Intrepid2
Intrepid2_CubatureDirectLineGaussDef.hpp
Go to the documentation of this file.
1 // @HEADER
2 // ************************************************************************
3 //
4 // Intrepid2 Package
5 // Copyright (2007) Sandia Corporation
6 //
7 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
8 // license for use of this work by or on behalf of the U.S. Government.
9 //
10 // Redistribution and use in source and binary forms, with or without
11 // modification, are permitted provided that the following conditions are
12 // met:
13 //
14 // 1. Redistributions of source code must retain the above copyright
15 // notice, this list of conditions and the following disclaimer.
16 //
17 // 2. Redistributions in binary form must reproduce the above copyright
18 // notice, this list of conditions and the following disclaimer in the
19 // documentation and/or other materials provided with the distribution.
20 //
21 // 3. Neither the name of the Corporation nor the names of the
22 // contributors may be used to endorse or promote products derived from
23 // this software without specific prior written permission.
24 //
25 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
26 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
28 // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
29 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
33 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
34 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36 //
37 // Questions? Contact Kyungjoo Kim (kyukim@sandia.gov), or
38 // Mauro Perego (mperego@sandia.gov)
39 //
40 // ************************************************************************
41 // @HEADER
42 
49 namespace Intrepid2 {
50 
51  template <typename SpT, typename PT, typename WT>
52  CubatureDirectLineGauss<SpT,PT,WT>::
53  CubatureDirectLineGauss(const ordinal_type degree)
54  : CubatureDirect<SpT,PT,WT>(degree, 1) {
55 
56  INTREPID2_TEST_FOR_EXCEPTION( degree < 0 ||
57  degree > static_cast<ordinal_type>(Parameters::MaxCubatureDegreeEdge), std::out_of_range,
58  ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree.");
59 
60  typedef Kokkos::DynRankView<PT,Kokkos::LayoutRight,Kokkos::HostSpace> pointViewHostType;
61  typedef Kokkos::DynRankView<WT,Kokkos::LayoutRight,Kokkos::HostSpace> weightViewHostType;
62 
63  this->cubatureData_.numPoints_ = cubatureDataStatic_[this->degree_].numPoints_;
64  {
65  // src
66  const pointViewHostType points_host(const_cast<PT*>( &(cubatureDataStatic_[this->degree_].points_[0][0]) ),
67  this->cubatureData_.numPoints_,
68  Parameters::MaxDimension);
69 
70  auto points = Kokkos::create_mirror_view(typename SpT::memory_space(), points_host);
71 
72  Kokkos::deep_copy(points,points_host);
73 
74  // dst
75  this->cubatureData_.points_ = Kokkos::DynRankView<PT,SpT>("CubatureDirectLineGauss::cubatureData_::points_",
76  this->cubatureData_.numPoints_,
77  Parameters::MaxDimension);
78  // copy
79  Kokkos::deep_copy(this->cubatureData_.points_ , points );
80  }
81  {
82  // src
83  const weightViewHostType weights(const_cast<PT*>( &(cubatureDataStatic_[this->degree_].weights_[0]) ),
84  this->cubatureData_.numPoints_);
85 
86  // dst
87  this->cubatureData_.weights_ = Kokkos::DynRankView<WT,SpT>("CubatureDirectLineGauss::cubatureData_::weights_",
88  this->cubatureData_.numPoints_);
89  // copy
90  Kokkos::deep_copy(Kokkos::subdynrankview(this->cubatureData_.weights_, Kokkos::ALL()) , Kokkos::subdynrankview(weights, Kokkos::ALL()));
91  }
92  }
93 
94  //-------------------------------------------------------------------------------------//
95  // Definition of cubature templates //
96  //-------------------------------------------------------------------------------------//
97 
98  /*
99  Cubature templates for lines are defined the reference cell:
100 
101  Line -> (-1,0,0),(1,0,0)
102  */
103 
104  /*
105  This static const member contains templates for Gauss(-Legendre) rules.
106  */
107 
108  template<typename SpT, typename PT, typename WT>
109  const typename CubatureDirect<SpT,PT,WT>::CubatureDataStatic
110  CubatureDirectLineGauss<SpT,PT,WT>::
111  cubatureDataStatic_[cubatureDataStaticSize] = {
112  // Collection of Gauss rules on [-1,1]
113  // The rule with array index i is exact for polynomials up to order i
114  {
115  1,
116  {{0e0, 0.0, 0.0}},
117  {2e0}
118  },
119  {
120  1,
121  {{0e0, 0.0, 0.0}},
122  {2e0}
123  },
124  {
125  2,
126  {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
127  {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
128  {1e0,
129  1e0}
130  },
131  {
132  2,
133  {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
134  {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
135  {1e0,
136  1e0}
137  },
138  {
139  3,
140  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
141  {0e0, 0.0, 0.0},
142  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
143  {5.555555555555555555555555555555555555556e-1,
144  8.888888888888888888888888888888888888889e-1,
145  5.555555555555555555555555555555555555556e-1}
146  },
147  {
148  3,
149  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
150  {0e0, 0.0, 0.0},
151  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
152  {5.555555555555555555555555555555555555556e-1,
153  8.888888888888888888888888888888888888889e-1,
154  5.555555555555555555555555555555555555556e-1}
155  },
156  {
157  4,
158  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
159  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
160  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
161  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
162  {3.478548451374538573730639492219994072353e-1,
163  6.521451548625461426269360507780005927647e-1,
164  6.521451548625461426269360507780005927647e-1,
165  3.478548451374538573730639492219994072353e-1}
166  },
167  {
168  4,
169  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
170  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
171  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
172  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
173  {3.478548451374538573730639492219994072353e-1,
174  6.521451548625461426269360507780005927647e-1,
175  6.521451548625461426269360507780005927647e-1,
176  3.478548451374538573730639492219994072353e-1}
177  },
178  {
179  5,
180  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
181  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
182  {0e0, 0.0, 0.0},
183  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
184  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
185  {2.369268850561890875142640407199173626433e-1,
186  4.786286704993664680412915148356381929123e-1,
187  5.688888888888888888888888888888888888889e-1,
188  4.786286704993664680412915148356381929123e-1,
189  2.369268850561890875142640407199173626433e-1}
190  },
191  {
192  5,
193  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
194  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
195  {0e0, 0.0, 0.0},
196  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
197  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
198  {2.369268850561890875142640407199173626433e-1,
199  4.786286704993664680412915148356381929123e-1,
200  5.688888888888888888888888888888888888889e-1,
201  4.786286704993664680412915148356381929123e-1,
202  2.369268850561890875142640407199173626433e-1}
203  },
204  {
205  6,
206  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
207  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
208  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
209  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
210  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
211  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
212  {1.713244923791703450402961421727328935268e-1,
213  3.607615730481386075698335138377161116615e-1,
214  4.679139345726910473898703439895509948117e-1,
215  4.679139345726910473898703439895509948117e-1,
216  3.607615730481386075698335138377161116615e-1,
217  1.713244923791703450402961421727328935268e-1}
218  },
219  {
220  6,
221  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
222  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
223  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
224  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
225  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
226  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
227  {1.713244923791703450402961421727328935268e-1,
228  3.607615730481386075698335138377161116615e-1,
229  4.679139345726910473898703439895509948117e-1,
230  4.679139345726910473898703439895509948117e-1,
231  3.607615730481386075698335138377161116615e-1,
232  1.713244923791703450402961421727328935268e-1}
233  },
234  {
235  7,
236  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
237  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
238  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
239  {0e0, 0.0, 0.0},
240  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
241  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
242  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
243  {1.294849661688696932706114326790820183286e-1,
244  2.797053914892766679014677714237795824869e-1,
245  3.818300505051189449503697754889751338784e-1,
246  4.179591836734693877551020408163265306122e-1,
247  3.818300505051189449503697754889751338784e-1,
248  2.797053914892766679014677714237795824869e-1,
249  1.294849661688696932706114326790820183286e-1}
250  },
251  {
252  7,
253  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
254  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
255  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
256  {0e0, 0.0, 0.0},
257  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
258  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
259  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
260  {1.294849661688696932706114326790820183286e-1,
261  2.797053914892766679014677714237795824869e-1,
262  3.818300505051189449503697754889751338784e-1,
263  4.179591836734693877551020408163265306122e-1,
264  3.818300505051189449503697754889751338784e-1,
265  2.797053914892766679014677714237795824869e-1,
266  1.294849661688696932706114326790820183286e-1}
267  },
268  {
269  8,
270  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
271  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
272  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
273  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
274  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
275  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
276  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
277  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
278  {1.012285362903762591525313543099621901154e-1,
279  2.223810344533744705443559944262408844301e-1,
280  3.137066458778872873379622019866013132603e-1,
281  3.626837833783619829651504492771956121941e-1,
282  3.626837833783619829651504492771956121941e-1,
283  3.137066458778872873379622019866013132603e-1,
284  2.223810344533744705443559944262408844301e-1,
285  1.012285362903762591525313543099621901154e-1}
286  },
287  {
288  8,
289  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
290  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
291  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
292  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
293  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
294  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
295  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
296  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
297  {1.012285362903762591525313543099621901154e-1,
298  2.223810344533744705443559944262408844301e-1,
299  3.137066458778872873379622019866013132603e-1,
300  3.626837833783619829651504492771956121941e-1,
301  3.626837833783619829651504492771956121941e-1,
302  3.137066458778872873379622019866013132603e-1,
303  2.223810344533744705443559944262408844301e-1,
304  1.012285362903762591525313543099621901154e-1}
305  },
306  {
307  9,
308  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
309  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
310  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
311  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
312  {0e0, 0.0, 0.0},
