Intrepid
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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 // Redistribution and use in source and binary forms, with or without
00011 // modification, are permitted provided that the following conditions are
00012 // met:
00013 //
00014 // 1. Redistributions of source code must retain the above copyright
00015 // notice, this list of conditions and the following disclaimer.
00016 //
00017 // 2. Redistributions in binary form must reproduce the above copyright
00018 // notice, this list of conditions and the following disclaimer in the
00019 // documentation and/or other materials provided with the distribution.
00020 //
00021 // 3. Neither the name of the Corporation nor the names of the
00022 // contributors may be used to endorse or promote products derived from
00023 // this software without specific prior written permission.
00024 //
00025 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
00026 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
00027 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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00035 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
00036 //
00037 // Questions? Contact Pavel Bochev  (pbboche@sandia.gov)
00038 //                    Denis Ridzal  (dridzal@sandia.gov), or
00039 //                    Kara Peterson (kjpeter@sandia.gov)
00040 //
00041 // ************************************************************************
00042 // @HEADER
00043 
00049 namespace Intrepid {
00050 
00051 template <class Scalar, class ArrayPoint, class ArrayWeight>
00052 CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::CubatureDirectLineGauss(const int degree) {
00053   this->degree_    = degree;
00054   this->dimension_ = 1;
00055   TEUCHOS_TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM),
00056                      std::out_of_range,
00057                      ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree.");
00058 } // end constructor
00059 
00060 
00061 
00062 template <class Scalar, class ArrayPoint, class ArrayWeight>
00063 const CubatureTemplate *  CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::exposeCubatureData() const {
00064   return cubature_data_;
00065 }
00066 
00067 
00068 
00069 template <class Scalar, class ArrayPoint, class ArrayWeight>
00070 int CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getMaxAccuracy() const {
00071   return INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM;
00072 }
00073 
00074 
00075 
00076 template <class Scalar, class ArrayPoint, class ArrayWeight>
00077 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getName() const {
00078   return cubature_name_;
00079 } // end getName
00080 
00081 
00082 
00083 template <class Scalar, class ArrayPoint, class ArrayWeight>
00084 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_name_ = "INTREPID_CUBATURE_LINE_GAUSS";
00085 
00086 
00087 //-------------------------------------------------------------------------------------//
00088 //                          Definition of cubature templates                           //
00089 //-------------------------------------------------------------------------------------//
00090 
00091 /*
00092    Cubature templates for lines are defined the reference cell:
00093 
00094    Line -> (-1,0,0),(1,0,0)
00095 */
00096 
00097 /*
00098    This static const member contains templates for Gauss(-Legendre) rules.
00099 */
00100 
00101 template <class Scalar, class ArrayPoint, class ArrayWeight>
00102 const CubatureTemplate CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_data_[INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM+1] =
00103 {
00104 
00105   // Collection of Gauss rules on [-1,1]
00106   // The rule with array index i is exact for polynomials up to order i
00107   {
00108     1,
00109     {{0e0, 0.0, 0.0}},
00110     {2e0}
00111   },
00112   {
00113     1,
00114     {{0e0, 0.0, 0.0}},
00115     {2e0}
00116   },
00117   {
00118     2,
00119     {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
00120      {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
00121     {1e0,
00122      1e0}
00123   },
00124   {
00125     2,
00126     {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
00127      {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
00128     {1e0,
00129      1e0}
00130   },
00131   {
00132     3,
00133     {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
00134      {0e0, 0.0, 0.0},
00135      {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
00136     {5.555555555555555555555555555555555555556e-1,
00137      8.888888888888888888888888888888888888889e-1,
00138      5.555555555555555555555555555555555555556e-1}
00139   },
00140   {
00141     3,
00142     {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
00143      {0e0, 0.0, 0.0},
00144      {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
00145     {5.555555555555555555555555555555555555556e-1,
00146      8.888888888888888888888888888888888888889e-1,
00147      5.555555555555555555555555555555555555556e-1}
00148   },
00149   {
00150     4,
00151     {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
00152      {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00153      {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00154      {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
00155     {3.478548451374538573730639492219994072353e-1,
00156      6.521451548625461426269360507780005927647e-1,
00157      6.521451548625461426269360507780005927647e-1,
00158      3.478548451374538573730639492219994072353e-1}
00159   },
00160   {
00161     4,
00162     {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
00163      {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00164      {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
00165      {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
00166     {3.478548451374538573730639492219994072353e-1,
00167      6.521451548625461426269360507780005927647e-1,
00168      6.521451548625461426269360507780005927647e-1,
00169      3.478548451374538573730639492219994072353e-1}
00170   },
00171   {
00172     5,
00173     {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
00174      {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00175      {0e0, 0.0, 0.0},
00176      {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00177      {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
00178     {2.369268850561890875142640407199173626433e-1,
00179      4.786286704993664680412915148356381929123e-1,
00180      5.688888888888888888888888888888888888889e-1,
00181      4.786286704993664680412915148356381929123e-1,
00182      2.369268850561890875142640407199173626433e-1}
00183   },
00184   {
00185     5,
00186     {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
00187      {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00188      {0e0, 0.0, 0.0},
00189      {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
00190      {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
00191     {2.369268850561890875142640407199173626433e-1,
00192      4.786286704993664680412915148356381929123e-1,
00193      5.688888888888888888888888888888888888889e-1,
00194      4.786286704993664680412915148356381929123e-1,
00195      2.369268850561890875142640407199173626433e-1}
00196   },
00197   {
00198     6,
00199     {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
00200      {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00201      {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00202      {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00203      {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00204      {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
00205     {1.713244923791703450402961421727328935268e-1,
00206      3.607615730481386075698335138377161116615e-1,
00207      4.679139345726910473898703439895509948117e-1,
00208      4.679139345726910473898703439895509948117e-1,
00209      3.607615730481386075698335138377161116615e-1,
00210      1.713244923791703450402961421727328935268e-1}
00211   },
00212   {
00213     6,
00214     {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
00215      {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00216      {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00217      {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
00218      {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
00219      {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
00220     {1.713244923791703450402961421727328935268e-1,
00221      3.607615730481386075698335138377161116615e-1,
00222      4.679139345726910473898703439895509948117e-1,
00223      4.679139345726910473898703439895509948117e-1,
00224      3.607615730481386075698335138377161116615e-1,
00225      1.713244923791703450402961421727328935268e-1}
00226   },
00227   {
00228     7,
00229     {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
00230      {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00231      {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00232      {0e0, 0.0, 0.0},
00233      {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00234      {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00235      {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
00236     {1.294849661688696932706114326790820183286e-1,
00237      2.797053914892766679014677714237795824869e-1,
00238      3.818300505051189449503697754889751338784e-1,
00239      4.179591836734693877551020408163265306122e-1,
00240      3.818300505051189449503697754889751338784e-1,
00241      2.797053914892766679014677714237795824869e-1,
00242      1.294849661688696932706114326790820183286e-1}
00243   },
00244   {
00245     7,
00246     {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
00247      {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00248      {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00249      {0e0, 0.0, 0.0},
00250      {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
00251      {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
00252      {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
00253     {1.294849661688696932706114326790820183286e-1,
00254      2.797053914892766679014677714237795824869e-1,
00255      3.818300505051189449503697754889751338784e-1,
00256      4.179591836734693877551020408163265306122e-1,
00257      3.818300505051189449503697754889751338784e-1,
00258      2.797053914892766679014677714237795824869e-1,
00259      1.294849661688696932706114326790820183286e-1}
00260   },
00261   {
00262     8,
00263     {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
00264      {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00265      {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00266      {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00267      {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00268      {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00269      {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00270      {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
00271     {1.012285362903762591525313543099621901154e-1,
00272      2.223810344533744705443559944262408844301e-1,
00273      3.137066458778872873379622019866013132603e-1,
00274      3.626837833783619829651504492771956121941e-1,
00275      3.626837833783619829651504492771956121941e-1,
00276      3.137066458778872873379622019866013132603e-1,
00277      2.223810344533744705443559944262408844301e-1,
00278      1.012285362903762591525313543099621901154e-1}
00279   },
00280   {
00281     8,
00282     {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
00283      {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00284      {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00285      {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00286      {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
00287      {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
00288      {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
00289      {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
00290     {1.012285362903762591525313543099621901154e-1,
00291      2.223810344533744705443559944262408844301e-1,
00292      3.137066458778872873379622019866013132603e-1,
00293      3.626837833783619829651504492771956121941e-1,
00294      3.626837833783619829651504492771956121941e-1,
00295      3.137066458778872873379622019866013132603e-1,
00296      2.223810344533744705443559944262408844301e-1,
00297      1.012285362903762591525313543099621901154e-1}
00298   },
00299   {
00300     9,
00301     {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
00302      {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00303      {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00304      {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00305      {0e0, 0.0, 0.0},
00306      {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00307      {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00308      {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00309      {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
00310     {8.127438836157441197189215811052365067566e-2,
00311      1.806481606948574040584720312429128095143e-1,
00312      2.606106964029354623187428694186328497718e-1,
00313      3.123470770400028400686304065844436655988e-1,
00314      3.302393550012597631645250692869740488788e-1,
00315      3.123470770400028400686304065844436655988e-1,
00316      2.606106964029354623187428694186328497718e-1,
00317      1.806481606948574040584720312429128095143e-1,
00318      8.127438836157441197189215811052365067566e-2}
00319   },
00320   {
00321     9,
00322     {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
00323      {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00324      {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00325      {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00326      {0e0, 0.0, 0.0},
00327      {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
00328      {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
00329      {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
00330      {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
00331     {8.127438836157441197189215811052365067566e-2,
00332      1.806481606948574040584720312429128095143e-1,
00333      2.606106964029354623187428694186328497718e-1,
00334      3.123470770400028400686304065844436655988e-1,
00335      3.302393550012597631645250692869740488788e-1,
00336      3.123470770400028400686304065844436655988e-1,
00337      2.606106964029354623187428694186328497718e-1,
00338      1.806481606948574040584720312429128095143e-1,
00339      8.127438836157441197189215811052365067566e-2}
00340   },
00341   {
00342     10,
00343     {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
00344      {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00345      {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00346      {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00347      {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00348      {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00349      {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00350      {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00351      {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00352      {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
00353     {6.667134430868813759356880989333179285786e-2,
00354      1.494513491505805931457763396576973324026e-1,
00355      2.190863625159820439955349342281631924588e-1,
00356      2.692667193099963550912269215694693528598e-1,
00357      2.95524224714752870173892994651338329421e-1,
00358      2.95524224714752870173892994651338329421e-1,
00359      2.692667193099963550912269215694693528598e-1,
00360      2.190863625159820439955349342281631924588e-1,
00361      1.494513491505805931457763396576973324026e-1,
00362      6.667134430868813759356880989333179285786e-2}
00363   },
00364   {
00365     10,
00366     {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
