points
00624      {.987992518020485428489565718586612581147     ,0.0, 0.0},
00625      {.937273392400705904307758947710209471244     ,0.0, 0.0},
00626      {.8482065834104272162006483207742168513663    ,0.0, 0.0},
00627      {.7244177313601700474161860546139380096309    ,0.0, 0.0},
00628      {.5709721726085388475372267372539106412384    ,0.0, 0.0},
00629      {.3941513470775633698972073709810454683628    ,0.0, 0.0},
00630      {.2011940939974345223006283033945962078128    ,0.0, 0.0},
00631      { 0                                           ,0.0, 0.0},
00632      {-.2011940939974345223006283033945962078128   ,0.0, 0.0},
00633      {-.3941513470775633698972073709810454683628   ,0.0, 0.0},
00634      {-.5709721726085388475372267372539106412384   ,0.0, 0.0},
00635      {-.7244177313601700474161860546139380096309   ,0.0, 0.0},
00636      {-.8482065834104272162006483207742168513663   ,0.0, 0.0},
00637      {-.937273392400705904307758947710209471244    ,0.0, 0.0},
00638      {-.987992518020485428489565718586612581147    ,0.0, 0.0}
00639     },
00640     { // weights
00641      .03075324199611726835462839357720441772175,
00642      .07036604748810812470926741645066733846671,
00643      .1071592204671719350118695466858693034155,
00644      .1395706779261543144478047945110283225209,
00645      .1662692058169939335532008604812088111309,
00646      .1861610000155622110268005618664228245062,
00647      .1984314853271115764561183264438393248187,
00648      .2025782419255612728806201999675193148387,
00649      .1984314853271115764561183264438393248187,
00650      .1861610000155622110268005618664228245062,
00651      .1662692058169939335532008604812088111309,
00652      .1395706779261543144478047945110283225209,
00653      .1071592204671719350118695466858693034155,
00654      .07036604748810812470926741645066733846671,
00655      .03075324199611726835462839357720441772175
00656     }
00657   },
00658   {
00659     15,
00660     { // points
00661      {.987992518020485428489565718586612581147     ,0.0, 0.0},
00662      {.937273392400705904307758947710209471244     ,0.0, 0.0},
00663      {.8482065834104272162006483207742168513663    ,0.0, 0.0},
00664      {.7244177313601700474161860546139380096309    ,0.0, 0.0},
00665      {.5709721726085388475372267372539106412384    ,0.0, 0.0},
00666      {.3941513470775633698972073709810454683628    ,0.0, 0.0},
00667      {.2011940939974345223006283033945962078128    ,0.0, 0.0},
00668      { 0                                           ,0.0, 0.0},
00669      {-.2011940939974345223006283033945962078128   ,0.0, 0.0},
00670      {-.3941513470775633698972073709810454683628   ,0.0, 0.0},
00671      {-.5709721726085388475372267372539106412384   ,0.0, 0.0},
00672      {-.7244177313601700474161860546139380096309   ,0.0, 0.0},
00673      {-.8482065834104272162006483207742168513663   ,0.0, 0.0},
00674      {-.937273392400705904307758947710209471244    ,0.0, 0.0},
00675      {-.987992518020485428489565718586612581147    ,0.0, 0.0}
00676     },
00677     { // weights
00678      .03075324199611726835462839357720441772175,
00679      .07036604748810812470926741645066733846671,
00680      .1071592204671719350118695466858693034155,
00681      .1395706779261543144478047945110283225209,
00682      .1662692058169939335532008604812088111309,
00683      .1861610000155622110268005618664228245062,
00684      .1984314853271115764561183264438393248187,
00685      .2025782419255612728806201999675193148387,
00686      .1984314853271115764561183264438393248187,
00687      .1861610000155622110268005618664228245062,
00688      .1662692058169939335532008604812088111309,
00689      .1395706779261543144478047945110283225209,
00690      .1071592204671719350118695466858693034155,
00691      .07036604748810812470926741645066733846671,
00692      .03075324199611726835462839357720441772175
00693     }
00694   },
00695   {
00696     16,
00697     { // points
00698      {.9894009349916499325961541734503326274263    ,0.0, 0.0},
00699      {.9445750230732325760779884155346083450911    ,0.0, 0.0},
00700      {.8656312023878317438804678977123931323873    ,0.0, 0.0},
00701      {.7554044083550030338951011948474422683538    ,0.0, 0.0},
00702      {.6178762444026437484466717640487910189919    ,0.0, 0.0},
00703      {.45801677765722738634241944298357757354      ,0.0, 0.0},
00704      {.2816035507792589132304605014604961064861    ,0.0, 0.0},
00705      {.09501250983763744018531933542495806313035   ,0.0, 0.0},
00706      {-.09501250983763744018531933542495806313035  ,0.0, 0.0},
00707      {-.2816035507792589132304605014604961064861   ,0.0, 0.0},
00708      {-.45801677765722738634241944298357757354     ,0.0, 0.0},
00709      {-.6178762444026437484466717640487910189919   ,0.0, 0.0},
00710      {-.7554044083550030338951011948474422683538   ,0.0, 0.0},
00711      {-.8656312023878317438804678977123931323873   ,0.0, 0.0},
00712      {-.9445750230732325760779884155346083450911   ,0.0, 0.0},
00713      {-.9894009349916499325961541734503326274263   ,0.0, 0.0}
00714     },
00715     { // weights
00716      .02715245941175409485178057245601810351227,
00717      .06225352393864789286284383699437769427499,
00718      .09515851168249278480992510760224622635526,
00719      .1246289712555338720524762821920164201449,
00720      .1495959888165767320815017305474785489705,
00721      .1691565193950025381893120790303599622116,
00722      .1826034150449235888667636679692199393836,
00723      .1894506104550684962853967232082831051469,
00724      .1894506104550684962853967232082831051469,
00725      .1826034150449235888667636679692199393836,
00726      .1691565193950025381893120790303599622116,
00727      .1495959888165767320815017305474785489705,
00728      .1246289712555338720524762821920164201449,
00729      .09515851168249278480992510760224622635526,
00730      .06225352393864789286284383699437769427499,
00731      .02715245941175409485178057245601810351227
00732     }
00733   },
00734   {
00735     16,
00736     { // points
00737      {.9894009349916499325961541734503326274263    ,0.0, 0.0},
00738      {.9445750230732325760779884155346083450911    ,0.0, 0.0},
00739      {.8656312023878317438804678977123931323873    ,0.0, 0.0},
00740      {.7554044083550030338951011948474422683538    ,0.0, 0.0},
00741      {.6178762444026437484466717640487910189919    ,0.0, 0.0},
00742      {.45801677765722738634241944298357757354      ,0.0, 0.0},
00743      {.2816035507792589132304605014604961064861    ,0.0, 0.0},
00744      {.09501250983763744018531933542495806313035   ,0.0, 0.0},
00745      {-.09501250983763744018531933542495806313035  ,0.0, 0.0},
00746      {-.2816035507792589132304605014604961064861   ,0.0, 0.0},
00747      {-.45801677765722738634241944298357757354     ,0.0, 0.0},
00748      {-.6178762444026437484466717640487910189919   ,0.0, 0.0},
00749      {-.7554044083550030338951011948474422683538   ,0.0, 0.0},
00750      {-.8656312023878317438804678977123931323873   ,0.0, 0.0},
00751      {-.9445750230732325760779884155346083450911   ,0.0, 0.0},
00752      {-.9894009349916499325961541734503326274263   ,0.0, 0.0}
00753     },
00754     { // weights
00755      .02715245941175409485178057245601810351227,
00756      .06225352393864789286284383699437769427499,
00757      .09515851168249278480992510760224622635526,
00758      .1246289712555338720524762821920164201449,
00759      .1495959888165767320815017305474785489705,
00760      .1691565193950025381893120790303599622116,
00761      .1826034150449235888667636679692199393836,
00762      .1894506104550684962853967232082831051469,
00763      .1894506104550684962853967232082831051469,
00764      .1826034150449235888667636679692199393836,
00765      .1691565193950025381893120790303599622116,
00766      .1495959888165767320815017305474785489705,
00767      .1246289712555338720524762821920164201449,
00768      .09515851168249278480992510760224622635526,
00769      .06225352393864789286284383699437769427499,
00770      .02715245941175409485178057245601810351227
00771     }
00772   },
00773   {
00774     17,
00775     { // points
00776      {.9905754753144173356754340199406652765078    ,0.0, 0.0},
00777      {.9506755217687677612227169578958030214434    ,0.0, 0.0},
00778      {.8802391537269859021229556944881556926234    ,0.0, 0.0},
00779      {.781514003896801406925230055520476050224     ,0.0, 0.0},
00780      {.6576711592166907658503022166430023351478    ,0.0, 0.0},
00781      {.5126905370864769678862465686295518745829    ,0.0, 0.0},
00782      {.3512317634538763152971855170953460050405    ,0.0, 0.0},
00783      {.1784841814958478558506774936540655574754    ,0.0, 0.0},
00784      { 0                                           ,0.0, 0.0},
00785      {-.1784841814958478558506774936540655574754   ,0.0, 0.0},
00786      {-.3512317634538763152971855170953460050405   ,0.0, 0.0},
00787      {-.5126905370864769678862465686295518745829   ,0.0, 0.0},
00788      {-.6576711592166907658503022166430023351478   ,0.0, 0.0},
00789      {-.781514003896801406925230055520476050224    ,0.0, 0.0},
00790      {-.8802391537269859021229556944881556926234   ,0.0, 0.0},
00791      {-.9506755217687677612227169578958030214434   ,0.0, 0.0},
00792      {-.9905754753144173356754340199406652765078   ,0.0, 0.0}
00793     },
00794     { // weights
00795      .0241483028685479319601100262875653246917,
00796      .05545952937398720112944016535824466051285,
00797      .08503614831717918088353537019106207385049,
00798      .1118838471934039710947883856263559267358,
00799      .1351363684685254732863199817023501973721,
00800      .1540457610768102880814315948019586119405,
00801      .1680041021564500445099706637883231550212,
00802      .1765627053669926463252709901131972391509,
00803       .1794464703562065254582656442618856214488,
00804       .1765627053669926463252709901131972391509,
00805       .1680041021564500445099706637883231550212,
00806       .1540457610768102880814315948019586119405,
00807       .1351363684685254732863199817023501973721,
00808       .1118838471934039710947883856263559267358,
00809       .08503614831717918088353537019106207385049,
00810       .05545952937398720112944016535824466051285,
00811       .0241483028685479319601100262875653246917
00812     }
00813   },
00814   {
00815     17,
00816     { // points
00817      {.9905754753144173356754340199406652765078    ,0.0, 0.0},
00818      {.9506755217687677612227169578958030214434    ,0.0, 0.0},
00819      {.8802391537269859021229556944881556926234    ,0.0, 0.0},
00820      {.781514003896801406925230055520476050224     ,0.0, 0.0},
00821      {.6576711592166907658503022166430023351478    ,0.0, 0.0},
00822      {.5126905370864769678862465686295518745829    ,0.0, 0.0},
00823      {.3512317634538763152971855170953460050405    ,0.0, 0.0},
00824      {.1784841814958478558506774936540655574754    ,0.0, 0.0},
00825      { 0                                           ,0.0, 0.0},
00826      {-.1784841814958478558506774936540655574754   ,0.0, 0.0},
00827      {-.3512317634538763152971855170953460050405   ,0.0, 0.0},
00828      {-.5126905370864769678862465686295518745829   ,0.0, 0.0},
00829      {-.6576711592166907658503022166430023351478   ,0.0, 0.0},
00830      {-.781514003896801406925230055520476050224    ,0.0, 0.0},
00831      {-.8802391537269859021229556944881556926234   ,0.0, 0.0},
00832      {-.9506755217687677612227169578958030214434   ,0.0, 0.0},
00833      {-.9905754753144173356754340199406652765078   ,0.0, 0.0}
00834     },
00835     { // weights
00836      .0241483028685479319601100262875653246917,
00837      .05545952937398720112944016535824466051285,
00838      .08503614831717918088353537019106207385049,
00839      .1118838471934039710947883856263559267358,
00840      .1351363684685254732863199817023501973721,
00841      .1540457610768102880814315948019586119405,
00842      .1680041021564500445099706637883231550212,
00843      .1765627053669926463252709901131972391509,
00844       .1794464703562065254582656442618856214488,
00845       .1765627053669926463252709901131972391509,
00846       .1680041021564500445099706637883231550212,
00847       .1540457610768102880814315948019586119405,
00848       .1351363684685254732863199817023501973721,
00849       .1118838471934039710947883856263559267358,
00850       .08503614831717918088353537019106207385049,
00851       .05545952937398720112944016535824466051285,
00852       .0241483028685479319601100262875653246917
00853     }
00854   },
00855   {
00856     18,
00857     { // points
00858      {.9915651684209309467300160047061507702526    ,0.0, 0.0},