313  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
314  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
315  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
316  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
317  {8.127438836157441197189215811052365067566e-2,
318  1.806481606948574040584720312429128095143e-1,
319  2.606106964029354623187428694186328497718e-1,
320  3.123470770400028400686304065844436655988e-1,
321  3.302393550012597631645250692869740488788e-1,
322  3.123470770400028400686304065844436655988e-1,
323  2.606106964029354623187428694186328497718e-1,
324  1.806481606948574040584720312429128095143e-1,
325  8.127438836157441197189215811052365067566e-2}
326  },
327  {
328  9,
329  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
330  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
331  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
332  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
333  {0e0, 0.0, 0.0},
334  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
335  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
336  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
337  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
338  {8.127438836157441197189215811052365067566e-2,
339  1.806481606948574040584720312429128095143e-1,
340  2.606106964029354623187428694186328497718e-1,
341  3.123470770400028400686304065844436655988e-1,
342  3.302393550012597631645250692869740488788e-1,
343  3.123470770400028400686304065844436655988e-1,
344  2.606106964029354623187428694186328497718e-1,
345  1.806481606948574040584720312429128095143e-1,
346  8.127438836157441197189215811052365067566e-2}
347  },
348  {
349  10,
350  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
351  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
352  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
353  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
354  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
355  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
356  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
357  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
358  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
359  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
360  {6.667134430868813759356880989333179285786e-2,
361  1.494513491505805931457763396576973324026e-1,
362  2.190863625159820439955349342281631924588e-1,
363  2.692667193099963550912269215694693528598e-1,
364  2.95524224714752870173892994651338329421e-1,
365  2.95524224714752870173892994651338329421e-1,
366  2.692667193099963550912269215694693528598e-1,
367  2.190863625159820439955349342281631924588e-1,
368  1.494513491505805931457763396576973324026e-1,
369  6.667134430868813759356880989333179285786e-2}
370  },
371  {
372  10,
373  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
374  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
375  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
376  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
377  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
378  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
379  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
380  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
381  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
382  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
383  {6.667134430868813759356880989333179285786e-2,
384  1.494513491505805931457763396576973324026e-1,
385  2.190863625159820439955349342281631924588e-1,
386  2.692667193099963550912269215694693528598e-1,
387  2.95524224714752870173892994651338329421e-1,
388  2.95524224714752870173892994651338329421e-1,
389  2.692667193099963550912269215694693528598e-1,
390  2.190863625159820439955349342281631924588e-1,
391  1.494513491505805931457763396576973324026e-1,
392  6.667134430868813759356880989333179285786e-2}
393  },
394  {
395  11,
396  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
397  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
398  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
399  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
400  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
401  {0e0, 0.0, 0.0},
402  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
403  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
404  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
405  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
406  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
407  {5.566856711617366648275372044254857872852e-2,
408  1.255803694649046246346942992239401001976e-1,
409  1.862902109277342514260976414316558916913e-1,
410  2.331937645919904799185237048431751394318e-1,
411  2.628045445102466621806888698905091953728e-1,
412  2.72925086777900630714483528336342189156e-1,
413  2.628045445102466621806888698905091953728e-1,
414  2.331937645919904799185237048431751394318e-1,
415  1.862902109277342514260976414316558916913e-1,
416  1.255803694649046246346942992239401001976e-1,
417  5.566856711617366648275372044254857872852e-2}
418  },
419  {
420  11,
421  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
422  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
423  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
424  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
425  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
426  {0e0, 0.0, 0.0},
427  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
428  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
429  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
430  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
431  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
432  {5.566856711617366648275372044254857872852e-2,
433  1.255803694649046246346942992239401001976e-1,
434  1.862902109277342514260976414316558916913e-1,
435  2.331937645919904799185237048431751394318e-1,
436  2.628045445102466621806888698905091953728e-1,
437  2.72925086777900630714483528336342189156e-1,
438  2.628045445102466621806888698905091953728e-1,
439  2.331937645919904799185237048431751394318e-1,
440  1.862902109277342514260976414316558916913e-1,
441  1.255803694649046246346942992239401001976e-1,
442  5.566856711617366648275372044254857872852e-2}
443  },
444  {
445  12,
446  { // points
447  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
448  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
449  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
450  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
451  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
452  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
453  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
454  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
455  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
456  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
457  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
458  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
459  },
460  { // weights
461  .04717533638651182719461596148501706031703,
462  .1069393259953184309602547181939962242146,
463  .160078328543346226334652529543359071872,
464  .2031674267230659217490644558097983765065,
465  .2334925365383548087608498989248780562594,
466  .2491470458134027850005624360429512108305,
467  .2491470458134027850005624360429512108305,
468  .2334925365383548087608498989248780562594,
469  .2031674267230659217490644558097983765065,
470  .160078328543346226334652529543359071872,
471  .1069393259953184309602547181939962242146,
472  .04717533638651182719461596148501706031703
473  }
474  },
475  {
476  12,
477  { // points
478  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
479  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
480  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
481  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
482  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
483  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
484  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
485  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
486  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
487  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
488  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
489  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
490  },
491  { // weights
492  .04717533638651182719461596148501706031703,
493  .1069393259953184309602547181939962242146,
494  .160078328543346226334652529543359071872,
495  .2031674267230659217490644558097983765065,
496  .2334925365383548087608498989248780562594,
497  .2491470458134027850005624360429512108305,
498  .2491470458134027850005624360429512108305,
499  .2334925365383548087608498989248780562594,
500  .2031674267230659217490644558097983765065,
501  .160078328543346226334652529543359071872,
502  .1069393259953184309602547181939962242146,
503  .04717533638651182719461596148501706031703
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  13,
541  { // points
542  {.984183054718588149472829448807109611065 ,0.0, 0.0},
543  {.9175983992229779652065478365007195123905 ,0.0, 0.0},
544  {.8015780907333099127942064895828598903056 ,0.0, 0.0},
545  {.6423493394403402206439846069955156500717 ,0.0, 0.0},
546  {.4484927510364468528779128521276398678019 ,0.0, 0.0},
547  {.2304583159551347940655281210979888352115 ,0.0, 0.0},
548  { 0 ,0.0, 0.0},
549  {-.2304583159551347940655281210979888352115 ,0.0, 0.0},
550  {-.4484927510364468528779128521276398678019 ,0.0, 0.0},
551  {-.6423493394403402206439846069955156500717 ,0.0, 0.0},
552  {-.8015780907333099127942064895828598903056 ,0.0, 0.0},
553  {-.9175983992229779652065478365007195123905 ,0.0, 0.0},
554  {-.984183054718588149472829448807109611065 ,0.0, 0.0}
555  },
556  { // weights
557  .04048400476531587952002159220098606004199,
558  .09212149983772844791442177595379712092368,
559  .1388735102197872384636017768688714676219,
560  .1781459807619457382800466919960979955128,
561  .2078160475368885023125232193060527633866,
562  .2262831802628972384120901860397766184348,
563  .2325515532308739101945895152688359481566,
564  .2262831802628972384120901860397766184348,
565  .2078160475368885023125232193060527633866,
566  .1781459807619457382800466919960979955128,
567  .1388735102197872384636017768688714676219,
568  .09212149983772844791442177595379712092368,
569  .04048400476531587952002159220098606004199
570  }
571  },
572  {
573  14,
574  { // points
575  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
576  {.928434883663573517336391139377874264477 ,0.0, 0.0},
577  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
578  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
579  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
580  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
581  {.108054948707343662066244650219834747612 ,0.0, 0.0},
582  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
583  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
584  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
585  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
586  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
587  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
588  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
589  },
590  { // weights
591  .03511946033175186303183287613819178061971,
592  .0801580871597602098056332770628543095837,
593  .1215185706879031846894148090724766259567,
594  .1572031671581935345696019386238421566057,
595  .1855383974779378137417165901251570362489,
596  .2051984637212956039659240656612180557103,
597  .215263853463157790195876443316260035275,
598  .215263853463157790195876443316260035275,
599  .2051984637212956039659240656612180557103,
600  .1855383974779378137417165901251570362489,
601  .1572031671581935345696019386238421566057,
602  .1215185706879031846894148090724766259567,
603  .0801580871597602098056332770628543095837,
604  .03511946033175186303183287613819178061971
605  }
606  },
607  {
608  14,
609  { // points
610  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
611  {.928434883663573517336391139377874264477 ,0.0, 0.0},
612  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
613  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
