Intrepid2
Intrepid2_CubatureDirectLineGaussDef.hpp
Go to the documentation of this file.
1 // @HEADER
2 // *****************************************************************************
3 // Intrepid2 Package
4 //
5 // Copyright 2007 NTESS and the Intrepid2 contributors.
6 // SPDX-License-Identifier: BSD-3-Clause
7 // *****************************************************************************
8 // @HEADER
9 
16 namespace Intrepid2 {
17 
18  template <typename DT, typename PT, typename WT>
19  CubatureDirectLineGauss<DT,PT,WT>::
20  CubatureDirectLineGauss(const ordinal_type degree)
21  : CubatureDirect<DT,PT,WT>(degree, 1) {
22 
23  INTREPID2_TEST_FOR_EXCEPTION( degree < 0 ||
24  degree > static_cast<ordinal_type>(Parameters::MaxCubatureDegreeEdge), std::out_of_range,
25  ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree.");
26 
27  typedef Kokkos::DynRankView<PT,Kokkos::LayoutRight,Kokkos::HostSpace> pointViewHostType;
28  typedef Kokkos::DynRankView<WT,Kokkos::LayoutRight,Kokkos::HostSpace> weightViewHostType;
29 
30  this->cubatureData_.numPoints_ = cubatureDataStatic_[this->degree_].numPoints_;
31  {
32  // src
33  const pointViewHostType points_host(const_cast<PT*>( &(cubatureDataStatic_[this->degree_].points_[0][0]) ),
34  this->cubatureData_.numPoints_,
35  Parameters::MaxDimension);
36 
37  auto points = Kokkos::create_mirror_view(typename DT::memory_space(), points_host);
38 
39  Kokkos::deep_copy(points,points_host);
40 
41  // dst
42  this->cubatureData_.points_ = Kokkos::DynRankView<PT,DT>("CubatureDirectLineGauss::cubatureData_::points_",
43  this->cubatureData_.numPoints_,
44  Parameters::MaxDimension);
45  // copy
46  Kokkos::deep_copy(this->cubatureData_.points_ , points );
47  }
48  {
49  // src
50  const weightViewHostType weights(const_cast<PT*>( &(cubatureDataStatic_[this->degree_].weights_[0]) ),
51  this->cubatureData_.numPoints_);
52 
53  // dst
54  this->cubatureData_.weights_ = Kokkos::DynRankView<WT,DT>("CubatureDirectLineGauss::cubatureData_::weights_",
55  this->cubatureData_.numPoints_);
56  // copy
57  Kokkos::deep_copy(Kokkos::subdynrankview(this->cubatureData_.weights_, Kokkos::ALL()) , Kokkos::subdynrankview(weights, Kokkos::ALL()));
58  }
59  }
60 
61  //-------------------------------------------------------------------------------------//
62  // Definition of cubature templates //
63  //-------------------------------------------------------------------------------------//
64 
65  /*
66  Cubature templates for lines are defined the reference cell:
67 
68  Line -> (-1,0,0),(1,0,0)
69  */
70 
71  /*
72  This static const member contains templates for Gauss(-Legendre) rules.
73  */
74 
75  template<typename DT, typename PT, typename WT>
76  const typename CubatureDirect<DT,PT,WT>::CubatureDataStatic
77  CubatureDirectLineGauss<DT,PT,WT>::
78  cubatureDataStatic_[cubatureDataStaticSize] = {
79  // Collection of Gauss rules on [-1,1]
80  // The rule with array index i is exact for polynomials up to order i
81  {
82  1,
83  {{0e0, 0.0, 0.0}},
84  {2e0}
85  },
86  {
87  1,
88  {{0e0, 0.0, 0.0}},
89  {2e0}
90  },
91  {
92  2,
93  {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
94  {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
95  {1e0,
96  1e0}
97  },
98  {
99  2,
100  {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
101  {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
102  {1e0,
103  1e0}
104  },
105  {
106  3,
107  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
108  {0e0, 0.0, 0.0},
109  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
110  {5.555555555555555555555555555555555555556e-1,
111  8.888888888888888888888888888888888888889e-1,
112  5.555555555555555555555555555555555555556e-1}
113  },
114  {
115  3,
116  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
117  {0e0, 0.0, 0.0},
118  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
119  {5.555555555555555555555555555555555555556e-1,
120  8.888888888888888888888888888888888888889e-1,
121  5.555555555555555555555555555555555555556e-1}
122  },
123  {
124  4,
125  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
126  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
127  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
128  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
129  {3.478548451374538573730639492219994072353e-1,
130  6.521451548625461426269360507780005927647e-1,
131  6.521451548625461426269360507780005927647e-1,
132  3.478548451374538573730639492219994072353e-1}
133  },
134  {
135  4,
136  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
137  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
138  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
139  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
140  {3.478548451374538573730639492219994072353e-1,
141  6.521451548625461426269360507780005927647e-1,
142  6.521451548625461426269360507780005927647e-1,
143  3.478548451374538573730639492219994072353e-1}
144  },
145  {
146  5,
147  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
148  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
149  {0e0, 0.0, 0.0},
150  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
151  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
152  {2.369268850561890875142640407199173626433e-1,
153  4.786286704993664680412915148356381929123e-1,
154  5.688888888888888888888888888888888888889e-1,
155  4.786286704993664680412915148356381929123e-1,
156  2.369268850561890875142640407199173626433e-1}
157  },
158  {
159  5,
160  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
161  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
162  {0e0, 0.0, 0.0},
163  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
164  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
165  {2.369268850561890875142640407199173626433e-1,
166  4.786286704993664680412915148356381929123e-1,
167  5.688888888888888888888888888888888888889e-1,
168  4.786286704993664680412915148356381929123e-1,
169  2.369268850561890875142640407199173626433e-1}
170  },
171  {
172  6,
173  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
174  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
175  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
176  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
177  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
178  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
179  {1.713244923791703450402961421727328935268e-1,
180  3.607615730481386075698335138377161116615e-1,
181  4.679139345726910473898703439895509948117e-1,
182  4.679139345726910473898703439895509948117e-1,
183  3.607615730481386075698335138377161116615e-1,
184  1.713244923791703450402961421727328935268e-1}
185  },
186  {
187  6,
188  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
189  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
190  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
191  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
192  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
193  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
194  {1.713244923791703450402961421727328935268e-1,
195  3.607615730481386075698335138377161116615e-1,
196  4.679139345726910473898703439895509948117e-1,
197  4.679139345726910473898703439895509948117e-1,
198  3.607615730481386075698335138377161116615e-1,
199  1.713244923791703450402961421727328935268e-1}
200  },
201  {
202  7,
203  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
204  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
205  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
206  {0e0, 0.0, 0.0},
207  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
208  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
209  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
210  {1.294849661688696932706114326790820183286e-1,
211  2.797053914892766679014677714237795824869e-1,
212  3.818300505051189449503697754889751338784e-1,
213  4.179591836734693877551020408163265306122e-1,
214  3.818300505051189449503697754889751338784e-1,
215  2.797053914892766679014677714237795824869e-1,
216  1.294849661688696932706114326790820183286e-1}
217  },
218  {
219  7,
220  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
221  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
222  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
223  {0e0, 0.0, 0.0},
224  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
225  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
226  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
227  {1.294849661688696932706114326790820183286e-1,
228  2.797053914892766679014677714237795824869e-1,
229  3.818300505051189449503697754889751338784e-1,
230  4.179591836734693877551020408163265306122e-1,
231  3.818300505051189449503697754889751338784e-1,
232  2.797053914892766679014677714237795824869e-1,
233  1.294849661688696932706114326790820183286e-1}
234  },
235  {
236  8,
237  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
238  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
239  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
240  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
241  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
242  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
243  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
244  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
245  {1.012285362903762591525313543099621901154e-1,
246  2.223810344533744705443559944262408844301e-1,
247  3.137066458778872873379622019866013132603e-1,
248  3.626837833783619829651504492771956121941e-1,
249  3.626837833783619829651504492771956121941e-1,
250  3.137066458778872873379622019866013132603e-1,
251  2.223810344533744705443559944262408844301e-1,
252  1.012285362903762591525313543099621901154e-1}
253  },
254  {
255  8,
256  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
257  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
258  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
259  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
260  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
261  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
262  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
263  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
264  {1.012285362903762591525313543099621901154e-1,
265  2.223810344533744705443559944262408844301e-1,
266  3.137066458778872873379622019866013132603e-1,
267  3.626837833783619829651504492771956121941e-1,
268  3.626837833783619829651504492771956121941e-1,
269  3.137066458778872873379622019866013132603e-1,
270  2.223810344533744705443559944262408844301e-1,
271  1.012285362903762591525313543099621901154e-1}
272  },
273  {
274  9,
275  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
276  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
277  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
278  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
279  {0e0, 0.0, 0.0},
280  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
281  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
282  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
283  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
284  {8.127438836157441197189215811052365067566e-2,
285  1.806481606948574040584720312429128095143e-1,
286  2.606106964029354623187428694186328497718e-1,
287  3.123470770400028400686304065844436655988e-1,
288  3.302393550012597631645250692869740488788e-1,
289  3.123470770400028400686304065844436655988e-1,
290  2.606106964029354623187428694186328497718e-1,
291  1.806481606948574040584720312429128095143e-1,
292  8.127438836157441197189215811052365067566e-2}
293  },
294  {
295  9,
296  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
297  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
298  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
299  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
300  {0e0, 0.0, 0.0},
301  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
302  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
303  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
304  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
305  {8.127438836157441197189215811052365067566e-2,
306  1.806481606948574040584720312429128095143e-1,
307  2.606106964029354623187428694186328497718e-1,
308  3.123470770400028400686304065844436655988e-1,
309  3.302393550012597631645250692869740488788e-1,
310  3.123470770400028400686304065844436655988e-1,
311  2.606106964029354623187428694186328497718e-1,
312  1.806481606948574040584720312429128095143e-1,
313  8.127438836157441197189215811052365067566e-2}
314  },
315  {
316  10,
317  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
318  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
319  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
320  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
321  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
322  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
323  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
324  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
325  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
326  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
327  {6.667134430868813759356880989333179285786e-2,
328  1.494513491505805931457763396576973324026e-1,
329  2.190863625159820439955349342281631924588e-1,
330  2.692667193099963550912269215694693528598e-1,
331  2.95524224714752870173892994651338329421e-1,
332  2.95524224714752870173892994651338329421e-1,
333  2.692667193099963550912269215694693528598e-1,
334  2.190863625159820439955349342281631924588e-1,
335  1.494513491505805931457763396576973324026e-1,
336  6.667134430868813759356880989333179285786e-2}
337  },
338  {
339  10,
340  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
341  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
342  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
343  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
344  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
345  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
346  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
347  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
348  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