00367      {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00368      {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00369      {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00370      {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00371      {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
00372      {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
00373      {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
00374      {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
00375      {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
00376     {6.667134430868813759356880989333179285786e-2,
00377      1.494513491505805931457763396576973324026e-1,
00378      2.190863625159820439955349342281631924588e-1,
00379      2.692667193099963550912269215694693528598e-1,
00380      2.95524224714752870173892994651338329421e-1,
00381      2.95524224714752870173892994651338329421e-1,
00382      2.692667193099963550912269215694693528598e-1,
00383      2.190863625159820439955349342281631924588e-1,
00384      1.494513491505805931457763396576973324026e-1,
00385      6.667134430868813759356880989333179285786e-2}
00386   },
00387   {
00388     11,
00389     {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
00390      {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00391      {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00392      {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00393      {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00394      {0e0, 0.0, 0.0},
00395      {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00396      {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00397      {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00398      {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00399      {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
00400     {5.566856711617366648275372044254857872852e-2,
00401      1.255803694649046246346942992239401001976e-1,
00402      1.862902109277342514260976414316558916913e-1,
00403      2.331937645919904799185237048431751394318e-1,
00404      2.628045445102466621806888698905091953728e-1,
00405      2.72925086777900630714483528336342189156e-1,
00406      2.628045445102466621806888698905091953728e-1,
00407      2.331937645919904799185237048431751394318e-1,
00408      1.862902109277342514260976414316558916913e-1,
00409      1.255803694649046246346942992239401001976e-1,
00410      5.566856711617366648275372044254857872852e-2}
00411   },
00412   {
00413     11,
00414     {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
00415      {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00416      {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00417      {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00418      {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00419      {0e0, 0.0, 0.0},
00420      {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
00421      {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
00422      {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
00423      {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
00424      {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
00425     {5.566856711617366648275372044254857872852e-2,
00426      1.255803694649046246346942992239401001976e-1,
00427      1.862902109277342514260976414316558916913e-1,
00428      2.331937645919904799185237048431751394318e-1,
00429      2.628045445102466621806888698905091953728e-1,
00430      2.72925086777900630714483528336342189156e-1,
00431      2.628045445102466621806888698905091953728e-1,
00432      2.331937645919904799185237048431751394318e-1,
00433      1.862902109277342514260976414316558916913e-1,
00434      1.255803694649046246346942992239401001976e-1,
00435      5.566856711617366648275372044254857872852e-2}
00436   },
00437   {
00438     12,
00439     { // points
00440      {.9815606342467192506905490901492808229602    ,0.0, 0.0},
00441      {.9041172563704748566784658661190961925376    ,0.0, 0.0},
00442      {.7699026741943046870368938332128180759849    ,0.0, 0.0},
00443      {.5873179542866174472967024189405342803691    ,0.0, 0.0},
00444      {.3678314989981801937526915366437175612564    ,0.0, 0.0},
00445      {.1252334085114689154724413694638531299834    ,0.0, 0.0},
00446      {-.1252334085114689154724413694638531299834   ,0.0, 0.0},
00447      {-.3678314989981801937526915366437175612564   ,0.0, 0.0},
00448      {-.5873179542866174472967024189405342803691   ,0.0, 0.0},
00449      {-.7699026741943046870368938332128180759849   ,0.0, 0.0},
00450      {-.9041172563704748566784658661190961925376   ,0.0, 0.0},
00451      {-.9815606342467192506905490901492808229602   ,0.0, 0.0}
00452     },
00453     { // weights
00454      .04717533638651182719461596148501706031703,
00455      .1069393259953184309602547181939962242146,
00456      .160078328543346226334652529543359071872,
00457      .2031674267230659217490644558097983765065,
00458      .2334925365383548087608498989248780562594,
00459      .2491470458134027850005624360429512108305,
00460       .2491470458134027850005624360429512108305,
00461       .2334925365383548087608498989248780562594,
00462       .2031674267230659217490644558097983765065,
00463       .160078328543346226334652529543359071872,
00464       .1069393259953184309602547181939962242146,
00465       .04717533638651182719461596148501706031703
00466     }
00467   },
00468   {
00469     12,
00470     { // points
00471      {.9815606342467192506905490901492808229602    ,0.0, 0.0},
00472      {.9041172563704748566784658661190961925376    ,0.0, 0.0},
00473      {.7699026741943046870368938332128180759849    ,0.0, 0.0},
00474      {.5873179542866174472967024189405342803691    ,0.0, 0.0},
00475      {.3678314989981801937526915366437175612564    ,0.0, 0.0},
00476      {.1252334085114689154724413694638531299834    ,0.0, 0.0},
00477      {-.1252334085114689154724413694638531299834   ,0.0, 0.0},
00478      {-.3678314989981801937526915366437175612564   ,0.0, 0.0},
00479      {-.5873179542866174472967024189405342803691   ,0.0, 0.0},
00480      {-.7699026741943046870368938332128180759849   ,0.0, 0.0},
00481      {-.9041172563704748566784658661190961925376   ,0.0, 0.0},
00482      {-.9815606342467192506905490901492808229602   ,0.0, 0.0}
00483     },
00484     { // weights
00485      .04717533638651182719461596148501706031703,
00486      .1069393259953184309602547181939962242146,
00487      .160078328543346226334652529543359071872,
00488      .2031674267230659217490644558097983765065,
00489      .2334925365383548087608498989248780562594,
00490      .2491470458134027850005624360429512108305,
00491       .2491470458134027850005624360429512108305,
00492       .2334925365383548087608498989248780562594,
00493       .2031674267230659217490644558097983765065,
00494       .160078328543346226334652529543359071872,
00495       .1069393259953184309602547181939962242146,
00496       .04717533638651182719461596148501706031703
00497     }
00498   },
00499   {
00500     13,
00501     { // points
00502      {.984183054718588149472829448807109611065     ,0.0, 0.0},
00503      {.9175983992229779652065478365007195123905    ,0.0, 0.0},
00504      {.8015780907333099127942064895828598903056    ,0.0, 0.0},
00505      {.6423493394403402206439846069955156500717    ,0.0, 0.0},
00506      {.4484927510364468528779128521276398678019    ,0.0, 0.0},
00507      {.2304583159551347940655281210979888352115    ,0.0, 0.0},
00508      { 0                                           ,0.0, 0.0},
00509      {-.2304583159551347940655281210979888352115   ,0.0, 0.0},
00510      {-.4484927510364468528779128521276398678019   ,0.0, 0.0},
00511      {-.6423493394403402206439846069955156500717   ,0.0, 0.0},
00512      {-.8015780907333099127942064895828598903056   ,0.0, 0.0},
00513      {-.9175983992229779652065478365007195123905   ,0.0, 0.0},
00514      {-.984183054718588149472829448807109611065    ,0.0, 0.0}
00515     },
00516     { // weights
00517      .04048400476531587952002159220098606004199,
00518      .09212149983772844791442177595379712092368,
00519      .1388735102197872384636017768688714676219,
00520      .1781459807619457382800466919960979955128,
00521      .2078160475368885023125232193060527633866,
00522      .2262831802628972384120901860397766184348,
00523      .2325515532308739101945895152688359481566,
00524      .2262831802628972384120901860397766184348,
00525      .2078160475368885023125232193060527633866,
00526      .1781459807619457382800466919960979955128,
00527      .1388735102197872384636017768688714676219,
00528      .09212149983772844791442177595379712092368,
00529      .04048400476531587952002159220098606004199
00530     }
00531   },
00532   {
00533     13,
00534     { // points
00535      {.984183054718588149472829448807109611065     ,0.0, 0.0},
00536      {.9175983992229779652065478365007195123905    ,0.0, 0.0},
00537      {.8015780907333099127942064895828598903056    ,0.0, 0.0},
00538      {.6423493394403402206439846069955156500717    ,0.0, 0.0},
00539      {.4484927510364468528779128521276398678019    ,0.0, 0.0},
00540      {.2304583159551347940655281210979888352115    ,0.0, 0.0},
00541      { 0                                           ,0.0, 0.0},
00542      {-.2304583159551347940655281210979888352115   ,0.0, 0.0},
00543      {-.4484927510364468528779128521276398678019   ,0.0, 0.0},
00544      {-.6423493394403402206439846069955156500717   ,0.0, 0.0},
00545      {-.8015780907333099127942064895828598903056   ,0.0, 0.0},
00546      {-.9175983992229779652065478365007195123905   ,0.0, 0.0},
00547      {-.984183054718588149472829448807109611065    ,0.0, 0.0}
00548     },
00549     { // weights
00550      .04048400476531587952002159220098606004199,
00551      .09212149983772844791442177595379712092368,
00552      .1388735102197872384636017768688714676219,
00553      .1781459807619457382800466919960979955128,
00554      .2078160475368885023125232193060527633866,
00555      .2262831802628972384120901860397766184348,
00556      .2325515532308739101945895152688359481566,
00557      .2262831802628972384120901860397766184348,
00558      .2078160475368885023125232193060527633866,
00559      .1781459807619457382800466919960979955128,
00560      .1388735102197872384636017768688714676219,
00561      .09212149983772844791442177595379712092368,
00562      .04048400476531587952002159220098606004199
00563     }
00564   },
00565   {
00566     14,
00567     { // points
00568      {.9862838086968123388415972667040528016761    ,0.0, 0.0},
00569      {.928434883663573517336391139377874264477     ,0.0, 0.0},
00570      {.8272013150697649931897947426503949610397    ,0.0, 0.0},
00571      {.6872929048116854701480198030193341375384    ,0.0, 0.0},
00572      {.5152486363581540919652907185511886623089    ,0.0, 0.0},
00573      {.3191123689278897604356718241684754668343    ,0.0, 0.0},
00574      {.108054948707343662066244650219834747612     ,0.0, 0.0},
00575      {-.108054948707343662066244650219834747612    ,0.0, 0.0},
00576      {-.3191123689278897604356718241684754668343   ,0.0, 0.0},
00577      {-.5152486363581540919652907185511886623089   ,0.0, 0.0},
00578      {-.6872929048116854701480198030193341375384   ,0.0, 0.0},
00579      {-.8272013150697649931897947426503949610397   ,0.0, 0.0},
00580      {-.928434883663573517336391139377874264477    ,0.0, 0.0},
00581      {-.9862838086968123388415972667040528016761   ,0.0, 0.0}
00582     },
00583     { // weights
00584      .03511946033175186303183287613819178061971,
00585      .0801580871597602098056332770628543095837,
00586      .1215185706879031846894148090724766259567,
00587      .1572031671581935345696019386238421566057,
00588      .1855383974779378137417165901251570362489,
00589      .2051984637212956039659240656612180557103,
00590      .215263853463157790195876443316260035275,
00591      .215263853463157790195876443316260035275,
00592      .2051984637212956039659240656612180557103,
00593      .1855383974779378137417165901251570362489,
00594      .1572031671581935345696019386238421566057,
00595      .1215185706879031846894148090724766259567,
00596      .0801580871597602098056332770628543095837,
00597      .03511946033175186303183287613819178061971
00598     }
00599   },
00600   {
00601     14,
00602     { // points
00603      {.9862838086968123388415972667040528016761    ,0.0, 0.0},
00604      {.928434883663573517336391139377874264477     ,0.0, 0.0},
00605      {.8272013150697649931897947426503949610397    ,0.0, 0.0},
00606      {.6872929048116854701480198030193341375384    ,0.0, 0.0},
00607      {.5152486363581540919652907185511886623089    ,0.0, 0.0},
00608      {.3191123689278897604356718241684754668343    ,0.0, 0.0},
00609      {.108054948707343662066244650219834747612     ,0.0, 0.0},
00610      {-.108054948707343662066244650219834747612    ,0.0, 0.0},
00611      {-.3191123689278897604356718241684754668343   ,0.0, 0.0},
00612      {-.5152486363581540919652907185511886623089   ,0.0, 0.0},
00613      {-.6872929048116854701480198030193341375384   ,0.0, 0.0},
00614      {-.8272013150697649931897947426503949610397   ,0.0, 0.0},
00615      {-.928434883663573517336391139377874264477    ,0.0, 0.0},
00616      {-.9862838086968123388415972667040528016761   ,0.0, 0.0}
00617     },
00618     { // weights
00619      .03511946033175186303183287613819178061971,
00620      .0801580871597602098056332770628543095837,
00621      .1215185706879031846894148090724766259567,
00622      .1572031671581935345696019386238421566057,
00623      .1855383974779378137417165901251570362489,
00624      .2051984637212956039659240656612180557103,
00625      .215263853463157790195876443316260035275,
00626      .215263853463157790195876443316260035275,
00627      .2051984637212956039659240656612180557103,
00628      .1855383974779378137417165901251570362489,
00629      .1572031671581935345696019386238421566057,
00630      .1215185706879031846894148090724766259567,
00631      .0801580871597602098056332770628543095837,
00632      .03511946033175186303183287613819178061971
00633     }
00634   },
00635   {
00636     15,
00637     { // points
00638      {.987992518020485428489565718586612581147     ,0.0, 0.0},
00639      {.937273392400705904307758947710209471244     ,0.0, 0.0},
00640      {.8482065834104272162006483207742168513663    ,0.0, 0.0},
00641      {.7244177313601700474161860546139380096309    ,0.0, 0.0},
00642      {.5709721726085388475372267372539106412384    ,0.0, 0.0},
00643      {.3941513470775633698972073709810454683628    ,0.0, 0.0},
00644      {.2011940939974345223006283033945962078128    ,0.0, 0.0},
00645      { 0                                           ,0.0, 0.0},
00646      {-.2011940939974345223006283033945962078128   ,0.0, 0.0},
00647      {-.3941513470775633698972073709810454683628   ,0.0, 0.0},
00648      {-.5709721726085388475372267372539106412384   ,0.0, 0.0},
00649      {-.7244177313601700474161860546139380096309   ,0.0, 0.0},
00650      {-.8482065834104272162006483207742168513663   ,0.0, 0.0},
00651      {-.937273392400705904307758947710209471244    ,0.0, 0.0},
00652      {-.987992518020485428489565718586612581147    ,0.0, 0.0}
00653     },
00654     { // weights
00655      .03075324199611726835462839357720441772175,
00656      .07036604748810812470926741645066733846671,
00657      .1071592204671719350118695466858693034155,
00658      .1395706779261543144478047945110283225209,
00659      .1662692058169939335532008604812088111309,
00660      .1861610000155622110268005618664228245062,
00661      .1984314853271115764561183264438393248187,
00662      .2025782419255612728806201999675193148387,
00663      .1984314853271115764561183264438393248187,
00664      .1861610000155622110268005618664228245062,
00665      .1662692058169939335532008604812088111309,
00666      .1395706779261543144478047945110283225209,
00667      .1071592204671719350118695466858693034155,
00668      .07036604748810812470926741645066733846671,
00669      .03075324199611726835462839357720441772175
00670     }
00671   },
00672   {
00673     15,
00674     { // points
00675      {.987992518020485428489565718586612581147     ,0.0, 0.0},
00676      {.937273392400705904307758947710209471244     ,0.0, 0.0},
00677      {.8482065834104272162006483207742168513663    ,0.0, 0.0},
00678      {.7244177313601700474161860546139380096309    ,0.0, 0.0},
00679      {.5709721726085388475372267372539106412384    ,0.0, 0.0},
00680      {.3941513470775633698972073709810454683628    ,0.0, 0.0},