614  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
615  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
616  {.108054948707343662066244650219834747612 ,0.0, 0.0},
617  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
618  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
619  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
620  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
621  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
622  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
623  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
624  },
625  { // weights
626  .03511946033175186303183287613819178061971,
627  .0801580871597602098056332770628543095837,
628  .1215185706879031846894148090724766259567,
629  .1572031671581935345696019386238421566057,
630  .1855383974779378137417165901251570362489,
631  .2051984637212956039659240656612180557103,
632  .215263853463157790195876443316260035275,
633  .215263853463157790195876443316260035275,
634  .2051984637212956039659240656612180557103,
635  .1855383974779378137417165901251570362489,
636  .1572031671581935345696019386238421566057,
637  .1215185706879031846894148090724766259567,
638  .0801580871597602098056332770628543095837,
639  .03511946033175186303183287613819178061971
640  }
641  },
642  {
643  15,
644  { // points
645  {.987992518020485428489565718586612581147 ,0.0, 0.0},
646  {.937273392400705904307758947710209471244 ,0.0, 0.0},
647  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
648  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
649  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
650  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
651  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
652  { 0 ,0.0, 0.0},
653  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
654  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
655  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
656  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
657  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
658  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
659  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
660  },
661  { // weights
662  .03075324199611726835462839357720441772175,
663  .07036604748810812470926741645066733846671,
664  .1071592204671719350118695466858693034155,
665  .1395706779261543144478047945110283225209,
666  .1662692058169939335532008604812088111309,
667  .1861610000155622110268005618664228245062,
668  .1984314853271115764561183264438393248187,
669  .2025782419255612728806201999675193148387,
670  .1984314853271115764561183264438393248187,
671  .1861610000155622110268005618664228245062,
672  .1662692058169939335532008604812088111309,
673  .1395706779261543144478047945110283225209,
674  .1071592204671719350118695466858693034155,
675  .07036604748810812470926741645066733846671,
676  .03075324199611726835462839357720441772175
677  }
678  },
679  {
680  15,
681  { // points
682  {.987992518020485428489565718586612581147 ,0.0, 0.0},
683  {.937273392400705904307758947710209471244 ,0.0, 0.0},
684  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
685  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
686  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
687  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
688  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
689  { 0 ,0.0, 0.0},
690  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
691  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
692  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
693  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
694  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
695  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
696  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
697  },
698  { // weights
699  .03075324199611726835462839357720441772175,
700  .07036604748810812470926741645066733846671,
701  .1071592204671719350118695466858693034155,
702  .1395706779261543144478047945110283225209,
703  .1662692058169939335532008604812088111309,
704  .1861610000155622110268005618664228245062,
705  .1984314853271115764561183264438393248187,
706  .2025782419255612728806201999675193148387,
707  .1984314853271115764561183264438393248187,
708  .1861610000155622110268005618664228245062,
709  .1662692058169939335532008604812088111309,
710  .1395706779261543144478047945110283225209,
711  .1071592204671719350118695466858693034155,
712  .07036604748810812470926741645066733846671,
713  .03075324199611726835462839357720441772175
714  }
715  },
716  {
717  16,
718  { // points
719  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
720  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
721  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
722  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
723  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
724  {.45801677765722738634241944298357757354 ,0.0, 0.0},
725  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
726  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
727  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
728  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
729  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
730  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
731  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
732  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
733  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
734  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
735  },
736  { // weights
737  .02715245941175409485178057245601810351227,
738  .06225352393864789286284383699437769427499,
739  .09515851168249278480992510760224622635526,
740  .1246289712555338720524762821920164201449,
741  .1495959888165767320815017305474785489705,
742  .1691565193950025381893120790303599622116,
743  .1826034150449235888667636679692199393836,
744  .1894506104550684962853967232082831051469,
745  .1894506104550684962853967232082831051469,
746  .1826034150449235888667636679692199393836,
747  .1691565193950025381893120790303599622116,
748  .1495959888165767320815017305474785489705,
749  .1246289712555338720524762821920164201449,
750  .09515851168249278480992510760224622635526,
751  .06225352393864789286284383699437769427499,
752  .02715245941175409485178057245601810351227
753  }
754  },
755  {
756  16,
757  { // points
758  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
759  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
760  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
761  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
762  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
763  {.45801677765722738634241944298357757354 ,0.0, 0.0},
764  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
765  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
766  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
767  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
768  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
769  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
770  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
771  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
772  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
773  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
774  },
775  { // weights
776  .02715245941175409485178057245601810351227,
777  .06225352393864789286284383699437769427499,
778  .09515851168249278480992510760224622635526,
779  .1246289712555338720524762821920164201449,
780  .1495959888165767320815017305474785489705,
781  .1691565193950025381893120790303599622116,
782  .1826034150449235888667636679692199393836,
783  .1894506104550684962853967232082831051469,
784  .1894506104550684962853967232082831051469,
785  .1826034150449235888667636679692199393836,
786  .1691565193950025381893120790303599622116,
787  .1495959888165767320815017305474785489705,
788  .1246289712555338720524762821920164201449,
789  .09515851168249278480992510760224622635526,
790  .06225352393864789286284383699437769427499,
791  .02715245941175409485178057245601810351227
792  }
793  },
794  {
795  17,
796  { // points
797  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
798  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
799  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
800  {.781514003896801406925230055520476050224 ,0.0, 0.0},
801  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
802  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
803  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
804  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
805  { 0 ,0.0, 0.0},
806  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
807  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
808  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
809  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
810  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
811  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
812  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
813  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
814  },
815  { // weights
816  .0241483028685479319601100262875653246917,
817  .05545952937398720112944016535824466051285,
818  .08503614831717918088353537019106207385049,
819  .1118838471934039710947883856263559267358,
820  .1351363684685254732863199817023501973721,
821  .1540457610768102880814315948019586119405,
822  .1680041021564500445099706637883231550212,
823  .1765627053669926463252709901131972391509,
824  .1794464703562065254582656442618856214488,
825  .1765627053669926463252709901131972391509,
826  .1680041021564500445099706637883231550212,
827  .1540457610768102880814315948019586119405,
828  .1351363684685254732863199817023501973721,
829  .1118838471934039710947883856263559267358,
830  .08503614831717918088353537019106207385049,
831  .05545952937398720112944016535824466051285,
832  .0241483028685479319601100262875653246917
833  }
834  },
835  {
836  17,
837  { // points
838  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
839  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
840  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
841  {.781514003896801406925230055520476050224 ,0.0, 0.0},
842  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
843  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
844  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
845  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
846  { 0 ,0.0, 0.0},
847  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
848  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
849  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
850  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
851  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
852  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
853  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
854  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
855  },
856  { // weights
857  .0241483028685479319601100262875653246917,
858  .05545952937398720112944016535824466051285,
859  .08503614831717918088353537019106207385049,
860  .1118838471934039710947883856263559267358,
861  .1351363684685254732863199817023501973721,
862  .1540457610768102880814315948019586119405,
863  .1680041021564500445099706637883231550212,
864  .1765627053669926463252709901131972391509,
865  .1794464703562065254582656442618856214488,
866  .1765627053669926463252709901131972391509,
867  .1680041021564500445099706637883231550212,
868  .1540457610768102880814315948019586119405,
869  .1351363684685254732863199817023501973721,
870  .1118838471934039710947883856263559267358,
871  .08503614831717918088353537019106207385049,
872  .05545952937398720112944016535824466051285,
873  .0241483028685479319601100262875653246917
874  }
875  },
876  {
877  18,
878  { // points
879  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
880  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
881  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
882  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
883  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
884  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
885  {.411751161462842646035931793833051637079 ,0.0, 0.0},
886  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