00859      {.9558239495713977551811958929297763099728    ,0.0, 0.0},
00860      {.8926024664975557392060605911271455154079    ,0.0, 0.0},
00861      {.8037049589725231156824174550145907971033    ,0.0, 0.0},
00862      {.6916870430603532078748910812888483894523    ,0.0, 0.0},
00863      {.5597708310739475346078715485253291369276    ,0.0, 0.0},
00864      {.411751161462842646035931793833051637079     ,0.0, 0.0},
00865      {.2518862256915055095889728548779112301629    ,0.0, 0.0},
00866      {.08477501304173530124226185293578381173332   ,0.0, 0.0},
00867      {-.08477501304173530124226185293578381173332  ,0.0, 0.0},
00868      {-.2518862256915055095889728548779112301629   ,0.0, 0.0},
00869      {-.411751161462842646035931793833051637079    ,0.0, 0.0},
00870      {-.5597708310739475346078715485253291369276   ,0.0, 0.0},
00871      {-.6916870430603532078748910812888483894523   ,0.0, 0.0},
00872      {-.8037049589725231156824174550145907971033   ,0.0, 0.0},
00873      {-.8926024664975557392060605911271455154079   ,0.0, 0.0},
00874      {-.9558239495713977551811958929297763099728   ,0.0, 0.0},
00875      {-.9915651684209309467300160047061507702526   ,0.0, 0.0}
00876     },
00877     { // weights
00878      .02161601352648331031334271026645246938769,
00879      .04971454889496979645333494620263864168087,
00880      .07642573025488905652912967761663652560532,
00881      .1009420441062871655628139849248346070628,
00882      .1225552067114784601845191268002015552282,
00883      .1406429146706506512047313037519472280955,
00884      .1546846751262652449254180038363747721932,
00885      .1642764837458327229860537764659275904123,
00886       .1691423829631435918406564701349866103341,
00887       .1691423829631435918406564701349866103341,
00888       .1642764837458327229860537764659275904123,
00889       .1546846751262652449254180038363747721932,
00890       .1406429146706506512047313037519472280955,
00891       .1225552067114784601845191268002015552282,
00892       .1009420441062871655628139849248346070628,
00893       .07642573025488905652912967761663652560532,
00894       .04971454889496979645333494620263864168087,
00895       .02161601352648331031334271026645246938769
00896     }
00897   },
00898   {
00899     18,
00900     { // points
00901      {.9915651684209309467300160047061507702526    ,0.0, 0.0},
00902      {.9558239495713977551811958929297763099728    ,0.0, 0.0},
00903      {.8926024664975557392060605911271455154079    ,0.0, 0.0},
00904      {.8037049589725231156824174550145907971033    ,0.0, 0.0},
00905      {.6916870430603532078748910812888483894523    ,0.0, 0.0},
00906      {.5597708310739475346078715485253291369276    ,0.0, 0.0},
00907      {.411751161462842646035931793833051637079     ,0.0, 0.0},
00908      {.2518862256915055095889728548779112301629    ,0.0, 0.0},
00909      {.08477501304173530124226185293578381173332   ,0.0, 0.0},
00910      {-.08477501304173530124226185293578381173332  ,0.0, 0.0},
00911      {-.2518862256915055095889728548779112301629   ,0.0, 0.0},
00912      {-.411751161462842646035931793833051637079    ,0.0, 0.0},
00913      {-.5597708310739475346078715485253291369276   ,0.0, 0.0},
00914      {-.6916870430603532078748910812888483894523   ,0.0, 0.0},
00915      {-.8037049589725231156824174550145907971033   ,0.0, 0.0},
00916      {-.8926024664975557392060605911271455154079   ,0.0, 0.0},
00917      {-.9558239495713977551811958929297763099728   ,0.0, 0.0},
00918      {-.9915651684209309467300160047061507702526   ,0.0, 0.0}
00919     },
00920     { // weights
00921      .02161601352648331031334271026645246938769,
00922      .04971454889496979645333494620263864168087,
00923      .07642573025488905652912967761663652560532,
00924      .1009420441062871655628139849248346070628,
00925      .1225552067114784601845191268002015552282,
00926      .1406429146706506512047313037519472280955,
00927      .1546846751262652449254180038363747721932,
00928      .1642764837458327229860537764659275904123,
00929       .1691423829631435918406564701349866103341,
00930       .1691423829631435918406564701349866103341,
00931       .1642764837458327229860537764659275904123,
00932       .1546846751262652449254180038363747721932,
00933       .1406429146706506512047313037519472280955,
00934       .1225552067114784601845191268002015552282,
00935       .1009420441062871655628139849248346070628,
00936       .07642573025488905652912967761663652560532,
00937       .04971454889496979645333494620263864168087,
00938       .02161601352648331031334271026645246938769
00939     }
00940   },
00941   {
00942     19,
00943     { // points
00944      {.9924068438435844031890176702532604935893    ,0.0, 0.0},
00945      {.9602081521348300308527788406876515266151    ,0.0, 0.0},
00946      {.9031559036148179016426609285323124878094    ,0.0, 0.0},
00947      {.8227146565371428249789224867127139017745    ,0.0, 0.0},
00948      {.7209661773352293786170958608237816296571    ,0.0, 0.0},
00949      {.6005453046616810234696381649462392798683    ,0.0, 0.0},
00950      {.4645707413759609457172671481041023679763    ,0.0, 0.0},
00951      {.3165640999636298319901173288498449178923    ,0.0, 0.0},
00952      {.1603586456402253758680961157407435495049    ,0.0, 0.0},
00953      { 0                                           ,0.0, 0.0},
00954      {-.1603586456402253758680961157407435495049   ,0.0, 0.0},
00955      {-.3165640999636298319901173288498449178923   ,0.0, 0.0},
00956      {-.4645707413759609457172671481041023679763   ,0.0, 0.0},
00957      {-.6005453046616810234696381649462392798683   ,0.0, 0.0},
00958      {-.7209661773352293786170958608237816296571   ,0.0, 0.0},
00959      {-.8227146565371428249789224867127139017745   ,0.0, 0.0},
00960      {-.9031559036148179016426609285323124878094   ,0.0, 0.0},
00961      {-.9602081521348300308527788406876515266151   ,0.0, 0.0},
00962      {-.9924068438435844031890176702532604935893   ,0.0, 0.0}
00963     },
00964     { // weights
00965      .01946178822972647703631204146443843575291,
00966      .04481422676569960033283815740199421195175,
00967      .06904454273764122658070825800601304496185,
00968      .09149002162244999946446209412383965266091,
00969      .1115666455473339947160239016817659974813,
00970      .1287539625393362276755157848568771170558,
00971      .1426067021736066117757461094419029724757,
00972      .152766042065859666778855400897662998461,
00973      .1589688433939543476499564394650472016788,
00974       .1610544498487836959791636253209167350399,
00975       .1589688433939543476499564394650472016788,
00976       .152766042065859666778855400897662998461,
00977       .1426067021736066117757461094419029724757,
00978       .1287539625393362276755157848568771170558,
00979       .1115666455473339947160239016817659974813,
00980       .09149002162244999946446209412383965266091,
00981       .06904454273764122658070825800601304496185,
00982       .04481422676569960033283815740199421195175,
00983       .01946178822972647703631204146443843575291
00984     }
00985   },
00986   {
00987     19,
00988     { // points
00989      {.9924068438435844031890176702532604935893    ,0.0, 0.0},
00990      {.9602081521348300308527788406876515266151    ,0.0, 0.0},
00991      {.9031559036148179016426609285323124878094    ,0.0, 0.0},
00992      {.8227146565371428249789224867127139017745    ,0.0, 0.0},
00993      {.7209661773352293786170958608237816296571    ,0.0, 0.0},
00994      {.6005453046616810234696381649462392798683    ,0.0, 0.0},
00995      {.4645707413759609457172671481041023679763    ,0.0, 0.0},
00996      {.3165640999636298319901173288498449178923    ,0.0, 0.0},
00997      {.1603586456402253758680961157407435495049    ,0.0, 0.0},
00998      { 0                                           ,0.0, 0.0},
00999      {-.1603586456402253758680961157407435495049   ,0.0, 0.0},
01000      {-.3165640999636298319901173288498449178923   ,0.0, 0.0},
01001      {-.4645707413759609457172671481041023679763   ,0.0, 0.0},
01002      {-.6005453046616810234696381649462392798683   ,0.0, 0.0},
01003      {-.7209661773352293786170958608237816296571   ,0.0, 0.0},
01004      {-.8227146565371428249789224867127139017745   ,0.0, 0.0},
01005      {-.9031559036148179016426609285323124878094   ,0.0, 0.0},
01006      {-.9602081521348300308527788406876515266151   ,0.0, 0.0},
01007      {-.9924068438435844031890176702532604935893   ,0.0, 0.0}
01008     },
01009     { // weights
01010      .01946178822972647703631204146443843575291,
01011      .04481422676569960033283815740199421195175,
01012      .06904454273764122658070825800601304496185,
01013      .09149002162244999946446209412383965266091,
01014      .1115666455473339947160239016817659974813,
01015      .1287539625393362276755157848568771170558,
01016      .1426067021736066117757461094419029724757,
01017      .152766042065859666778855400897662998461,
01018      .1589688433939543476499564394650472016788,
01019       .1610544498487836959791636253209167350399,
01020       .1589688433939543476499564394650472016788,
01021       .152766042065859666778855400897662998461,
01022       .1426067021736066117757461094419029724757,
01023       .1287539625393362276755157848568771170558,
01024       .1115666455473339947160239016817659974813,
01025       .09149002162244999946446209412383965266091,
01026       .06904454273764122658070825800601304496185,
01027       .04481422676569960033283815740199421195175,
01028       .01946178822972647703631204146443843575291
01029     }
01030   },
01031   {
01032     20,
01033     { // points
01034      {.9931285991850949247861223884713202782226    ,0.0, 0.0},
01035      {.9639719272779137912676661311972772219121    ,0.0, 0.0},
01036      {.9122344282513259058677524412032981130492    ,0.0, 0.0},
01037      {.8391169718222188233945290617015206853296    ,0.0, 0.0},
01038      {.7463319064601507926143050703556415903107    ,0.0, 0.0},
01039      {.6360536807265150254528366962262859367434    ,0.0, 0.0},
01040      {.5108670019508270980043640509552509984255    ,0.0, 0.0},
01041      {.3737060887154195606725481770249272373957    ,0.0, 0.0},
01042      {.2277858511416450780804961953685746247431    ,0.0, 0.0},
01043      {.0765265211334973337546404093988382110048    ,0.0, 0.0},
01044      {-.0765265211334973337546404093988382110048   ,0.0, 0.0},
01045      {-.2277858511416450780804961953685746247431   ,0.0, 0.0},
01046      {-.3737060887154195606725481770249272373957   ,0.0, 0.0},
01047      {-.5108670019508270980043640509552509984255   ,0.0, 0.0},
01048      {-.6360536807265150254528366962262859367434   ,0.0, 0.0},
01049      {-.7463319064601507926143050703556415903107   ,0.0, 0.0},
01050      {-.8391169718222188233945290617015206853296   ,0.0, 0.0},
01051      {-.9122344282513259058677524412032981130492   ,0.0, 0.0},
01052      {-.9639719272779137912676661311972772219121   ,0.0, 0.0},
01053      {-.9931285991850949247861223884713202782226   ,0.0, 0.0}
01054     },
01055     { // weights
01056      .01761400713915211831186196235185281636214,
01057      .04060142980038694133103995227493210987909,
01058      .0626720483341090635695065351870416063516,
01059      .08327674157670474872475814322204620610018,
01060      .1019301198172404350367501354803498761667,
01061      .118194531961518417312377377711382287005,
01062      .1316886384491766268984944997481631349161,
01063      .1420961093183820513292983250671649330345,
01064      .1491729864726037467878287370019694366927,
01065      .1527533871307258506980843319550975934919,
01066       .1527533871307258506980843319550975934919,
01067       .1491729864726037467878287370019694366927,
01068       .1420961093183820513292983250671649330345,
01069       .1316886384491766268984944997481631349161,
01070       .118194531961518417312377377711382287005,
01071       .1019301198172404350367501354803498761667,
01072       .08327674157670474872475814322204620610018,
01073       .0626720483341090635695065351870416063516,
01074       .04060142980038694133103995227493210987909,
01075       .01761400713915211831186196235185281636214
01076     }
01077   },
01078   {
01079     20,
01080     { // points
01081      {.9931285991850949247861223884713202782226    ,0.0, 0.0},
01082      {.9639719272779137912676661311972772219121    ,0.0, 0.0},
01083      {.9122344282513259058677524412032981130492    ,0.0, 0.0},
01084      {.8391169718222188233945290617015206853296    ,0.0, 0.0},
01085      {.7463319064601507926143050703556415903107    ,0.0, 0.0},
01086      {.6360536807265150254528366962262859367434    ,0.0, 0.0},
01087      {.5108670019508270980043640509552509984255    ,0.0, 0.0},