00681      {.2011940939974345223006283033945962078128    ,0.0, 0.0},
00682      { 0                                           ,0.0, 0.0},
00683      {-.2011940939974345223006283033945962078128   ,0.0, 0.0},
00684      {-.3941513470775633698972073709810454683628   ,0.0, 0.0},
00685      {-.5709721726085388475372267372539106412384   ,0.0, 0.0},
00686      {-.7244177313601700474161860546139380096309   ,0.0, 0.0},
00687      {-.8482065834104272162006483207742168513663   ,0.0, 0.0},
00688      {-.937273392400705904307758947710209471244    ,0.0, 0.0},
00689      {-.987992518020485428489565718586612581147    ,0.0, 0.0}
00690     },
00691     { // weights
00692      .03075324199611726835462839357720441772175,
00693      .07036604748810812470926741645066733846671,
00694      .1071592204671719350118695466858693034155,
00695      .1395706779261543144478047945110283225209,
00696      .1662692058169939335532008604812088111309,
00697      .1861610000155622110268005618664228245062,
00698      .1984314853271115764561183264438393248187,
00699      .2025782419255612728806201999675193148387,
00700      .1984314853271115764561183264438393248187,
00701      .1861610000155622110268005618664228245062,
00702      .1662692058169939335532008604812088111309,
00703      .1395706779261543144478047945110283225209,
00704      .1071592204671719350118695466858693034155,
00705      .07036604748810812470926741645066733846671,
00706      .03075324199611726835462839357720441772175
00707     }
00708   },
00709   {
00710     16,
00711     { // points
00712      {.9894009349916499325961541734503326274263    ,0.0, 0.0},
00713      {.9445750230732325760779884155346083450911    ,0.0, 0.0},
00714      {.8656312023878317438804678977123931323873    ,0.0, 0.0},
00715      {.7554044083550030338951011948474422683538    ,0.0, 0.0},
00716      {.6178762444026437484466717640487910189919    ,0.0, 0.0},
00717      {.45801677765722738634241944298357757354      ,0.0, 0.0},
00718      {.2816035507792589132304605014604961064861    ,0.0, 0.0},
00719      {.09501250983763744018531933542495806313035   ,0.0, 0.0},
00720      {-.09501250983763744018531933542495806313035  ,0.0, 0.0},
00721      {-.2816035507792589132304605014604961064861   ,0.0, 0.0},
00722      {-.45801677765722738634241944298357757354     ,0.0, 0.0},
00723      {-.6178762444026437484466717640487910189919   ,0.0, 0.0},
00724      {-.7554044083550030338951011948474422683538   ,0.0, 0.0},
00725      {-.8656312023878317438804678977123931323873   ,0.0, 0.0},
00726      {-.9445750230732325760779884155346083450911   ,0.0, 0.0},
00727      {-.9894009349916499325961541734503326274263   ,0.0, 0.0}
00728     },
00729     { // weights
00730      .02715245941175409485178057245601810351227,
00731      .06225352393864789286284383699437769427499,
00732      .09515851168249278480992510760224622635526,
00733      .1246289712555338720524762821920164201449,
00734      .1495959888165767320815017305474785489705,
00735      .1691565193950025381893120790303599622116,
00736      .1826034150449235888667636679692199393836,
00737      .1894506104550684962853967232082831051469,
00738      .1894506104550684962853967232082831051469,
00739      .1826034150449235888667636679692199393836,
00740      .1691565193950025381893120790303599622116,
00741      .1495959888165767320815017305474785489705,
00742      .1246289712555338720524762821920164201449,
00743      .09515851168249278480992510760224622635526,
00744      .06225352393864789286284383699437769427499,
00745      .02715245941175409485178057245601810351227
00746     }
00747   },
00748   {
00749     16,
00750     { // points
00751      {.9894009349916499325961541734503326274263    ,0.0, 0.0},
00752      {.9445750230732325760779884155346083450911    ,0.0, 0.0},
00753      {.8656312023878317438804678977123931323873    ,0.0, 0.0},
00754      {.7554044083550030338951011948474422683538    ,0.0, 0.0},
00755      {.6178762444026437484466717640487910189919    ,0.0, 0.0},
00756      {.45801677765722738634241944298357757354      ,0.0, 0.0},
00757      {.2816035507792589132304605014604961064861    ,0.0, 0.0},
00758      {.09501250983763744018531933542495806313035   ,0.0, 0.0},
00759      {-.09501250983763744018531933542495806313035  ,0.0, 0.0},
00760      {-.2816035507792589132304605014604961064861   ,0.0, 0.0},
00761      {-.45801677765722738634241944298357757354     ,0.0, 0.0},
00762      {-.6178762444026437484466717640487910189919   ,0.0, 0.0},
00763      {-.7554044083550030338951011948474422683538   ,0.0, 0.0},
00764      {-.8656312023878317438804678977123931323873   ,0.0, 0.0},
00765      {-.9445750230732325760779884155346083450911   ,0.0, 0.0},
00766      {-.9894009349916499325961541734503326274263   ,0.0, 0.0}
00767     },
00768     { // weights
00769      .02715245941175409485178057245601810351227,
00770      .06225352393864789286284383699437769427499,
00771      .09515851168249278480992510760224622635526,
00772      .1246289712555338720524762821920164201449,
00773      .1495959888165767320815017305474785489705,
00774      .1691565193950025381893120790303599622116,
00775      .1826034150449235888667636679692199393836,
00776      .1894506104550684962853967232082831051469,
00777      .1894506104550684962853967232082831051469,
00778      .1826034150449235888667636679692199393836,
00779      .1691565193950025381893120790303599622116,
00780      .1495959888165767320815017305474785489705,
00781      .1246289712555338720524762821920164201449,
00782      .09515851168249278480992510760224622635526,
00783      .06225352393864789286284383699437769427499,
00784      .02715245941175409485178057245601810351227
00785     }
00786   },
00787   {
00788     17,
00789     { // points
00790      {.9905754753144173356754340199406652765078    ,0.0, 0.0},
00791      {.9506755217687677612227169578958030214434    ,0.0, 0.0},
00792      {.8802391537269859021229556944881556926234    ,0.0, 0.0},
00793      {.781514003896801406925230055520476050224     ,0.0, 0.0},
00794      {.6576711592166907658503022166430023351478    ,0.0, 0.0},
00795      {.5126905370864769678862465686295518745829    ,0.0, 0.0},
00796      {.3512317634538763152971855170953460050405    ,0.0, 0.0},
00797      {.1784841814958478558506774936540655574754    ,0.0, 0.0},
00798      { 0                                           ,0.0, 0.0},
00799      {-.1784841814958478558506774936540655574754   ,0.0, 0.0},
00800      {-.3512317634538763152971855170953460050405   ,0.0, 0.0},
00801      {-.5126905370864769678862465686295518745829   ,0.0, 0.0},
00802      {-.6576711592166907658503022166430023351478   ,0.0, 0.0},
00803      {-.781514003896801406925230055520476050224    ,0.0, 0.0},
00804      {-.8802391537269859021229556944881556926234   ,0.0, 0.0},
00805      {-.9506755217687677612227169578958030214434   ,0.0, 0.0},
00806      {-.9905754753144173356754340199406652765078   ,0.0, 0.0}
00807     },
00808     { // weights
00809      .0241483028685479319601100262875653246917,
00810      .05545952937398720112944016535824466051285,
00811      .08503614831717918088353537019106207385049,
00812      .1118838471934039710947883856263559267358,
00813      .1351363684685254732863199817023501973721,
00814      .1540457610768102880814315948019586119405,
00815      .1680041021564500445099706637883231550212,
00816      .1765627053669926463252709901131972391509,
00817       .1794464703562065254582656442618856214488,
00818       .1765627053669926463252709901131972391509,
00819       .1680041021564500445099706637883231550212,
00820       .1540457610768102880814315948019586119405,
00821       .1351363684685254732863199817023501973721,
00822       .1118838471934039710947883856263559267358,
00823       .08503614831717918088353537019106207385049,
00824       .05545952937398720112944016535824466051285,
00825       .0241483028685479319601100262875653246917
00826     }
00827   },
00828   {
00829     17,
00830     { // points
00831      {.9905754753144173356754340199406652765078    ,0.0, 0.0},
00832      {.9506755217687677612227169578958030214434    ,0.0, 0.0},
00833      {.8802391537269859021229556944881556926234    ,0.0, 0.0},
00834      {.781514003896801406925230055520476050224     ,0.0, 0.0},
00835      {.6576711592166907658503022166430023351478    ,0.0, 0.0},
00836      {.5126905370864769678862465686295518745829    ,0.0, 0.0},
00837      {.3512317634538763152971855170953460050405    ,0.0, 0.0},
00838      {.1784841814958478558506774936540655574754    ,0.0, 0.0},
00839      { 0                                           ,0.0, 0.0},
00840      {-.1784841814958478558506774936540655574754   ,0.0, 0.0},
00841      {-.3512317634538763152971855170953460050405   ,0.0, 0.0},
00842      {-.5126905370864769678862465686295518745829   ,0.0, 0.0},
00843      {-.6576711592166907658503022166430023351478   ,0.0, 0.0},
00844      {-.781514003896801406925230055520476050224    ,0.0, 0.0},
00845      {-.8802391537269859021229556944881556926234   ,0.0, 0.0},
00846      {-.9506755217687677612227169578958030214434   ,0.0, 0.0},
00847      {-.9905754753144173356754340199406652765078   ,0.0, 0.0}
00848     },
00849     { // weights
00850      .0241483028685479319601100262875653246917,
00851      .05545952937398720112944016535824466051285,
00852      .08503614831717918088353537019106207385049,
00853      .1118838471934039710947883856263559267358,
00854      .1351363684685254732863199817023501973721,
00855      .1540457610768102880814315948019586119405,
00856      .1680041021564500445099706637883231550212,
00857      .1765627053669926463252709901131972391509,
00858       .1794464703562065254582656442618856214488,
00859       .1765627053669926463252709901131972391509,
00860       .1680041021564500445099706637883231550212,
00861       .1540457610768102880814315948019586119405,
00862       .1351363684685254732863199817023501973721,
00863       .1118838471934039710947883856263559267358,
00864       .08503614831717918088353537019106207385049,
00865       .05545952937398720112944016535824466051285,
00866       .0241483028685479319601100262875653246917
00867     }
00868   },
00869   {
00870     18,
00871     { // points
00872      {.9915651684209309467300160047061507702526    ,0.0, 0.0},
00873      {.9558239495713977551811958929297763099728    ,0.0, 0.0},
00874      {.8926024664975557392060605911271455154079    ,0.0, 0.0},
00875      {.8037049589725231156824174550145907971033    ,0.0, 0.0},
00876      {.6916870430603532078748910812888483894523    ,0.0, 0.0},
00877      {.5597708310739475346078715485253291369276    ,0.0, 0.0},
00878      {.411751161462842646035931793833051637079     ,0.0, 0.0},
00879      {.2518862256915055095889728548779112301629    ,0.0, 0.0},
00880      {.08477501304173530124226185293578381173332   ,0.0, 0.0},
00881      {-.08477501304173530124226185293578381173332  ,0.0, 0.0},
00882      {-.2518862256915055095889728548779112301629   ,0.0, 0.0},
00883      {-.411751161462842646035931793833051637079    ,0.0, 0.0},
00884      {-.5597708310739475346078715485253291369276   ,0.0, 0.0},
00885      {-.6916870430603532078748910812888483894523   ,0.0, 0.0},
00886      {-.8037049589725231156824174550145907971033   ,0.0, 0.0},
00887      {-.8926024664975557392060605911271455154079   ,0.0, 0.0},
00888      {-.9558239495713977551811958929297763099728   ,0.0, 0.0},
00889      {-.9915651684209309467300160047061507702526   ,0.0, 0.0}
00890     },
00891     { // weights
00892      .02161601352648331031334271026645246938769,
00893      .04971454889496979645333494620263864168087,
00894      .07642573025488905652912967761663652560532,
00895      .1009420441062871655628139849248346070628,
00896      .1225552067114784601845191268002015552282,
00897      .1406429146706506512047313037519472280955,
00898      .1546846751262652449254180038363747721932,
00899      .1642764837458327229860537764659275904123,
00900       .1691423829631435918406564701349866103341,
00901       .1691423829631435918406564701349866103341,
00902       .1642764837458327229860537764659275904123,
00903       .1546846751262652449254180038363747721932,
00904       .1406429146706506512047313037519472280955,
00905       .1225552067114784601845191268002015552282,
00906       .1009420441062871655628139849248346070628,
00907       .07642573025488905652912967761663652560532,
00908       .04971454889496979645333494620263864168087,
00909       .02161601352648331031334271026645246938769
00910     }
00911   },
00912   {
00913     18,
00914     { // points
00915      {.9915651684209309467300160047061507702526    ,0.0, 0.0},
00916      {.9558239495713977551811958929297763099728    ,0.0, 0.0},
00917      {.8926024664975557392060605911271455154079    ,0.0, 0.0},
00918      {.8037049589725231156824174550145907971033    ,0.0, 0.0},
00919      {.6916870430603532078748910812888483894523    ,0.0, 0.0},
00920      {.5597708310739475346078715485253291369276    ,0.0, 0.0},
00921      {.411751161462842646035931793833051637079     ,0.0, 0.0},
00922      {.2518862256915055095889728548779112301629    ,0.0, 0.0},
00923      {.08477501304173530124226185293578381173332   ,0.0, 0.0},
00924      {-.08477501304173530124226185293578381173332  ,0.0, 0.0},
00925      {-.2518862256915055095889728548779112301629   ,0.0, 0.0},
00926      {-.411751161462842646035931793833051637079    ,0.0, 0.0},
00927      {-.5597708310739475346078715485253291369276   ,0.0, 0.0},
00928      {-.6916870430603532078748910812888483894523   ,0.0, 0.0},
00929      {-.8037049589725231156824174550145907971033   ,0.0, 0.0},
00930      {-.8926024664975557392060605911271455154079   ,0.0, 0.0},
00931      {-.9558239495713977551811958929297763099728   ,0.0, 0.0},
00932      {-.9915651684209309467300160047061507702526   ,0.0, 0.0}
00933     },
00934     { // weights
00935      .02161601352648331031334271026645246938769,
00936      .04971454889496979645333494620263864168087,
00937      .07642573025488905652912967761663652560532,
00938      .1009420441062871655628139849248346070628,
00939      .1225552067114784601845191268002015552282,
00940      .1406429146706506512047313037519472280955,
00941      .1546846751262652449254180038363747721932,
00942      .1642764837458327229860537764659275904123,
00943       .1691423829631435918406564701349866103341,
00944       .1691423829631435918406564701349866103341,
00945       .1642764837458327229860537764659275904123,
00946       .1546846751262652449254180038363747721932,
00947       .1406429146706506512047313037519472280955,
00948       .1225552067114784601845191268002015552282,
00949       .1009420441062871655628139849248346070628,
00950       .07642573025488905652912967761663652560532,
00951       .04971454889496979645333494620263864168087,
00952       .02161601352648331031334271026645246938769
00953     }
00954   },
00955   {
00956     19,
00957     { // points
00958      {.9924068438435844031890176702532604935893    ,0.0, 0.0},
00959      {.9602081521348300308527788406876515266151    ,0.0, 0.0},
00960      {.9031559036148179016426609285323124878094    ,0.0, 0.0},
00961      {.8227146565371428249789224867127139017745    ,0.0, 0.0},
00962      {.7209661773352293786170958608237816296571    ,0.0, 0.0},
00963      {.6005453046616810234696381649462392798683    ,0.0, 0.0},
00964      {.4645707413759609457172671481041023679763    ,0.0, 0.0},
00965      {.3165640999636298319901173288498449178923    ,0.0, 0.0},
00966      {.1603586456402253758680961157407435495049    ,0.0, 0.0},
00967      { 0                                           ,0.0, 0.0},
00968      {-.1603586456402253758680961157407435495049   ,0.0, 0.0},
00969      {-.3165640999636298319901173288498449178923   ,0.0, 0.0},
00970      {-.4645707413759609457172671481041023679763   ,0.0, 0.0},
00971      {-.6005453046616810234696381649462392798683   ,0.0, 0.0},
00972      {-.7209661773352293786170958608237816296571   ,0.0, 0.0},
00973      {-.8227146565371428249789224867127139017745   ,0.0, 0.0},
00974      {-.9031559036148179016426609285323124878094   ,0.0, 0.0},
00975      {-.9602081521348300308527788406876515266151   ,0.0, 0.0},
00976      {-.9924068438435844031890176702532604935893   ,0.0, 0.0}
00977     },
00978     { // weights
00979      .01946178822972647703631204146443843575291,
00980      .04481422676569960033283815740199421195175,
00981      .06904454273764122658070825800601304496185,
00982      .09149002162244999946446209412383965266091,