887  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
888  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
889  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
890  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
891  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
892  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
893  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
894  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
895  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
896  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
897  },
898  { // weights
899  .02161601352648331031334271026645246938769,
900  .04971454889496979645333494620263864168087,
901  .07642573025488905652912967761663652560532,
902  .1009420441062871655628139849248346070628,
903  .1225552067114784601845191268002015552282,
904  .1406429146706506512047313037519472280955,
905  .1546846751262652449254180038363747721932,
906  .1642764837458327229860537764659275904123,
907  .1691423829631435918406564701349866103341,
908  .1691423829631435918406564701349866103341,
909  .1642764837458327229860537764659275904123,
910  .1546846751262652449254180038363747721932,
911  .1406429146706506512047313037519472280955,
912  .1225552067114784601845191268002015552282,
913  .1009420441062871655628139849248346070628,
914  .07642573025488905652912967761663652560532,
915  .04971454889496979645333494620263864168087,
916  .02161601352648331031334271026645246938769
917  }
918  },
919  {
920  18,
921  { // points
922  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
923  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
924  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
925  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
926  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
927  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
928  {.411751161462842646035931793833051637079 ,0.0, 0.0},
929  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
930  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
931  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
932  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
933  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
934  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
935  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
936  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
937  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
938  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
939  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
940  },
941  { // weights
942  .02161601352648331031334271026645246938769,
943  .04971454889496979645333494620263864168087,
944  .07642573025488905652912967761663652560532,
945  .1009420441062871655628139849248346070628,
946  .1225552067114784601845191268002015552282,
947  .1406429146706506512047313037519472280955,
948  .1546846751262652449254180038363747721932,
949  .1642764837458327229860537764659275904123,
950  .1691423829631435918406564701349866103341,
951  .1691423829631435918406564701349866103341,
952  .1642764837458327229860537764659275904123,
953  .1546846751262652449254180038363747721932,
954  .1406429146706506512047313037519472280955,
955  .1225552067114784601845191268002015552282,
956  .1009420441062871655628139849248346070628,
957  .07642573025488905652912967761663652560532,
958  .04971454889496979645333494620263864168087,
959  .02161601352648331031334271026645246938769
960  }
961  },
962  {
963  19,
964  { // points
965  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
966  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
967  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
968  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
969  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
970  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
971  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
972  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
973  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
974  { 0 ,0.0, 0.0},
975  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
976  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
977  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
978  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
979  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
980  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
981  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
982  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
983  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
984  },
985  { // weights
986  .01946178822972647703631204146443843575291,
987  .04481422676569960033283815740199421195175,
988  .06904454273764122658070825800601304496185,
989  .09149002162244999946446209412383965266091,
990  .1115666455473339947160239016817659974813,
991  .1287539625393362276755157848568771170558,
992  .1426067021736066117757461094419029724757,
993  .152766042065859666778855400897662998461,
994  .1589688433939543476499564394650472016788,
995  .1610544498487836959791636253209167350399,
996  .1589688433939543476499564394650472016788,
997  .152766042065859666778855400897662998461,
998  .1426067021736066117757461094419029724757,
999  .1287539625393362276755157848568771170558,
1000  .1115666455473339947160239016817659974813,
1001  .09149002162244999946446209412383965266091,
1002  .06904454273764122658070825800601304496185,
1003  .04481422676569960033283815740199421195175,
1004  .01946178822972647703631204146443843575291
1005  }
1006  },
1007  {
1008  19,
1009  { // points
1010  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
1011  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
1012  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
1013  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
1014  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
1015  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
1016  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
1017  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
1018  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
1019  { 0 ,0.0, 0.0},
1020  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
1021  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
1022  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
1023  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
1024  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
1025  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
1026  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
1027  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
1028  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
1029  },
1030  { // weights
1031  .01946178822972647703631204146443843575291,
1032  .04481422676569960033283815740199421195175,
1033  .06904454273764122658070825800601304496185,
1034  .09149002162244999946446209412383965266091,
1035  .1115666455473339947160239016817659974813,
1036  .1287539625393362276755157848568771170558,
1037  .1426067021736066117757461094419029724757,
1038  .152766042065859666778855400897662998461,
1039  .1589688433939543476499564394650472016788,
1040  .1610544498487836959791636253209167350399,
1041  .1589688433939543476499564394650472016788,
1042  .152766042065859666778855400897662998461,
1043  .1426067021736066117757461094419029724757,
1044  .1287539625393362276755157848568771170558,
1045  .1115666455473339947160239016817659974813,
1046  .09149002162244999946446209412383965266091,
1047  .06904454273764122658070825800601304496185,
1048  .04481422676569960033283815740199421195175,
1049  .01946178822972647703631204146443843575291
1050  }
1051  },
1052  {
1053  20,
1054  { // points
1055  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1056  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1057  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1058  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1059  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1060  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1061  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1062  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1063  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1064  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1065  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1066  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1067  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1068  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1069  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1070  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1071  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1072  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1073  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1074  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1075  },
1076  { // weights
1077  .01761400713915211831186196235185281636214,
1078  .04060142980038694133103995227493210987909,
1079  .0626720483341090635695065351870416063516,
1080  .08327674157670474872475814322204620610018,
1081  .1019301198172404350367501354803498761667,
1082  .118194531961518417312377377711382287005,
1083  .1316886384491766268984944997481631349161,
1084  .1420961093183820513292983250671649330345,
1085  .1491729864726037467878287370019694366927,
1086  .1527533871307258506980843319550975934919,
1087  .1527533871307258506980843319550975934919,
1088  .1491729864726037467878287370019694366927,
1089  .1420961093183820513292983250671649330345,
1090  .1316886384491766268984944997481631349161,
1091  .118194531961518417312377377711382287005,
1092  .1019301198172404350367501354803498761667,
1093  .08327674157670474872475814322204620610018,
1094  .0626720483341090635695065351870416063516,
1095  .04060142980038694133103995227493210987909,
1096  .01761400713915211831186196235185281636214
1097  }
1098  },
1099  {
1100  20,
1101  { // points
1102  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1103  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1104  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1105  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1106  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1107  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1108  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1109  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1110  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1111  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1112  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1113  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1114  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1115  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1116  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1117  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1118  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1119  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1120  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1121  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1122  },
1123  { // weights
1124  .01761400713915211831186196235185281636214,
1125  .04060142980038694133103995227493210987909,
1126  .0626720483341090635695065351870416063516,
1127  .08327674157670474872475814322204620610018,
1128  .1019301198172404350367501354803498761667,
1129  .118194531961518417312377377711382287005,
1130  .1316886384491766268984944997481631349161,
1131  .1420961093183820513292983250671649330345,
1132  .1491729864726037467878287370019694366927,
1133  .1527533871307258506980843319550975934919,
1134  .1527533871307258506980843319550975934919,
1135  .1491729864726037467878287370019694366927,
1136  .1420961093183820513292983250671649330345,
1137  .1316886384491766268984944997481631349161,
1138  .118194531961518417312377377711382287005,
1139  .1019301198172404350367501354803498761667,
1140  .08327674157670474872475814322204620610018,
1141  .0626720483341090635695065351870416063516,
1142  .04060142980038694133103995227493210987909,
1143  .01761400713915211831186196235185281636214
1144  }
1145  },
1146  {
1147  21,
1148  { // points