01088      {.3737060887154195606725481770249272373957    ,0.0, 0.0},
01089      {.2277858511416450780804961953685746247431    ,0.0, 0.0},
01090      {.0765265211334973337546404093988382110048    ,0.0, 0.0},
01091      {-.0765265211334973337546404093988382110048   ,0.0, 0.0},
01092      {-.2277858511416450780804961953685746247431   ,0.0, 0.0},
01093      {-.3737060887154195606725481770249272373957   ,0.0, 0.0},
01094      {-.5108670019508270980043640509552509984255   ,0.0, 0.0},
01095      {-.6360536807265150254528366962262859367434   ,0.0, 0.0},
01096      {-.7463319064601507926143050703556415903107   ,0.0, 0.0},
01097      {-.8391169718222188233945290617015206853296   ,0.0, 0.0},
01098      {-.9122344282513259058677524412032981130492   ,0.0, 0.0},
01099      {-.9639719272779137912676661311972772219121   ,0.0, 0.0},
01100      {-.9931285991850949247861223884713202782226   ,0.0, 0.0}
01101     },
01102     { // weights
01103      .01761400713915211831186196235185281636214,
01104      .04060142980038694133103995227493210987909,
01105      .0626720483341090635695065351870416063516,
01106      .08327674157670474872475814322204620610018,
01107      .1019301198172404350367501354803498761667,
01108      .118194531961518417312377377711382287005,
01109      .1316886384491766268984944997481631349161,
01110      .1420961093183820513292983250671649330345,
01111      .1491729864726037467878287370019694366927,
01112      .1527533871307258506980843319550975934919,
01113       .1527533871307258506980843319550975934919,
01114       .1491729864726037467878287370019694366927,
01115       .1420961093183820513292983250671649330345,
01116       .1316886384491766268984944997481631349161,
01117       .118194531961518417312377377711382287005,
01118       .1019301198172404350367501354803498761667,
01119       .08327674157670474872475814322204620610018,
01120       .0626720483341090635695065351870416063516,
01121       .04060142980038694133103995227493210987909,
01122       .01761400713915211831186196235185281636214
01123     }
01124   },
01125   {
01126     21,
01127     { // points
01128      {.9937521706203895002602420359379409291933    ,0.0, 0.0},
01129      {.9672268385663062943166222149076951614247    ,0.0, 0.0},
01130      {.9200993341504008287901871337149688941591    ,0.0, 0.0},
01131      {.8533633645833172836472506385875676702761    ,0.0, 0.0},
01132      {.768439963475677908615877851306228034821     ,0.0, 0.0},
01133      {.667138804197412319305966669990339162597     ,0.0, 0.0},
01134      {.5516188358872198070590187967243132866221    ,0.0, 0.0},
01135      {.4243421202074387835736688885437880520964    ,0.0, 0.0},
01136      {.288021316802401096600792516064600319909     ,0.0, 0.0},
01137      {.1455618541608950909370309823386863301163    ,0.0, 0.0},
01138      {0                                            ,0.0, 0.0},
01139      {-.1455618541608950909370309823386863301163   ,0.0, 0.0},
01140      {-.288021316802401096600792516064600319909    ,0.0, 0.0},
01141      {-.4243421202074387835736688885437880520964   ,0.0, 0.0},
01142      {-.5516188358872198070590187967243132866221   ,0.0, 0.0},
01143      {-.667138804197412319305966669990339162597    ,0.0, 0.0},
01144      {-.768439963475677908615877851306228034821    ,0.0, 0.0},
01145      {-.8533633645833172836472506385875676702761   ,0.0, 0.0},
01146      {-.9200993341504008287901871337149688941591   ,0.0, 0.0},
01147      {-.9672268385663062943166222149076951614247   ,0.0, 0.0},
01148      {-.9937521706203895002602420359379409291933   ,0.0, 0.0}
01149     },
01150     { // weights
01151      .01601722825777433332422461685847101526589,
01152      .03695378977085249379995066829932966618894,
01153      .05713442542685720828363582647244795749129,
01154      .07610011362837930201705165330018317922615,
01155      .09344442345603386155328974111393208848353,
01156      .1087972991671483776634745780701056420337,
01157      .1218314160537285341953671771257335983563,
01158      .132268938633337461781052574496775604329,
01159      .1398873947910731547221334238675831108928,
01160      .1445244039899700590638271665537525436099,
01161       .1460811336496904271919851476833711882448,
01162      .1445244039899700590638271665537525436099,
01163      .1398873947910731547221334238675831108928,
01164      .132268938633337461781052574496775604329,
01165      .1218314160537285341953671771257335983563,
01166      .1087972991671483776634745780701056420337,
01167      .09344442345603386155328974111393208848353,
01168      .07610011362837930201705165330018317922615,
01169      .05713442542685720828363582647244795749129,
01170      .03695378977085249379995066829932966618894,
01171      .01601722825777433332422461685847101526589
01172     }
01173   },
01174   {
01175     21,
01176     { // points
01177      {.9937521706203895002602420359379409291933    ,0.0, 0.0},
01178      {.9672268385663062943166222149076951614247    ,0.0, 0.0},
01179      {.9200993341504008287901871337149688941591    ,0.0, 0.0},
01180      {.8533633645833172836472506385875676702761    ,0.0, 0.0},
01181      {.768439963475677908615877851306228034821     ,0.0, 0.0},
01182      {.667138804197412319305966669990339162597     ,0.0, 0.0},
01183      {.5516188358872198070590187967243132866221    ,0.0, 0.0},
01184      {.4243421202074387835736688885437880520964    ,0.0, 0.0},
01185      {.288021316802401096600792516064600319909     ,0.0, 0.0},
01186      {.1455618541608950909370309823386863301163    ,0.0, 0.0},
01187      {0                                            ,0.0, 0.0},
01188      {-.1455618541608950909370309823386863301163   ,0.0, 0.0},
01189      {-.288021316802401096600792516064600319909    ,0.0, 0.0},
01190      {-.4243421202074387835736688885437880520964   ,0.0, 0.0},
01191      {-.5516188358872198070590187967243132866221   ,0.0, 0.0},
01192      {-.667138804197412319305966669990339162597    ,0.0, 0.0},
01193      {-.768439963475677908615877851306228034821    ,0.0, 0.0},
01194      {-.8533633645833172836472506385875676702761   ,0.0, 0.0},
01195      {-.9200993341504008287901871337149688941591   ,0.0, 0.0},
01196      {-.9672268385663062943166222149076951614247   ,0.0, 0.0},
01197      {-.9937521706203895002602420359379409291933   ,0.0, 0.0}
01198     },
01199     { // weights
01200      .01601722825777433332422461685847101526589,
01201      .03695378977085249379995066829932966618894,
01202      .05713442542685720828363582647244795749129,
01203      .07610011362837930201705165330018317922615,
01204      .09344442345603386155328974111393208848353,
01205      .1087972991671483776634745780701056420337,
01206      .1218314160537285341953671771257335983563,
01207      .132268938633337461781052574496775604329,
01208      .1398873947910731547221334238675831108928,
01209      .1445244039899700590638271665537525436099,
01210       .1460811336496904271919851476833711882448,
01211      .1445244039899700590638271665537525436099,
01212      .1398873947910731547221334238675831108928,
01213      .132268938633337461781052574496775604329,
01214      .1218314160537285341953671771257335983563,
01215      .1087972991671483776634745780701056420337,
01216      .09344442345603386155328974111393208848353,
01217      .07610011362837930201705165330018317922615,
01218      .05713442542685720828363582647244795749129,
01219      .03695378977085249379995066829932966618894,
01220      .01601722825777433332422461685847101526589
01221     }
01222   },
01223   {
01224     22,
01225     { // points
01226      {.9942945854823992920730314211612989803931    ,0.0, 0.0},
01227      {.970060497835428727123950986765268710806     ,0.0, 0.0},
01228      {.9269567721871740005206929392590531966353    ,0.0, 0.0},
01229      {.8658125777203001365364256370193787290848    ,0.0, 0.0},
01230      {.7878168059792081620042779554083515213882    ,0.0, 0.0},
01231      {.6944872631866827800506898357622567712673    ,0.0, 0.0},
01232      {.5876404035069115929588769276386473488776    ,0.0, 0.0},
01233      {.4693558379867570264063307109664063460953    ,0.0, 0.0},
01234      {.3419358208920842251581474204273796195592    ,0.0, 0.0},
01235      {.2078604266882212854788465339195457342157    ,0.0, 0.0},
01236      {.0697392733197222212138417961186280818223    ,0.0, 0.0},
01237      {-.0697392733197222212138417961186280818223   ,0.0, 0.0},
01238      {-.2078604266882212854788465339195457342157   ,0.0, 0.0},
01239      {-.3419358208920842251581474204273796195592   ,0.0, 0.0},
01240      {-.4693558379867570264063307109664063460953   ,0.0, 0.0},
01241      {-.5876404035069115929588769276386473488776   ,0.0, 0.0},
01242      {-.6944872631866827800506898357622567712673   ,0.0, 0.0},
01243      {-.7878168059792081620042779554083515213882   ,0.0, 0.0},
01244      {-.8658125777203001365364256370193787290848   ,0.0, 0.0},
01245      {-.9269567721871740005206929392590531966353   ,0.0, 0.0},
01246      {-.970060497835428727123950986765268710806    ,0.0, 0.0},
01247      {-.9942945854823992920730314211612989803931   ,0.0, 0.0}
01248     },
01249     { // weights
01250      .01462799529827220068499109804718544519021,
01251      .03377490158481415479330224686591290134917,
01252      .05229333515268328594031205127321125611215,
01253      .06979646842452048809496141893021765739878,
01254      .08594160621706772741444368137270286618914,
01255      .1004141444428809649320788378305362823508,
01256      .1129322960805392183934006074217843191143,
01257      .1232523768105124242855609861548144719594,
01258      .1311735047870623707329649925303074458757,
01259      .1365414983460151713525738312315173965864,
01260      .1392518728556319933754102483418099578739,
01261       .1392518728556319933754102483418099578739,
01262       .1365414983460151713525738312315173965864,
01263       .1311735047870623707329649925303074458757,
01264       .1232523768105124242855609861548144719594,
01265       .1129322960805392183934006074217843191143,
01266       .1004141444428809649320788378305362823508,
01267       .08594160621706772741444368137270286618914,
01268       .06979646842452048809496141893021765739878,
01269       .05229333515268328594031205127321125611215,
01270       .03377490158481415479330224686591290134917,
01271       .01462799529827220068499109804718544519021
01272     }
01273   },
01274   {
01275     22,
01276     { // points
01277      {.9942945854823992920730314211612989803931    ,0.0, 0.0},
01278      {.970060497835428727123950986765268710806     ,0.0, 0.0},
01279      {.9269567721871740005206929392590531966353    ,0.0, 0.0},
01280      {.8658125777203001365364256370193787290848    ,0.0, 0.0},
01281      {.7878168059792081620042779554083515213882    ,0.0, 0.0},
01282      {.6944872631866827800506898357622567712673    ,0.0, 0.0},
01283      {.5876404035069115929588769276386473488776    ,0.0, 0.0},
01284      {.4693558379867570264063307109664063460953    ,0.0, 0.0},
01285      {.3419358208920842251581474204273796195592    ,0.0, 0.0},
01286      {.2078604266882212854788465339195457342157    ,0.0, 0.0},
01287      {.0697392733197222212138417961186280818223    ,0.0, 0.0},
01288      {-.0697392733197222212138417961186280818223   ,0.0, 0.0},
01289      {-.2078604266882212854788465339195457342157   ,0.0, 0.0},
01290      {-.3419358208920842251581474204273796195592   ,0.0, 0.0},
01291      {-.4693558379867570264063307109664063460953   ,0.0, 0.0},
01292      {-.5876404035069115929588769276386473488776   ,0.0, 0.0},
01293      {-.6944872631866827800506898357622567712673   ,0.0, 0.0},
01294      {-.7878168059792081620042779554083515213882   ,0.0, 0.0},
01295      {-.8658125777203001365364256370193787290848   ,0.0, 0.0},
01296      {-.9269567721871740005206929392590531966353   ,0.0, 0.0},
01297      {-.970060497835428727123950986765268710806    ,0.0, 0.0},
01298      {-.9942945854823992920730314211612989803931   ,0.0, 0.0}
01299     },
01300     { // weights
01301      .01462799529827220068499109804718544519021,
01302      .03377490158481415479330224686591290134917,
01303      .05229333515268328594031205127321125611215,
01304      .06979646842452048809496141893021765739878,
01305      .08594160621706772741444368137270286618914,
01306      .1004141444428809649320788378305362823508,
01307      .1129322960805392183934006074217843191143,
01308      .1232523768105124242855609861548144719594,
01309      .1311735047870623707329649925303074458757,
01310      .1365414983460151713525738312315173965864,
01311      .1392518728556319933754102483418099578739,
01312       .1392518728556319933754102483418099578739,
01313       .1365414983460151713525738312315173965864,