349  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
350  {6.667134430868813759356880989333179285786e-2,
351  1.494513491505805931457763396576973324026e-1,
352  2.190863625159820439955349342281631924588e-1,
353  2.692667193099963550912269215694693528598e-1,
354  2.95524224714752870173892994651338329421e-1,
355  2.95524224714752870173892994651338329421e-1,
356  2.692667193099963550912269215694693528598e-1,
357  2.190863625159820439955349342281631924588e-1,
358  1.494513491505805931457763396576973324026e-1,
359  6.667134430868813759356880989333179285786e-2}
360  },
361  {
362  11,
363  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
364  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
365  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
366  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
367  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
368  {0e0, 0.0, 0.0},
369  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
370  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
371  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
372  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
373  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
374  {5.566856711617366648275372044254857872852e-2,
375  1.255803694649046246346942992239401001976e-1,
376  1.862902109277342514260976414316558916913e-1,
377  2.331937645919904799185237048431751394318e-1,
378  2.628045445102466621806888698905091953728e-1,
379  2.72925086777900630714483528336342189156e-1,
380  2.628045445102466621806888698905091953728e-1,
381  2.331937645919904799185237048431751394318e-1,
382  1.862902109277342514260976414316558916913e-1,
383  1.255803694649046246346942992239401001976e-1,
384  5.566856711617366648275372044254857872852e-2}
385  },
386  {
387  11,
388  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
389  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
390  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
391  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
392  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
393  {0e0, 0.0, 0.0},
394  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
395  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
396  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
397  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
398  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
399  {5.566856711617366648275372044254857872852e-2,
400  1.255803694649046246346942992239401001976e-1,
401  1.862902109277342514260976414316558916913e-1,
402  2.331937645919904799185237048431751394318e-1,
403  2.628045445102466621806888698905091953728e-1,
404  2.72925086777900630714483528336342189156e-1,
405  2.628045445102466621806888698905091953728e-1,
406  2.331937645919904799185237048431751394318e-1,
407  1.862902109277342514260976414316558916913e-1,
408  1.255803694649046246346942992239401001976e-1,
409  5.566856711617366648275372044254857872852e-2}
410  },
411  {
412  12,
413  { // points
414  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
415  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
416  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
417  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
418  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
419  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
420  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
421  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
422  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
423  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
424  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
425  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
426  },
427  { // weights
428  .04717533638651182719461596148501706031703,
429  .1069393259953184309602547181939962242146,
430  .160078328543346226334652529543359071872,
431  .2031674267230659217490644558097983765065,
432  .2334925365383548087608498989248780562594,
433  .2491470458134027850005624360429512108305,
434  .2491470458134027850005624360429512108305,
435  .2334925365383548087608498989248780562594,
436  .2031674267230659217490644558097983765065,
437  .160078328543346226334652529543359071872,
438  .1069393259953184309602547181939962242146,
439  .04717533638651182719461596148501706031703
440  }
441  },
442  {
443  12,
444  { // points
445  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
446  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
447  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
448  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
449  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
450  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
451  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
452  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
453  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
454  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
455  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
456  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
457  },
458  { // weights
459  .04717533638651182719461596148501706031703,
460  .1069393259953184309602547181939962242146,
461  .160078328543346226334652529543359071872,
462  .2031674267230659217490644558097983765065,
463  .2334925365383548087608498989248780562594,
464  .2491470458134027850005624360429512108305,
465  .2491470458134027850005624360429512108305,
466  .2334925365383548087608498989248780562594,
467  .2031674267230659217490644558097983765065,
468  .160078328543346226334652529543359071872,
469  .1069393259953184309602547181939962242146,
470  .04717533638651182719461596148501706031703
471  }
472  },
473  {
474  13,
475  { // points
476  {.984183054718588149472829448807109611065 ,0.0, 0.0},
477  {.9175983992229779652065478365007195123905 ,0.0, 0.0},
478  {.8015780907333099127942064895828598903056 ,0.0, 0.0},
479  {.6423493394403402206439846069955156500717 ,0.0, 0.0},
480  {.4484927510364468528779128521276398678019 ,0.0, 0.0},
481  {.2304583159551347940655281210979888352115 ,0.0, 0.0},
482  { 0 ,0.0, 0.0},
483  {-.2304583159551347940655281210979888352115 ,0.0, 0.0},
484  {-.4484927510364468528779128521276398678019 ,0.0, 0.0},
485  {-.6423493394403402206439846069955156500717 ,0.0, 0.0},
486  {-.8015780907333099127942064895828598903056 ,0.0, 0.0},
487  {-.9175983992229779652065478365007195123905 ,0.0, 0.0},
488  {-.984183054718588149472829448807109611065 ,0.0, 0.0}
489  },
490  { // weights
491  .04048400476531587952002159220098606004199,
492  .09212149983772844791442177595379712092368,
493  .1388735102197872384636017768688714676219,
494  .1781459807619457382800466919960979955128,
495  .2078160475368885023125232193060527633866,
496  .2262831802628972384120901860397766184348,
497  .2325515532308739101945895152688359481566,
498  .2262831802628972384120901860397766184348,
499  .2078160475368885023125232193060527633866,
500  .1781459807619457382800466919960979955128,
501  .1388735102197872384636017768688714676219,
502  .09212149983772844791442177595379712092368,
503  .04048400476531587952002159220098606004199
504  }
505  },
506  {
507  13,
508  { // points
509  {.984183054718588149472829448807109611065 ,0.0, 0.0},
510  {.9175983992229779652065478365007195123905 ,0.0, 0.0},
511  {.8015780907333099127942064895828598903056 ,0.0, 0.0},
512  {.6423493394403402206439846069955156500717 ,0.0, 0.0},
513  {.4484927510364468528779128521276398678019 ,0.0, 0.0},
514  {.2304583159551347940655281210979888352115 ,0.0, 0.0},
515  { 0 ,0.0, 0.0},
516  {-.2304583159551347940655281210979888352115 ,0.0, 0.0},
517  {-.4484927510364468528779128521276398678019 ,0.0, 0.0},
518  {-.6423493394403402206439846069955156500717 ,0.0, 0.0},
519  {-.8015780907333099127942064895828598903056 ,0.0, 0.0},
520  {-.9175983992229779652065478365007195123905 ,0.0, 0.0},
521  {-.984183054718588149472829448807109611065 ,0.0, 0.0}
522  },
523  { // weights
524  .04048400476531587952002159220098606004199,
525  .09212149983772844791442177595379712092368,
526  .1388735102197872384636017768688714676219,
527  .1781459807619457382800466919960979955128,
528  .2078160475368885023125232193060527633866,
529  .2262831802628972384120901860397766184348,
530  .2325515532308739101945895152688359481566,
531  .2262831802628972384120901860397766184348,
532  .2078160475368885023125232193060527633866,
533  .1781459807619457382800466919960979955128,
534  .1388735102197872384636017768688714676219,
535  .09212149983772844791442177595379712092368,
536  .04048400476531587952002159220098606004199
537  }
538  },
539  {
540  14,
541  { // points
542  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
543  {.928434883663573517336391139377874264477 ,0.0, 0.0},
544  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
545  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
546  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
547  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
548  {.108054948707343662066244650219834747612 ,0.0, 0.0},
549  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
550  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
551  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
552  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
553  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
554  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
555  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
556  },
557  { // weights
558  .03511946033175186303183287613819178061971,
559  .0801580871597602098056332770628543095837,
560  .1215185706879031846894148090724766259567,
561  .1572031671581935345696019386238421566057,
562  .1855383974779378137417165901251570362489,
563  .2051984637212956039659240656612180557103,
564  .215263853463157790195876443316260035275,
565  .215263853463157790195876443316260035275,
566  .2051984637212956039659240656612180557103,
567  .1855383974779378137417165901251570362489,
568  .1572031671581935345696019386238421566057,
569  .1215185706879031846894148090724766259567,
570  .0801580871597602098056332770628543095837,
571  .03511946033175186303183287613819178061971
572  }
573  },
574  {
575  14,
576  { // points
577  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
578  {.928434883663573517336391139377874264477 ,0.0, 0.0},
579  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
580  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
581  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
582  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
583  {.108054948707343662066244650219834747612 ,0.0, 0.0},
584  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
585  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
586  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
587  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
588  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
589  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
590  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
591  },
592  { // weights
593  .03511946033175186303183287613819178061971,
594  .0801580871597602098056332770628543095837,
595  .1215185706879031846894148090724766259567,
596  .1572031671581935345696019386238421566057,
597  .1855383974779378137417165901251570362489,
598  .2051984637212956039659240656612180557103,
599  .215263853463157790195876443316260035275,
600  .215263853463157790195876443316260035275,
601  .2051984637212956039659240656612180557103,
602  .1855383974779378137417165901251570362489,
603  .1572031671581935345696019386238421566057,
604  .1215185706879031846894148090724766259567,
605  .0801580871597602098056332770628543095837,
606  .03511946033175186303183287613819178061971
607  }
608  },
609  {
610  15,
611  { // points
612  {.987992518020485428489565718586612581147 ,0.0, 0.0},
613  {.937273392400705904307758947710209471244 ,0.0, 0.0},
614  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
615  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
616  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
617  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
618  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
619  { 0 ,0.0, 0.0},
620  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
621  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
622  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
623  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
624  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
625  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
626  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
627  },
628  { // weights
629  .03075324199611726835462839357720441772175,
630  .07036604748810812470926741645066733846671,
631  .1071592204671719350118695466858693034155,
632  .1395706779261543144478047945110283225209,
633  .1662692058169939335532008604812088111309,
634  .1861610000155622110268005618664228245062,
635  .1984314853271115764561183264438393248187,
636  .2025782419255612728806201999675193148387,
637  .1984314853271115764561183264438393248187,
638  .1861610000155622110268005618664228245062,
639  .1662692058169939335532008604812088111309,
640  .1395706779261543144478047945110283225209,
641  .1071592204671719350118695466858693034155,
642  .07036604748810812470926741645066733846671,
643  .03075324199611726835462839357720441772175
644  }
645  },
646  {
647  15,
648  { // points
649  {.987992518020485428489565718586612581147 ,0.0, 0.0},
650  {.937273392400705904307758947710209471244 ,0.0, 0.0},
651  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
652  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
653  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
654  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
655  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
656  { 0 ,0.0, 0.0},
657  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
658  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
659  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
660  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
661  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
662  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
663  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
664  },
665  { // weights
666  .03075324199611726835462839357720441772175,
667  .07036604748810812470926741645066733846671,
668  .1071592204671719350118695466858693034155,