1149  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1150  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1151  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1152  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1153  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1154  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1155  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1156  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1157  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1158  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1159  {0 ,0.0, 0.0},
1160  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1161  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1162  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1163  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1164  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1165  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1166  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1167  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1168  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1169  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1170  },
1171  { // weights
1172  .01601722825777433332422461685847101526589,
1173  .03695378977085249379995066829932966618894,
1174  .05713442542685720828363582647244795749129,
1175  .07610011362837930201705165330018317922615,
1176  .09344442345603386155328974111393208848353,
1177  .1087972991671483776634745780701056420337,
1178  .1218314160537285341953671771257335983563,
1179  .132268938633337461781052574496775604329,
1180  .1398873947910731547221334238675831108928,
1181  .1445244039899700590638271665537525436099,
1182  .1460811336496904271919851476833711882448,
1183  .1445244039899700590638271665537525436099,
1184  .1398873947910731547221334238675831108928,
1185  .132268938633337461781052574496775604329,
1186  .1218314160537285341953671771257335983563,
1187  .1087972991671483776634745780701056420337,
1188  .09344442345603386155328974111393208848353,
1189  .07610011362837930201705165330018317922615,
1190  .05713442542685720828363582647244795749129,
1191  .03695378977085249379995066829932966618894,
1192  .01601722825777433332422461685847101526589
1193  }
1194  },
1195  {
1196  21,
1197  { // points
1198  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1199  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1200  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1201  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1202  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1203  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1204  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1205  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1206  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1207  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1208  {0 ,0.0, 0.0},
1209  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1210  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1211  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1212  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1213  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1214  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1215  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1216  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1217  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1218  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1219  },
1220  { // weights
1221  .01601722825777433332422461685847101526589,
1222  .03695378977085249379995066829932966618894,
1223  .05713442542685720828363582647244795749129,
1224  .07610011362837930201705165330018317922615,
1225  .09344442345603386155328974111393208848353,
1226  .1087972991671483776634745780701056420337,
1227  .1218314160537285341953671771257335983563,
1228  .132268938633337461781052574496775604329,
1229  .1398873947910731547221334238675831108928,
1230  .1445244039899700590638271665537525436099,
1231  .1460811336496904271919851476833711882448,
1232  .1445244039899700590638271665537525436099,
1233  .1398873947910731547221334238675831108928,
1234  .132268938633337461781052574496775604329,
1235  .1218314160537285341953671771257335983563,
1236  .1087972991671483776634745780701056420337,
1237  .09344442345603386155328974111393208848353,
1238  .07610011362837930201705165330018317922615,
1239  .05713442542685720828363582647244795749129,
1240  .03695378977085249379995066829932966618894,
1241  .01601722825777433332422461685847101526589
1242  }
1243  },
1244  {
1245  22,
1246  { // points
1247  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1248  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1249  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1250  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1251  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1252  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1253  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1254  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1255  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1256  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1257  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1258  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1259  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1260  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1261  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1262  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1263  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1264  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1265  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1266  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1267  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1268  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1269  },
1270  { // weights
1271  .01462799529827220068499109804718544519021,
1272  .03377490158481415479330224686591290134917,
1273  .05229333515268328594031205127321125611215,
1274  .06979646842452048809496141893021765739878,
1275  .08594160621706772741444368137270286618914,
1276  .1004141444428809649320788378305362823508,
1277  .1129322960805392183934006074217843191143,
1278  .1232523768105124242855609861548144719594,
1279  .1311735047870623707329649925303074458757,
1280  .1365414983460151713525738312315173965864,
1281  .1392518728556319933754102483418099578739,
1282  .1392518728556319933754102483418099578739,
1283  .1365414983460151713525738312315173965864,
1284  .1311735047870623707329649925303074458757,
1285  .1232523768105124242855609861548144719594,
1286  .1129322960805392183934006074217843191143,
1287  .1004141444428809649320788378305362823508,
1288  .08594160621706772741444368137270286618914,
1289  .06979646842452048809496141893021765739878,
1290  .05229333515268328594031205127321125611215,
1291  .03377490158481415479330224686591290134917,
1292  .01462799529827220068499109804718544519021
1293  }
1294  },
1295  {
1296  22,
1297  { // points
1298  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1299  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1300  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1301  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1302  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1303  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1304  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1305  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1306  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1307  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1308  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1309  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1310  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1311  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1312  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1313  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1314  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1315  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1316  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1317  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1318  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1319  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1320  },
1321  { // weights
1322  .01462799529827220068499109804718544519021,
1323  .03377490158481415479330224686591290134917,
1324  .05229333515268328594031205127321125611215,
1325  .06979646842452048809496141893021765739878,
1326  .08594160621706772741444368137270286618914,
1327  .1004141444428809649320788378305362823508,
1328  .1129322960805392183934006074217843191143,
1329  .1232523768105124242855609861548144719594,
1330  .1311735047870623707329649925303074458757,
1331  .1365414983460151713525738312315173965864,
1332  .1392518728556319933754102483418099578739,
1333  .1392518728556319933754102483418099578739,
1334  .1365414983460151713525738312315173965864,
1335  .1311735047870623707329649925303074458757,
1336  .1232523768105124242855609861548144719594,
1337  .1129322960805392183934006074217843191143,
1338  .1004141444428809649320788378305362823508,
1339  .08594160621706772741444368137270286618914,
1340  .06979646842452048809496141893021765739878,
1341  .05229333515268328594031205127321125611215,
1342  .03377490158481415479330224686591290134917,
1343  .01462799529827220068499109804718544519021
1344  }
1345  },
1346  {
1347  23,
1348  { // points
1349  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1350  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1351  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1352  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1353  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1354  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1355  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1356  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1357  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1358  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1359  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1360  {0 ,0.0, 0.0},
1361  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1362  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1363  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1364  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1365  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1366  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1367  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1368  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1369  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1370  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1371  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1372  },
1373  { // weights
1374  .01341185948714177208130949345861506497662,
1375  .03098800585697944431069421964188450538377,
1376  .04803767173108466857164107163203399656122,
1377  .06423242140852585212716961515891099803916,
1378  .07928141177671895492289252474204322691371,
1379  .09291576606003514747701861736976464860346,
1380  .1048920914645414100740861850147438548585,
1381  .1149966402224113649416435129339613014914,
1382  .1230490843067295304675784006720096548159,
1383  .1289057221880821499785953393997936532597,
1384  .132462039404696617371642464703316925805,
1385  .1336545721861061753514571105458443385832,
1386  .132462039404696617371642464703316925805,
1387  .1289057221880821499785953393997936532597,
1388  .1230490843067295304675784006720096548159,
1389  .1149966402224113649416435129339613014914,
1390  .1048920914645414100740861850147438548585,
1391  .09291576606003514747701861736976464860346,
1392  .07928141177671895492289252474204322691371,
1393  .06423242140852585212716961515891099803916,
1394  .04803767173108466857164107163203399656122,
1395  .03098800585697944431069421964188450538377,
1396  .01341185948714177208130949345861506497662
1397  }
1398  },
1399  {
1400  23,
1401  { // points
1402  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1403  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1404  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1405  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1406  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1407  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1408  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1409  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1410  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1411  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1412  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1413  {0 ,0.0, 0.0},