01314       .1311735047870623707329649925303074458757,
01315       .1232523768105124242855609861548144719594,
01316       .1129322960805392183934006074217843191143,
01317       .1004141444428809649320788378305362823508,
01318       .08594160621706772741444368137270286618914,
01319       .06979646842452048809496141893021765739878,
01320       .05229333515268328594031205127321125611215,
01321       .03377490158481415479330224686591290134917,
01322       .01462799529827220068499109804718544519021
01323     }
01324   },
01325   {
01326     23,
01327     { // points
01328      {.9947693349975521235239257154455743605736    ,0.0, 0.0},
01329      {.9725424712181152319560240768207773751816    ,0.0, 0.0},
01330      {.9329710868260161023491969890384229782357    ,0.0, 0.0},
01331      {.8767523582704416673781568859341456716389    ,0.0, 0.0},
01332      {.8048884016188398921511184069967785579414    ,0.0, 0.0},
01333      {.7186613631319501944616244837486188483299    ,0.0, 0.0},
01334      {.6196098757636461563850973116495956533872    ,0.0, 0.0},
01335      {.5095014778460075496897930478668464305448    ,0.0, 0.0},
01336      {.3903010380302908314214888728806054585781    ,0.0, 0.0},
01337      {.264135680970344930533869538283309602979     ,0.0, 0.0},
01338      {.1332568242984661109317426822417661370104    ,0.0, 0.0},
01339      {0                                            ,0.0, 0.0},
01340      {-.1332568242984661109317426822417661370104   ,0.0, 0.0},
01341      {-.264135680970344930533869538283309602979    ,0.0, 0.0},
01342      {-.3903010380302908314214888728806054585781   ,0.0, 0.0},
01343      {-.5095014778460075496897930478668464305448   ,0.0, 0.0},
01344      {-.6196098757636461563850973116495956533872   ,0.0, 0.0},
01345      {-.7186613631319501944616244837486188483299   ,0.0, 0.0},
01346      {-.8048884016188398921511184069967785579414   ,0.0, 0.0},
01347      {-.8767523582704416673781568859341456716389   ,0.0, 0.0},
01348      {-.9329710868260161023491969890384229782357   ,0.0, 0.0},
01349      {-.9725424712181152319560240768207773751816   ,0.0, 0.0},
01350      {-.9947693349975521235239257154455743605736   ,0.0, 0.0}
01351     },
01352     { // weights
01353      .01341185948714177208130949345861506497662,
01354      .03098800585697944431069421964188450538377,
01355      .04803767173108466857164107163203399656122,
01356      .06423242140852585212716961515891099803916,
01357      .07928141177671895492289252474204322691371,
01358      .09291576606003514747701861736976464860346,
01359      .1048920914645414100740861850147438548585,
01360      .1149966402224113649416435129339613014914,
01361      .1230490843067295304675784006720096548159,
01362      .1289057221880821499785953393997936532597,
01363      .132462039404696617371642464703316925805,
01364       .1336545721861061753514571105458443385832,
01365       .132462039404696617371642464703316925805,
01366       .1289057221880821499785953393997936532597,
01367       .1230490843067295304675784006720096548159,
01368       .1149966402224113649416435129339613014914,
01369       .1048920914645414100740861850147438548585,
01370       .09291576606003514747701861736976464860346,
01371       .07928141177671895492289252474204322691371,
01372       .06423242140852585212716961515891099803916,
01373       .04803767173108466857164107163203399656122,
01374       .03098800585697944431069421964188450538377,
01375       .01341185948714177208130949345861506497662
01376     }
01377   },
01378   {
01379     23,
01380     { // points
01381      {.9947693349975521235239257154455743605736    ,0.0, 0.0},
01382      {.9725424712181152319560240768207773751816    ,0.0, 0.0},
01383      {.9329710868260161023491969890384229782357    ,0.0, 0.0},
01384      {.8767523582704416673781568859341456716389    ,0.0, 0.0},
01385      {.8048884016188398921511184069967785579414    ,0.0, 0.0},
01386      {.7186613631319501944616244837486188483299    ,0.0, 0.0},
01387      {.6196098757636461563850973116495956533872    ,0.0, 0.0},
01388      {.5095014778460075496897930478668464305448    ,0.0, 0.0},
01389      {.3903010380302908314214888728806054585781    ,0.0, 0.0},
01390      {.264135680970344930533869538283309602979     ,0.0, 0.0},
01391      {.1332568242984661109317426822417661370104    ,0.0, 0.0},
01392      {0                                            ,0.0, 0.0},
01393      {-.1332568242984661109317426822417661370104   ,0.0, 0.0},
01394      {-.264135680970344930533869538283309602979    ,0.0, 0.0},
01395      {-.3903010380302908314214888728806054585781   ,0.0, 0.0},
01396      {-.5095014778460075496897930478668464305448   ,0.0, 0.0},
01397      {-.6196098757636461563850973116495956533872   ,0.0, 0.0},
01398      {-.7186613631319501944616244837486188483299   ,0.0, 0.0},
01399      {-.8048884016188398921511184069967785579414   ,0.0, 0.0},
01400      {-.8767523582704416673781568859341456716389   ,0.0, 0.0},
01401      {-.9329710868260161023491969890384229782357   ,0.0, 0.0},
01402      {-.9725424712181152319560240768207773751816   ,0.0, 0.0},
01403      {-.9947693349975521235239257154455743605736   ,0.0, 0.0}
01404     },
01405     { // weights
01406      .01341185948714177208130949345861506497662,
01407      .03098800585697944431069421964188450538377,
01408      .04803767173108466857164107163203399656122,
01409      .06423242140852585212716961515891099803916,
01410      .07928141177671895492289252474204322691371,
01411      .09291576606003514747701861736976464860346,
01412      .1048920914645414100740861850147438548585,
01413      .1149966402224113649416435129339613014914,
01414      .1230490843067295304675784006720096548159,
01415      .1289057221880821499785953393997936532597,
01416      .132462039404696617371642464703316925805,
01417       .1336545721861061753514571105458443385832,
01418       .132462039404696617371642464703316925805,
01419       .1289057221880821499785953393997936532597,
01420       .1230490843067295304675784006720096548159,
01421       .1149966402224113649416435129339613014914,
01422       .1048920914645414100740861850147438548585,
01423       .09291576606003514747701861736976464860346,
01424       .07928141177671895492289252474204322691371,
01425       .06423242140852585212716961515891099803916,
01426       .04803767173108466857164107163203399656122,
01427       .03098800585697944431069421964188450538377,
01428       .01341185948714177208130949345861506497662
01429     }
01430   },
01431   {
01432     24,
01433     { // points
01434      {.9951872199970213601799974097007368118746    ,0.0, 0.0},
01435      {.9747285559713094981983919930081690617412    ,0.0, 0.0},
01436      {.9382745520027327585236490017087214496548    ,0.0, 0.0},
01437      {.8864155270044010342131543419821967550873    ,0.0, 0.0},
01438      {.8200019859739029219539498726697452080761    ,0.0, 0.0},
01439      {.7401241915785543642438281030999784255233    ,0.0, 0.0},
01440      {.6480936519369755692524957869107476266697    ,0.0, 0.0},
01441      {.5454214713888395356583756172183723700108    ,0.0, 0.0},
01442      {.4337935076260451384870842319133497124524    ,0.0, 0.0},
01443      {.3150426796961633743867932913198102407865    ,0.0, 0.0},
01444      {.1911188674736163091586398207570696318404    ,0.0, 0.0},
01445      {.064056892862605626085043082624745038591     ,0.0, 0.0},
01446      {-.064056892862605626085043082624745038591    ,0.0, 0.0},
01447      {-.1911188674736163091586398207570696318404   ,0.0, 0.0},
01448      {-.3150426796961633743867932913198102407865   ,0.0, 0.0},
01449      {-.4337935076260451384870842319133497124524   ,0.0, 0.0},
01450      {-.5454214713888395356583756172183723700108   ,0.0, 0.0},
01451      {-.6480936519369755692524957869107476266697   ,0.0, 0.0},
01452      {-.7401241915785543642438281030999784255233   ,0.0, 0.0},
01453      {-.8200019859739029219539498726697452080761   ,0.0, 0.0},
01454      {-.8864155270044010342131543419821967550873   ,0.0, 0.0},
01455      {-.9382745520027327585236490017087214496548   ,0.0, 0.0},
01456      {-.9747285559713094981983919930081690617412   ,0.0, 0.0},
01457      {-.9951872199970213601799974097007368118746   ,0.0, 0.0}
01458     },
01459     { // weights
01460      .01234122979998719954680566707003729157591,
01461      .0285313886289336631813078159518782864492,
01462      .04427743881741980616860274821133822885931,
01463      .0592985849154367807463677585001085845412,
01464      .07334648141108030573403361525311651811934,
01465      .08619016153195327591718520298374266718508,
01466      .09761865210411388826988066446424715442792,
01467      .1074442701159656347825773424466062227946,
01468      .1155056680537256013533444839067835598623,
01469      .121670472927803391204463153476262425607,
01470      .1258374563468282961213753825111836887264,
01471      .1279381953467521569740561652246953718517,
01472      .1279381953467521569740561652246953718517,
01473       .1258374563468282961213753825111836887264,
01474       .121670472927803391204463153476262425607,
01475       .1155056680537256013533444839067835598623,
01476       .1074442701159656347825773424466062227946,
01477       .09761865210411388826988066446424715442792,
01478       .08619016153195327591718520298374266718508,
01479       .07334648141108030573403361525311651811934,
01480       .0592985849154367807463677585001085845412,
01481       .04427743881741980616860274821133822885931,
01482       .0285313886289336631813078159518782864492,
01483       .01234122979998719954680566707003729157591
01484     }
01485   },
01486   {
01487     24,
01488     { // points
01489      {.9951872199970213601799974097007368118746    ,0.0, 0.0},
01490      {.9747285559713094981983919930081690617412    ,0.0, 0.0},
01491      {.9382745520027327585236490017087214496548    ,0.0, 0.0},
01492      {.8864155270044010342131543419821967550873    ,0.0, 0.0},
01493      {.8200019859739029219539498726697452080761    ,0.0, 0.0},
01494      {.7401241915785543642438281030999784255233    ,0.0, 0.0},
01495      {.6480936519369755692524957869107476266697    ,0.0, 0.0},
01496      {.5454214713888395356583756172183723700108    ,0.0, 0.0},
01497      {.4337935076260451384870842319133497124524    ,0.0, 0.0},
01498      {.3150426796961633743867932913198102407865    ,0.0, 0.0},
01499      {.1911188674736163091586398207570696318404    ,0.0, 0.0},
01500      {.064056892862605626085043082624745038591     ,0.0, 0.0},
01501      {-.064056892862605626085043082624745038591    ,0.0, 0.0},
01502      {-.1911188674736163091586398207570696318404   ,0.0, 0.0},
01503      {-.3150426796961633743867932913198102407865   ,0.0, 0.0},
01504      {-.4337935076260451384870842319133497124524   ,0.0, 0.0},
01505      {-.5454214713888395356583756172183723700108   ,0.0, 0.0},
01506      {-.6480936519369755692524957869107476266697   ,0.0, 0.0},
01507      {-.7401241915785543642438281030999784255233   ,0.0, 0.0},
01508      {-.8200019859739029219539498726697452080761   ,0.0, 0.0},
01509      {-.8864155270044010342131543419821967550873   ,0.0, 0.0},
01510      {-.9382745520027327585236490017087214496548   ,0.0, 0.0},
01511      {-.9747285559713094981983919930081690617412   ,0.0, 0.0},
01512      {-.9951872199970213601799974097007368118746   ,0.0, 0.0}
01513     },
01514     { // weights
01515      .01234122979998719954680566707003729157591,
01516      .0285313886289336631813078159518782864492,
01517      .04427743881741980616860274821133822885931,
01518      .0592985849154367807463677585001085845412,
01519      .07334648141108030573403361525311651811934,
01520      .08619016153195327591718520298374266718508,
01521      .09761865210411388826988066446424715442792,
01522      .1074442701159656347825773424466062227946,
01523      .1155056680537256013533444839067835598623,
01524      .121670472927803391204463153476262425607,
01525      .1258374563468282961213753825111836887264,
01526      .1279381953467521569740561652246953718517,
01527      .1279381953467521569740561652246953718517,
01528       .1258374563468282961213753825111836887264,
01529       .121670472927803391204463153476262425607,
01530       .1155056680537256013533444839067835598623,
01531       .1074442701159656347825773424466062227946,
01532       .09761865210411388826988066446424715442792,
01533       .08619016153195327591718520298374266718508,
01534       .07334648141108030573403361525311651811934,
01535       .0592985849154367807463677585001085845412,
01536       .04427743881741980616860274821133822885931,
01537       .0285313886289336631813078159518782864492,
01538       .01234122979998719954680566707003729157591