669  .1395706779261543144478047945110283225209,
670  .1662692058169939335532008604812088111309,
671  .1861610000155622110268005618664228245062,
672  .1984314853271115764561183264438393248187,
673  .2025782419255612728806201999675193148387,
674  .1984314853271115764561183264438393248187,
675  .1861610000155622110268005618664228245062,
676  .1662692058169939335532008604812088111309,
677  .1395706779261543144478047945110283225209,
678  .1071592204671719350118695466858693034155,
679  .07036604748810812470926741645066733846671,
680  .03075324199611726835462839357720441772175
681  }
682  },
683  {
684  16,
685  { // points
686  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
687  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
688  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
689  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
690  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
691  {.45801677765722738634241944298357757354 ,0.0, 0.0},
692  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
693  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
694  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
695  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
696  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
697  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
698  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
699  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
700  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
701  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
702  },
703  { // weights
704  .02715245941175409485178057245601810351227,
705  .06225352393864789286284383699437769427499,
706  .09515851168249278480992510760224622635526,
707  .1246289712555338720524762821920164201449,
708  .1495959888165767320815017305474785489705,
709  .1691565193950025381893120790303599622116,
710  .1826034150449235888667636679692199393836,
711  .1894506104550684962853967232082831051469,
712  .1894506104550684962853967232082831051469,
713  .1826034150449235888667636679692199393836,
714  .1691565193950025381893120790303599622116,
715  .1495959888165767320815017305474785489705,
716  .1246289712555338720524762821920164201449,
717  .09515851168249278480992510760224622635526,
718  .06225352393864789286284383699437769427499,
719  .02715245941175409485178057245601810351227
720  }
721  },
722  {
723  16,
724  { // points
725  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
726  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
727  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
728  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
729  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
730  {.45801677765722738634241944298357757354 ,0.0, 0.0},
731  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
732  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
733  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
734  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
735  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
736  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
737  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
738  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
739  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
740  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
741  },
742  { // weights
743  .02715245941175409485178057245601810351227,
744  .06225352393864789286284383699437769427499,
745  .09515851168249278480992510760224622635526,
746  .1246289712555338720524762821920164201449,
747  .1495959888165767320815017305474785489705,
748  .1691565193950025381893120790303599622116,
749  .1826034150449235888667636679692199393836,
750  .1894506104550684962853967232082831051469,
751  .1894506104550684962853967232082831051469,
752  .1826034150449235888667636679692199393836,
753  .1691565193950025381893120790303599622116,
754  .1495959888165767320815017305474785489705,
755  .1246289712555338720524762821920164201449,
756  .09515851168249278480992510760224622635526,
757  .06225352393864789286284383699437769427499,
758  .02715245941175409485178057245601810351227
759  }
760  },
761  {
762  17,
763  { // points
764  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
765  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
766  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
767  {.781514003896801406925230055520476050224 ,0.0, 0.0},
768  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
769  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
770  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
771  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
772  { 0 ,0.0, 0.0},
773  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
774  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
775  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
776  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
777  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
778  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
779  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
780  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
781  },
782  { // weights
783  .0241483028685479319601100262875653246917,
784  .05545952937398720112944016535824466051285,
785  .08503614831717918088353537019106207385049,
786  .1118838471934039710947883856263559267358,
787  .1351363684685254732863199817023501973721,
788  .1540457610768102880814315948019586119405,
789  .1680041021564500445099706637883231550212,
790  .1765627053669926463252709901131972391509,
791  .1794464703562065254582656442618856214488,
792  .1765627053669926463252709901131972391509,
793  .1680041021564500445099706637883231550212,
794  .1540457610768102880814315948019586119405,
795  .1351363684685254732863199817023501973721,
796  .1118838471934039710947883856263559267358,
797  .08503614831717918088353537019106207385049,
798  .05545952937398720112944016535824466051285,
799  .0241483028685479319601100262875653246917
800  }
801  },
802  {
803  17,
804  { // points
805  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
806  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
807  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
808  {.781514003896801406925230055520476050224 ,0.0, 0.0},
809  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
810  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
811  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
812  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
813  { 0 ,0.0, 0.0},
814  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
815  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
816  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
817  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
818  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
819  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
820  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
821  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
822  },
823  { // weights
824  .0241483028685479319601100262875653246917,
825  .05545952937398720112944016535824466051285,
826  .08503614831717918088353537019106207385049,
827  .1118838471934039710947883856263559267358,
828  .1351363684685254732863199817023501973721,
829  .1540457610768102880814315948019586119405,
830  .1680041021564500445099706637883231550212,
831  .1765627053669926463252709901131972391509,
832  .1794464703562065254582656442618856214488,
833  .1765627053669926463252709901131972391509,
834  .1680041021564500445099706637883231550212,
835  .1540457610768102880814315948019586119405,
836  .1351363684685254732863199817023501973721,
837  .1118838471934039710947883856263559267358,
838  .08503614831717918088353537019106207385049,
839  .05545952937398720112944016535824466051285,
840  .0241483028685479319601100262875653246917
841  }
842  },
843  {
844  18,
845  { // points
846  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
847  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
848  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
849  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
850  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
851  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
852  {.411751161462842646035931793833051637079 ,0.0, 0.0},
853  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
854  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
855  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
856  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
857  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
858  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
859  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
860  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
861  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
862  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
863  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
864  },
865  { // weights
866  .02161601352648331031334271026645246938769,
867  .04971454889496979645333494620263864168087,
868  .07642573025488905652912967761663652560532,
869  .1009420441062871655628139849248346070628,
870  .1225552067114784601845191268002015552282,
871  .1406429146706506512047313037519472280955,
872  .1546846751262652449254180038363747721932,
873  .1642764837458327229860537764659275904123,
874  .1691423829631435918406564701349866103341,
875  .1691423829631435918406564701349866103341,
876  .1642764837458327229860537764659275904123,
877  .1546846751262652449254180038363747721932,
878  .1406429146706506512047313037519472280955,
879  .1225552067114784601845191268002015552282,
880  .1009420441062871655628139849248346070628,
881  .07642573025488905652912967761663652560532,
882  .04971454889496979645333494620263864168087,
883  .02161601352648331031334271026645246938769
884  }
885  },
886  {
887  18,
888  { // points
889  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
890  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
891  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
892  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
893  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
894  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
895  {.411751161462842646035931793833051637079 ,0.0, 0.0},
896  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
897  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
898  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
899  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
900  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
901  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
902  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
903  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
904  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
905  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
906  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
907  },
908  { // weights
909  .02161601352648331031334271026645246938769,
910  .04971454889496979645333494620263864168087,
911  .07642573025488905652912967761663652560532,
912  .1009420441062871655628139849248346070628,
913  .1225552067114784601845191268002015552282,
914  .1406429146706506512047313037519472280955,
915  .1546846751262652449254180038363747721932,
916  .1642764837458327229860537764659275904123,
917  .1691423829631435918406564701349866103341,
918  .1691423829631435918406564701349866103341,
919  .1642764837458327229860537764659275904123,
920  .1546846751262652449254180038363747721932,
921  .1406429146706506512047313037519472280955,
922  .1225552067114784601845191268002015552282,
923  .1009420441062871655628139849248346070628,
924  .07642573025488905652912967761663652560532,
925  .04971454889496979645333494620263864168087,
926  .02161601352648331031334271026645246938769
927  }
928  },
929  {
930  19,
931  { // points
932  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
933  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
934  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
935  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
936  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
937  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
938  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
939  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
940  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
941  { 0 ,0.0, 0.0},
942  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
943  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
944  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
945  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
946  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
947  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
948  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
949  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
950  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
951  },
952  { // weights
953  .01946178822972647703631204146443843575291,
954  .04481422676569960033283815740199421195175,
955  .06904454273764122658070825800601304496185,
956  .09149002162244999946446209412383965266091,
957  .1115666455473339947160239016817659974813,
958  .1287539625393362276755157848568771170558,
959  .1426067021736066117757461094419029724757,
960  .152766042065859666778855400897662998461,
961  .1589688433939543476499564394650472016788,
962  .1610544498487836959791636253209167350399,
963  .1589688433939543476499564394650472016788,
964  .152766042065859666778855400897662998461,
965  .1426067021736066117757461094419029724757,
966  .1287539625393362276755157848568771170558,
967  .1115666455473339947160239016817659974813,
968  .09149002162244999946446209412383965266091,
969  .06904454273764122658070825800601304496185,
970  .04481422676569960033283815740199421195175,
971  .01946178822972647703631204146443843575291
972  }
973  },
974  {
975  19,
976  { // points
977  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
978  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
979  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
980  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
981  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
982  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
983  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