00983      .1115666455473339947160239016817659974813,
00984      .1287539625393362276755157848568771170558,
00985      .1426067021736066117757461094419029724757,
00986      .152766042065859666778855400897662998461,
00987      .1589688433939543476499564394650472016788,
00988       .1610544498487836959791636253209167350399,
00989       .1589688433939543476499564394650472016788,
00990       .152766042065859666778855400897662998461,
00991       .1426067021736066117757461094419029724757,
00992       .1287539625393362276755157848568771170558,
00993       .1115666455473339947160239016817659974813,
00994       .09149002162244999946446209412383965266091,
00995       .06904454273764122658070825800601304496185,
00996       .04481422676569960033283815740199421195175,
00997       .01946178822972647703631204146443843575291
00998     }
00999   },
01000   {
01001     19,
01002     { // points
01003      {.9924068438435844031890176702532604935893    ,0.0, 0.0},
01004      {.9602081521348300308527788406876515266151    ,0.0, 0.0},
01005      {.9031559036148179016426609285323124878094    ,0.0, 0.0},
01006      {.8227146565371428249789224867127139017745    ,0.0, 0.0},
01007      {.7209661773352293786170958608237816296571    ,0.0, 0.0},
01008      {.6005453046616810234696381649462392798683    ,0.0, 0.0},
01009      {.4645707413759609457172671481041023679763    ,0.0, 0.0},
01010      {.3165640999636298319901173288498449178923    ,0.0, 0.0},
01011      {.1603586456402253758680961157407435495049    ,0.0, 0.0},
01012      { 0                                           ,0.0, 0.0},
01013      {-.1603586456402253758680961157407435495049   ,0.0, 0.0},
01014      {-.3165640999636298319901173288498449178923   ,0.0, 0.0},
01015      {-.4645707413759609457172671481041023679763   ,0.0, 0.0},
01016      {-.6005453046616810234696381649462392798683   ,0.0, 0.0},
01017      {-.7209661773352293786170958608237816296571   ,0.0, 0.0},
01018      {-.8227146565371428249789224867127139017745   ,0.0, 0.0},
01019      {-.9031559036148179016426609285323124878094   ,0.0, 0.0},
01020      {-.9602081521348300308527788406876515266151   ,0.0, 0.0},
01021      {-.9924068438435844031890176702532604935893   ,0.0, 0.0}
01022     },
01023     { // weights
01024      .01946178822972647703631204146443843575291,
01025      .04481422676569960033283815740199421195175,
01026      .06904454273764122658070825800601304496185,
01027      .09149002162244999946446209412383965266091,
01028      .1115666455473339947160239016817659974813,
01029      .1287539625393362276755157848568771170558,
01030      .1426067021736066117757461094419029724757,
01031      .152766042065859666778855400897662998461,
01032      .1589688433939543476499564394650472016788,
01033       .1610544498487836959791636253209167350399,
01034       .1589688433939543476499564394650472016788,
01035       .152766042065859666778855400897662998461,
01036       .1426067021736066117757461094419029724757,
01037       .1287539625393362276755157848568771170558,
01038       .1115666455473339947160239016817659974813,
01039       .09149002162244999946446209412383965266091,
01040       .06904454273764122658070825800601304496185,
01041       .04481422676569960033283815740199421195175,
01042       .01946178822972647703631204146443843575291
01043     }
01044   },
01045   {
01046     20,
01047     { // points
01048      {.9931285991850949247861223884713202782226    ,0.0, 0.0},
01049      {.9639719272779137912676661311972772219121    ,0.0, 0.0},
01050      {.9122344282513259058677524412032981130492    ,0.0, 0.0},
01051      {.8391169718222188233945290617015206853296    ,0.0, 0.0},
01052      {.7463319064601507926143050703556415903107    ,0.0, 0.0},
01053      {.6360536807265150254528366962262859367434    ,0.0, 0.0},
01054      {.5108670019508270980043640509552509984255    ,0.0, 0.0},
01055      {.3737060887154195606725481770249272373957    ,0.0, 0.0},
01056      {.2277858511416450780804961953685746247431    ,0.0, 0.0},
01057      {.0765265211334973337546404093988382110048    ,0.0, 0.0},
01058      {-.0765265211334973337546404093988382110048   ,0.0, 0.0},
01059      {-.2277858511416450780804961953685746247431   ,0.0, 0.0},
01060      {-.3737060887154195606725481770249272373957   ,0.0, 0.0},
01061      {-.5108670019508270980043640509552509984255   ,0.0, 0.0},
01062      {-.6360536807265150254528366962262859367434   ,0.0, 0.0},
01063      {-.7463319064601507926143050703556415903107   ,0.0, 0.0},
01064      {-.8391169718222188233945290617015206853296   ,0.0, 0.0},
01065      {-.9122344282513259058677524412032981130492   ,0.0, 0.0},
01066      {-.9639719272779137912676661311972772219121   ,0.0, 0.0},
01067      {-.9931285991850949247861223884713202782226   ,0.0, 0.0}
01068     },
01069     { // weights
01070      .01761400713915211831186196235185281636214,
01071      .04060142980038694133103995227493210987909,
01072      .0626720483341090635695065351870416063516,
01073      .08327674157670474872475814322204620610018,
01074      .1019301198172404350367501354803498761667,
01075      .118194531961518417312377377711382287005,
01076      .1316886384491766268984944997481631349161,
01077      .1420961093183820513292983250671649330345,
01078      .1491729864726037467878287370019694366927,
01079      .1527533871307258506980843319550975934919,
01080       .1527533871307258506980843319550975934919,
01081       .1491729864726037467878287370019694366927,
01082       .1420961093183820513292983250671649330345,
01083       .1316886384491766268984944997481631349161,
01084       .118194531961518417312377377711382287005,
01085       .1019301198172404350367501354803498761667,
01086       .08327674157670474872475814322204620610018,
01087       .0626720483341090635695065351870416063516,
01088       .04060142980038694133103995227493210987909,
01089       .01761400713915211831186196235185281636214
01090     }
01091   },
01092   {
01093     20,
01094     { // points
01095      {.9931285991850949247861223884713202782226    ,0.0, 0.0},
01096      {.9639719272779137912676661311972772219121    ,0.0, 0.0},
01097      {.9122344282513259058677524412032981130492    ,0.0, 0.0},
01098      {.8391169718222188233945290617015206853296    ,0.0, 0.0},
01099      {.7463319064601507926143050703556415903107    ,0.0, 0.0},
01100      {.6360536807265150254528366962262859367434    ,0.0, 0.0},
01101      {.5108670019508270980043640509552509984255    ,0.0, 0.0},
01102      {.3737060887154195606725481770249272373957    ,0.0, 0.0},
01103      {.2277858511416450780804961953685746247431    ,0.0, 0.0},
01104      {.0765265211334973337546404093988382110048    ,0.0, 0.0},
01105      {-.0765265211334973337546404093988382110048   ,0.0, 0.0},
01106      {-.2277858511416450780804961953685746247431   ,0.0, 0.0},
01107      {-.3737060887154195606725481770249272373957   ,0.0, 0.0},
01108      {-.5108670019508270980043640509552509984255   ,0.0, 0.0},
01109      {-.6360536807265150254528366962262859367434   ,0.0, 0.0},
01110      {-.7463319064601507926143050703556415903107   ,0.0, 0.0},
01111      {-.8391169718222188233945290617015206853296   ,0.0, 0.0},
01112      {-.9122344282513259058677524412032981130492   ,0.0, 0.0},
01113      {-.9639719272779137912676661311972772219121   ,0.0, 0.0},
01114      {-.9931285991850949247861223884713202782226   ,0.0, 0.0}
01115     },
01116     { // weights
01117      .01761400713915211831186196235185281636214,
01118      .04060142980038694133103995227493210987909,
01119      .0626720483341090635695065351870416063516,
01120      .08327674157670474872475814322204620610018,
01121      .1019301198172404350367501354803498761667,
01122      .118194531961518417312377377711382287005,
01123      .1316886384491766268984944997481631349161,
01124      .1420961093183820513292983250671649330345,
01125      .1491729864726037467878287370019694366927,
01126      .1527533871307258506980843319550975934919,
01127       .1527533871307258506980843319550975934919,
01128       .1491729864726037467878287370019694366927,
01129       .1420961093183820513292983250671649330345,
01130       .1316886384491766268984944997481631349161,
01131       .118194531961518417312377377711382287005,
01132       .1019301198172404350367501354803498761667,
01133       .08327674157670474872475814322204620610018,
01134       .0626720483341090635695065351870416063516,
01135       .04060142980038694133103995227493210987909,
01136       .01761400713915211831186196235185281636214
01137     }
01138   },
01139   {
01140     21,
01141     { // points
01142      {.9937521706203895002602420359379409291933    ,0.0, 0.0},
01143      {.9672268385663062943166222149076951614247    ,0.0, 0.0},
01144      {.9200993341504008287901871337149688941591    ,0.0, 0.0},
01145      {.8533633645833172836472506385875676702761    ,0.0, 0.0},
01146      {.768439963475677908615877851306228034821     ,0.0, 0.0},
01147      {.667138804197412319305966669990339162597     ,0.0, 0.0},
01148      {.5516188358872198070590187967243132866221    ,0.0, 0.0},
01149      {.4243421202074387835736688885437880520964    ,0.0, 0.0},
01150      {.288021316802401096600792516064600319909     ,0.0, 0.0},
01151      {.1455618541608950909370309823386863301163    ,0.0, 0.0},
01152      {0                                            ,0.0, 0.0},
01153      {-.1455618541608950909370309823386863301163   ,0.0, 0.0},
01154      {-.288021316802401096600792516064600319909    ,0.0, 0.0},
01155      {-.4243421202074387835736688885437880520964   ,0.0, 0.0},
01156      {-.5516188358872198070590187967243132866221   ,0.0, 0.0},
01157      {-.667138804197412319305966669990339162597    ,0.0, 0.0},
01158      {-.768439963475677908615877851306228034821    ,0.0, 0.0},
01159      {-.8533633645833172836472506385875676702761   ,0.0, 0.0},
01160      {-.9200993341504008287901871337149688941591   ,0.0, 0.0},
01161      {-.9672268385663062943166222149076951614247   ,0.0, 0.0},
01162      {-.9937521706203895002602420359379409291933   ,0.0, 0.0}
01163     },
01164     { // weights
01165      .01601722825777433332422461685847101526589,
01166      .03695378977085249379995066829932966618894,
01167      .05713442542685720828363582647244795749129,
01168      .07610011362837930201705165330018317922615,
01169      .09344442345603386155328974111393208848353,
01170      .1087972991671483776634745780701056420337,
01171      .1218314160537285341953671771257335983563,
01172      .132268938633337461781052574496775604329,
01173      .1398873947910731547221334238675831108928,
01174      .1445244039899700590638271665537525436099,
01175       .1460811336496904271919851476833711882448,
01176      .1445244039899700590638271665537525436099,
01177      .1398873947910731547221334238675831108928,
01178      .132268938633337461781052574496775604329,
01179      .1218314160537285341953671771257335983563,
01180      .1087972991671483776634745780701056420337,
01181      .09344442345603386155328974111393208848353,
01182      .07610011362837930201705165330018317922615,
01183      .05713442542685720828363582647244795749129,
01184      .03695378977085249379995066829932966618894,
01185      .01601722825777433332422461685847101526589
01186     }
01187   },
01188   {
01189     21,
01190     { // points
01191      {.9937521706203895002602420359379409291933    ,0.0, 0.0},
01192      {.9672268385663062943166222149076951614247    ,0.0, 0.0},
01193      {.9200993341504008287901871337149688941591    ,0.0, 0.0},
01194      {.8533633645833172836472506385875676702761    ,0.0, 0.0},
01195      {.768439963475677908615877851306228034821     ,0.0, 0.0},
01196      {.667138804197412319305966669990339162597     ,0.0, 0.0},
01197      {.5516188358872198070590187967243132866221    ,0.0, 0.0},
01198      {.4243421202074387835736688885437880520964    ,0.0, 0.0},
01199      {.288021316802401096600792516064600319909     ,0.0, 0.0},
01200      {.1455618541608950909370309823386863301163    ,0.0, 0.0},
01201      {0                                            ,0.0, 0.0},
01202      {-.1455618541608950909370309823386863301163   ,0.0, 0.0},
01203      {-.288021316802401096600792516064600319909    ,0.0, 0.0},
01204      {-.4243421202074387835736688885437880520964   ,0.0, 0.0},
01205      {-.5516188358872198070590187967243132866221   ,0.0, 0.0},
01206      {-.667138804197412319305966669990339162597    ,0.0, 0.0},
01207      {-.768439963475677908615877851306228034821    ,0.0, 0.0},
01208      {-.8533633645833172836472506385875676702761   ,0.0, 0.0},
01209      {-.9200993341504008287901871337149688941591   ,0.0, 0.0},
01210      {-.9672268385663062943166222149076951614247   ,0.0, 0.0},
01211      {-.9937521706203895002602420359379409291933   ,0.0, 0.0}
01212     },
01213     { // weights
01214      .01601722825777433332422461685847101526589,
01215      .03695378977085249379995066829932966618894,
01216      .05713442542685720828363582647244795749129,
01217      .07610011362837930201705165330018317922615,
01218      .09344442345603386155328974111393208848353,
01219      .1087972991671483776634745780701056420337,
01220      .1218314160537285341953671771257335983563,
01221      .132268938633337461781052574496775604329,
01222      .1398873947910731547221334238675831108928,
01223      .1445244039899700590638271665537525436099,
01224       .1460811336496904271919851476833711882448,
01225      .1445244039899700590638271665537525436099,
01226      .1398873947910731547221334238675831108928,
01227      .132268938633337461781052574496775604329,
01228      .1218314160537285341953671771257335983563,
01229      .1087972991671483776634745780701056420337,
01230      .09344442345603386155328974111393208848353,
01231      .07610011362837930201705165330018317922615,
01232      .05713442542685720828363582647244795749129,
01233      .03695378977085249379995066829932966618894,
01234      .01601722825777433332422461685847101526589
01235     }
01236   },
01237   {
01238     22,
01239     { // points
01240      {.9942945854823992920730314211612989803931    ,0.0, 0.0},
01241      {.970060497835428727123950986765268710806     ,0.0, 0.0},
01242      {.9269567721871740005206929392590531966353    ,0.0, 0.0},
01243      {.8658125777203001365364256370193787290848    ,0.0, 0.0},
01244      {.7878168059792081620042779554083515213882    ,0.0, 0.0},
01245      {.6944872631866827800506898357622567712673    ,0.0, 0.0},
01246      {.5876404035069115929588769276386473488776    ,0.0, 0.0},
01247      {.4693558379867570264063307109664063460953    ,0.0, 0.0},
01248      {.3419358208920842251581474204273796195592    ,0.0, 0.0},
01249      {.2078604266882212854788465339195457342157    ,0.0, 0.0},
01250      {.0697392733197222212138417961186280818223    ,0.0, 0.0},
01251      {-.0697392733197222212138417961186280818223   ,0.0, 0.0},
01252      {-.2078604266882212854788465339195457342157   ,0.0, 0.0},
01253      {-.3419358208920842251581474204273796195592   ,0.0, 0.0},
01254      {-.4693558379867570264063307109664063460953   ,0.0, 0.0},
01255      {-.5876404035069115929588769276386473488776   ,0.0, 0.0},
01256      {-.6944872631866827800506898357622567712673   ,0.0, 0.0},
01257      {-.7878168059792081620042779554083515213882   ,0.0, 0.0},
01258      {-.8658125777203001365364256370193787290848   ,0.0, 0.0},
01259      {-.9269567721871740005206929392590531966353   ,0.0, 0.0},
01260      {-.970060497835428727123950986765268710806    ,0.0, 0.0},
01261      {-.9942945854823992920730314211612989803931   ,0.0, 0.0}
01262     },
01263     { // weights
01264      .01462799529827220068499109804718544519021,
01265      .03377490158481415479330224686591290134917,
01266      .05229333515268328594031205127321125611215,
01267      .06979646842452048809496141893021765739878,
01268      .08594160621706772741444368137270286618914,
01269      .1004141444428809649320788378305362823508,
01270      .1129322960805392183934006074217843191143,
01271      .1232523768105124242855609861548144719594,
01272      .1311735047870623707329649925303074458757,
01273      .1365414983460151713525738312315173965864,
01274      .1392518728556319933754102483418099578739,
01275       .1392518728556319933754102483418099578739,
01276       .1365414983460151713525738312315173965864,
01277       .1311735047870623707329649925303074458757,
01278       .1232523768105124242855609861548144719594,
01279       .1129322960805392183934006074217843191143,
01280       .1004141444428809649320788378305362823508,