01539     }
01540   },
01541   {
01542     25,
01543     { // points
01544      {.9955569697904980979087849468939016172576    ,0.0, 0.0},
01545      {.9766639214595175114983153864795940677454    ,0.0, 0.0},
01546      {.9429745712289743394140111696584705319052    ,0.0, 0.0},
01547      {.8949919978782753688510420067828049541746    ,0.0, 0.0},
01548      {.833442628760834001421021108693569569461     ,0.0, 0.0},
01549      {.7592592630373576305772828652043609763875    ,0.0, 0.0},
01550      {.6735663684734683644851206332476221758834    ,0.0, 0.0},
01551      {.5776629302412229677236898416126540673957    ,0.0, 0.0},
01552      {.4730027314457149605221821150091920413318    ,0.0, 0.0},
01553      {.3611723058093878377358217301276406674221    ,0.0, 0.0},
01554      {.2438668837209884320451903627974515864056    ,0.0, 0.0},
01555      {.1228646926107103963873598188080368055322    ,0.0, 0.0},
01556      {0                                            ,0.0, 0.0},
01557      {-.1228646926107103963873598188080368055322   ,0.0, 0.0},
01558      {-.2438668837209884320451903627974515864056   ,0.0, 0.0},
01559      {-.3611723058093878377358217301276406674221   ,0.0, 0.0},
01560      {-.4730027314457149605221821150091920413318   ,0.0, 0.0},
01561      {-.5776629302412229677236898416126540673957   ,0.0, 0.0},
01562      {-.6735663684734683644851206332476221758834   ,0.0, 0.0},
01563      {-.7592592630373576305772828652043609763875   ,0.0, 0.0},
01564      {-.833442628760834001421021108693569569461    ,0.0, 0.0},
01565      {-.8949919978782753688510420067828049541746   ,0.0, 0.0},
01566      {-.9429745712289743394140111696584705319052   ,0.0, 0.0},
01567      {-.9766639214595175114983153864795940677454   ,0.0, 0.0},
01568      {-.9955569697904980979087849468939016172576   ,0.0, 0.0}
01569     },
01570     { // weights
01571      .01139379850102628794790296411323477360332,
01572      .02635498661503213726190181529529914493596,
01573      .04093915670130631265562348771164595366085,
01574      .05490469597583519192593689154047332416011,
01575      .06803833381235691720718718565670796855471,
01576      .08014070033500101801323495966911130229023,
01577      .09102826198296364981149722070289165338099,
01578      .1005359490670506442022068903926858269885,
01579      .1085196244742636531160939570501166193401,
01580      .1148582591457116483393255458695558086409,
01581      .1194557635357847722281781265129010473902,
01582      .1222424429903100416889595189458515058351,
01583       .1231760537267154512039028730790501424382,
01584       .1222424429903100416889595189458515058351,
01585       .1194557635357847722281781265129010473902,
01586       .1148582591457116483393255458695558086409,
01587       .1085196244742636531160939570501166193401,
01588       .1005359490670506442022068903926858269885,
01589       .09102826198296364981149722070289165338099,
01590       .08014070033500101801323495966911130229023,
01591      .06803833381235691720718718565670796855471,
01592       .05490469597583519192593689154047332416011,
01593       .04093915670130631265562348771164595366085,
01594       .02635498661503213726190181529529914493596,
01595       .01139379850102628794790296411323477360332
01596     }
01597   },
01598   {
01599     25,
01600     { // points
01601      {.9955569697904980979087849468939016172576    ,0.0, 0.0},
01602      {.9766639214595175114983153864795940677454    ,0.0, 0.0},
01603      {.9429745712289743394140111696584705319052    ,0.0, 0.0},
01604      {.8949919978782753688510420067828049541746    ,0.0, 0.0},
01605      {.833442628760834001421021108693569569461     ,0.0, 0.0},
01606      {.7592592630373576305772828652043609763875    ,0.0, 0.0},
01607      {.6735663684734683644851206332476221758834    ,0.0, 0.0},
01608      {.5776629302412229677236898416126540673957    ,0.0, 0.0},
01609      {.4730027314457149605221821150091920413318    ,0.0, 0.0},
01610      {.3611723058093878377358217301276406674221    ,0.0, 0.0},
01611      {.2438668837209884320451903627974515864056    ,0.0, 0.0},
01612      {.1228646926107103963873598188080368055322    ,0.0, 0.0},
01613      {0                                            ,0.0, 0.0},
01614      {-.1228646926107103963873598188080368055322   ,0.0, 0.0},
01615      {-.2438668837209884320451903627974515864056   ,0.0, 0.0},
01616      {-.3611723058093878377358217301276406674221   ,0.0, 0.0},
01617      {-.4730027314457149605221821150091920413318   ,0.0, 0.0},
01618      {-.5776629302412229677236898416126540673957   ,0.0, 0.0},
01619      {-.6735663684734683644851206332476221758834   ,0.0, 0.0},
01620      {-.7592592630373576305772828652043609763875   ,0.0, 0.0},
01621      {-.833442628760834001421021108693569569461    ,0.0, 0.0},
01622      {-.8949919978782753688510420067828049541746   ,0.0, 0.0},
01623      {-.9429745712289743394140111696584705319052   ,0.0, 0.0},
01624      {-.9766639214595175114983153864795940677454   ,0.0, 0.0},
01625      {-.9955569697904980979087849468939016172576   ,0.0, 0.0}
01626     },
01627     { // weights
01628      .01139379850102628794790296411323477360332,
01629      .02635498661503213726190181529529914493596,
01630      .04093915670130631265562348771164595366085,
01631      .05490469597583519192593689154047332416011,
01632      .06803833381235691720718718565670796855471,
01633      .08014070033500101801323495966911130229023,
01634      .09102826198296364981149722070289165338099,
01635      .1005359490670506442022068903926858269885,
01636      .1085196244742636531160939570501166193401,
01637      .1148582591457116483393255458695558086409,
01638      .1194557635357847722281781265129010473902,
01639      .1222424429903100416889595189458515058351,
01640       .1231760537267154512039028730790501424382,
01641       .1222424429903100416889595189458515058351,
01642       .1194557635357847722281781265129010473902,
01643       .1148582591457116483393255458695558086409,
01644       .1085196244742636531160939570501166193401,
01645       .1005359490670506442022068903926858269885,
01646       .09102826198296364981149722070289165338099,
01647       .08014070033500101801323495966911130229023,
01648      .06803833381235691720718718565670796855471,
01649       .05490469597583519192593689154047332416011,
01650       .04093915670130631265562348771164595366085,
01651       .02635498661503213726190181529529914493596,
01652       .01139379850102628794790296411323477360332
01653     }
01654   },
01655   {
01656     26,
01657     { // points
01658      {.9958857011456169290032169593229060259569    ,0.0, 0.0},
01659      {.9783854459564709911005803543119263054469    ,0.0, 0.0},
01660      {.9471590666617142501359152835180367545207    ,0.0, 0.0},
01661      {.9026378619843070742176655992312102513411    ,0.0, 0.0},
01662      {.8454459427884980187975070614678381615721    ,0.0, 0.0},
01663      {.7763859488206788561929672472422838669762    ,0.0, 0.0},
01664      {.6964272604199572648638139137294246978608    ,0.0, 0.0},
01665      {.6066922930176180632319787469168870544353    ,0.0, 0.0},
01666      {.5084407148245057176957030647255691753763    ,0.0, 0.0},
01667      {.4030517551234863064810773770988831036599    ,0.0, 0.0},
01668      {.2920048394859568951428353820778302968847    ,0.0, 0.0},
01669      {.1768588203568901839690577484183447499774    ,0.0, 0.0},
01670      {.05923009342931320709371857519840336079023   ,0.0, 0.0},
01671      {-.05923009342931320709371857519840336079023  ,0.0, 0.0},
01672      {-.1768588203568901839690577484183447499774   ,0.0, 0.0},
01673      {-.2920048394859568951428353820778302968847   ,0.0, 0.0},
01674      {-.4030517551234863064810773770988831036599   ,0.0, 0.0},
01675      {-.5084407148245057176957030647255691753763   ,0.0, 0.0},
01676      {-.6066922930176180632319787469168870544353   ,0.0, 0.0},
01677      {-.6964272604199572648638139137294246978608   ,0.0, 0.0},
01678      {-.7763859488206788561929672472422838669762   ,0.0, 0.0},
01679      {-.8454459427884980187975070614678381615721   ,0.0, 0.0},
01680      {-.9026378619843070742176655992312102513411   ,0.0, 0.0},
01681      {-.9471590666617142501359152835180367545207   ,0.0, 0.0},
01682      {-.9783854459564709911005803543119263054469   ,0.0, 0.0},
01683      {-.9958857011456169290032169593229060259569   ,0.0, 0.0}
01684     },
01685     { // weights
01686      .01055137261734300715565118768525197790435,
01687      .0244178510926319087896158275197884002405,
01688      .03796238329436276395030314124885049469077,
01689      .05097582529714781199831990072407337952588,
01690      .06327404632957483553945368990704509572222,
01691      .07468414976565974588707579610284833863875,
01692      .08504589431348523921044776507998169658392,
01693      .09421380035591414846366488306730319854917,
01694      .1020591610944254232384140702534307923272,
01695      .1084718405285765906565794267279975822894,
01696      .113361816546319666549440718442598145246,
01697      .116660443485296582044662507540362213632,
01698       .1183214152792622765163710857004686846499,
01699        .1183214152792622765163710857004686846499,
01700       .116660443485296582044662507540362213632,
01701       .113361816546319666549440718442598145246,
01702       .1084718405285765906565794267279975822894,
01703       .1020591610944254232384140702534307923272,
01704       .09421380035591414846366488306730319854917,
01705       .08504589431348523921044776507998169658392,
01706       .07468414976565974588707579610284833863875,
01707       .06327404632957483553945368990704509572222,
01708       .05097582529714781199831990072407337952588,
01709       .03796238329436276395030314124885049469077,
01710       .0244178510926319087896158275197884002405,
01711       .01055137261734300715565118768525197790435
01712     }
01713   },
01714   {
01715     26,
01716     { // points
01717      {.9958857011456169290032169593229060259569    ,0.0, 0.0},
01718      {.9783854459564709911005803543119263054469    ,0.0, 0.0},
01719      {.9471590666617142501359152835180367545207    ,0.0, 0.0},
01720      {.9026378619843070742176655992312102513411    ,0.0, 0.0},
01721      {.8454459427884980187975070614678381615721    ,0.0, 0.0},
01722      {.7763859488206788561929672472422838669762    ,0.0, 0.0},
01723      {.6964272604199572648638139137294246978608    ,0.0, 0.0},
01724      {.6066922930176180632319787469168870544353    ,0.0, 0.0},
01725      {.5084407148245057176957030647255691753763    ,0.0, 0.0},
01726      {.4030517551234863064810773770988831036599    ,0.0, 0.0},
01727      {.2920048394859568951428353820778302968847    ,0.0, 0.0},
01728      {.1768588203568901839690577484183447499774    ,0.0, 0.0},
01729      {.05923009342931320709371857519840336079023   ,0.0, 0.0},
01730      {-.05923009342931320709371857519840336079023  ,0.0, 0.0},
01731      {-.1768588203568901839690577484183447499774   ,0.0, 0.0},
01732      {-.2920048394859568951428353820778302968847   ,0.0, 0.0},
01733      {-.4030517551234863064810773770988831036599   ,0.0, 0.0},
01734      {-.5084407148245057176957030647255691753763   ,0.0, 0.0},
01735      {-.6066922930176180632319787469168870544353   ,0.0, 0.0},
01736      {-.6964272604199572648638139137294246978608   ,0.0, 0.0},
01737      {-.7763859488206788561929672472422838669762   ,0.0, 0.0},
01738      {-.8454459427884980187975070614678381615721   ,0.0, 0.0},
01739      {-.9026378619843070742176655992312102513411   ,0.0, 0.0},
01740      {-.9471590666617142501359152835180367545207   ,0.0, 0.0},
01741      {-.9783854459564709911005803543119263054469   ,0.0, 0.0},
01742      {-.9958857011456169290032169593229060259569   ,0.0, 0.0}
01743     },
01744     { // weights
01745      .01055137261734300715565118768525197790435,
01746      .0244178510926319087896158275197884002405,
01747      .03796238329436276395030314124885049469077,
01748      .05097582529714781199831990072407337952588,
01749      .06327404632957483553945368990704509572222,
01750      .07468414976565974588707579610284833863875,
01751      .08504589431348523921044776507998169658392,
01752      .09421380035591414846366488306730319854917,
01753      .1020591610944254232384140702534307923272,
01754      .1084718405285765906565794267279975822894,
01755      .113361816546319666549440718442598145246,
01756      .116660443485296582044662507540362213632,
01757       .1183214152792622765163710857004686846499,
01758        .1183214152792622765163710857004686846499,
01759       .116660443485296582044662507540362213632,
01760       .113361816546319666549440718442598145246,
01761       .1084718405285765906565794267279975822894,