1414  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1415  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1416  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1417  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1418  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1419  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1420  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1421  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1422  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1423  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1424  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1425  },
1426  { // weights
1427  .01341185948714177208130949345861506497662,
1428  .03098800585697944431069421964188450538377,
1429  .04803767173108466857164107163203399656122,
1430  .06423242140852585212716961515891099803916,
1431  .07928141177671895492289252474204322691371,
1432  .09291576606003514747701861736976464860346,
1433  .1048920914645414100740861850147438548585,
1434  .1149966402224113649416435129339613014914,
1435  .1230490843067295304675784006720096548159,
1436  .1289057221880821499785953393997936532597,
1437  .132462039404696617371642464703316925805,
1438  .1336545721861061753514571105458443385832,
1439  .132462039404696617371642464703316925805,
1440  .1289057221880821499785953393997936532597,
1441  .1230490843067295304675784006720096548159,
1442  .1149966402224113649416435129339613014914,
1443  .1048920914645414100740861850147438548585,
1444  .09291576606003514747701861736976464860346,
1445  .07928141177671895492289252474204322691371,
1446  .06423242140852585212716961515891099803916,
1447  .04803767173108466857164107163203399656122,
1448  .03098800585697944431069421964188450538377,
1449  .01341185948714177208130949345861506497662
1450  }
1451  },
1452  {
1453  24,
1454  { // points
1455  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1456  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1457  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1458  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1459  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1460  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1461  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1462  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1463  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1464  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1465  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1466  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1467  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1468  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1469  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1470  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1471  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1472  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1473  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1474  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1475  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1476  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1477  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1478  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1479  },
1480  { // weights
1481  .01234122979998719954680566707003729157591,
1482  .0285313886289336631813078159518782864492,
1483  .04427743881741980616860274821133822885931,
1484  .0592985849154367807463677585001085845412,
1485  .07334648141108030573403361525311651811934,
1486  .08619016153195327591718520298374266718508,
1487  .09761865210411388826988066446424715442792,
1488  .1074442701159656347825773424466062227946,
1489  .1155056680537256013533444839067835598623,
1490  .121670472927803391204463153476262425607,
1491  .1258374563468282961213753825111836887264,
1492  .1279381953467521569740561652246953718517,
1493  .1279381953467521569740561652246953718517,
1494  .1258374563468282961213753825111836887264,
1495  .121670472927803391204463153476262425607,
1496  .1155056680537256013533444839067835598623,
1497  .1074442701159656347825773424466062227946,
1498  .09761865210411388826988066446424715442792,
1499  .08619016153195327591718520298374266718508,
1500  .07334648141108030573403361525311651811934,
1501  .0592985849154367807463677585001085845412,
1502  .04427743881741980616860274821133822885931,
1503  .0285313886289336631813078159518782864492,
1504  .01234122979998719954680566707003729157591
1505  }
1506  },
1507  {
1508  24,
1509  { // points
1510  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1511  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1512  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1513  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1514  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1515  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1516  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1517  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1518  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1519  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1520  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1521  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1522  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1523  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1524  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1525  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1526  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1527  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1528  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1529  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1530  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1531  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1532  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1533  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1534  },
1535  { // weights
1536  .01234122979998719954680566707003729157591,
1537  .0285313886289336631813078159518782864492,
1538  .04427743881741980616860274821133822885931,
1539  .0592985849154367807463677585001085845412,
1540  .07334648141108030573403361525311651811934,
1541  .08619016153195327591718520298374266718508,
1542  .09761865210411388826988066446424715442792,
1543  .1074442701159656347825773424466062227946,
1544  .1155056680537256013533444839067835598623,
1545  .121670472927803391204463153476262425607,
1546  .1258374563468282961213753825111836887264,
1547  .1279381953467521569740561652246953718517,
1548  .1279381953467521569740561652246953718517,
1549  .1258374563468282961213753825111836887264,
1550  .121670472927803391204463153476262425607,
1551  .1155056680537256013533444839067835598623,
1552  .1074442701159656347825773424466062227946,
1553  .09761865210411388826988066446424715442792,
1554  .08619016153195327591718520298374266718508,
1555  .07334648141108030573403361525311651811934,
1556  .0592985849154367807463677585001085845412,
1557  .04427743881741980616860274821133822885931,
1558  .0285313886289336631813078159518782864492,
1559  .01234122979998719954680566707003729157591
1560  }
1561  },
1562  {
1563  25,
1564  { // points
1565  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1566  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1567  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1568  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1569  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1570  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1571  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1572  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1573  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1574  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1575  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1576  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1577  {0 ,0.0, 0.0},
1578  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1579  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1580  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1581  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1582  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1583  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1584  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1585  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1586  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1587  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1588  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1589  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1590  },
1591  { // weights
1592  .01139379850102628794790296411323477360332,
1593  .02635498661503213726190181529529914493596,
1594  .04093915670130631265562348771164595366085,
1595  .05490469597583519192593689154047332416011,
1596  .06803833381235691720718718565670796855471,
1597  .08014070033500101801323495966911130229023,
1598  .09102826198296364981149722070289165338099,
1599  .1005359490670506442022068903926858269885,
1600  .1085196244742636531160939570501166193401,
1601  .1148582591457116483393255458695558086409,
1602  .1194557635357847722281781265129010473902,
1603  .1222424429903100416889595189458515058351,
1604  .1231760537267154512039028730790501424382,
1605  .1222424429903100416889595189458515058351,
1606  .1194557635357847722281781265129010473902,
1607  .1148582591457116483393255458695558086409,
1608  .1085196244742636531160939570501166193401,
1609  .1005359490670506442022068903926858269885,
1610  .09102826198296364981149722070289165338099,
1611  .08014070033500101801323495966911130229023,
1612  .06803833381235691720718718565670796855471,
1613  .05490469597583519192593689154047332416011,
1614  .04093915670130631265562348771164595366085,
1615  .02635498661503213726190181529529914493596,
1616  .01139379850102628794790296411323477360332
1617  }
1618  },
1619  {
1620  25,
1621  { // points
1622  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1623  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1624  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1625  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1626  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1627  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1628  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1629  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1630  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1631  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1632  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1633  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1634  {0 ,0.0, 0.0},
1635  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1636  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1637  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1638  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1639  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1640  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1641  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1642  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1643  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1644  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1645  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1646  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1647  },
1648  { // weights
1649  .01139379850102628794790296411323477360332,
1650  .02635498661503213726190181529529914493596,
1651  .04093915670130631265562348771164595366085,
1652  .05490469597583519192593689154047332416011,
1653  .06803833381235691720718718565670796855471,
1654  .08014070033500101801323495966911130229023,
1655  .09102826198296364981149722070289165338099,
1656  .1005359490670506442022068903926858269885,
1657  .1085196244742636531160939570501166193401,
1658  .1148582591457116483393255458695558086409,
1659  .1194557635357847722281781265129010473902,
1660  .1222424429903100416889595189458515058351,