01281       .08594160621706772741444368137270286618914,
01282       .06979646842452048809496141893021765739878,
01283       .05229333515268328594031205127321125611215,
01284       .03377490158481415479330224686591290134917,
01285       .01462799529827220068499109804718544519021
01286     }
01287   },
01288   {
01289     22,
01290     { // points
01291      {.9942945854823992920730314211612989803931    ,0.0, 0.0},
01292      {.970060497835428727123950986765268710806     ,0.0, 0.0},
01293      {.9269567721871740005206929392590531966353    ,0.0, 0.0},
01294      {.8658125777203001365364256370193787290848    ,0.0, 0.0},
01295      {.7878168059792081620042779554083515213882    ,0.0, 0.0},
01296      {.6944872631866827800506898357622567712673    ,0.0, 0.0},
01297      {.5876404035069115929588769276386473488776    ,0.0, 0.0},
01298      {.4693558379867570264063307109664063460953    ,0.0, 0.0},
01299      {.3419358208920842251581474204273796195592    ,0.0, 0.0},
01300      {.2078604266882212854788465339195457342157    ,0.0, 0.0},
01301      {.0697392733197222212138417961186280818223    ,0.0, 0.0},
01302      {-.0697392733197222212138417961186280818223   ,0.0, 0.0},
01303      {-.2078604266882212854788465339195457342157   ,0.0, 0.0},
01304      {-.3419358208920842251581474204273796195592   ,0.0, 0.0},
01305      {-.4693558379867570264063307109664063460953   ,0.0, 0.0},
01306      {-.5876404035069115929588769276386473488776   ,0.0, 0.0},
01307      {-.6944872631866827800506898357622567712673   ,0.0, 0.0},
01308      {-.7878168059792081620042779554083515213882   ,0.0, 0.0},
01309      {-.8658125777203001365364256370193787290848   ,0.0, 0.0},
01310      {-.9269567721871740005206929392590531966353   ,0.0, 0.0},
01311      {-.970060497835428727123950986765268710806    ,0.0, 0.0},
01312      {-.9942945854823992920730314211612989803931   ,0.0, 0.0}
01313     },
01314     { // weights
01315      .01462799529827220068499109804718544519021,
01316      .03377490158481415479330224686591290134917,
01317      .05229333515268328594031205127321125611215,
01318      .06979646842452048809496141893021765739878,
01319      .08594160621706772741444368137270286618914,
01320      .1004141444428809649320788378305362823508,
01321      .1129322960805392183934006074217843191143,
01322      .1232523768105124242855609861548144719594,
01323      .1311735047870623707329649925303074458757,
01324      .1365414983460151713525738312315173965864,
01325      .1392518728556319933754102483418099578739,
01326       .1392518728556319933754102483418099578739,
01327       .1365414983460151713525738312315173965864,
01328       .1311735047870623707329649925303074458757,
01329       .1232523768105124242855609861548144719594,
01330       .1129322960805392183934006074217843191143,
01331       .1004141444428809649320788378305362823508,
01332       .08594160621706772741444368137270286618914,
01333       .06979646842452048809496141893021765739878,
01334       .05229333515268328594031205127321125611215,
01335       .03377490158481415479330224686591290134917,
01336       .01462799529827220068499109804718544519021
01337     }
01338   },
01339   {
01340     23,
01341     { // points
01342      {.9947693349975521235239257154455743605736    ,0.0, 0.0},
01343      {.9725424712181152319560240768207773751816    ,0.0, 0.0},
01344      {.9329710868260161023491969890384229782357    ,0.0, 0.0},
01345      {.8767523582704416673781568859341456716389    ,0.0, 0.0},
01346      {.8048884016188398921511184069967785579414    ,0.0, 0.0},
01347      {.7186613631319501944616244837486188483299    ,0.0, 0.0},
01348      {.6196098757636461563850973116495956533872    ,0.0, 0.0},
01349      {.5095014778460075496897930478668464305448    ,0.0, 0.0},
01350      {.3903010380302908314214888728806054585781    ,0.0, 0.0},
01351      {.264135680970344930533869538283309602979     ,0.0, 0.0},
01352      {.1332568242984661109317426822417661370104    ,0.0, 0.0},
01353      {0                                            ,0.0, 0.0},
01354      {-.1332568242984661109317426822417661370104   ,0.0, 0.0},
01355      {-.264135680970344930533869538283309602979    ,0.0, 0.0},
01356      {-.3903010380302908314214888728806054585781   ,0.0, 0.0},
01357      {-.5095014778460075496897930478668464305448   ,0.0, 0.0},
01358      {-.6196098757636461563850973116495956533872   ,0.0, 0.0},
01359      {-.7186613631319501944616244837486188483299   ,0.0, 0.0},
01360      {-.8048884016188398921511184069967785579414   ,0.0, 0.0},
01361      {-.8767523582704416673781568859341456716389   ,0.0, 0.0},
01362      {-.9329710868260161023491969890384229782357   ,0.0, 0.0},
01363      {-.9725424712181152319560240768207773751816   ,0.0, 0.0},
01364      {-.9947693349975521235239257154455743605736   ,0.0, 0.0}
01365     },
01366     { // weights
01367      .01341185948714177208130949345861506497662,
01368      .03098800585697944431069421964188450538377,
01369      .04803767173108466857164107163203399656122,
01370      .06423242140852585212716961515891099803916,
01371      .07928141177671895492289252474204322691371,
01372      .09291576606003514747701861736976464860346,
01373      .1048920914645414100740861850147438548585,
01374      .1149966402224113649416435129339613014914,
01375      .1230490843067295304675784006720096548159,
01376      .1289057221880821499785953393997936532597,
01377      .132462039404696617371642464703316925805,
01378       .1336545721861061753514571105458443385832,
01379       .132462039404696617371642464703316925805,
01380       .1289057221880821499785953393997936532597,
01381       .1230490843067295304675784006720096548159,
01382       .1149966402224113649416435129339613014914,
01383       .1048920914645414100740861850147438548585,
01384       .09291576606003514747701861736976464860346,
01385       .07928141177671895492289252474204322691371,
01386       .06423242140852585212716961515891099803916,
01387       .04803767173108466857164107163203399656122,
01388       .03098800585697944431069421964188450538377,
01389       .01341185948714177208130949345861506497662
01390     }
01391   },
01392   {
01393     23,
01394     { // points
01395      {.9947693349975521235239257154455743605736    ,0.0, 0.0},
01396      {.9725424712181152319560240768207773751816    ,0.0, 0.0},
01397      {.9329710868260161023491969890384229782357    ,0.0, 0.0},
01398      {.8767523582704416673781568859341456716389    ,0.0, 0.0},
01399      {.8048884016188398921511184069967785579414    ,0.0, 0.0},
01400      {.7186613631319501944616244837486188483299    ,0.0, 0.0},
01401      {.6196098757636461563850973116495956533872    ,0.0, 0.0},
01402      {.5095014778460075496897930478668464305448    ,0.0, 0.0},
01403      {.3903010380302908314214888728806054585781    ,0.0, 0.0},
01404      {.264135680970344930533869538283309602979     ,0.0, 0.0},
01405      {.1332568242984661109317426822417661370104    ,0.0, 0.0},
01406      {0                                            ,0.0, 0.0},
01407      {-.1332568242984661109317426822417661370104   ,0.0, 0.0},
01408      {-.264135680970344930533869538283309602979    ,0.0, 0.0},
01409      {-.3903010380302908314214888728806054585781   ,0.0, 0.0},
01410      {-.5095014778460075496897930478668464305448   ,0.0, 0.0},
01411      {-.6196098757636461563850973116495956533872   ,0.0, 0.0},
01412      {-.7186613631319501944616244837486188483299   ,0.0, 0.0},
01413      {-.8048884016188398921511184069967785579414   ,0.0, 0.0},
01414      {-.8767523582704416673781568859341456716389   ,0.0, 0.0},
01415      {-.9329710868260161023491969890384229782357   ,0.0, 0.0},
01416      {-.9725424712181152319560240768207773751816   ,0.0, 0.0},
01417      {-.9947693349975521235239257154455743605736   ,0.0, 0.0}
01418     },
01419     { // weights
01420      .01341185948714177208130949345861506497662,
01421      .03098800585697944431069421964188450538377,
01422      .04803767173108466857164107163203399656122,
01423      .06423242140852585212716961515891099803916,
01424      .07928141177671895492289252474204322691371,
01425      .09291576606003514747701861736976464860346,
01426      .1048920914645414100740861850147438548585,
01427      .1149966402224113649416435129339613014914,
01428      .1230490843067295304675784006720096548159,
01429      .1289057221880821499785953393997936532597,
01430      .132462039404696617371642464703316925805,
01431       .1336545721861061753514571105458443385832,
01432       .132462039404696617371642464703316925805,
01433       .1289057221880821499785953393997936532597,
01434       .1230490843067295304675784006720096548159,
01435       .1149966402224113649416435129339613014914,
01436       .1048920914645414100740861850147438548585,
01437       .09291576606003514747701861736976464860346,
01438       .07928141177671895492289252474204322691371,
01439       .06423242140852585212716961515891099803916,
01440       .04803767173108466857164107163203399656122,
01441       .03098800585697944431069421964188450538377,
01442       .01341185948714177208130949345861506497662
01443     }
01444   },
01445   {
01446     24,
01447     { // points
01448      {.9951872199970213601799974097007368118746    ,0.0, 0.0},
01449      {.9747285559713094981983919930081690617412    ,0.0, 0.0},
01450      {.9382745520027327585236490017087214496548    ,0.0, 0.0},
01451      {.8864155270044010342131543419821967550873    ,0.0, 0.0},
01452      {.8200019859739029219539498726697452080761    ,0.0, 0.0},
01453      {.7401241915785543642438281030999784255233    ,0.0, 0.0},
01454      {.6480936519369755692524957869107476266697    ,0.0, 0.0},
01455      {.5454214713888395356583756172183723700108    ,0.0, 0.0},
01456      {.4337935076260451384870842319133497124524    ,0.0, 0.0},
01457      {.3150426796961633743867932913198102407865    ,0.0, 0.0},
01458      {.1911188674736163091586398207570696318404    ,0.0, 0.0},
01459      {.064056892862605626085043082624745038591     ,0.0, 0.0},
01460      {-.064056892862605626085043082624745038591    ,0.0, 0.0},
01461      {-.1911188674736163091586398207570696318404   ,0.0, 0.0},
01462      {-.3150426796961633743867932913198102407865   ,0.0, 0.0},
01463      {-.4337935076260451384870842319133497124524   ,0.0, 0.0},
01464      {-.5454214713888395356583756172183723700108   ,0.0, 0.0},
01465      {-.6480936519369755692524957869107476266697   ,0.0, 0.0},
01466      {-.7401241915785543642438281030999784255233   ,0.0, 0.0},
01467      {-.8200019859739029219539498726697452080761   ,0.0, 0.0},
01468      {-.8864155270044010342131543419821967550873   ,0.0, 0.0},
01469      {-.9382745520027327585236490017087214496548   ,0.0, 0.0},
01470      {-.9747285559713094981983919930081690617412   ,0.0, 0.0},
01471      {-.9951872199970213601799974097007368118746   ,0.0, 0.0}
01472     },
01473     { // weights
01474      .01234122979998719954680566707003729157591,
01475      .0285313886289336631813078159518782864492,
01476      .04427743881741980616860274821133822885931,
01477      .0592985849154367807463677585001085845412,
01478      .07334648141108030573403361525311651811934,
01479      .08619016153195327591718520298374266718508,
01480      .09761865210411388826988066446424715442792,
01481      .1074442701159656347825773424466062227946,
01482      .1155056680537256013533444839067835598623,
01483      .121670472927803391204463153476262425607,
01484      .1258374563468282961213753825111836887264,
01485      .1279381953467521569740561652246953718517,
01486      .1279381953467521569740561652246953718517,
01487       .1258374563468282961213753825111836887264,
01488       .121670472927803391204463153476262425607,
01489       .1155056680537256013533444839067835598623,
01490       .1074442701159656347825773424466062227946,
01491       .09761865210411388826988066446424715442792,
01492       .08619016153195327591718520298374266718508,
01493       .07334648141108030573403361525311651811934,
01494       .0592985849154367807463677585001085845412,
01495       .04427743881741980616860274821133822885931,
01496       .0285313886289336631813078159518782864492,
01497       .01234122979998719954680566707003729157591
01498     }
01499   },
01500   {
01501     24,
01502     { // points
01503      {.9951872199970213601799974097007368118746    ,0.0, 0.0},
01504      {.9747285559713094981983919930081690617412    ,0.0, 0.0},
01505      {.9382745520027327585236490017087214496548    ,0.0, 0.0},
01506      {.8864155270044010342131543419821967550873    ,0.0, 0.0},
01507      {.8200019859739029219539498726697452080761    ,0.0, 0.0},
01508      {.7401241915785543642438281030999784255233    ,0.0, 0.0},
01509      {.6480936519369755692524957869107476266697    ,0.0, 0.0},
01510      {.5454214713888395356583756172183723700108    ,0.0, 0.0},
01511      {.4337935076260451384870842319133497124524    ,0.0, 0.0},
01512      {.3150426796961633743867932913198102407865    ,0.0, 0.0},
01513      {.1911188674736163091586398207570696318404    ,0.0, 0.0},
01514      {.064056892862605626085043082624745038591     ,0.0, 0.0},
01515      {-.064056892862605626085043082624745038591    ,0.0, 0.0},
01516      {-.1911188674736163091586398207570696318404   ,0.0, 0.0},
01517      {-.3150426796961633743867932913198102407865   ,0.0, 0.0},
01518      {-.4337935076260451384870842319133497124524   ,0.0, 0.0},
01519      {-.5454214713888395356583756172183723700108   ,0.0, 0.0},
01520      {-.6480936519369755692524957869107476266697   ,0.0, 0.0},
01521      {-.7401241915785543642438281030999784255233   ,0.0, 0.0},
01522      {-.8200019859739029219539498726697452080761   ,0.0, 0.0},
01523      {-.8864155270044010342131543419821967550873   ,0.0, 0.0},
01524      {-.9382745520027327585236490017087214496548   ,0.0, 0.0},
01525      {-.9747285559713094981983919930081690617412   ,0.0, 0.0},
01526      {-.9951872199970213601799974097007368118746   ,0.0, 0.0}
01527     },
01528     { // weights
01529      .01234122979998719954680566707003729157591,
01530      .0285313886289336631813078159518782864492,
01531      .04427743881741980616860274821133822885931,
01532      .0592985849154367807463677585001085845412,
01533      .07334648141108030573403361525311651811934,
01534      .08619016153195327591718520298374266718508,
01535      .09761865210411388826988066446424715442792,
01536      .1074442701159656347825773424466062227946,
01537      .1155056680537256013533444839067835598623,
01538      .121670472927803391204463153476262425607,
01539      .1258374563468282961213753825111836887264,
01540      .1279381953467521569740561652246953718517,
01541      .1279381953467521569740561652246953718517,
01542       .1258374563468282961213753825111836887264,
01543       .121670472927803391204463153476262425607,
01544       .1155056680537256013533444839067835598623,
01545       .1074442701159656347825773424466062227946,
01546       .09761865210411388826988066446424715442792,
01547       .08619016153195327591718520298374266718508,
01548       .07334648141108030573403361525311651811934,
01549       .0592985849154367807463677585001085845412,
01550       .04427743881741980616860274821133822885931,
01551       .0285313886289336631813078159518782864492,
01552       .01234122979998719954680566707003729157591
01553     }
01554   },
01555   {
01556     25,
01557     { // points
01558      {.9955569697904980979087849468939016172576    ,0.0, 0.0},
01559      {.9766639214595175114983153864795940677454    ,0.0, 0.0},
01560      {.9429745712289743394140111696584705319052    ,0.0, 0.0},
01561      {.8949919978782753688510420067828049541746    ,0.0, 0.0},
01562      {.833442628760834001421021108693569569461     ,0.0, 0.0},
01563      {.7592592630373576305772828652043609763875    ,0.0, 0.0},
01564      {.6735663684734683644851206332476221758834    ,0.0, 0.0},
01565      {.5776629302412229677236898416126540673957    ,0.0, 0.0},
01566      {.4730027314457149605221821150091920413318    ,0.0, 0.0},
01567      {.3611723058093878377358217301276406674221    ,0.0, 0.0},
01568      {.2438668837209884320451903627974515864056    ,0.0, 0.0},
01569      {.1228646926107103963873598188080368055322    ,0.0, 0.0},
01570      {0                                            ,0.0, 0.0},
01571      {-.1228646926107103963873598188080368055322   ,0.0, 0.0},
01572      {-.2438668837209884320451903627974515864056   ,0.0, 0.0},
01573      {-.3611723058093878377358217301276406674221   ,0.0, 0.0},