01762       .1020591610944254232384140702534307923272,
01763       .09421380035591414846366488306730319854917,
01764       .08504589431348523921044776507998169658392,
01765       .07468414976565974588707579610284833863875,
01766       .06327404632957483553945368990704509572222,
01767       .05097582529714781199831990072407337952588,
01768       .03796238329436276395030314124885049469077,
01769       .0244178510926319087896158275197884002405,
01770       .01055137261734300715565118768525197790435
01771     }
01772   },
01773   {
01774     27,
01775     { // points
01776      {.9961792628889885669388872083812299902607    ,0.0, 0.0},
01777      {.9799234759615012228558733556610471845676    ,0.0, 0.0},
01778      {.9509005578147050068519080306438828930926    ,0.0, 0.0},
01779      {.909482320677491104300645018209689254948     ,0.0, 0.0},
01780      {.8562079080182944903027372227068427977643    ,0.0, 0.0},
01781      {.7917716390705082271443973441072707329194    ,0.0, 0.0},
01782      {.7170134737394236992948162116423395497507    ,0.0, 0.0},
01783      {.6329079719464951409277346376344886121031    ,0.0, 0.0},
01784      {.5405515645794568949003009415599828209592    ,0.0, 0.0},
01785      {.4411482517500268805859741556892814524477    ,0.0, 0.0},
01786      {.33599390363850889973031903420728454179      ,0.0, 0.0},
01787      {.2264593654395368588572391073602301711794    ,0.0, 0.0},
01788      {.1139725856095299669328949838699766271733    ,0.0, 0.0},
01789      {0                                            ,0.0, 0.0},
01790      {-.1139725856095299669328949838699766271733   ,0.0, 0.0},
01791      {-.2264593654395368588572391073602301711794   ,0.0, 0.0},
01792      {-.33599390363850889973031903420728454179     ,0.0, 0.0},
01793      {-.4411482517500268805859741556892814524477   ,0.0, 0.0},
01794      {-.5405515645794568949003009415599828209592   ,0.0, 0.0},
01795      {-.6329079719464951409277346376344886121031   ,0.0, 0.0},
01796      {-.7170134737394236992948162116423395497507   ,0.0, 0.0},
01797      {-.7917716390705082271443973441072707329194   ,0.0, 0.0},
01798      {-.8562079080182944903027372227068427977643   ,0.0, 0.0},
01799      {-.909482320677491104300645018209689254948    ,0.0, 0.0},
01800      {-.9509005578147050068519080306438828930926   ,0.0, 0.0},
01801      {-.9799234759615012228558733556610471845676   ,0.0, 0.0},
01802      {-.9961792628889885669388872083812299902607   ,0.0, 0.0}
01803     },
01804     { // weights
01805      .009798996051294360261150055091259098098226,
01806      .02268623159618062319603420644676148881277,
01807      .03529705375741971102257828930471164113614,
01808      .04744941252061506270409671011418471822473,
01809      .05898353685983359911030083371953163316524,
01810      .06974882376624559298432288835666727613282,
01811      .07960486777305777126307495900984240297615,
01812      .08842315854375695019432280285374911105654,
01813      .09608872737002850756565264655810585916021,
01814      .1025016378177457986712477115326638093244,
01815      .107578285788533187212162984426657404819,
01816      .1112524883568451926721630960428486748329,
01817      .1134763461089651486203699480920992579205,
01818       .1142208673789569890450457369018352486807,
01819       .1134763461089651486203699480920992579205,
01820       .1112524883568451926721630960428486748329,
01821       .107578285788533187212162984426657404819,
01822       .1025016378177457986712477115326638093244,
01823       .09608872737002850756565264655810585916021,
01824       .08842315854375695019432280285374911105654,
01825       .07960486777305777126307495900984240297615,
01826       .06974882376624559298432288835666727613282,
01827       .05898353685983359911030083371953163316524,
01828       .04744941252061506270409671011418471822473,
01829       .03529705375741971102257828930471164113614,
01830       .02268623159618062319603420644676148881277,
01831       .009798996051294360261150055091259098098226
01832     }
01833   },
01834   {
01835     27,
01836     { // points
01837      {.9961792628889885669388872083812299902607    ,0.0, 0.0},
01838      {.9799234759615012228558733556610471845676    ,0.0, 0.0},
01839      {.9509005578147050068519080306438828930926    ,0.0, 0.0},
01840      {.909482320677491104300645018209689254948     ,0.0, 0.0},
01841      {.8562079080182944903027372227068427977643    ,0.0, 0.0},
01842      {.7917716390705082271443973441072707329194    ,0.0, 0.0},
01843      {.7170134737394236992948162116423395497507    ,0.0, 0.0},
01844      {.6329079719464951409277346376344886121031    ,0.0, 0.0},
01845      {.5405515645794568949003009415599828209592    ,0.0, 0.0},
01846      {.4411482517500268805859741556892814524477    ,0.0, 0.0},
01847      {.33599390363850889973031903420728454179      ,0.0, 0.0},
01848      {.2264593654395368588572391073602301711794    ,0.0, 0.0},
01849      {.1139725856095299669328949838699766271733    ,0.0, 0.0},
01850      {0                                            ,0.0, 0.0},
01851      {-.1139725856095299669328949838699766271733   ,0.0, 0.0},
01852      {-.2264593654395368588572391073602301711794   ,0.0, 0.0},
01853      {-.33599390363850889973031903420728454179     ,0.0, 0.0},
01854      {-.4411482517500268805859741556892814524477   ,0.0, 0.0},
01855      {-.5405515645794568949003009415599828209592   ,0.0, 0.0},
01856      {-.6329079719464951409277346376344886121031   ,0.0, 0.0},
01857      {-.7170134737394236992948162116423395497507   ,0.0, 0.0},
01858      {-.7917716390705082271443973441072707329194   ,0.0, 0.0},
01859      {-.8562079080182944903027372227068427977643   ,0.0, 0.0},
01860      {-.909482320677491104300645018209689254948    ,0.0, 0.0},
01861      {-.9509005578147050068519080306438828930926   ,0.0, 0.0},
01862      {-.9799234759615012228558733556610471845676   ,0.0, 0.0},
01863      {-.9961792628889885669388872083812299902607   ,0.0, 0.0}
01864     },
01865     { // weights
01866      .009798996051294360261150055091259098098226,
01867      .02268623159618062319603420644676148881277,
01868      .03529705375741971102257828930471164113614,
01869      .04744941252061506270409671011418471822473,
01870      .05898353685983359911030083371953163316524,
01871      .06974882376624559298432288835666727613282,
01872      .07960486777305777126307495900984240297615,
01873      .08842315854375695019432280285374911105654,
01874      .09608872737002850756565264655810585916021,
01875      .1025016378177457986712477115326638093244,
01876      .107578285788533187212162984426657404819,
01877      .1112524883568451926721630960428486748329,
01878      .1134763461089651486203699480920992579205,
01879       .1142208673789569890450457369018352486807,
01880       .1134763461089651486203699480920992579205,
01881       .1112524883568451926721630960428486748329,
01882       .107578285788533187212162984426657404819,
01883       .1025016378177457986712477115326638093244,
01884       .09608872737002850756565264655810585916021,
01885       .08842315854375695019432280285374911105654,
01886       .07960486777305777126307495900984240297615,
01887       .06974882376624559298432288835666727613282,
01888       .05898353685983359911030083371953163316524,
01889       .04744941252061506270409671011418471822473,
01890       .03529705375741971102257828930471164113614,
01891       .02268623159618062319603420644676148881277,
01892       .009798996051294360261150055091259098098226
01893     }
01894   },
01895   {
01896     28,
01897     { // points
01898      {.9964424975739544499504363904833109917501    ,0.0, 0.0},
01899      {.9813031653708727536945599458078302764442    ,0.0, 0.0},
01900      {.9542592806289381972541018397052155890034    ,0.0, 0.0},
01901      {.9156330263921320738696894233299271463525    ,0.0, 0.0},
01902      {.8658925225743950489422545673796868043419    ,0.0, 0.0},
01903      {.8056413709171791714478859554252776586717    ,0.0, 0.0},
01904      {.7356108780136317720281445102925343680161    ,0.0, 0.0},
01905      {.6566510940388649612198981765067428215696    ,0.0, 0.0},
01906      {.5697204718114017193080032833564309331247    ,0.0, 0.0},
01907      {.4758742249551182610344118476674340426272    ,0.0, 0.0},
01908      {.3762515160890787102213572095560869828717    ,0.0, 0.0},
01909      {.2720616276351780776768263561257697348248    ,0.0, 0.0},
01910      {.1645692821333807712814717778911654571457    ,0.0, 0.0},
01911      {.0550792898840342704265165273418799778508    ,0.0, 0.0},
01912      {-.0550792898840342704265165273418799778508   ,0.0, 0.0},
01913      {-.1645692821333807712814717778911654571457   ,0.0, 0.0},
01914      {-.2720616276351780776768263561257697348248   ,0.0, 0.0},
01915      {-.3762515160890787102213572095560869828717   ,0.0, 0.0},
01916      {-.4758742249551182610344118476674340426272   ,0.0, 0.0},
01917      {-.5697204718114017193080032833564309331247   ,0.0, 0.0},
01918      {-.6566510940388649612198981765067428215696   ,0.0, 0.0},
01919      {-.7356108780136317720281445102925343680161   ,0.0, 0.0},
01920      {-.8056413709171791714478859554252776586717   ,0.0, 0.0},
01921      {-.8658925225743950489422545673796868043419   ,0.0, 0.0},
01922      {-.9156330263921320738696894233299271463525   ,0.0, 0.0},
01923      {-.9542592806289381972541018397052155890034   ,0.0, 0.0},
01924      {-.9813031653708727536945599458078302764442   ,0.0, 0.0},
01925      {-.9964424975739544499504363904833109917501   ,0.0, 0.0}
01926     },
01927     { // weights
01928      .009124282593094517738816153922951706240344,
01929      .02113211259277125975150038099326543445137,
01930      .03290142778230437997763081917053204598153,
01931      .04427293475900422783958787765320739061499,
01932      .05510734567571674543148291822694559121906,
01933      .06527292396699959579339756677550463635364,
01934      .07464621423456877902393188717302203802164,
01935      .08311341722890121839039649824433247986113,
01936      .09057174439303284094218603133678412982286,
01937      .09693065799792991585048900609544060176503,
01938      .1021129675780607698142166385057121350466,
01939      .1060557659228464179104164369968108287899,
01940      .1087111922582941352535715193036733678753,
01941      .1100470130164751962823762656018176139566,
01942       .1100470130164751962823762656018176139566,
01943       .1087111922582941352535715193036733678753,
01944       .1060557659228464179104164369968108287899,
01945       .1021129675780607698142166385057121350466,
01946       .09693065799792991585048900609544060176503,
01947       .09057174439303284094218603133678412982286,
01948       .08311341722890121839039649824433247986113,
01949       .07464621423456877902393188717302203802164,
01950       .06527292396699959579339756677550463635364,
01951       .05510734567571674543148291822694559121906,
01952       .04427293475900422783958787765320739061499,
01953       .03290142778230437997763081917053204598153,
01954       .02113211259277125975150038099326543445137,
01955       .009124282593094517738816153922951706240344
01956     }
01957   },
01958   {
01959     28,
01960     { // points
01961      {.9964424975739544499504363904833109917501    ,0.0, 0.0},
01962      {.9813031653708727536945599458078302764442    ,0.0, 0.0},
01963      {.9542592806289381972541018397052155890034    ,0.0, 0.0},
01964      {.9156330263921320738696894233299271463525    ,0.0, 0.0},
01965      {.8658925225743950489422545673796868043419    ,0.0, 0.0},
01966      {.8056413709171791714478859554252776586717    ,0.0, 0.0},
01967      {.7356108780136317720281445102925343680161    ,0.0, 0.0},
01968      {.6566510940388649612198981765067428215696    ,0.0, 0.0},
01969      {.5697204718114017193080032833564309331247    ,0.0, 0.0},
01970      {.4758742249551182610344118476674340426272    ,0.0, 0.0},
01971      {.3762515160890787102213572095560869828717    ,0.0, 0.0},
01972      {.2720616276351780776768263561257697348248    ,0.0, 0.0},
01973      {.1645692821333807712814717778911654571457    ,0.0, 0.0},
01974      {.0550792898840342704265165273418799778508    ,0.0, 0.0},
01975      {-.0550792898840342704265165273418799778508   ,0.0, 0.0},
01976      {-.1645692821333807712814717778911654571457   ,0.0, 0.0},
01977      {-.2720616276351780776768263561257697348248   ,0.0, 0.0},
01978      {-.3762515160890787102213572095560869828717   ,0.0, 0.0},
01979      {-.4758742249551182610344118476674340426272   ,0.0, 0.0},
01980      {-.5697204718114017193080032833564309331247   ,0.0, 0.0},
01981      {-.6566510940388649612198981765067428215696   ,0.0, 0.0},
01982      {-.7356108780136317720281445102925343680161   ,0.0, 0.0},