984  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
985  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
986  { 0 ,0.0, 0.0},
987  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
988  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
989  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
990  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
991  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
992  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
993  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
994  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
995  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
996  },
997  { // weights
998  .01946178822972647703631204146443843575291,
999  .04481422676569960033283815740199421195175,
1000  .06904454273764122658070825800601304496185,
1001  .09149002162244999946446209412383965266091,
1002  .1115666455473339947160239016817659974813,
1003  .1287539625393362276755157848568771170558,
1004  .1426067021736066117757461094419029724757,
1005  .152766042065859666778855400897662998461,
1006  .1589688433939543476499564394650472016788,
1007  .1610544498487836959791636253209167350399,
1008  .1589688433939543476499564394650472016788,
1009  .152766042065859666778855400897662998461,
1010  .1426067021736066117757461094419029724757,
1011  .1287539625393362276755157848568771170558,
1012  .1115666455473339947160239016817659974813,
1013  .09149002162244999946446209412383965266091,
1014  .06904454273764122658070825800601304496185,
1015  .04481422676569960033283815740199421195175,
1016  .01946178822972647703631204146443843575291
1017  }
1018  },
1019  {
1020  20,
1021  { // points
1022  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1023  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1024  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1025  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1026  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1027  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1028  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1029  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1030  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1031  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1032  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1033  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1034  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1035  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1036  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1037  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1038  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1039  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1040  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1041  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1042  },
1043  { // weights
1044  .01761400713915211831186196235185281636214,
1045  .04060142980038694133103995227493210987909,
1046  .0626720483341090635695065351870416063516,
1047  .08327674157670474872475814322204620610018,
1048  .1019301198172404350367501354803498761667,
1049  .118194531961518417312377377711382287005,
1050  .1316886384491766268984944997481631349161,
1051  .1420961093183820513292983250671649330345,
1052  .1491729864726037467878287370019694366927,
1053  .1527533871307258506980843319550975934919,
1054  .1527533871307258506980843319550975934919,
1055  .1491729864726037467878287370019694366927,
1056  .1420961093183820513292983250671649330345,
1057  .1316886384491766268984944997481631349161,
1058  .118194531961518417312377377711382287005,
1059  .1019301198172404350367501354803498761667,
1060  .08327674157670474872475814322204620610018,
1061  .0626720483341090635695065351870416063516,
1062  .04060142980038694133103995227493210987909,
1063  .01761400713915211831186196235185281636214
1064  }
1065  },
1066  {
1067  20,
1068  { // points
1069  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1070  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1071  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1072  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1073  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1074  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1075  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1076  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1077  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1078  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1079  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1080  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1081  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1082  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1083  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1084  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1085  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1086  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1087  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1088  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1089  },
1090  { // weights
1091  .01761400713915211831186196235185281636214,
1092  .04060142980038694133103995227493210987909,
1093  .0626720483341090635695065351870416063516,
1094  .08327674157670474872475814322204620610018,
1095  .1019301198172404350367501354803498761667,
1096  .118194531961518417312377377711382287005,
1097  .1316886384491766268984944997481631349161,
1098  .1420961093183820513292983250671649330345,
1099  .1491729864726037467878287370019694366927,
1100  .1527533871307258506980843319550975934919,
1101  .1527533871307258506980843319550975934919,
1102  .1491729864726037467878287370019694366927,
1103  .1420961093183820513292983250671649330345,
1104  .1316886384491766268984944997481631349161,
1105  .118194531961518417312377377711382287005,
1106  .1019301198172404350367501354803498761667,
1107  .08327674157670474872475814322204620610018,
1108  .0626720483341090635695065351870416063516,
1109  .04060142980038694133103995227493210987909,
1110  .01761400713915211831186196235185281636214
1111  }
1112  },
1113  {
1114  21,
1115  { // points
1116  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1117  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1118  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1119  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1120  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1121  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1122  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1123  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1124  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1125  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1126  {0 ,0.0, 0.0},
1127  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1128  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1129  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1130  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1131  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1132  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1133  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1134  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1135  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1136  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1137  },
1138  { // weights
1139  .01601722825777433332422461685847101526589,
1140  .03695378977085249379995066829932966618894,
1141  .05713442542685720828363582647244795749129,
1142  .07610011362837930201705165330018317922615,
1143  .09344442345603386155328974111393208848353,
1144  .1087972991671483776634745780701056420337,
1145  .1218314160537285341953671771257335983563,
1146  .132268938633337461781052574496775604329,
1147  .1398873947910731547221334238675831108928,
1148  .1445244039899700590638271665537525436099,
1149  .1460811336496904271919851476833711882448,
1150  .1445244039899700590638271665537525436099,
1151  .1398873947910731547221334238675831108928,
1152  .132268938633337461781052574496775604329,
1153  .1218314160537285341953671771257335983563,
1154  .1087972991671483776634745780701056420337,
1155  .09344442345603386155328974111393208848353,
1156  .07610011362837930201705165330018317922615,
1157  .05713442542685720828363582647244795749129,
1158  .03695378977085249379995066829932966618894,
1159  .01601722825777433332422461685847101526589
1160  }
1161  },
1162  {
1163  21,
1164  { // points
1165  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1166  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1167  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1168  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1169  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1170  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1171  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1172  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1173  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1174  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1175  {0 ,0.0, 0.0},
1176  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1177  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1178  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1179  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1180  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1181  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1182  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1183  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1184  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1185  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1186  },
1187  { // weights
1188  .01601722825777433332422461685847101526589,
1189  .03695378977085249379995066829932966618894,
1190  .05713442542685720828363582647244795749129,
1191  .07610011362837930201705165330018317922615,
1192  .09344442345603386155328974111393208848353,
1193  .1087972991671483776634745780701056420337,
1194  .1218314160537285341953671771257335983563,
1195  .132268938633337461781052574496775604329,
1196  .1398873947910731547221334238675831108928,
1197  .1445244039899700590638271665537525436099,
1198  .1460811336496904271919851476833711882448,
1199  .1445244039899700590638271665537525436099,
1200  .1398873947910731547221334238675831108928,
1201  .132268938633337461781052574496775604329,
1202  .1218314160537285341953671771257335983563,
1203  .1087972991671483776634745780701056420337,
1204  .09344442345603386155328974111393208848353,
1205  .07610011362837930201705165330018317922615,
1206  .05713442542685720828363582647244795749129,
1207  .03695378977085249379995066829932966618894,
1208  .01601722825777433332422461685847101526589
1209  }
1210  },
1211  {
1212  22,
1213  { // points
1214  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1215  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1216  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1217  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1218  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1219  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1220  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1221  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1222  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1223  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1224  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1225  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1226  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1227  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1228  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1229  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1230  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1231  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1232  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1233  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1234  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1235  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1236  },
1237  { // weights
1238  .01462799529827220068499109804718544519021,
1239  .03377490158481415479330224686591290134917,
1240  .05229333515268328594031205127321125611215,
1241  .06979646842452048809496141893021765739878,
1242  .08594160621706772741444368137270286618914,
1243  .1004141444428809649320788378305362823508,
1244  .1129322960805392183934006074217843191143,
1245  .1232523768105124242855609861548144719594,
1246  .1311735047870623707329649925303074458757,
1247  .1365414983460151713525738312315173965864,
1248  .1392518728556319933754102483418099578739,
1249  .1392518728556319933754102483418099578739,
1250  .1365414983460151713525738312315173965864,
1251  .1311735047870623707329649925303074458757,
1252  .1232523768105124242855609861548144719594,
1253  .1129322960805392183934006074217843191143,
1254  .1004141444428809649320788378305362823508,
1255  .08594160621706772741444368137270286618914,
1256  .06979646842452048809496141893021765739878,
1257  .05229333515268328594031205127321125611215,
1258  .03377490158481415479330224686591290134917,
1259  .01462799529827220068499109804718544519021
1260  }
1261  },
1262  {
1263  22,
1264  { // points
1265  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1266  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1267  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1268  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1269  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1270  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1271  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1272  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1273  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1274  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1275  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1276  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1277  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1278  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1279  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1280  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1281  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1282  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1283  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1284  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1285  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1286  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1287  },