01574      {-.4730027314457149605221821150091920413318   ,0.0, 0.0},
01575      {-.5776629302412229677236898416126540673957   ,0.0, 0.0},
01576      {-.6735663684734683644851206332476221758834   ,0.0, 0.0},
01577      {-.7592592630373576305772828652043609763875   ,0.0, 0.0},
01578      {-.833442628760834001421021108693569569461    ,0.0, 0.0},
01579      {-.8949919978782753688510420067828049541746   ,0.0, 0.0},
01580      {-.9429745712289743394140111696584705319052   ,0.0, 0.0},
01581      {-.9766639214595175114983153864795940677454   ,0.0, 0.0},
01582      {-.9955569697904980979087849468939016172576   ,0.0, 0.0}
01583     },
01584     { // weights
01585      .01139379850102628794790296411323477360332,
01586      .02635498661503213726190181529529914493596,
01587      .04093915670130631265562348771164595366085,
01588      .05490469597583519192593689154047332416011,
01589      .06803833381235691720718718565670796855471,
01590      .08014070033500101801323495966911130229023,
01591      .09102826198296364981149722070289165338099,
01592      .1005359490670506442022068903926858269885,
01593      .1085196244742636531160939570501166193401,
01594      .1148582591457116483393255458695558086409,
01595      .1194557635357847722281781265129010473902,
01596      .1222424429903100416889595189458515058351,
01597       .1231760537267154512039028730790501424382,
01598       .1222424429903100416889595189458515058351,
01599       .1194557635357847722281781265129010473902,
01600       .1148582591457116483393255458695558086409,
01601       .1085196244742636531160939570501166193401,
01602       .1005359490670506442022068903926858269885,
01603       .09102826198296364981149722070289165338099,
01604       .08014070033500101801323495966911130229023,
01605      .06803833381235691720718718565670796855471,
01606       .05490469597583519192593689154047332416011,
01607       .04093915670130631265562348771164595366085,
01608       .02635498661503213726190181529529914493596,
01609       .01139379850102628794790296411323477360332
01610     }
01611   },
01612   {
01613     25,
01614     { // points
01615      {.9955569697904980979087849468939016172576    ,0.0, 0.0},
01616      {.9766639214595175114983153864795940677454    ,0.0, 0.0},
01617      {.9429745712289743394140111696584705319052    ,0.0, 0.0},
01618      {.8949919978782753688510420067828049541746    ,0.0, 0.0},
01619      {.833442628760834001421021108693569569461     ,0.0, 0.0},
01620      {.7592592630373576305772828652043609763875    ,0.0, 0.0},
01621      {.6735663684734683644851206332476221758834    ,0.0, 0.0},
01622      {.5776629302412229677236898416126540673957    ,0.0, 0.0},
01623      {.4730027314457149605221821150091920413318    ,0.0, 0.0},
01624      {.3611723058093878377358217301276406674221    ,0.0, 0.0},
01625      {.2438668837209884320451903627974515864056    ,0.0, 0.0},
01626      {.1228646926107103963873598188080368055322    ,0.0, 0.0},
01627      {0                                            ,0.0, 0.0},
01628      {-.1228646926107103963873598188080368055322   ,0.0, 0.0},
01629      {-.2438668837209884320451903627974515864056   ,0.0, 0.0},
01630      {-.3611723058093878377358217301276406674221   ,0.0, 0.0},
01631      {-.4730027314457149605221821150091920413318   ,0.0, 0.0},
01632      {-.5776629302412229677236898416126540673957   ,0.0, 0.0},
01633      {-.6735663684734683644851206332476221758834   ,0.0, 0.0},
01634      {-.7592592630373576305772828652043609763875   ,0.0, 0.0},
01635      {-.833442628760834001421021108693569569461    ,0.0, 0.0},
01636      {-.8949919978782753688510420067828049541746   ,0.0, 0.0},
01637      {-.9429745712289743394140111696584705319052   ,0.0, 0.0},
01638      {-.9766639214595175114983153864795940677454   ,0.0, 0.0},
01639      {-.9955569697904980979087849468939016172576   ,0.0, 0.0}
01640     },
01641     { // weights
01642      .01139379850102628794790296411323477360332,
01643      .02635498661503213726190181529529914493596,
01644      .04093915670130631265562348771164595366085,
01645      .05490469597583519192593689154047332416011,
01646      .06803833381235691720718718565670796855471,
01647      .08014070033500101801323495966911130229023,
01648      .09102826198296364981149722070289165338099,
01649      .1005359490670506442022068903926858269885,
01650      .1085196244742636531160939570501166193401,
01651      .1148582591457116483393255458695558086409,
01652      .1194557635357847722281781265129010473902,
01653      .1222424429903100416889595189458515058351,
01654       .1231760537267154512039028730790501424382,
01655       .1222424429903100416889595189458515058351,
01656       .1194557635357847722281781265129010473902,
01657       .1148582591457116483393255458695558086409,
01658       .1085196244742636531160939570501166193401,
01659       .1005359490670506442022068903926858269885,
01660       .09102826198296364981149722070289165338099,
01661       .08014070033500101801323495966911130229023,
01662      .06803833381235691720718718565670796855471,
01663       .05490469597583519192593689154047332416011,
01664       .04093915670130631265562348771164595366085,
01665       .02635498661503213726190181529529914493596,
01666       .01139379850102628794790296411323477360332
01667     }
01668   },
01669   {
01670     26,
01671     { // points
01672      {.9958857011456169290032169593229060259569    ,0.0, 0.0},
01673      {.9783854459564709911005803543119263054469    ,0.0, 0.0},
01674      {.9471590666617142501359152835180367545207    ,0.0, 0.0},
01675      {.9026378619843070742176655992312102513411    ,0.0, 0.0},
01676      {.8454459427884980187975070614678381615721    ,0.0, 0.0},
01677      {.7763859488206788561929672472422838669762    ,0.0, 0.0},
01678      {.6964272604199572648638139137294246978608    ,0.0, 0.0},
01679      {.6066922930176180632319787469168870544353    ,0.0, 0.0},
01680      {.5084407148245057176957030647255691753763    ,0.0, 0.0},
01681      {.4030517551234863064810773770988831036599    ,0.0, 0.0},
01682      {.2920048394859568951428353820778302968847    ,0.0, 0.0},
01683      {.1768588203568901839690577484183447499774    ,0.0, 0.0},
01684      {.05923009342931320709371857519840336079023   ,0.0, 0.0},
01685      {-.05923009342931320709371857519840336079023  ,0.0, 0.0},
01686      {-.1768588203568901839690577484183447499774   ,0.0, 0.0},
01687      {-.2920048394859568951428353820778302968847   ,0.0, 0.0},
01688      {-.4030517551234863064810773770988831036599   ,0.0, 0.0},
01689      {-.5084407148245057176957030647255691753763   ,0.0, 0.0},
01690      {-.6066922930176180632319787469168870544353   ,0.0, 0.0},
01691      {-.6964272604199572648638139137294246978608   ,0.0, 0.0},
01692      {-.7763859488206788561929672472422838669762   ,0.0, 0.0},
01693      {-.8454459427884980187975070614678381615721   ,0.0, 0.0},
01694      {-.9026378619843070742176655992312102513411   ,0.0, 0.0},
01695      {-.9471590666617142501359152835180367545207   ,0.0, 0.0},
01696      {-.9783854459564709911005803543119263054469   ,0.0, 0.0},
01697      {-.9958857011456169290032169593229060259569   ,0.0, 0.0}
01698     },
01699     { // weights
01700      .01055137261734300715565118768525197790435,
01701      .0244178510926319087896158275197884002405,
01702      .03796238329436276395030314124885049469077,
01703      .05097582529714781199831990072407337952588,
01704      .06327404632957483553945368990704509572222,
01705      .07468414976565974588707579610284833863875,
01706      .08504589431348523921044776507998169658392,
01707      .09421380035591414846366488306730319854917,
01708      .1020591610944254232384140702534307923272,
01709      .1084718405285765906565794267279975822894,
01710      .113361816546319666549440718442598145246,
01711      .116660443485296582044662507540362213632,
01712       .1183214152792622765163710857004686846499,
01713        .1183214152792622765163710857004686846499,
01714       .116660443485296582044662507540362213632,
01715       .113361816546319666549440718442598145246,
01716       .1084718405285765906565794267279975822894,
01717       .1020591610944254232384140702534307923272,
01718       .09421380035591414846366488306730319854917,
01719       .08504589431348523921044776507998169658392,
01720       .07468414976565974588707579610284833863875,
01721       .06327404632957483553945368990704509572222,
01722       .05097582529714781199831990072407337952588,
01723       .03796238329436276395030314124885049469077,
01724       .0244178510926319087896158275197884002405,
01725       .01055137261734300715565118768525197790435
01726     }
01727   },
01728   {
01729     26,
01730     { // points
01731      {.9958857011456169290032169593229060259569    ,0.0, 0.0},
01732      {.9783854459564709911005803543119263054469    ,0.0, 0.0},
01733      {.9471590666617142501359152835180367545207    ,0.0, 0.0},
01734      {.9026378619843070742176655992312102513411    ,0.0, 0.0},
01735      {.8454459427884980187975070614678381615721    ,0.0, 0.0},
01736      {.7763859488206788561929672472422838669762    ,0.0, 0.0},
01737      {.6964272604199572648638139137294246978608    ,0.0, 0.0},
01738      {.6066922930176180632319787469168870544353    ,0.0, 0.0},
01739      {.5084407148245057176957030647255691753763    ,0.0, 0.0},
01740      {.4030517551234863064810773770988831036599    ,0.0, 0.0},
01741      {.2920048394859568951428353820778302968847    ,0.0, 0.0},
01742      {.1768588203568901839690577484183447499774    ,0.0, 0.0},
01743      {.05923009342931320709371857519840336079023   ,0.0, 0.0},
01744      {-.05923009342931320709371857519840336079023  ,0.0, 0.0},
01745      {-.1768588203568901839690577484183447499774   ,0.0, 0.0},
01746      {-.2920048394859568951428353820778302968847   ,0.0, 0.0},
01747      {-.4030517551234863064810773770988831036599   ,0.0, 0.0},
01748      {-.5084407148245057176957030647255691753763   ,0.0, 0.0},
01749      {-.6066922930176180632319787469168870544353   ,0.0, 0.0},
01750      {-.6964272604199572648638139137294246978608   ,0.0, 0.0},
01751      {-.7763859488206788561929672472422838669762   ,0.0, 0.0},
01752      {-.8454459427884980187975070614678381615721   ,0.0, 0.0},
01753      {-.9026378619843070742176655992312102513411   ,0.0, 0.0},
01754      {-.9471590666617142501359152835180367545207   ,0.0, 0.0},
01755      {-.9783854459564709911005803543119263054469   ,0.0, 0.0},
01756      {-.9958857011456169290032169593229060259569   ,0.0, 0.0}
01757     },
01758     { // weights
01759      .01055137261734300715565118768525197790435,
01760      .0244178510926319087896158275197884002405,
01761      .03796238329436276395030314124885049469077,
01762      .05097582529714781199831990072407337952588,
01763      .06327404632957483553945368990704509572222,
01764      .07468414976565974588707579610284833863875,
01765      .08504589431348523921044776507998169658392,
01766      .09421380035591414846366488306730319854917,
01767      .1020591610944254232384140702534307923272,
01768      .1084718405285765906565794267279975822894,
01769      .113361816546319666549440718442598145246,
01770      .116660443485296582044662507540362213632,
01771       .1183214152792622765163710857004686846499,
01772        .1183214152792622765163710857004686846499,
01773       .116660443485296582044662507540362213632,
01774       .113361816546319666549440718442598145246,
01775       .1084718405285765906565794267279975822894,
01776       .1020591610944254232384140702534307923272,
01777       .09421380035591414846366488306730319854917,
01778       .08504589431348523921044776507998169658392,
01779       .07468414976565974588707579610284833863875,
01780       .06327404632957483553945368990704509572222,
01781       .05097582529714781199831990072407337952588,
01782       .03796238329436276395030314124885049469077,
01783       .0244178510926319087896158275197884002405,
01784       .01055137261734300715565118768525197790435
01785     }
01786   },
01787   {
01788     27,
01789     { // points
01790      {.9961792628889885669388872083812299902607    ,0.0, 0.0},
01791      {.9799234759615012228558733556610471845676    ,0.0, 0.0},
01792      {.9509005578147050068519080306438828930926    ,0.0, 0.0},
01793      {.909482320677491104300645018209689254948     ,0.0, 0.0},
01794      {.8562079080182944903027372227068427977643    ,0.0, 0.0},
01795      {.7917716390705082271443973441072707329194    ,0.0, 0.0},
01796      {.7170134737394236992948162116423395497507    ,0.0, 0.0},
01797      {.6329079719464951409277346376344886121031    ,0.0, 0.0},
01798      {.5405515645794568949003009415599828209592    ,0.0, 0.0},
01799      {.4411482517500268805859741556892814524477    ,0.0, 0.0},
01800      {.33599390363850889973031903420728454179      ,0.0, 0.0},
01801      {.2264593654395368588572391073602301711794    ,0.0, 0.0},
01802      {.1139725856095299669328949838699766271733    ,0.0, 0.0},
01803      {0                                            ,0.0, 0.0},
01804      {-.1139725856095299669328949838699766271733   ,0.0, 0.0},
01805      {-.2264593654395368588572391073602301711794   ,0.0, 0.0},
01806      {-.33599390363850889973031903420728454179     ,0.0, 0.0},
01807      {-.4411482517500268805859741556892814524477   ,0.0, 0.0},
01808      {-.5405515645794568949003009415599828209592   ,0.0, 0.0},
01809      {-.6329079719464951409277346376344886121031   ,0.0, 0.0},
01810      {-.7170134737394236992948162116423395497507   ,0.0, 0.0},
01811      {-.7917716390705082271443973441072707329194   ,0.0, 0.0},
01812      {-.8562079080182944903027372227068427977643   ,0.0, 0.0},
01813      {-.909482320677491104300645018209689254948    ,0.0, 0.0},
01814      {-.9509005578147050068519080306438828930926   ,0.0, 0.0},
01815      {-.9799234759615012228558733556610471845676   ,0.0, 0.0},
01816      {-.9961792628889885669388872083812299902607   ,0.0, 0.0}
01817     },
01818     { // weights
01819      .009798996051294360261150055091259098098226,
01820      .02268623159618062319603420644676148881277,
01821      .03529705375741971102257828930471164113614,
01822      .04744941252061506270409671011418471822473,
01823      .05898353685983359911030083371953163316524,
01824      .06974882376624559298432288835666727613282,
01825      .07960486777305777126307495900984240297615,
01826      .08842315854375695019432280285374911105654,
01827      .09608872737002850756565264655810585916021,
01828      .1025016378177457986712477115326638093244,
01829      .107578285788533187212162984426657404819,
01830      .1112524883568451926721630960428486748329,
01831      .1134763461089651486203699480920992579205,
01832       .1142208673789569890450457369018352486807,
01833       .1134763461089651486203699480920992579205,
01834       .1112524883568451926721630960428486748329,
01835       .107578285788533187212162984426657404819,
01836       .1025016378177457986712477115326638093244,
01837       .09608872737002850756565264655810585916021,
01838       .08842315854375695019432280285374911105654,
01839       .07960486777305777126307495900984240297615,
01840       .06974882376624559298432288835666727613282,
01841       .05898353685983359911030083371953163316524,
01842       .04744941252061506270409671011418471822473,
01843       .03529705375741971102257828930471164113614,
01844       .02268623159618062319603420644676148881277,
01845       .009798996051294360261150055091259098098226
01846     }
01847   },
01848   {
01849     27,
01850     { // points
01851      {.9961792628889885669388872083812299902607    ,0.0, 0.0},
01852      {.9799234759615012228558733556610471845676    ,0.0, 0.0},
01853      {.9509005578147050068519080306438828930926    ,0.0, 0.0},
01854      {.909482320677491104300645018209689254948     ,0.0, 0.0},
01855      {.8562079080182944903027372227068427977643    ,0.0, 0.0},
01856      {.7917716390705082271443973441072707329194    ,0.0, 0.0},
01857      {.7170134737394236992948162116423395497507    ,0.0, 0.0},
01858      {.6329079719464951409277346376344886121031    ,0.0, 0.0},
01859      {.5405515645794568949003009415599828209592    ,0.0, 0.0},
01860      {.4411482517500268805859741556892814524477    ,0.0, 0.0},
01861      {.33599390363850889973031903420728454179      ,0.0, 0.0},
01862      {.2264593654395368588572391073602301711794    ,0.0, 0.0},
01863      {.1139725856095299669328949838699766271733    ,0.0, 0.0},
01864      {0                                            ,0.0, 0.0},