01983      {-.8056413709171791714478859554252776586717   ,0.0, 0.0},
01984      {-.8658925225743950489422545673796868043419   ,0.0, 0.0},
01985      {-.9156330263921320738696894233299271463525   ,0.0, 0.0},
01986      {-.9542592806289381972541018397052155890034   ,0.0, 0.0},
01987      {-.9813031653708727536945599458078302764442   ,0.0, 0.0},
01988      {-.9964424975739544499504363904833109917501   ,0.0, 0.0}
01989     },
01990     { // weights
01991      .009124282593094517738816153922951706240344,
01992      .02113211259277125975150038099326543445137,
01993      .03290142778230437997763081917053204598153,
01994      .04427293475900422783958787765320739061499,
01995      .05510734567571674543148291822694559121906,
01996      .06527292396699959579339756677550463635364,
01997      .07464621423456877902393188717302203802164,
01998      .08311341722890121839039649824433247986113,
01999      .09057174439303284094218603133678412982286,
02000      .09693065799792991585048900609544060176503,
02001      .1021129675780607698142166385057121350466,
02002      .1060557659228464179104164369968108287899,
02003      .1087111922582941352535715193036733678753,
02004      .1100470130164751962823762656018176139566,
02005       .1100470130164751962823762656018176139566,
02006       .1087111922582941352535715193036733678753,
02007       .1060557659228464179104164369968108287899,
02008       .1021129675780607698142166385057121350466,
02009       .09693065799792991585048900609544060176503,
02010       .09057174439303284094218603133678412982286,
02011       .08311341722890121839039649824433247986113,
02012       .07464621423456877902393188717302203802164,
02013       .06527292396699959579339756677550463635364,
02014       .05510734567571674543148291822694559121906,
02015       .04427293475900422783958787765320739061499,
02016       .03290142778230437997763081917053204598153,
02017       .02113211259277125975150038099326543445137,
02018       .009124282593094517738816153922951706240344
02019     }
02020   },
02021   {
02022     29,
02023     { // points
02024      {.9966794422605965861631915325493538856518    ,0.0, 0.0},
02025      {.9825455052614131748709260157863769561068    ,0.0, 0.0},
02026      {.9572855957780877257982080369808235637376    ,0.0, 0.0},
02027      {.9211802329530587850937534360831064254088    ,0.0, 0.0},
02028      {.8746378049201027904177934212565785469106    ,0.0, 0.0},
02029      {.81818548761525244498957221457878497563      ,0.0, 0.0},
02030      {.7524628517344771339126100772121381902126    ,0.0, 0.0},
02031      {.6782145376026865151561850053919859263883    ,0.0, 0.0},
02032      {.5962817971382278203795862111889897800782    ,0.0, 0.0},
02033      {.5075929551242276421026279196275201533512    ,0.0, 0.0},
02034      {.4131528881740086638907065860316168233234    ,0.0, 0.0},
02035      {.3140316378676399349481959231910474482584    ,0.0, 0.0},
02036      {.2113522861660010745063757289029374990567    ,0.0, 0.0},
02037      {.1062782301326792301709823924303769809172    ,0.0, 0.0},
02038      {0                                            ,0.0, 0.0},
02039      {-.1062782301326792301709823924303769809172   ,0.0, 0.0},
02040      {-.2113522861660010745063757289029374990567   ,0.0, 0.0},
02041      {-.3140316378676399349481959231910474482584   ,0.0, 0.0},
02042      {-.4131528881740086638907065860316168233234   ,0.0, 0.0},
02043      {-.5075929551242276421026279196275201533512   ,0.0, 0.0},
02044      {-.5962817971382278203795862111889897800782   ,0.0, 0.0},
02045      {-.6782145376026865151561850053919859263883   ,0.0, 0.0},
02046      {-.7524628517344771339126100772121381902126   ,0.0, 0.0},
02047      {-.81818548761525244498957221457878497563     ,0.0, 0.0},
02048      {-.8746378049201027904177934212565785469106   ,0.0, 0.0},
02049      {-.9211802329530587850937534360831064254088   ,0.0, 0.0},
02050      {-.9572855957780877257982080369808235637376   ,0.0, 0.0},
02051      {-.9825455052614131748709260157863769561068   ,0.0, 0.0},
02052      {-.9966794422605965861631915325493538856518   ,0.0, 0.0}
02053     },
02054     { // weights
02055      .008516903878746409654263813302249803002399,
02056      .01973208505612270598385980164039563114961,
02057      .03074049220209362264440852537461674974712,
02058      .04140206251868283610483001011407692153349,
02059      .05159482690249792391259438117954259791962,
02060      .06120309065707913854210984802390704492406,
02061      .07011793325505127856958148694887917310239,
02062      .07823832713576378382814488865968033136688,
02063      .0854722573661725275453448492972080713817,
02064      .09173775713925876334796641107711080689823,
02065      .09696383409440860630190007488268875917636,
02066      .1010912737599149661218205469074973636476,
02067      .1040733100777293739133284712851200689107,
02068      .1058761550973209414065913278521878930748,
02069       .1064793817183142442465111269096775683302,
02070       .1058761550973209414065913278521878930748,
02071       .1040733100777293739133284712851200689107,
02072       .1010912737599149661218205469074973636476,
02073       .09696383409440860630190007488268875917636,
02074       .09173775713925876334796641107711080689823,
02075       .0854722573661725275453448492972080713817,
02076       .07823832713576378382814488865968033136688,
02077       .07011793325505127856958148694887917310239,
02078       .06120309065707913854210984802390704492406,
02079       .05159482690249792391259438117954259791962,
02080       .04140206251868283610483001011407692153349,
02081       .03074049220209362264440852537461674974712,
02082       .01973208505612270598385980164039563114961,
02083       .008516903878746409654263813302249803002399
02084     }
02085   },
02086   {
02087     29,
02088     { // points
02089      {.9966794422605965861631915325493538856518    ,0.0, 0.0},
02090      {.9825455052614131748709260157863769561068    ,0.0, 0.0},
02091      {.9572855957780877257982080369808235637376    ,0.0, 0.0},
02092      {.9211802329530587850937534360831064254088    ,0.0, 0.0},
02093      {.8746378049201027904177934212565785469106    ,0.0, 0.0},
02094      {.81818548761525244498957221457878497563      ,0.0, 0.0},
02095      {.7524628517344771339126100772121381902126    ,0.0, 0.0},
02096      {.6782145376026865151561850053919859263883    ,0.0, 0.0},
02097      {.5962817971382278203795862111889897800782    ,0.0, 0.0},
02098      {.5075929551242276421026279196275201533512    ,0.0, 0.0},
02099      {.4131528881740086638907065860316168233234    ,0.0, 0.0},
02100      {.3140316378676399349481959231910474482584    ,0.0, 0.0},
02101      {.2113522861660010745063757289029374990567    ,0.0, 0.0},
02102      {.1062782301326792301709823924303769809172    ,0.0, 0.0},
02103      {0                                            ,0.0, 0.0},
02104      {-.1062782301326792301709823924303769809172   ,0.0, 0.0},
02105      {-.2113522861660010745063757289029374990567   ,0.0, 0.0},
02106      {-.3140316378676399349481959231910474482584   ,0.0, 0.0},
02107      {-.4131528881740086638907065860316168233234   ,0.0, 0.0},
02108      {-.5075929551242276421026279196275201533512   ,0.0, 0.0},
02109      {-.5962817971382278203795862111889897800782   ,0.0, 0.0},
02110      {-.6782145376026865151561850053919859263883   ,0.0, 0.0},
02111      {-.7524628517344771339126100772121381902126   ,0.0, 0.0},
02112      {-.81818548761525244498957221457878497563     ,0.0, 0.0},
02113      {-.8746378049201027904177934212565785469106   ,0.0, 0.0},
02114      {-.9211802329530587850937534360831064254088   ,0.0, 0.0},
02115      {-.9572855957780877257982080369808235637376   ,0.0, 0.0},
02116      {-.9825455052614131748709260157863769561068   ,0.0, 0.0},
02117      {-.9966794422605965861631915325493538856518   ,0.0, 0.0}
02118     },
02119     { // weights
02120      .008516903878746409654263813302249803002399,
02121      .01973208505612270598385980164039563114961,
02122      .03074049220209362264440852537461674974712,
02123      .04140206251868283610483001011407692153349,
02124      .05159482690249792391259438117954259791962,
02125      .06120309065707913854210984802390704492406,
02126      .07011793325505127856958148694887917310239,
02127      .07823832713576378382814488865968033136688,
02128      .0854722573661725275453448492972080713817,
02129      .09173775713925876334796641107711080689823,
02130      .09696383409440860630190007488268875917636,
02131      .1010912737599149661218205469074973636476,
02132      .1040733100777293739133284712851200689107,
02133      .1058761550973209414065913278521878930748,
02134       .1064793817183142442465111269096775683302,
02135       .1058761550973209414065913278521878930748,
02136       .1040733100777293739133284712851200689107,
02137       .1010912737599149661218205469074973636476,
02138       .09696383409440860630190007488268875917636,
02139       .09173775713925876334796641107711080689823,
02140       .0854722573661725275453448492972080713817,
02141       .07823832713576378382814488865968033136688,
02142       .07011793325505127856958148694887917310239,
02143       .06120309065707913854210984802390704492406,
02144       .05159482690249792391259438117954259791962,
02145       .04140206251868283610483001011407692153349,
02146       .03074049220209362264440852537461674974712,
02147       .01973208505612270598385980164039563114961,
02148       .008516903878746409654263813302249803002399
02149     }
02150   },
02151   {
02152     30,
02153     { // points
02154      {.9968934840746495402716300509186952833409    ,0.0, 0.0},
02155      {.9836681232797472099700325816056628019403    ,0.0, 0.0},
02156      {.9600218649683075122168710255817976629304    ,0.0, 0.0},
02157      {.9262000474292743258793242770804740040865    ,0.0, 0.0},
02158      {.8825605357920526815431164625302255900567    ,0.0, 0.0},
02159      {.8295657623827683974428981197325019164391    ,0.0, 0.0},
02160      {.7677774321048261949179773409745031316949    ,0.0, 0.0},
02161      {.6978504947933157969322923880266400683824    ,0.0, 0.0},
02162      {.6205261829892428611404775564311892992074    ,0.0, 0.0},
02163      {.5366241481420198992641697933110727941642    ,0.0, 0.0},
02164      {.4470337695380891767806099003228540001624    ,0.0, 0.0},
02165      {.3527047255308781134710372070893738606536    ,0.0, 0.0},
02166      {.2546369261678898464398051298178051078828    ,0.0, 0.0},
02167      {.1538699136085835469637946727432559204186    ,0.0, 0.0},
02168      {.05147184255531769583302521316672257374914   ,0.0, 0.0},
02169      {-.05147184255531769583302521316672257374914  ,0.0, 0.0},
02170      {-.1538699136085835469637946727432559204186   ,0.0, 0.0},
02171      {-.2546369261678898464398051298178051078828   ,0.0, 0.0},
02172      {-.3527047255308781134710372070893738606536   ,0.0, 0.0},
02173      {-.4470337695380891767806099003228540001624   ,0.0, 0.0},
02174      {-.5366241481420198992641697933110727941642   ,0.0, 0.0},
02175      {-.6205261829892428611404775564311892992074   ,0.0, 0.0},
02176      {-.6978504947933157969322923880266400683824   ,0.0, 0.0},
02177      {-.7677774321048261949179773409745031316949   ,0.0, 0.0},
02178      {-.8295657623827683974428981197325019164391   ,0.0, 0.0},
02179      {-.8825605357920526815431164625302255900567   ,0.0, 0.0},
02180      {-.9262000474292743258793242770804740040865   ,0.0, 0.0},
02181      {-.9600218649683075122168710255817976629304   ,0.0, 0.0},
02182      {-.9836681232797472099700325816056628019403   ,0.0, 0.0},
02183      {-.9968934840746495402716300509186952833409   ,0.0, 0.0}
02184     },
02185     { // weights
02186      .007968192496166605615465883474673622450481,
02187      .01846646831109095914230213191204726909621,
02188      .02878470788332336934971917961129204363959,
02189      .0387991925696270495968019364463476920332,
02190      .04840267283059405290293814042280751781527,
02191      .05749315621761906648172168940205612879712,
02192      .06597422988218049512812851511596236123744,
02193      .07375597473770520626824385002219073415377,
02194      .08075589522942021535469493846052973087589,
02195      .08689978720108297980238753071512570257675,
02196      .09212252223778612871763270708761876719691,
02197      .09636873717464425963946862635180986509641,
02198      .09959342058679526706278028210356947652987,
02199      .1017623897484055045964289521685540446327,
02200      .1028526528935588403412856367054150438684,
02201       .1028526528935588403412856367054150438684,
02202       .1017623897484055045964289521685540446327,