1288  { // weights
1289  .01462799529827220068499109804718544519021,
1290  .03377490158481415479330224686591290134917,
1291  .05229333515268328594031205127321125611215,
1292  .06979646842452048809496141893021765739878,
1293  .08594160621706772741444368137270286618914,
1294  .1004141444428809649320788378305362823508,
1295  .1129322960805392183934006074217843191143,
1296  .1232523768105124242855609861548144719594,
1297  .1311735047870623707329649925303074458757,
1298  .1365414983460151713525738312315173965864,
1299  .1392518728556319933754102483418099578739,
1300  .1392518728556319933754102483418099578739,
1301  .1365414983460151713525738312315173965864,
1302  .1311735047870623707329649925303074458757,
1303  .1232523768105124242855609861548144719594,
1304  .1129322960805392183934006074217843191143,
1305  .1004141444428809649320788378305362823508,
1306  .08594160621706772741444368137270286618914,
1307  .06979646842452048809496141893021765739878,
1308  .05229333515268328594031205127321125611215,
1309  .03377490158481415479330224686591290134917,
1310  .01462799529827220068499109804718544519021
1311  }
1312  },
1313  {
1314  23,
1315  { // points
1316  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1317  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1318  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1319  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1320  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1321  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1322  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1323  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1324  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1325  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1326  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1327  {0 ,0.0, 0.0},
1328  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1329  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1330  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1331  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1332  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1333  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1334  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1335  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1336  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1337  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1338  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1339  },
1340  { // weights
1341  .01341185948714177208130949345861506497662,
1342  .03098800585697944431069421964188450538377,
1343  .04803767173108466857164107163203399656122,
1344  .06423242140852585212716961515891099803916,
1345  .07928141177671895492289252474204322691371,
1346  .09291576606003514747701861736976464860346,
1347  .1048920914645414100740861850147438548585,
1348  .1149966402224113649416435129339613014914,
1349  .1230490843067295304675784006720096548159,
1350  .1289057221880821499785953393997936532597,
1351  .132462039404696617371642464703316925805,
1352  .1336545721861061753514571105458443385832,
1353  .132462039404696617371642464703316925805,
1354  .1289057221880821499785953393997936532597,
1355  .1230490843067295304675784006720096548159,
1356  .1149966402224113649416435129339613014914,
1357  .1048920914645414100740861850147438548585,
1358  .09291576606003514747701861736976464860346,
1359  .07928141177671895492289252474204322691371,
1360  .06423242140852585212716961515891099803916,
1361  .04803767173108466857164107163203399656122,
1362  .03098800585697944431069421964188450538377,
1363  .01341185948714177208130949345861506497662
1364  }
1365  },
1366  {
1367  23,
1368  { // points
1369  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1370  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1371  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1372  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1373  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1374  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1375  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1376  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1377  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1378  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1379  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1380  {0 ,0.0, 0.0},
1381  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1382  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1383  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1384  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1385  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1386  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1387  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1388  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1389  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1390  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1391  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1392  },
1393  { // weights
1394  .01341185948714177208130949345861506497662,
1395  .03098800585697944431069421964188450538377,
1396  .04803767173108466857164107163203399656122,
1397  .06423242140852585212716961515891099803916,
1398  .07928141177671895492289252474204322691371,
1399  .09291576606003514747701861736976464860346,
1400  .1048920914645414100740861850147438548585,
1401  .1149966402224113649416435129339613014914,
1402  .1230490843067295304675784006720096548159,
1403  .1289057221880821499785953393997936532597,
1404  .132462039404696617371642464703316925805,
1405  .1336545721861061753514571105458443385832,
1406  .132462039404696617371642464703316925805,
1407  .1289057221880821499785953393997936532597,
1408  .1230490843067295304675784006720096548159,
1409  .1149966402224113649416435129339613014914,
1410  .1048920914645414100740861850147438548585,
1411  .09291576606003514747701861736976464860346,
1412  .07928141177671895492289252474204322691371,
1413  .06423242140852585212716961515891099803916,
1414  .04803767173108466857164107163203399656122,
1415  .03098800585697944431069421964188450538377,
1416  .01341185948714177208130949345861506497662
1417  }
1418  },
1419  {
1420  24,
1421  { // points
1422  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1423  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1424  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1425  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1426  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1427  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1428  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1429  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1430  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1431  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1432  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1433  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1434  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1435  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1436  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1437  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1438  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1439  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1440  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1441  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1442  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1443  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1444  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1445  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1446  },
1447  { // weights
1448  .01234122979998719954680566707003729157591,
1449  .0285313886289336631813078159518782864492,
1450  .04427743881741980616860274821133822885931,
1451  .0592985849154367807463677585001085845412,
1452  .07334648141108030573403361525311651811934,
1453  .08619016153195327591718520298374266718508,
1454  .09761865210411388826988066446424715442792,
1455  .1074442701159656347825773424466062227946,
1456  .1155056680537256013533444839067835598623,
1457  .121670472927803391204463153476262425607,
1458  .1258374563468282961213753825111836887264,
1459  .1279381953467521569740561652246953718517,
1460  .1279381953467521569740561652246953718517,
1461  .1258374563468282961213753825111836887264,
1462  .121670472927803391204463153476262425607,
1463  .1155056680537256013533444839067835598623,
1464  .1074442701159656347825773424466062227946,
1465  .09761865210411388826988066446424715442792,
1466  .08619016153195327591718520298374266718508,
1467  .07334648141108030573403361525311651811934,
1468  .0592985849154367807463677585001085845412,
1469  .04427743881741980616860274821133822885931,
1470  .0285313886289336631813078159518782864492,
1471  .01234122979998719954680566707003729157591
1472  }
1473  },
1474  {
1475  24,
1476  { // points
1477  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1478  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1479  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1480  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1481  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1482  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1483  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1484  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1485  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1486  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1487  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1488  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1489  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1490  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1491  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1492  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1493  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1494  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1495  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1496  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1497  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1498  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1499  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1500  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1501  },
1502  { // weights
1503  .01234122979998719954680566707003729157591,
1504  .0285313886289336631813078159518782864492,
1505  .04427743881741980616860274821133822885931,
1506  .0592985849154367807463677585001085845412,
1507  .07334648141108030573403361525311651811934,
1508  .08619016153195327591718520298374266718508,
1509  .09761865210411388826988066446424715442792,
1510  .1074442701159656347825773424466062227946,
1511  .1155056680537256013533444839067835598623,
1512  .121670472927803391204463153476262425607,
1513  .1258374563468282961213753825111836887264,
1514  .1279381953467521569740561652246953718517,
1515  .1279381953467521569740561652246953718517,
1516  .1258374563468282961213753825111836887264,
1517  .121670472927803391204463153476262425607,
1518  .1155056680537256013533444839067835598623,
1519  .1074442701159656347825773424466062227946,
1520  .09761865210411388826988066446424715442792,
1521  .08619016153195327591718520298374266718508,
1522  .07334648141108030573403361525311651811934,
1523  .0592985849154367807463677585001085845412,
1524  .04427743881741980616860274821133822885931,
1525  .0285313886289336631813078159518782864492,
1526  .01234122979998719954680566707003729157591
1527  }
1528  },
1529  {
1530  25,
1531  { // points
1532  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1533  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1534  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1535  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1536  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1537  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1538  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1539  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1540  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1541  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1542  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1543  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1544  {0 ,0.0, 0.0},
1545  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1546  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1547  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1548  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1549  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1550  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1551  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1552  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1553  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1554  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1555  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1556  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1557  },
1558  { // weights
1559  .01139379850102628794790296411323477360332,
1560  .02635498661503213726190181529529914493596,
1561  .04093915670130631265562348771164595366085,
1562  .05490469597583519192593689154047332416011,
1563  .06803833381235691720718718565670796855471,
1564  .08014070033500101801323495966911130229023,
1565  .09102826198296364981149722070289165338099,
1566  .1005359490670506442022068903926858269885,
1567  .1085196244742636531160939570501166193401,
1568  .1148582591457116483393255458695558086409,
1569  .1194557635357847722281781265129010473902,
1570  .1222424429903100416889595189458515058351,
1571  .1231760537267154512039028730790501424382,
1572  .1222424429903100416889595189458515058351,
1573  .1194557635357847722281781265129010473902,
1574  .1148582591457116483393255458695558086409,
1575  .1085196244742636531160939570501166193401,
1576  .1005359490670506442022068903926858269885,
1577  .09102826198296364981149722070289165338099,
1578  .08014070033500101801323495966911130229023,
1579  .06803833381235691720718718565670796855471,
1580  .05490469597583519192593689154047332416011,
1581  .04093915670130631265562348771164595366085,