01865      {-.1139725856095299669328949838699766271733   ,0.0, 0.0},
01866      {-.2264593654395368588572391073602301711794   ,0.0, 0.0},
01867      {-.33599390363850889973031903420728454179     ,0.0, 0.0},
01868      {-.4411482517500268805859741556892814524477   ,0.0, 0.0},
01869      {-.5405515645794568949003009415599828209592   ,0.0, 0.0},
01870      {-.6329079719464951409277346376344886121031   ,0.0, 0.0},
01871      {-.7170134737394236992948162116423395497507   ,0.0, 0.0},
01872      {-.7917716390705082271443973441072707329194   ,0.0, 0.0},
01873      {-.8562079080182944903027372227068427977643   ,0.0, 0.0},
01874      {-.909482320677491104300645018209689254948    ,0.0, 0.0},
01875      {-.9509005578147050068519080306438828930926   ,0.0, 0.0},
01876      {-.9799234759615012228558733556610471845676   ,0.0, 0.0},
01877      {-.9961792628889885669388872083812299902607   ,0.0, 0.0}
01878     },
01879     { // weights
01880      .009798996051294360261150055091259098098226,
01881      .02268623159618062319603420644676148881277,
01882      .03529705375741971102257828930471164113614,
01883      .04744941252061506270409671011418471822473,
01884      .05898353685983359911030083371953163316524,
01885      .06974882376624559298432288835666727613282,
01886      .07960486777305777126307495900984240297615,
01887      .08842315854375695019432280285374911105654,
01888      .09608872737002850756565264655810585916021,
01889      .1025016378177457986712477115326638093244,
01890      .107578285788533187212162984426657404819,
01891      .1112524883568451926721630960428486748329,
01892      .1134763461089651486203699480920992579205,
01893       .1142208673789569890450457369018352486807,
01894       .1134763461089651486203699480920992579205,
01895       .1112524883568451926721630960428486748329,
01896       .107578285788533187212162984426657404819,
01897       .1025016378177457986712477115326638093244,
01898       .09608872737002850756565264655810585916021,
01899       .08842315854375695019432280285374911105654,
01900       .07960486777305777126307495900984240297615,
01901       .06974882376624559298432288835666727613282,
01902       .05898353685983359911030083371953163316524,
01903       .04744941252061506270409671011418471822473,
01904       .03529705375741971102257828930471164113614,
01905       .02268623159618062319603420644676148881277,
01906       .009798996051294360261150055091259098098226
01907     }
01908   },
01909   {
01910     28,
01911     { // points
01912      {.9964424975739544499504363904833109917501    ,0.0, 0.0},
01913      {.9813031653708727536945599458078302764442    ,0.0, 0.0},
01914      {.9542592806289381972541018397052155890034    ,0.0, 0.0},
01915      {.9156330263921320738696894233299271463525    ,0.0, 0.0},
01916      {.8658925225743950489422545673796868043419    ,0.0, 0.0},
01917      {.8056413709171791714478859554252776586717    ,0.0, 0.0},
01918      {.7356108780136317720281445102925343680161    ,0.0, 0.0},
01919      {.6566510940388649612198981765067428215696    ,0.0, 0.0},
01920      {.5697204718114017193080032833564309331247    ,0.0, 0.0},
01921      {.4758742249551182610344118476674340426272    ,0.0, 0.0},
01922      {.3762515160890787102213572095560869828717    ,0.0, 0.0},
01923      {.2720616276351780776768263561257697348248    ,0.0, 0.0},
01924      {.1645692821333807712814717778911654571457    ,0.0, 0.0},
01925      {.0550792898840342704265165273418799778508    ,0.0, 0.0},
01926      {-.0550792898840342704265165273418799778508   ,0.0, 0.0},
01927      {-.1645692821333807712814717778911654571457   ,0.0, 0.0},
01928      {-.2720616276351780776768263561257697348248   ,0.0, 0.0},
01929      {-.3762515160890787102213572095560869828717   ,0.0, 0.0},
01930      {-.4758742249551182610344118476674340426272   ,0.0, 0.0},
01931      {-.5697204718114017193080032833564309331247   ,0.0, 0.0},
01932      {-.6566510940388649612198981765067428215696   ,0.0, 0.0},
01933      {-.7356108780136317720281445102925343680161   ,0.0, 0.0},
01934      {-.8056413709171791714478859554252776586717   ,0.0, 0.0},
01935      {-.8658925225743950489422545673796868043419   ,0.0, 0.0},
01936      {-.9156330263921320738696894233299271463525   ,0.0, 0.0},
01937      {-.9542592806289381972541018397052155890034   ,0.0, 0.0},
01938      {-.9813031653708727536945599458078302764442   ,0.0, 0.0},
01939      {-.9964424975739544499504363904833109917501   ,0.0, 0.0}
01940     },
01941     { // weights
01942      .009124282593094517738816153922951706240344,
01943      .02113211259277125975150038099326543445137,
01944      .03290142778230437997763081917053204598153,
01945      .04427293475900422783958787765320739061499,
01946      .05510734567571674543148291822694559121906,
01947      .06527292396699959579339756677550463635364,
01948      .07464621423456877902393188717302203802164,
01949      .08311341722890121839039649824433247986113,
01950      .09057174439303284094218603133678412982286,
01951      .09693065799792991585048900609544060176503,
01952      .1021129675780607698142166385057121350466,
01953      .1060557659228464179104164369968108287899,
01954      .1087111922582941352535715193036733678753,
01955      .1100470130164751962823762656018176139566,
01956       .1100470130164751962823762656018176139566,
01957       .1087111922582941352535715193036733678753,
01958       .1060557659228464179104164369968108287899,
01959       .1021129675780607698142166385057121350466,
01960       .09693065799792991585048900609544060176503,
01961       .09057174439303284094218603133678412982286,
01962       .08311341722890121839039649824433247986113,
01963       .07464621423456877902393188717302203802164,
01964       .06527292396699959579339756677550463635364,
01965       .05510734567571674543148291822694559121906,
01966       .04427293475900422783958787765320739061499,
01967       .03290142778230437997763081917053204598153,
01968       .02113211259277125975150038099326543445137,
01969       .009124282593094517738816153922951706240344
01970     }
01971   },
01972   {
01973     28,
01974     { // points
01975      {.9964424975739544499504363904833109917501    ,0.0, 0.0},
01976      {.9813031653708727536945599458078302764442    ,0.0, 0.0},
01977      {.9542592806289381972541018397052155890034    ,0.0, 0.0},
01978      {.9156330263921320738696894233299271463525    ,0.0, 0.0},
01979      {.8658925225743950489422545673796868043419    ,0.0, 0.0},
01980      {.8056413709171791714478859554252776586717    ,0.0, 0.0},
01981      {.7356108780136317720281445102925343680161    ,0.0, 0.0},
01982      {.6566510940388649612198981765067428215696    ,0.0, 0.0},
01983      {.5697204718114017193080032833564309331247    ,0.0, 0.0},
01984      {.4758742249551182610344118476674340426272    ,0.0, 0.0},
01985      {.3762515160890787102213572095560869828717    ,0.0, 0.0},
01986      {.2720616276351780776768263561257697348248    ,0.0, 0.0},
01987      {.1645692821333807712814717778911654571457    ,0.0, 0.0},
01988      {.0550792898840342704265165273418799778508    ,0.0, 0.0},
01989      {-.0550792898840342704265165273418799778508   ,0.0, 0.0},
01990      {-.1645692821333807712814717778911654571457   ,0.0, 0.0},
01991      {-.2720616276351780776768263561257697348248   ,0.0, 0.0},
01992      {-.3762515160890787102213572095560869828717   ,0.0, 0.0},
01993      {-.4758742249551182610344118476674340426272   ,0.0, 0.0},
01994      {-.5697204718114017193080032833564309331247   ,0.0, 0.0},
01995      {-.6566510940388649612198981765067428215696   ,0.0, 0.0},
01996      {-.7356108780136317720281445102925343680161   ,0.0, 0.0},
01997      {-.8056413709171791714478859554252776586717   ,0.0, 0.0},
01998      {-.8658925225743950489422545673796868043419   ,0.0, 0.0},
01999      {-.9156330263921320738696894233299271463525   ,0.0, 0.0},
02000      {-.9542592806289381972541018397052155890034   ,0.0, 0.0},
02001      {-.9813031653708727536945599458078302764442   ,0.0, 0.0},
02002      {-.9964424975739544499504363904833109917501   ,0.0, 0.0}
02003     },
02004     { // weights
02005      .009124282593094517738816153922951706240344,
02006      .02113211259277125975150038099326543445137,
02007      .03290142778230437997763081917053204598153,
02008      .04427293475900422783958787765320739061499,
02009      .05510734567571674543148291822694559121906,
02010      .06527292396699959579339756677550463635364,
02011      .07464621423456877902393188717302203802164,
02012      .08311341722890121839039649824433247986113,
02013      .09057174439303284094218603133678412982286,
02014      .09693065799792991585048900609544060176503,
02015      .1021129675780607698142166385057121350466,
02016      .1060557659228464179104164369968108287899,
02017      .1087111922582941352535715193036733678753,
02018      .1100470130164751962823762656018176139566,
02019       .1100470130164751962823762656018176139566,
02020       .1087111922582941352535715193036733678753,
02021       .1060557659228464179104164369968108287899,
02022       .1021129675780607698142166385057121350466,
02023       .09693065799792991585048900609544060176503,
02024       .09057174439303284094218603133678412982286,
02025       .08311341722890121839039649824433247986113,
02026       .07464621423456877902393188717302203802164,
02027       .06527292396699959579339756677550463635364,
02028       .05510734567571674543148291822694559121906,
02029       .04427293475900422783958787765320739061499,
02030       .03290142778230437997763081917053204598153,
02031       .02113211259277125975150038099326543445137,
02032       .009124282593094517738816153922951706240344
02033     }
02034   },
02035   {
02036     29,
02037     { // points
02038      {.9966794422605965861631915325493538856518    ,0.0, 0.0},
02039      {.9825455052614131748709260157863769561068    ,0.0, 0.0},
02040      {.9572855957780877257982080369808235637376    ,0.0, 0.0},
02041      {.9211802329530587850937534360831064254088    ,0.0, 0.0},
02042      {.8746378049201027904177934212565785469106    ,0.0, 0.0},
02043      {.81818548761525244498957221457878497563      ,0.0, 0.0},
02044      {.7524628517344771339126100772121381902126    ,0.0, 0.0},
02045      {.6782145376026865151561850053919859263883    ,0.0, 0.0},
02046      {.5962817971382278203795862111889897800782    ,0.0, 0.0},
02047      {.5075929551242276421026279196275201533512    ,0.0, 0.0},
02048      {.4131528881740086638907065860316168233234    ,0.0, 0.0},
02049      {.3140316378676399349481959231910474482584    ,0.0, 0.0},
02050      {.2113522861660010745063757289029374990567    ,0.0, 0.0},
02051      {.1062782301326792301709823924303769809172    ,0.0, 0.0},
02052      {0                                            ,0.0, 0.0},
02053      {-.1062782301326792301709823924303769809172   ,0.0, 0.0},
02054      {-.2113522861660010745063757289029374990567   ,0.0, 0.0},
02055      {-.3140316378676399349481959231910474482584   ,0.0, 0.0},
02056      {-.4131528881740086638907065860316168233234   ,0.0, 0.0},
02057      {-.5075929551242276421026279196275201533512   ,0.0, 0.0},
02058      {-.5962817971382278203795862111889897800782   ,0.0, 0.0},
02059      {-.6782145376026865151561850053919859263883   ,0.0, 0.0},
02060      {-.7524628517344771339126100772121381902126   ,0.0, 0.0},
02061      {-.81818548761525244498957221457878497563     ,0.0, 0.0},
02062      {-.8746378049201027904177934212565785469106   ,0.0, 0.0},
02063      {-.9211802329530587850937534360831064254088   ,0.0, 0.0},
02064      {-.9572855957780877257982080369808235637376   ,0.0, 0.0},
02065      {-.9825455052614131748709260157863769561068   ,0.0, 0.0},
02066      {-.9966794422605965861631915325493538856518   ,0.0, 0.0}
02067     },
02068     { // weights
02069      .008516903878746409654263813302249803002399,
02070      .01973208505612270598385980164039563114961,
02071      .03074049220209362264440852537461674974712,
02072      .04140206251868283610483001011407692153349,
02073      .05159482690249792391259438117954259791962,
02074      .06120309065707913854210984802390704492406,
02075      .07011793325505127856958148694887917310239,
02076      .07823832713576378382814488865968033136688,
02077      .0854722573661725275453448492972080713817,
02078      .09173775713925876334796641107711080689823,
02079      .09696383409440860630190007488268875917636,
02080      .1010912737599149661218205469074973636476,
02081      .1040733100777293739133284712851200689107,
02082      .1058761550973209414065913278521878930748,
02083       .1064793817183142442465111269096775683302,
02084       .1058761550973209414065913278521878930748,
02085       .1040733100777293739133284712851200689107,
02086       .1010912737599149661218205469074973636476,
02087       .09696383409440860630190007488268875917636,
02088       .09173775713925876334796641107711080689823,
02089       .0854722573661725275453448492972080713817,
02090       .07823832713576378382814488865968033136688,
02091       .07011793325505127856958148694887917310239,
02092       .06120309065707913854210984802390704492406,
02093       .05159482690249792391259438117954259791962,
02094       .04140206251868283610483001011407692153349,
02095       .03074049220209362264440852537461674974712,
02096       .01973208505612270598385980164039563114961,
02097       .008516903878746409654263813302249803002399
02098     }
02099   },
02100   {
02101     29,
02102     { // points
02103      {.9966794422605965861631915325493538856518    ,0.0, 0.0},
02104      {.9825455052614131748709260157863769561068    ,0.0, 0.0},
02105      {.9572855957780877257982080369808235637376    ,0.0, 0.0},
02106      {.9211802329530587850937534360831064254088    ,0.0, 0.0},
02107      {.8746378049201027904177934212565785469106    ,0.0, 0.0},
02108      {.81818548761525244498957221457878497563      ,0.0, 0.0},
02109      {.7524628517344771339126100772121381902126    ,0.0, 0.0},
02110      {.6782145376026865151561850053919859263883    ,0.0, 0.0},
02111      {.5962817971382278203795862111889897800782    ,0.0, 0.0},
02112      {.5075929551242276421026279196275201533512    ,0.0, 0.0},
02113      {.4131528881740086638907065860316168233234    ,0.0, 0.0},
02114      {.3140316378676399349481959231910474482584    ,0.0, 0.0},
02115      {.2113522861660010745063757289029374990567    ,0.0, 0.0},
02116      {.1062782301326792301709823924303769809172    ,0.0, 0.0},
02117      {0                                            ,0.0, 0.0},
02118      {-.1062782301326792301709823924303769809172   ,0.0, 0.0},
02119      {-.2113522861660010745063757289029374990567   ,0.0, 0.0},
02120      {-.3140316378676399349481959231910474482584   ,0.0, 0.0},
02121      {-.4131528881740086638907065860316168233234   ,0.0, 0.0},
02122      {-.5075929551242276421026279196275201533512   ,0.0, 0.0},
02123      {-.5962817971382278203795862111889897800782   ,0.0, 0.0},
02124      {-.6782145376026865151561850053919859263883   ,0.0, 0.0},
02125      {-.7524628517344771339126100772121381902126   ,0.0, 0.0},
02126      {-.81818548761525244498957221457878497563     ,0.0, 0.0},
02127      {-.8746378049201027904177934212565785469106   ,0.0, 0.0},
02128      {-.9211802329530587850937534360831064254088   ,0.0, 0.0},
02129      {-.9572855957780877257982080369808235637376   ,0.0, 0.0},
02130      {-.9825455052614131748709260157863769561068   ,0.0, 0.0},
02131      {-.9966794422605965861631915325493538856518   ,0.0, 0.0}
02132     },
02133     { // weights
02134      .008516903878746409654263813302249803002399,
02135      .01973208505612270598385980164039563114961,
02136      .03074049220209362264440852537461674974712,
02137      .04140206251868283610483001011407692153349,
02138      .05159482690249792391259438117954259791962,
02139      .06120309065707913854210984802390704492406,
02140      .07011793325505127856958148694887917310239,
02141      .07823832713576378382814488865968033136688,
02142      .0854722573661725275453448492972080713817,
02143      .09173775713925876334796641107711080689823,
02144      .09696383409440860630190007488268875917636,
02145      .1010912737599149661218205469074973636476,
02146      .1040733100777293739133284712851200689107,
02147      .1058761550973209414065913278521878930748,
02148       .1064793817183142442465111269096775683302,
02149       .1058761550973209414065913278521878930748,
02150       .1040733100777293739133284712851200689107,