1661  .1231760537267154512039028730790501424382,
1662  .1222424429903100416889595189458515058351,
1663  .1194557635357847722281781265129010473902,
1664  .1148582591457116483393255458695558086409,
1665  .1085196244742636531160939570501166193401,
1666  .1005359490670506442022068903926858269885,
1667  .09102826198296364981149722070289165338099,
1668  .08014070033500101801323495966911130229023,
1669  .06803833381235691720718718565670796855471,
1670  .05490469597583519192593689154047332416011,
1671  .04093915670130631265562348771164595366085,
1672  .02635498661503213726190181529529914493596,
1673  .01139379850102628794790296411323477360332
1674  }
1675  },
1676  {
1677  26,
1678  { // points
1679  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1680  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1681  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1682  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1683  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1684  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1685  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1686  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1687  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1688  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1689  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1690  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1691  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1692  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1693  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1694  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1695  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1696  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1697  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1698  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1699  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1700  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1701  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1702  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1703  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1704  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1705  },
1706  { // weights
1707  .01055137261734300715565118768525197790435,
1708  .0244178510926319087896158275197884002405,
1709  .03796238329436276395030314124885049469077,
1710  .05097582529714781199831990072407337952588,
1711  .06327404632957483553945368990704509572222,
1712  .07468414976565974588707579610284833863875,
1713  .08504589431348523921044776507998169658392,
1714  .09421380035591414846366488306730319854917,
1715  .1020591610944254232384140702534307923272,
1716  .1084718405285765906565794267279975822894,
1717  .113361816546319666549440718442598145246,
1718  .116660443485296582044662507540362213632,
1719  .1183214152792622765163710857004686846499,
1720  .1183214152792622765163710857004686846499,
1721  .116660443485296582044662507540362213632,
1722  .113361816546319666549440718442598145246,
1723  .1084718405285765906565794267279975822894,
1724  .1020591610944254232384140702534307923272,
1725  .09421380035591414846366488306730319854917,
1726  .08504589431348523921044776507998169658392,
1727  .07468414976565974588707579610284833863875,
1728  .06327404632957483553945368990704509572222,
1729  .05097582529714781199831990072407337952588,
1730  .03796238329436276395030314124885049469077,
1731  .0244178510926319087896158275197884002405,
1732  .01055137261734300715565118768525197790435
1733  }
1734  },
1735  {
1736  26,
1737  { // points
1738  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1739  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1740  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1741  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1742  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1743  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1744  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1745  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1746  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1747  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1748  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1749  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1750  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1751  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1752  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1753  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1754  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1755  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1756  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1757  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1758  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1759  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1760  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1761  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1762  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1763  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1764  },
1765  { // weights
1766  .01055137261734300715565118768525197790435,
1767  .0244178510926319087896158275197884002405,
1768  .03796238329436276395030314124885049469077,
1769  .05097582529714781199831990072407337952588,
1770  .06327404632957483553945368990704509572222,
1771  .07468414976565974588707579610284833863875,
1772  .08504589431348523921044776507998169658392,
1773  .09421380035591414846366488306730319854917,
1774  .1020591610944254232384140702534307923272,
1775  .1084718405285765906565794267279975822894,
1776  .113361816546319666549440718442598145246,
1777  .116660443485296582044662507540362213632,
1778  .1183214152792622765163710857004686846499,
1779  .1183214152792622765163710857004686846499,
1780  .116660443485296582044662507540362213632,
1781  .113361816546319666549440718442598145246,
1782  .1084718405285765906565794267279975822894,
1783  .1020591610944254232384140702534307923272,
1784  .09421380035591414846366488306730319854917,
1785  .08504589431348523921044776507998169658392,
1786  .07468414976565974588707579610284833863875,
1787  .06327404632957483553945368990704509572222,
1788  .05097582529714781199831990072407337952588,
1789  .03796238329436276395030314124885049469077,
1790  .0244178510926319087896158275197884002405,
1791  .01055137261734300715565118768525197790435
1792  }
1793  },
1794  {
1795  27,
1796  { // points
1797  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1798  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1799  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1800  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1801  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1802  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1803  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1804  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1805  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1806  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1807  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1808  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1809  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1810  {0 ,0.0, 0.0},
1811  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1812  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1813  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1814  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1815  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1816  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1817  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1818  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1819  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1820  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1821  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1822  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1823  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1824  },
1825  { // weights
1826  .009798996051294360261150055091259098098226,
1827  .02268623159618062319603420644676148881277,
1828  .03529705375741971102257828930471164113614,
1829  .04744941252061506270409671011418471822473,
1830  .05898353685983359911030083371953163316524,
1831  .06974882376624559298432288835666727613282,
1832  .07960486777305777126307495900984240297615,
1833  .08842315854375695019432280285374911105654,
1834  .09608872737002850756565264655810585916021,
1835  .1025016378177457986712477115326638093244,
1836  .107578285788533187212162984426657404819,
1837  .1112524883568451926721630960428486748329,
1838  .1134763461089651486203699480920992579205,
1839  .1142208673789569890450457369018352486807,
1840  .1134763461089651486203699480920992579205,
1841  .1112524883568451926721630960428486748329,
1842  .107578285788533187212162984426657404819,
1843  .1025016378177457986712477115326638093244,
1844  .09608872737002850756565264655810585916021,
1845  .08842315854375695019432280285374911105654,
1846  .07960486777305777126307495900984240297615,
1847  .06974882376624559298432288835666727613282,
1848  .05898353685983359911030083371953163316524,
1849  .04744941252061506270409671011418471822473,
1850  .03529705375741971102257828930471164113614,
1851  .02268623159618062319603420644676148881277,
1852  .009798996051294360261150055091259098098226
1853  }
1854  },
1855  {
1856  27,
1857  { // points
1858  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1859  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1860  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1861  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1862  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1863  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1864  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1865  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1866  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1867  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1868  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1869  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1870  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1871  {0 ,0.0, 0.0},
1872  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1873  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1874  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1875  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1876  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1877  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1878  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1879  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1880  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1881  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1882  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1883  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1884  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1885  },
1886  { // weights
1887  .009798996051294360261150055091259098098226,
1888  .02268623159618062319603420644676148881277,
1889  .03529705375741971102257828930471164113614,
1890  .04744941252061506270409671011418471822473,
1891  .05898353685983359911030083371953163316524,
1892  .06974882376624559298432288835666727613282,
1893  .07960486777305777126307495900984240297615,
1894  .08842315854375695019432280285374911105654,
1895  .09608872737002850756565264655810585916021,
1896  .1025016378177457986712477115326638093244,
1897  .107578285788533187212162984426657404819,
1898  .1112524883568451926721630960428486748329,
1899  .1134763461089651486203699480920992579205,
1900  .1142208673789569890450457369018352486807,
1901  .1134763461089651486203699480920992579205,
1902  .1112524883568451926721630960428486748329,
1903  .107578285788533187212162984426657404819,
1904  .1025016378177457986712477115326638093244,
1905  .09608872737002850756565264655810585916021,
1906  .08842315854375695019432280285374911105654,
1907  .07960486777305777126307495900984240297615,
1908  .06974882376624559298432288835666727613282,
1909  .05898353685983359911030083371953163316524,
1910  .04744941252061506270409671011418471822473,
1911  .03529705375741971102257828930471164113614,
1912  .02268623159618062319603420644676148881277,