1582  .02635498661503213726190181529529914493596,
1583  .01139379850102628794790296411323477360332
1584  }
1585  },
1586  {
1587  25,
1588  { // points
1589  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1590  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1591  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1592  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1593  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1594  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1595  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1596  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1597  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1598  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1599  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1600  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1601  {0 ,0.0, 0.0},
1602  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1603  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1604  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1605  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1606  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1607  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1608  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1609  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1610  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1611  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1612  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1613  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1614  },
1615  { // weights
1616  .01139379850102628794790296411323477360332,
1617  .02635498661503213726190181529529914493596,
1618  .04093915670130631265562348771164595366085,
1619  .05490469597583519192593689154047332416011,
1620  .06803833381235691720718718565670796855471,
1621  .08014070033500101801323495966911130229023,
1622  .09102826198296364981149722070289165338099,
1623  .1005359490670506442022068903926858269885,
1624  .1085196244742636531160939570501166193401,
1625  .1148582591457116483393255458695558086409,
1626  .1194557635357847722281781265129010473902,
1627  .1222424429903100416889595189458515058351,
1628  .1231760537267154512039028730790501424382,
1629  .1222424429903100416889595189458515058351,
1630  .1194557635357847722281781265129010473902,
1631  .1148582591457116483393255458695558086409,
1632  .1085196244742636531160939570501166193401,
1633  .1005359490670506442022068903926858269885,
1634  .09102826198296364981149722070289165338099,
1635  .08014070033500101801323495966911130229023,
1636  .06803833381235691720718718565670796855471,
1637  .05490469597583519192593689154047332416011,
1638  .04093915670130631265562348771164595366085,
1639  .02635498661503213726190181529529914493596,
1640  .01139379850102628794790296411323477360332
1641  }
1642  },
1643  {
1644  26,
1645  { // points
1646  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1647  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1648  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1649  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1650  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1651  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1652  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1653  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1654  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1655  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1656  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1657  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1658  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1659  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1660  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1661  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1662  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1663  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1664  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1665  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1666  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1667  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1668  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1669  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1670  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1671  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1672  },
1673  { // weights
1674  .01055137261734300715565118768525197790435,
1675  .0244178510926319087896158275197884002405,
1676  .03796238329436276395030314124885049469077,
1677  .05097582529714781199831990072407337952588,
1678  .06327404632957483553945368990704509572222,
1679  .07468414976565974588707579610284833863875,
1680  .08504589431348523921044776507998169658392,
1681  .09421380035591414846366488306730319854917,
1682  .1020591610944254232384140702534307923272,
1683  .1084718405285765906565794267279975822894,
1684  .113361816546319666549440718442598145246,
1685  .116660443485296582044662507540362213632,
1686  .1183214152792622765163710857004686846499,
1687  .1183214152792622765163710857004686846499,
1688  .116660443485296582044662507540362213632,
1689  .113361816546319666549440718442598145246,
1690  .1084718405285765906565794267279975822894,
1691  .1020591610944254232384140702534307923272,
1692  .09421380035591414846366488306730319854917,
1693  .08504589431348523921044776507998169658392,
1694  .07468414976565974588707579610284833863875,
1695  .06327404632957483553945368990704509572222,
1696  .05097582529714781199831990072407337952588,
1697  .03796238329436276395030314124885049469077,
1698  .0244178510926319087896158275197884002405,
1699  .01055137261734300715565118768525197790435
1700  }
1701  },
1702  {
1703  26,
1704  { // points
1705  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1706  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1707  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1708  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1709  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1710  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1711  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1712  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1713  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1714  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1715  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1716  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1717  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1718  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1719  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1720  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1721  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1722  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1723  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1724  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1725  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1726  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1727  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1728  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1729  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1730  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1731  },
1732  { // weights
1733  .01055137261734300715565118768525197790435,
1734  .0244178510926319087896158275197884002405,
1735  .03796238329436276395030314124885049469077,
1736  .05097582529714781199831990072407337952588,
1737  .06327404632957483553945368990704509572222,
1738  .07468414976565974588707579610284833863875,
1739  .08504589431348523921044776507998169658392,
1740  .09421380035591414846366488306730319854917,
1741  .1020591610944254232384140702534307923272,
1742  .1084718405285765906565794267279975822894,
1743  .113361816546319666549440718442598145246,
1744  .116660443485296582044662507540362213632,
1745  .1183214152792622765163710857004686846499,
1746  .1183214152792622765163710857004686846499,
1747  .116660443485296582044662507540362213632,
1748  .113361816546319666549440718442598145246,
1749  .1084718405285765906565794267279975822894,
1750  .1020591610944254232384140702534307923272,
1751  .09421380035591414846366488306730319854917,
1752  .08504589431348523921044776507998169658392,
1753  .07468414976565974588707579610284833863875,
1754  .06327404632957483553945368990704509572222,
1755  .05097582529714781199831990072407337952588,
1756  .03796238329436276395030314124885049469077,
1757  .0244178510926319087896158275197884002405,
1758  .01055137261734300715565118768525197790435
1759  }
1760  },
1761  {
1762  27,
1763  { // points
1764  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1765  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1766  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1767  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1768  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1769  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1770  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1771  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1772  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1773  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1774  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1775  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1776  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1777  {0 ,0.0, 0.0},
1778  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1779  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1780  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1781  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1782  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1783  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1784  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1785  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1786  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1787  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1788  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1789  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1790  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1791  },
1792  { // weights
1793  .009798996051294360261150055091259098098226,
1794  .02268623159618062319603420644676148881277,
1795  .03529705375741971102257828930471164113614,
1796  .04744941252061506270409671011418471822473,
1797  .05898353685983359911030083371953163316524,
1798  .06974882376624559298432288835666727613282,
1799  .07960486777305777126307495900984240297615,
1800  .08842315854375695019432280285374911105654,
1801  .09608872737002850756565264655810585916021,
1802  .1025016378177457986712477115326638093244,
1803  .107578285788533187212162984426657404819,
1804  .1112524883568451926721630960428486748329,
1805  .1134763461089651486203699480920992579205,
1806  .1142208673789569890450457369018352486807,
1807  .1134763461089651486203699480920992579205,
1808  .1112524883568451926721630960428486748329,
1809  .107578285788533187212162984426657404819,
1810  .1025016378177457986712477115326638093244,
1811  .09608872737002850756565264655810585916021,
1812  .08842315854375695019432280285374911105654,
1813  .07960486777305777126307495900984240297615,
1814  .06974882376624559298432288835666727613282,
1815  .05898353685983359911030083371953163316524,
1816  .04744941252061506270409671011418471822473,
1817  .03529705375741971102257828930471164113614,
1818  .02268623159618062319603420644676148881277,
1819  .009798996051294360261150055091259098098226
1820  }
1821  },
1822  {
1823  27,
1824  { // points
1825  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1826  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1827  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1828  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1829  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1830  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1831  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1832  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1833  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1834  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1835  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1836  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1837  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1838  {0 ,0.0, 0.0},
1839  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1840  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1841  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1842  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1843  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1844  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1845  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1846  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1847  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1848  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1849  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1850  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1851  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1852  },
1853  { // weights
1854  .009798996051294360261150055091259098098226,
1855  .02268623159618062319603420644676148881277,
1856  .03529705375741971102257828930471164113614,
1857  .04744941252061506270409671011418471822473,
1858  .05898353685983359911030083371953163316524,
1859  .06974882376624559298432288835666727613282,
1860  .07960486777305777126307495900984240297615,
1861  .08842315854375695019432280285374911105654,
1862  .09608872737002850756565264655810585916021,
1863  .1025016378177457986712477115326638093244,
1864  .107578285788533187212162984426657404819,
1865  .1112524883568451926721630960428486748329,
1866  .1134763461089651486203699480920992579205,
1867  .1142208673789569890450457369018352486807,
1868  .1134763461089651486203699480920992579205,
1869  .1112524883568451926721630960428486748329,
1870  .107578285788533187212162984426657404819,
1871  .1025016378177457986712477115326638093244,
1872  .09608872737002850756565264655810585916021,
1873  .08842315854375695019432280285374911105654,
1874  .07960486777305777126307495900984240297615,
1875  .06974882376624559298432288835666727613282,
1876  .05898353685983359911030083371953163316524,