02203       .09959342058679526706278028210356947652987,
02204       .09636873717464425963946862635180986509641,
02205       .09212252223778612871763270708761876719691,
02206       .08689978720108297980238753071512570257675,
02207       .08075589522942021535469493846052973087589,
02208       .07375597473770520626824385002219073415377,
02209       .06597422988218049512812851511596236123744,
02210       .05749315621761906648172168940205612879712,
02211       .04840267283059405290293814042280751781527,
02212       .0387991925696270495968019364463476920332,
02213       .02878470788332336934971917961129204363959,
02214       .01846646831109095914230213191204726909621,
02215       .007968192496166605615465883474673622450481
02216     }
02217   },
02218   {
02219     30,
02220     { // points
02221      {.9968934840746495402716300509186952833409    ,0.0, 0.0},
02222      {.9836681232797472099700325816056628019403    ,0.0, 0.0},
02223      {.9600218649683075122168710255817976629304    ,0.0, 0.0},
02224      {.9262000474292743258793242770804740040865    ,0.0, 0.0},
02225      {.8825605357920526815431164625302255900567    ,0.0, 0.0},
02226      {.8295657623827683974428981197325019164391    ,0.0, 0.0},
02227      {.7677774321048261949179773409745031316949    ,0.0, 0.0},
02228      {.6978504947933157969322923880266400683824    ,0.0, 0.0},
02229      {.6205261829892428611404775564311892992074    ,0.0, 0.0},
02230      {.5366241481420198992641697933110727941642    ,0.0, 0.0},
02231      {.4470337695380891767806099003228540001624    ,0.0, 0.0},
02232      {.3527047255308781134710372070893738606536    ,0.0, 0.0},
02233      {.2546369261678898464398051298178051078828    ,0.0, 0.0},
02234      {.1538699136085835469637946727432559204186    ,0.0, 0.0},
02235      {.05147184255531769583302521316672257374914   ,0.0, 0.0},
02236      {-.05147184255531769583302521316672257374914  ,0.0, 0.0},
02237      {-.1538699136085835469637946727432559204186   ,0.0, 0.0},
02238      {-.2546369261678898464398051298178051078828   ,0.0, 0.0},
02239      {-.3527047255308781134710372070893738606536   ,0.0, 0.0},
02240      {-.4470337695380891767806099003228540001624   ,0.0, 0.0},
02241      {-.5366241481420198992641697933110727941642   ,0.0, 0.0},
02242      {-.6205261829892428611404775564311892992074   ,0.0, 0.0},
02243      {-.6978504947933157969322923880266400683824   ,0.0, 0.0},
02244      {-.7677774321048261949179773409745031316949   ,0.0, 0.0},
02245      {-.8295657623827683974428981197325019164391   ,0.0, 0.0},
02246      {-.8825605357920526815431164625302255900567   ,0.0, 0.0},
02247      {-.9262000474292743258793242770804740040865   ,0.0, 0.0},
02248      {-.9600218649683075122168710255817976629304   ,0.0, 0.0},
02249      {-.9836681232797472099700325816056628019403   ,0.0, 0.0},
02250      {-.9968934840746495402716300509186952833409   ,0.0, 0.0}
02251     },
02252     { // weights
02253      .007968192496166605615465883474673622450481,
02254      .01846646831109095914230213191204726909621,
02255      .02878470788332336934971917961129204363959,
02256      .0387991925696270495968019364463476920332,
02257      .04840267283059405290293814042280751781527,
02258      .05749315621761906648172168940205612879712,
02259      .06597422988218049512812851511596236123744,
02260      .07375597473770520626824385002219073415377,
02261      .08075589522942021535469493846052973087589,
02262      .08689978720108297980238753071512570257675,
02263      .09212252223778612871763270708761876719691,
02264      .09636873717464425963946862635180986509641,
02265      .09959342058679526706278028210356947652987,
02266      .1017623897484055045964289521685540446327,
02267      .1028526528935588403412856367054150438684,
02268       .1028526528935588403412856367054150438684,
02269       .1017623897484055045964289521685540446327,
02270       .09959342058679526706278028210356947652987,
02271       .09636873717464425963946862635180986509641,
02272       .09212252223778612871763270708761876719691,
02273       .08689978720108297980238753071512570257675,
02274       .08075589522942021535469493846052973087589,
02275       .07375597473770520626824385002219073415377,
02276       .06597422988218049512812851511596236123744,
02277       .05749315621761906648172168940205612879712,
02278       .04840267283059405290293814042280751781527,
02279       .0387991925696270495968019364463476920332,
02280       .02878470788332336934971917961129204363959,
02281       .01846646831109095914230213191204726909621,
02282       .007968192496166605615465883474673622450481
02283     }
02284   },
02285   {
02286     31,
02287     { // points
02288      {.9970874818194770740556265542231025082514    ,0.0, 0.0},
02289      {.9846859096651524840024651667346847109385    ,0.0, 0.0},
02290      {.9625039250929496617890524041058583018972    ,0.0, 0.0},
02291      {.9307569978966481649569457597292635128134    ,0.0, 0.0},
02292      {.8897600299482710433741920089821592615436    ,0.0, 0.0},
02293      {.8399203201462673400869045359401783560547    ,0.0, 0.0},
02294      {.7817331484166249404063600201946844910954    ,0.0, 0.0},
02295      {.7157767845868532839059708653664859558902    ,0.0, 0.0},
02296      {.6427067229242603461844182032325014539917    ,0.0, 0.0},
02297      {.5632491614071492627209449235951614279486    ,0.0, 0.0},
02298      {.4781937820449024804405940393564857484395    ,0.0, 0.0},
02299      {.3883859016082329430613514612875201019851    ,0.0, 0.0},
02300      {.2947180699817016166179038976717043387529    ,0.0, 0.0},
02301      {.1981211993355706287724129960328339377748    ,0.0, 0.0},
02302      {.099555312152341520325174790118940733839     ,0.0, 0.0},
02303      {0                                            ,0.0, 0.0},
02304      {-.099555312152341520325174790118940733839    ,0.0, 0.0},
02305      {-.1981211993355706287724129960328339377748   ,0.0, 0.0},
02306      {-.2947180699817016166179038976717043387529   ,0.0, 0.0},
02307      {-.3883859016082329430613514612875201019851   ,0.0, 0.0},
02308      {-.4781937820449024804405940393564857484395   ,0.0, 0.0},
02309      {-.5632491614071492627209449235951614279486   ,0.0, 0.0},
02310      {-.6427067229242603461844182032325014539917   ,0.0, 0.0},
02311      {-.7157767845868532839059708653664859558902   ,0.0, 0.0},
02312      {-.7817331484166249404063600201946844910954   ,0.0, 0.0},
02313      {-.8399203201462673400869045359401783560547   ,0.0, 0.0},
02314      {-.8897600299482710433741920089821592615436   ,0.0, 0.0},
02315      {-.9307569978966481649569457597292635128134   ,0.0, 0.0},
02316      {-.9625039250929496617890524041058583018972   ,0.0, 0.0},
02317      {-.9846859096651524840024651667346847109385   ,0.0, 0.0},
02318      {-.9970874818194770740556265542231025082514   ,0.0, 0.0}
02319     },
02320     { // weights
02321      .007470831579248775858696875032212407022151,
02322      .01731862079031058246315799608682114136627,
02323      .02700901918497942180060870809193215614236,
02324      .03643227391238546402439201046780344232715,
02325      .04549370752720110290231585789462967726355,
02326      .05410308242491685371166625908662004272039,
02327      .06217478656102842691034354368669666715873,
02328      .06962858323541036616775612625512571051509,
02329      .07639038659877661642635767490133064492576,
02330      .08239299176158926390382336743196177061577,
02331      .08757674060847787612619806969533309222926,
02332      .09189011389364147821536287160715012549731,
02333      .09529024291231951280720419748759668454132,
02334      .09774333538632872509347401097899670383573,
02335      .09922501122667230787487551442861501401754,
02336      .09972054479342645142753383373434943964325,
02337      .09922501122667230787487551442861501401754,
02338       .09774333538632872509347401097899670383573,
02339       .09529024291231951280720419748759668454132,
02340       .09189011389364147821536287160715012549731,
02341       .08757674060847787612619806969533309222926,
02342       .08239299176158926390382336743196177061577,
02343       .07639038659877661642635767490133064492576,
02344       .06962858323541036616775612625512571051509,
02345       .06217478656102842691034354368669666715873,
02346       .05410308242491685371166625908662004272039,
02347       .04549370752720110290231585789462967726355,
02348       .03643227391238546402439201046780344232715,
02349       .02700901918497942180060870809193215614236,
02350       .01731862079031058246315799608682114136627,
02351       .007470831579248775858696875032212407022151
02352     }
02353   },
02354   {
02355     31,
02356     { // points
02357      {.9970874818194770740556265542231025082514    ,0.0, 0.0},
02358      {.9846859096651524840024651667346847109385    ,0.0, 0.0},
02359      {.9625039250929496617890524041058583018972    ,0.0, 0.0},
02360      {.9307569978966481649569457597292635128134    ,0.0, 0.0},
02361      {.8897600299482710433741920089821592615436    ,0.0, 0.0},
02362      {.8399203201462673400869045359401783560547    ,0.0, 0.0},
02363      {.7817331484166249404063600201946844910954    ,0.0, 0.0},
02364      {.7157767845868532839059708653664859558902    ,0.0, 0.0},
02365      {.6427067229242603461844182032325014539917    ,0.0, 0.0},
02366      {.5632491614071492627209449235951614279486    ,0.0, 0.0},
02367      {.4781937820449024804405940393564857484395    ,0.0, 0.0},
02368      {.3883859016082329430613514612875201019851    ,0.0, 0.0},
02369      {.2947180699817016166179038976717043387529    ,0.0, 0.0},
02370      {.1981211993355706287724129960328339377748    ,0.0, 0.0},
02371      {.099555312152341520325174790118940733839     ,0.0, 0.0},
02372      {0                                            ,0.0, 0.0},
02373      {-.099555312152341520325174790118940733839    ,0.0, 0.0},
02374      {-.1981211993355706287724129960328339377748   ,0.0, 0.0},
02375      {-.2947180699817016166179038976717043387529   ,0.0, 0.0},
02376      {-.3883859016082329430613514612875201019851   ,0.0, 0.0},
02377      {-.4781937820449024804405940393564857484395   ,0.0, 0.0},
02378      {-.5632491614071492627209449235951614279486   ,0.0, 0.0},
02379      {-.6427067229242603461844182032325014539917   ,0.0, 0.0},
02380      {-.7157767845868532839059708653664859558902   ,0.0, 0.0},
02381      {-.7817331484166249404063600201946844910954   ,0.0, 0.0},
02382      {-.8399203201462673400869045359401783560547   ,0.0, 0.0},
02383      {-.8897600299482710433741920089821592615436   ,0.0, 0.0},
02384      {-.9307569978966481649569457597292635128134   ,0.0, 0.0},
02385      {-.9625039250929496617890524041058583018972   ,0.0, 0.0},
02386      {-.9846859096651524840024651667346847109385   ,0.0, 0.0},
02387      {-.9970874818194770740556265542231025082514   ,0.0, 0.0}
02388     },
02389     { // weights
02390      .007470831579248775858696875032212407022151,
02391      .01731862079031058246315799608682114136627,
02392      .02700901918497942180060870809193215614236,
02393      .03643227391238546402439201046780344232715,
02394      .04549370752720110290231585789462967726355,
02395      .05410308242491685371166625908662004272039,
02396      .06217478656102842691034354368669666715873,
02397      .06962858323541036616775612625512571051509,
02398      .07639038659877661642635767490133064492576,
02399      .08239299176158926390382336743196177061577,
02400      .08757674060847787612619806969533309222926,
02401      .09189011389364147821536287160715012549731,
02402      .09529024291231951280720419748759668454132,
02403      .09774333538632872509347401097899670383573,
02404      .09922501122667230787487551442861501401754,
02405      .09972054479342645142753383373434943964325,
02406      .09922501122667230787487551442861501401754,
02407       .09774333538632872509347401097899670383573,
02408       .09529024291231951280720419748759668454132,
02409       .09189011389364147821536287160715012549731,
02410       .08757674060847787612619806969533309222926,
02411       .08239299176158926390382336743196177061577,
02412       .07639038659877661642635767490133064492576,
02413       .06962858323541036616775612625512571051509,
02414       .06217478656102842691034354368669666715873,
02415       .05410308242491685371166625908662004272039,
02416       .04549370752720110290231585789462967726355,
02417       .03643227391238546402439201046780344232715,
02418       .02700901918497942180060870809193215614236,
02419       .01731862079031058246315799608682114136627,
02420       .007470831579248775858696875032212407022151
02421     }
02422   } // end Gauss
02423 
02424 };
02425     
02426 } // end namespace Intrepid