02151       .1010912737599149661218205469074973636476,
02152       .09696383409440860630190007488268875917636,
02153       .09173775713925876334796641107711080689823,
02154       .0854722573661725275453448492972080713817,
02155       .07823832713576378382814488865968033136688,
02156       .07011793325505127856958148694887917310239,
02157       .06120309065707913854210984802390704492406,
02158       .05159482690249792391259438117954259791962,
02159       .04140206251868283610483001011407692153349,
02160       .03074049220209362264440852537461674974712,
02161       .01973208505612270598385980164039563114961,
02162       .008516903878746409654263813302249803002399
02163     }
02164   },
02165   {
02166     30,
02167     { // points
02168      {.9968934840746495402716300509186952833409    ,0.0, 0.0},
02169      {.9836681232797472099700325816056628019403    ,0.0, 0.0},
02170      {.9600218649683075122168710255817976629304    ,0.0, 0.0},
02171      {.9262000474292743258793242770804740040865    ,0.0, 0.0},
02172      {.8825605357920526815431164625302255900567    ,0.0, 0.0},
02173      {.8295657623827683974428981197325019164391    ,0.0, 0.0},
02174      {.7677774321048261949179773409745031316949    ,0.0, 0.0},
02175      {.6978504947933157969322923880266400683824    ,0.0, 0.0},
02176      {.6205261829892428611404775564311892992074    ,0.0, 0.0},
02177      {.5366241481420198992641697933110727941642    ,0.0, 0.0},
02178      {.4470337695380891767806099003228540001624    ,0.0, 0.0},
02179      {.3527047255308781134710372070893738606536    ,0.0, 0.0},
02180      {.2546369261678898464398051298178051078828    ,0.0, 0.0},
02181      {.1538699136085835469637946727432559204186    ,0.0, 0.0},
02182      {.05147184255531769583302521316672257374914   ,0.0, 0.0},
02183      {-.05147184255531769583302521316672257374914  ,0.0, 0.0},
02184      {-.1538699136085835469637946727432559204186   ,0.0, 0.0},
02185      {-.2546369261678898464398051298178051078828   ,0.0, 0.0},
02186      {-.3527047255308781134710372070893738606536   ,0.0, 0.0},
02187      {-.4470337695380891767806099003228540001624   ,0.0, 0.0},
02188      {-.5366241481420198992641697933110727941642   ,0.0, 0.0},
02189      {-.6205261829892428611404775564311892992074   ,0.0, 0.0},
02190      {-.6978504947933157969322923880266400683824   ,0.0, 0.0},
02191      {-.7677774321048261949179773409745031316949   ,0.0, 0.0},
02192      {-.8295657623827683974428981197325019164391   ,0.0, 0.0},
02193      {-.8825605357920526815431164625302255900567   ,0.0, 0.0},
02194      {-.9262000474292743258793242770804740040865   ,0.0, 0.0},
02195      {-.9600218649683075122168710255817976629304   ,0.0, 0.0},
02196      {-.9836681232797472099700325816056628019403   ,0.0, 0.0},
02197      {-.9968934840746495402716300509186952833409   ,0.0, 0.0}
02198     },
02199     { // weights
02200      .007968192496166605615465883474673622450481,
02201      .01846646831109095914230213191204726909621,
02202      .02878470788332336934971917961129204363959,
02203      .0387991925696270495968019364463476920332,
02204      .04840267283059405290293814042280751781527,
02205      .05749315621761906648172168940205612879712,
02206      .06597422988218049512812851511596236123744,
02207      .07375597473770520626824385002219073415377,
02208      .08075589522942021535469493846052973087589,
02209      .08689978720108297980238753071512570257675,
02210      .09212252223778612871763270708761876719691,
02211      .09636873717464425963946862635180986509641,
02212      .09959342058679526706278028210356947652987,
02213      .1017623897484055045964289521685540446327,
02214      .1028526528935588403412856367054150438684,
02215       .1028526528935588403412856367054150438684,
02216       .1017623897484055045964289521685540446327,
02217       .09959342058679526706278028210356947652987,
02218       .09636873717464425963946862635180986509641,
02219       .09212252223778612871763270708761876719691,
02220       .08689978720108297980238753071512570257675,
02221       .08075589522942021535469493846052973087589,
02222       .07375597473770520626824385002219073415377,
02223       .06597422988218049512812851511596236123744,
02224       .05749315621761906648172168940205612879712,
02225       .04840267283059405290293814042280751781527,
02226       .0387991925696270495968019364463476920332,
02227       .02878470788332336934971917961129204363959,
02228       .01846646831109095914230213191204726909621,
02229       .007968192496166605615465883474673622450481
02230     }
02231   },
02232   {
02233     30,
02234     { // points
02235      {.9968934840746495402716300509186952833409    ,0.0, 0.0},
02236      {.9836681232797472099700325816056628019403    ,0.0, 0.0},
02237      {.9600218649683075122168710255817976629304    ,0.0, 0.0},
02238      {.9262000474292743258793242770804740040865    ,0.0, 0.0},
02239      {.8825605357920526815431164625302255900567    ,0.0, 0.0},
02240      {.8295657623827683974428981197325019164391    ,0.0, 0.0},
02241      {.7677774321048261949179773409745031316949    ,0.0, 0.0},
02242      {.6978504947933157969322923880266400683824    ,0.0, 0.0},
02243      {.6205261829892428611404775564311892992074    ,0.0, 0.0},
02244      {.5366241481420198992641697933110727941642    ,0.0, 0.0},
02245      {.4470337695380891767806099003228540001624    ,0.0, 0.0},
02246      {.3527047255308781134710372070893738606536    ,0.0, 0.0},
02247      {.2546369261678898464398051298178051078828    ,0.0, 0.0},
02248      {.1538699136085835469637946727432559204186    ,0.0, 0.0},
02249      {.05147184255531769583302521316672257374914   ,0.0, 0.0},
02250      {-.05147184255531769583302521316672257374914  ,0.0, 0.0},
02251      {-.1538699136085835469637946727432559204186   ,0.0, 0.0},
02252      {-.2546369261678898464398051298178051078828   ,0.0, 0.0},
02253      {-.3527047255308781134710372070893738606536   ,0.0, 0.0},
02254      {-.4470337695380891767806099003228540001624   ,0.0, 0.0},
02255      {-.5366241481420198992641697933110727941642   ,0.0, 0.0},
02256      {-.6205261829892428611404775564311892992074   ,0.0, 0.0},
02257      {-.6978504947933157969322923880266400683824   ,0.0, 0.0},
02258      {-.7677774321048261949179773409745031316949   ,0.0, 0.0},
02259      {-.8295657623827683974428981197325019164391   ,0.0, 0.0},
02260      {-.8825605357920526815431164625302255900567   ,0.0, 0.0},
02261      {-.9262000474292743258793242770804740040865   ,0.0, 0.0},
02262      {-.9600218649683075122168710255817976629304   ,0.0, 0.0},
02263      {-.9836681232797472099700325816056628019403   ,0.0, 0.0},
02264      {-.9968934840746495402716300509186952833409   ,0.0, 0.0}
02265     },
02266     { // weights
02267      .007968192496166605615465883474673622450481,
02268      .01846646831109095914230213191204726909621,
02269      .02878470788332336934971917961129204363959,
02270      .0387991925696270495968019364463476920332,
02271      .04840267283059405290293814042280751781527,
02272      .05749315621761906648172168940205612879712,
02273      .06597422988218049512812851511596236123744,
02274      .07375597473770520626824385002219073415377,
02275      .08075589522942021535469493846052973087589,
02276      .08689978720108297980238753071512570257675,
02277      .09212252223778612871763270708761876719691,
02278      .09636873717464425963946862635180986509641,
02279      .09959342058679526706278028210356947652987,
02280      .1017623897484055045964289521685540446327,
02281      .1028526528935588403412856367054150438684,
02282       .1028526528935588403412856367054150438684,
02283       .1017623897484055045964289521685540446327,
02284       .09959342058679526706278028210356947652987,
02285       .09636873717464425963946862635180986509641,
02286       .09212252223778612871763270708761876719691,
02287       .08689978720108297980238753071512570257675,
02288       .08075589522942021535469493846052973087589,
02289       .07375597473770520626824385002219073415377,
02290       .06597422988218049512812851511596236123744,
02291       .05749315621761906648172168940205612879712,
02292       .04840267283059405290293814042280751781527,
02293       .0387991925696270495968019364463476920332,
02294       .02878470788332336934971917961129204363959,
02295       .01846646831109095914230213191204726909621,
02296       .007968192496166605615465883474673622450481
02297     }
02298   },
02299   {
02300     31,
02301     { // points
02302      {.9970874818194770740556265542231025082514    ,0.0, 0.0},
02303      {.9846859096651524840024651667346847109385    ,0.0, 0.0},
02304      {.9625039250929496617890524041058583018972    ,0.0, 0.0},
02305      {.9307569978966481649569457597292635128134    ,0.0, 0.0},
02306      {.8897600299482710433741920089821592615436    ,0.0, 0.0},
02307      {.8399203201462673400869045359401783560547    ,0.0, 0.0},
02308      {.7817331484166249404063600201946844910954    ,0.0, 0.0},
02309      {.7157767845868532839059708653664859558902    ,0.0, 0.0},
02310      {.6427067229242603461844182032325014539917    ,0.0, 0.0},
02311      {.5632491614071492627209449235951614279486    ,0.0, 0.0},
02312      {.4781937820449024804405940393564857484395    ,0.0, 0.0},
02313      {.3883859016082329430613514612875201019851    ,0.0, 0.0},
02314      {.2947180699817016166179038976717043387529    ,0.0, 0.0},
02315      {.1981211993355706287724129960328339377748    ,0.0, 0.0},
02316      {.099555312152341520325174790118940733839     ,0.0, 0.0},
02317      {0                                            ,0.0, 0.0},
02318      {-.099555312152341520325174790118940733839    ,0.0, 0.0},
02319      {-.1981211993355706287724129960328339377748   ,0.0, 0.0},
02320      {-.2947180699817016166179038976717043387529   ,0.0, 0.0},
02321      {-.3883859016082329430613514612875201019851   ,0.0, 0.0},
02322      {-.4781937820449024804405940393564857484395   ,0.0, 0.0},
02323      {-.5632491614071492627209449235951614279486   ,0.0, 0.0},
02324      {-.6427067229242603461844182032325014539917   ,0.0, 0.0},
02325      {-.7157767845868532839059708653664859558902   ,0.0, 0.0},
02326      {-.7817331484166249404063600201946844910954   ,0.0, 0.0},
02327      {-.8399203201462673400869045359401783560547   ,0.0, 0.0},
02328      {-.8897600299482710433741920089821592615436   ,0.0, 0.0},
02329      {-.9307569978966481649569457597292635128134   ,0.0, 0.0},
02330      {-.9625039250929496617890524041058583018972   ,0.0, 0.0},
02331      {-.9846859096651524840024651667346847109385   ,0.0, 0.0},
02332      {-.9970874818194770740556265542231025082514   ,0.0, 0.0}
02333     },
02334     { // weights
02335      .007470831579248775858696875032212407022151,
02336      .01731862079031058246315799608682114136627,
02337      .02700901918497942180060870809193215614236,
02338      .03643227391238546402439201046780344232715,
02339      .04549370752720110290231585789462967726355,
02340      .05410308242491685371166625908662004272039,
02341      .06217478656102842691034354368669666715873,
02342      .06962858323541036616775612625512571051509,
02343      .07639038659877661642635767490133064492576,
02344      .08239299176158926390382336743196177061577,
02345      .08757674060847787612619806969533309222926,
02346      .09189011389364147821536287160715012549731,
02347      .09529024291231951280720419748759668454132,
02348      .09774333538632872509347401097899670383573,
02349      .09922501122667230787487551442861501401754,
02350      .09972054479342645142753383373434943964325,
02351      .09922501122667230787487551442861501401754,
02352       .09774333538632872509347401097899670383573,
02353       .09529024291231951280720419748759668454132,
02354       .09189011389364147821536287160715012549731,
02355       .08757674060847787612619806969533309222926,
02356       .08239299176158926390382336743196177061577,
02357       .07639038659877661642635767490133064492576,
02358       .06962858323541036616775612625512571051509,
02359       .06217478656102842691034354368669666715873,
02360       .05410308242491685371166625908662004272039,
02361       .04549370752720110290231585789462967726355,
02362       .03643227391238546402439201046780344232715,
02363       .02700901918497942180060870809193215614236,
02364       .01731862079031058246315799608682114136627,
02365       .007470831579248775858696875032212407022151
02366     }
02367   },
02368   {
02369     31,
02370     { // points
02371      {.9970874818194770740556265542231025082514    ,0.0, 0.0},
02372      {.9846859096651524840024651667346847109385    ,0.0, 0.0},
02373      {.9625039250929496617890524041058583018972    ,0.0, 0.0},
02374      {.9307569978966481649569457597292635128134    ,0.0, 0.0},
02375      {.8897600299482710433741920089821592615436    ,0.0, 0.0},
02376      {.8399203201462673400869045359401783560547    ,0.0, 0.0},
02377      {.7817331484166249404063600201946844910954    ,0.0, 0.0},
02378      {.7157767845868532839059708653664859558902    ,0.0, 0.0},
02379      {.6427067229242603461844182032325014539917    ,0.0, 0.0},
02380      {.5632491614071492627209449235951614279486    ,0.0, 0.0},
02381      {.4781937820449024804405940393564857484395    ,0.0, 0.0},
02382      {.3883859016082329430613514612875201019851    ,0.0, 0.0},
02383      {.2947180699817016166179038976717043387529    ,0.0, 0.0},
02384      {.1981211993355706287724129960328339377748    ,0.0, 0.0},
02385      {.099555312152341520325174790118940733839     ,0.0, 0.0},
02386      {0                                            ,0.0, 0.0},
02387      {-.099555312152341520325174790118940733839    ,0.0, 0.0},
02388      {-.1981211993355706287724129960328339377748   ,0.0, 0.0},
02389      {-.2947180699817016166179038976717043387529   ,0.0, 0.0},
02390      {-.3883859016082329430613514612875201019851   ,0.0, 0.0},
02391      {-.4781937820449024804405940393564857484395   ,0.0, 0.0},
02392      {-.5632491614071492627209449235951614279486   ,0.0, 0.0},
02393      {-.6427067229242603461844182032325014539917   ,0.0, 0.0},
02394      {-.7157767845868532839059708653664859558902   ,0.0, 0.0},
02395      {-.7817331484166249404063600201946844910954   ,0.0, 0.0},
02396      {-.8399203201462673400869045359401783560547   ,0.0, 0.0},
02397      {-.8897600299482710433741920089821592615436   ,0.0, 0.0},
02398      {-.9307569978966481649569457597292635128134   ,0.0, 0.0},
02399      {-.9625039250929496617890524041058583018972   ,0.0, 0.0},
02400      {-.9846859096651524840024651667346847109385   ,0.0, 0.0},
02401      {-.9970874818194770740556265542231025082514   ,0.0, 0.0}
02402     },
02403     { // weights
02404      .007470831579248775858696875032212407022151,
02405      .01731862079031058246315799608682114136627,
02406      .02700901918497942180060870809193215614236,
02407      .03643227391238546402439201046780344232715,
02408      .04549370752720110290231585789462967726355,
02409      .05410308242491685371166625908662004272039,
02410      .06217478656102842691034354368669666715873,
02411      .06962858323541036616775612625512571051509,
02412      .07639038659877661642635767490133064492576,
02413      .08239299176158926390382336743196177061577,
02414      .08757674060847787612619806969533309222926,
02415      .09189011389364147821536287160715012549731,
02416      .09529024291231951280720419748759668454132,
02417      .09774333538632872509347401097899670383573,
02418      .09922501122667230787487551442861501401754,
02419      .09972054479342645142753383373434943964325,
02420      .09922501122667230787487551442861501401754,
02421       .09774333538632872509347401097899670383573,
02422       .09529024291231951280720419748759668454132,
02423       .09189011389364147821536287160715012549731,
02424       .08757674060847787612619806969533309222926,
02425       .08239299176158926390382336743196177061577,
02426       .07639038659877661642635767490133064492576,
02427       .06962858323541036616775612625512571051509,
02428       .06217478656102842691034354368669666715873,
02429       .05410308242491685371166625908662004272039,
02430       .04549370752720110290231585789462967726355,
02431       .03643227391238546402439201046780344232715,
02432       .02700901918497942180060870809193215614236,
02433       .01731862079031058246315799608682114136627,
02434       .007470831579248775858696875032212407022151
02435     }
02436   } // end Gauss
02437 
02438 };
02439     
02440 } // end namespace Intrepid