1877  .04744941252061506270409671011418471822473,
1878  .03529705375741971102257828930471164113614,
1879  .02268623159618062319603420644676148881277,
1880  .009798996051294360261150055091259098098226
1881  }
1882  },
1883  {
1884  28,
1885  { // points
1886  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1887  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1888  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1889  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1890  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1891  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1892  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1893  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1894  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1895  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1896  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1897  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1898  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1899  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1900  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1901  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1902  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1903  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
1904  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
1905  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
1906  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
1907  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
1908  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
1909  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
1910  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
1911  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
1912  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
1913  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
1914  },
1915  { // weights
1916  .009124282593094517738816153922951706240344,
1917  .02113211259277125975150038099326543445137,
1918  .03290142778230437997763081917053204598153,
1919  .04427293475900422783958787765320739061499,
1920  .05510734567571674543148291822694559121906,
1921  .06527292396699959579339756677550463635364,
1922  .07464621423456877902393188717302203802164,
1923  .08311341722890121839039649824433247986113,
1924  .09057174439303284094218603133678412982286,
1925  .09693065799792991585048900609544060176503,
1926  .1021129675780607698142166385057121350466,
1927  .1060557659228464179104164369968108287899,
1928  .1087111922582941352535715193036733678753,
1929  .1100470130164751962823762656018176139566,
1930  .1100470130164751962823762656018176139566,
1931  .1087111922582941352535715193036733678753,
1932  .1060557659228464179104164369968108287899,
1933  .1021129675780607698142166385057121350466,
1934  .09693065799792991585048900609544060176503,
1935  .09057174439303284094218603133678412982286,
1936  .08311341722890121839039649824433247986113,
1937  .07464621423456877902393188717302203802164,
1938  .06527292396699959579339756677550463635364,
1939  .05510734567571674543148291822694559121906,
1940  .04427293475900422783958787765320739061499,
1941  .03290142778230437997763081917053204598153,
1942  .02113211259277125975150038099326543445137,
1943  .009124282593094517738816153922951706240344
1944  }
1945  },
1946  {
1947  28,
1948  { // points
1949  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1950  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1951  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1952  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1953  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1954  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1955  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1956  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1957  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1958  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1959  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1960  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1961  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1962  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1963  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1964  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1965  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1966  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
1967  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
1968  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
1969  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
1970  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
1971  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
1972  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
1973  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
1974  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
1975  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
1976  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
1977  },
1978  { // weights
1979  .009124282593094517738816153922951706240344,
1980  .02113211259277125975150038099326543445137,
1981  .03290142778230437997763081917053204598153,
1982  .04427293475900422783958787765320739061499,
1983  .05510734567571674543148291822694559121906,
1984  .06527292396699959579339756677550463635364,
1985  .07464621423456877902393188717302203802164,
1986  .08311341722890121839039649824433247986113,
1987  .09057174439303284094218603133678412982286,
1988  .09693065799792991585048900609544060176503,
1989  .1021129675780607698142166385057121350466,
1990  .1060557659228464179104164369968108287899,
1991  .1087111922582941352535715193036733678753,
1992  .1100470130164751962823762656018176139566,
1993  .1100470130164751962823762656018176139566,
1994  .1087111922582941352535715193036733678753,
1995  .1060557659228464179104164369968108287899,
1996  .1021129675780607698142166385057121350466,
1997  .09693065799792991585048900609544060176503,
1998  .09057174439303284094218603133678412982286,
1999  .08311341722890121839039649824433247986113,
2000  .07464621423456877902393188717302203802164,
2001  .06527292396699959579339756677550463635364,
2002  .05510734567571674543148291822694559121906,
2003  .04427293475900422783958787765320739061499,
2004  .03290142778230437997763081917053204598153,
2005  .02113211259277125975150038099326543445137,
2006  .009124282593094517738816153922951706240344
2007  }
2008  },
2009  {
2010  29,
2011  { // points
2012  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2013  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2014  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2015  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2016  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2017  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2018  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2019  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2020  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2021  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2022  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2023  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2024  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2025  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2026  {0 ,0.0, 0.0},
2027  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2028  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2029  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2030  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2031  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2032  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2033  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2034  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2035  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2036  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2037  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2038  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2039  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2040  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2041  },
2042  { // weights
2043  .008516903878746409654263813302249803002399,
2044  .01973208505612270598385980164039563114961,
2045  .03074049220209362264440852537461674974712,
2046  .04140206251868283610483001011407692153349,
2047  .05159482690249792391259438117954259791962,
2048  .06120309065707913854210984802390704492406,
2049  .07011793325505127856958148694887917310239,
2050  .07823832713576378382814488865968033136688,
2051  .0854722573661725275453448492972080713817,
2052  .09173775713925876334796641107711080689823,
2053  .09696383409440860630190007488268875917636,
2054  .1010912737599149661218205469074973636476,
2055  .1040733100777293739133284712851200689107,
2056  .1058761550973209414065913278521878930748,
2057  .1064793817183142442465111269096775683302,
2058  .1058761550973209414065913278521878930748,
2059  .1040733100777293739133284712851200689107,
2060  .1010912737599149661218205469074973636476,
2061  .09696383409440860630190007488268875917636,
2062  .09173775713925876334796641107711080689823,
2063  .0854722573661725275453448492972080713817,
2064  .07823832713576378382814488865968033136688,
2065  .07011793325505127856958148694887917310239,
2066  .06120309065707913854210984802390704492406,
2067  .05159482690249792391259438117954259791962,
2068  .04140206251868283610483001011407692153349,
2069  .03074049220209362264440852537461674974712,
2070  .01973208505612270598385980164039563114961,
2071  .008516903878746409654263813302249803002399
2072  }
2073  },
2074  {
2075  29,
2076  { // points
2077  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2078  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2079  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2080  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2081  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2082  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2083  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2084  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2085  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2086  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2087  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2088  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2089  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2090  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2091  {0 ,0.0, 0.0},
2092  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2093  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2094  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2095  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2096  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2097  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2098  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2099  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2100  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2101  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2102  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2103  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2104  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2105  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2106  },
2107  { // weights
2108  .008516903878746409654263813302249803002399,
2109  .01973208505612270598385980164039563114961,
2110  .03074049220209362264440852537461674974712,
2111  .04140206251868283610483001011407692153349,
2112  .05159482690249792391259438117954259791962,
2113  .06120309065707913854210984802390704492406,
2114  .07011793325505127856958148694887917310239,
2115  .07823832713576378382814488865968033136688,
2116  .0854722573661725275453448492972080713817,
2117  .09173775713925876334796641107711080689823,
2118  .09696383409440860630190007488268875917636,
2119  .1010912737599149661218205469074973636476,
2120  .1040733100777293739133284712851200689107,
2121  .1058761550973209414065913278521878930748,
2122  .1064793817183142442465111269096775683302,
2123  .1058761550973209414065913278521878930748,
2124  .1040733100777293739133284712851200689107,
2125  .1010912737599149661218205469074973636476,
2126  .09696383409440860630190007488268875917636,
2127  .09173775713925876334796641107711080689823,
2128  .0854722573661725275453448492972080713817,
2129  .07823832713576378382814488865968033136688,
2130  .07011793325505127856958148694887917310239,
2131  .06120309065707913854210984802390704492406,
2132  .05159482690249792391259438117954259791962,
2133  .04140206251868283610483001011407692153349,
2134  .03074049220209362264440852537461674974712,
2135  .01973208505612270598385980164039563114961,
2136  .008516903878746409654263813302249803002399
2137  }
2138  },
2139  {
2140  30,
2141  { // points
2142  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2143  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2144  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2145  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2146  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2147  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2148  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2149  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2150  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2151  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2152  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2153  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2154  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2155  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2156  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2157  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2158  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2159  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2160  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2161  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2162  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2163  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2164  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2165  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2166  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2167  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2168  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2169  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2170  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2171  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2172  },
2173  { // weights
2174  .007968192496166605615465883474673622450481,
2175  .01846646831109095914230213191204726909621,
2176  .02878470788332336934971917961129204363959,
2177  .0387991925696270495968019364463476920332,
2178  .04840267283059405290293814042280751781527,
2179  .05749315621761906648172168940205612879712,
2180  .06597422988218049512812851511596236123744,
2181  .07375597473770520626824385002219073415377,
2182  .08075589522942021535469493846052973087589,
2183  .08689978720108297980238753071512570257675,
2184  .09212252223778612871763270708761876719691,
2185  .09636873717464425963946862635180986509641,
2186  .09959342058679526706278028210356947652987,
2187  .1017623897484055045964289521685540446327,
2188  .1028526528935588403412856367054150438684,
2189  .1028526528935588403412856367054150438684,
2190  .1017623897484055045964289521685540446327,
2191  .09959342058679526706278028210356947652987,
2192  .09636873717464425963946862635180986509641,
2193  .09212252223778612871763270708761876719691,
2194  .08689978720108297980238753071512570257675,
2195  .08075589522942021535469493846052973087589,
2196  .07375597473770520626824385002219073415377,
2197  .06597422988218049512812851511596236123744,
2198  .05749315621761906648172168940205612879712,
2199  .04840267283059405290293814042280751781527,
2200  .0387991925696270495968019364463476920332,
2201  .02878470788332336934971917961129204363959,
2202  .01846646831109095914230213191204726909621,
2203  .007968192496166605615465883474673622450481
2204  }
2205  },
2206  {
2207  30,
2208  { // points
2209  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2210  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2211  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2212  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2213  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2214  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2215  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2216  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2217  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2218  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2219  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2220  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2221  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2222  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2223  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2224  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2225  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2226  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2227  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2228  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2229  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2230  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2231  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2232  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2233  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2234  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2235  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2236  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2237  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2238  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2239  },
2240  { // weights
2241  .007968192496166605615465883474673622450481,
2242  .01846646831109095914230213191204726909621,
2243  .02878470788332336934971917961129204363959,
2244  .0387991925696270495968019364463476920332,
2245  .04840267283059405290293814042280751781527,
2246  .05749315621761906648172168940205612879712,
2247  .06597422988218049512812851511596236123744,
2248  .07375597473770520626824385002219073415377,
2249  .08075589522942021535469493846052973087589,
2250  .08689978720108297980238753071512570257675,
2251  .09212252223778612871763270708761876719691,
2252  .09636873717464425963946862635180986509641,
2253  .09959342058679526706278028210356947652987,
2254  .1017623897484055045964289521685540446327,
2255  .1028526528935588403412856367054150438684,
2256  .1028526528935588403412856367054150438684,
2257  .1017623897484055045964289521685540446327,
2258  .09959342058679526706278028210356947652987,
2259  .09636873717464425963946862635180986509641,
2260  .09212252223778612871763270708761876719691,
2261  .08689978720108297980238753071512570257675,
2262  .08075589522942021535469493846052973087589,
2263  .07375597473770520626824385002219073415377,
2264  .06597422988218049512812851511596236123744,
2265  .05749315621761906648172168940205612879712,
2266  .04840267283059405290293814042280751781527,
2267  .0387991925696270495968019364463476920332,
2268  .02878470788332336934971917961129204363959,
2269  .01846646831109095914230213191204726909621,
2270  .007968192496166605615465883474673622450481
2271  }
2272  },
2273  {
2274  31,
2275  { // points
2276  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2277  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2278  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2279  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2280  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2281  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2282  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2283  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2284  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2285  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2286  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2287  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2288  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2289  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2290  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2291  {0 ,0.0, 0.0},
2292  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2293  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2294  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2295  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2296  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2297  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2298  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2299  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2300  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2301  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2302  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2303  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2304  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2305  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2306  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2307  },
2308  { // weights
2309  .007470831579248775858696875032212407022151,
2310  .01731862079031058246315799608682114136627,
2311  .02700901918497942180060870809193215614236,
2312  .03643227391238546402439201046780344232715,
2313  .04549370752720110290231585789462967726355,
2314  .05410308242491685371166625908662004272039,
2315  .06217478656102842691034354368669666715873,
2316  .06962858323541036616775612625512571051509,
2317  .07639038659877661642635767490133064492576,
2318  .08239299176158926390382336743196177061577,
2319  .08757674060847787612619806969533309222926,
2320  .09189011389364147821536287160715012549731,
2321  .09529024291231951280720419748759668454132,
2322  .09774333538632872509347401097899670383573,
2323  .09922501122667230787487551442861501401754,
2324  .09972054479342645142753383373434943964325,
2325  .09922501122667230787487551442861501401754,
2326  .09774333538632872509347401097899670383573,
2327  .09529024291231951280720419748759668454132,
2328  .09189011389364147821536287160715012549731,
2329  .08757674060847787612619806969533309222926,
2330  .08239299176158926390382336743196177061577,
2331  .07639038659877661642635767490133064492576,
2332  .06962858323541036616775612625512571051509,
2333  .06217478656102842691034354368669666715873,
2334  .05410308242491685371166625908662004272039,
2335  .04549370752720110290231585789462967726355,
2336  .03643227391238546402439201046780344232715,
2337  .02700901918497942180060870809193215614236,
2338  .01731862079031058246315799608682114136627,
2339  .007470831579248775858696875032212407022151
2340  }
2341  },
2342  {
2343  31,
2344  { // points
2345  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2346  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2347  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2348  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2349  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2350  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2351  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2352  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2353  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2354  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2355  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2356  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2357  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2358  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2359  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2360  {0 ,0.0, 0.0},
2361  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2362  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2363  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2364  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2365  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2366  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2367  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2368  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2369  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2370  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2371  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2372  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2373  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2374  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2375  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2376  },
2377  { // weights
2378  .007470831579248775858696875032212407022151,
2379  .01731862079031058246315799608682114136627,
2380  .02700901918497942180060870809193215614236,
2381  .03643227391238546402439201046780344232715,
2382  .04549370752720110290231585789462967726355,
2383  .05410308242491685371166625908662004272039,
2384  .06217478656102842691034354368669666715873,
2385  .06962858323541036616775612625512571051509,
2386  .07639038659877661642635767490133064492576,
2387  .08239299176158926390382336743196177061577,
2388  .08757674060847787612619806969533309222926,
2389  .09189011389364147821536287160715012549731,
2390  .09529024291231951280720419748759668454132,
2391  .09774333538632872509347401097899670383573,
2392  .09922501122667230787487551442861501401754,
2393  .09972054479342645142753383373434943964325,
2394  .09922501122667230787487551442861501401754,
2395  .09774333538632872509347401097899670383573,
2396  .09529024291231951280720419748759668454132,
2397  .09189011389364147821536287160715012549731,
2398  .08757674060847787612619806969533309222926,
2399  .08239299176158926390382336743196177061577,
2400  .07639038659877661642635767490133064492576,
2401  .06962858323541036616775612625512571051509,
2402  .06217478656102842691034354368669666715873,
2403  .05410308242491685371166625908662004272039,
2404  .04549370752720110290231585789462967726355,
2405  .03643227391238546402439201046780344232715,
2406  .02700901918497942180060870809193215614236,
2407  .01731862079031058246315799608682114136627,
2408  .007470831579248775858696875032212407022151
2409  }
2410  } // end Gauss
2411  };
2412 
2413 } // end namespace Intrepid2
Intrepid2::Parameters::MaxDimension
static constexpr ordinal_type MaxDimension
The maximum ambient space dimension.
Definition: Intrepid2_Types.hpp:114
Intrepid2::CubatureDirect::CubatureData::weights_
Kokkos::DynRankView< weightValueType, DeviceType > weights_
Array with the associated cubature weights.
Definition: Intrepid2_CubatureDirect.hpp:80
Intrepid2::CubatureDirectLineGauss
Defines Gauss integration rules on a line.
Definition: Intrepid2_CubatureDirectLineGauss.hpp:30
Intrepid2::CubatureDirectLineGauss::cubatureDataStatic_
static const CubatureDataStatic cubatureDataStatic_[cubatureDataStaticSize]
Complete set of data defining line Gauss(-Legendre) rules.
Definition: Intrepid2_CubatureDirectLineGauss.hpp:45
Intrepid2::CubatureDirect::cubatureData_
CubatureData cubatureData_
Cubature data on device.
Definition: Intrepid2_CubatureDirect.hpp:95
Intrepid2::CubatureDirect::CubatureDataStatic::numPoints_
ordinal_type numPoints_
Number of cubature points stored in the template.
Definition: Intrepid2_CubatureDirect.hpp:54
Intrepid2::CubatureDirectLineGauss::CubatureDirectLineGauss
CubatureDirectLineGauss(const ordinal_type degree=0)
Constructor.
Definition: Intrepid2_CubatureDirectLineGaussDef.hpp:20
Intrepid2::CubatureDirect
Defines direct cubature (integration) rules in Intrepid.
Definition: Intrepid2_CubatureDirect.hpp:43
Intrepid2::CubatureDirect::CubatureDataStatic
Cubature data is defined on the host space and is static.
Definition: Intrepid2_CubatureDirect.hpp:50
Intrepid2::Parameters::MaxCubatureDegreeEdge
static constexpr ordinal_type MaxCubatureDegreeEdge
The maximum degree of the polynomial that can be integrated exactly by a direct edge rule...
Definition: Intrepid2_Types.hpp:106
Intrepid2::CubatureDirect::CubatureData::points_
Kokkos::DynRankView< pointValueType, DeviceType > points_
Array with the (X,Y,Z) coordinates of the cubature points.
Definition: Intrepid2_CubatureDirect.hpp:76
Intrepid2::CubatureDirect::CubatureData::numPoints_
ordinal_type numPoints_
Number of cubature points stored in the template.
Definition: Intrepid2_CubatureDirect.hpp:72
Intrepid2::CubatureDirect::degree_
ordinal_type degree_
The degree of polynomials that are integrated exactly by this cubature rule.
Definition: Intrepid2_CubatureDirect.hpp:87
Generated by   doxygen 1.8.5