1913  .009798996051294360261150055091259098098226
1914  }
1915  },
1916  {
1917  28,
1918  { // points
1919  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1920  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1921  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1922  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1923  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1924  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1925  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1926  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1927  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1928  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1929  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1930  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1931  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1932  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1933  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1934  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1935  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1936  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
1937  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
1938  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
1939  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
1940  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
1941  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
1942  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
1943  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
1944  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
1945  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
1946  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
1947  },
1948  { // weights
1949  .009124282593094517738816153922951706240344,
1950  .02113211259277125975150038099326543445137,
1951  .03290142778230437997763081917053204598153,
1952  .04427293475900422783958787765320739061499,
1953  .05510734567571674543148291822694559121906,
1954  .06527292396699959579339756677550463635364,
1955  .07464621423456877902393188717302203802164,
1956  .08311341722890121839039649824433247986113,
1957  .09057174439303284094218603133678412982286,
1958  .09693065799792991585048900609544060176503,
1959  .1021129675780607698142166385057121350466,
1960  .1060557659228464179104164369968108287899,
1961  .1087111922582941352535715193036733678753,
1962  .1100470130164751962823762656018176139566,
1963  .1100470130164751962823762656018176139566,
1964  .1087111922582941352535715193036733678753,
1965  .1060557659228464179104164369968108287899,
1966  .1021129675780607698142166385057121350466,
1967  .09693065799792991585048900609544060176503,
1968  .09057174439303284094218603133678412982286,
1969  .08311341722890121839039649824433247986113,
1970  .07464621423456877902393188717302203802164,
1971  .06527292396699959579339756677550463635364,
1972  .05510734567571674543148291822694559121906,
1973  .04427293475900422783958787765320739061499,
1974  .03290142778230437997763081917053204598153,
1975  .02113211259277125975150038099326543445137,
1976  .009124282593094517738816153922951706240344
1977  }
1978  },
1979  {
1980  28,
1981  { // points
1982  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1983  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1984  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1985  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1986  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1987  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1988  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1989  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1990  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1991  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1992  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1993  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1994  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1995  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1996  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1997  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1998  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1999  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
2000  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
2001  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
2002  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
2003  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
2004  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
2005  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
2006  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
2007  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
2008  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
2009  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
2010  },
2011  { // weights
2012  .009124282593094517738816153922951706240344,
2013  .02113211259277125975150038099326543445137,
2014  .03290142778230437997763081917053204598153,
2015  .04427293475900422783958787765320739061499,
2016  .05510734567571674543148291822694559121906,
2017  .06527292396699959579339756677550463635364,
2018  .07464621423456877902393188717302203802164,
2019  .08311341722890121839039649824433247986113,
2020  .09057174439303284094218603133678412982286,
2021  .09693065799792991585048900609544060176503,
2022  .1021129675780607698142166385057121350466,
2023  .1060557659228464179104164369968108287899,
2024  .1087111922582941352535715193036733678753,
2025  .1100470130164751962823762656018176139566,
2026  .1100470130164751962823762656018176139566,
2027  .1087111922582941352535715193036733678753,
2028  .1060557659228464179104164369968108287899,
2029  .1021129675780607698142166385057121350466,
2030  .09693065799792991585048900609544060176503,
2031  .09057174439303284094218603133678412982286,
2032  .08311341722890121839039649824433247986113,
2033  .07464621423456877902393188717302203802164,
2034  .06527292396699959579339756677550463635364,
2035  .05510734567571674543148291822694559121906,
2036  .04427293475900422783958787765320739061499,
2037  .03290142778230437997763081917053204598153,
2038  .02113211259277125975150038099326543445137,
2039  .009124282593094517738816153922951706240344
2040  }
2041  },
2042  {
2043  29,
2044  { // points
2045  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2046  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2047  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2048  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2049  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2050  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2051  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2052  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2053  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2054  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2055  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2056  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2057  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2058  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2059  {0 ,0.0, 0.0},
2060  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2061  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2062  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2063  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2064  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2065  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2066  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2067  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2068  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2069  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2070  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2071  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2072  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2073  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2074  },
2075  { // weights
2076  .008516903878746409654263813302249803002399,
2077  .01973208505612270598385980164039563114961,
2078  .03074049220209362264440852537461674974712,
2079  .04140206251868283610483001011407692153349,
2080  .05159482690249792391259438117954259791962,
2081  .06120309065707913854210984802390704492406,
2082  .07011793325505127856958148694887917310239,
2083  .07823832713576378382814488865968033136688,
2084  .0854722573661725275453448492972080713817,
2085  .09173775713925876334796641107711080689823,
2086  .09696383409440860630190007488268875917636,
2087  .1010912737599149661218205469074973636476,
2088  .1040733100777293739133284712851200689107,
2089  .1058761550973209414065913278521878930748,
2090  .1064793817183142442465111269096775683302,
2091  .1058761550973209414065913278521878930748,
2092  .1040733100777293739133284712851200689107,
2093  .1010912737599149661218205469074973636476,
2094  .09696383409440860630190007488268875917636,
2095  .09173775713925876334796641107711080689823,
2096  .0854722573661725275453448492972080713817,
2097  .07823832713576378382814488865968033136688,
2098  .07011793325505127856958148694887917310239,
2099  .06120309065707913854210984802390704492406,
2100  .05159482690249792391259438117954259791962,
2101  .04140206251868283610483001011407692153349,
2102  .03074049220209362264440852537461674974712,
2103  .01973208505612270598385980164039563114961,
2104  .008516903878746409654263813302249803002399
2105  }
2106  },
2107  {
2108  29,
2109  { // points
2110  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2111  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2112  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2113  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2114  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2115  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2116  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2117  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2118  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2119  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2120  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2121  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2122  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2123  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2124  {0 ,0.0, 0.0},
2125  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2126  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2127  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2128  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2129  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2130  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2131  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2132  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2133  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2134  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2135  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2136  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2137  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2138  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2139  },
2140  { // weights
2141  .008516903878746409654263813302249803002399,
2142  .01973208505612270598385980164039563114961,
2143  .03074049220209362264440852537461674974712,
2144  .04140206251868283610483001011407692153349,
2145  .05159482690249792391259438117954259791962,
2146  .06120309065707913854210984802390704492406,
2147  .07011793325505127856958148694887917310239,
2148  .07823832713576378382814488865968033136688,
2149  .0854722573661725275453448492972080713817,
2150  .09173775713925876334796641107711080689823,
2151  .09696383409440860630190007488268875917636,
2152  .1010912737599149661218205469074973636476,
2153  .1040733100777293739133284712851200689107,
2154  .1058761550973209414065913278521878930748,
2155  .1064793817183142442465111269096775683302,
2156  .1058761550973209414065913278521878930748,
2157  .1040733100777293739133284712851200689107,
2158  .1010912737599149661218205469074973636476,
2159  .09696383409440860630190007488268875917636,
2160  .09173775713925876334796641107711080689823,
2161  .0854722573661725275453448492972080713817,
2162  .07823832713576378382814488865968033136688,
2163  .07011793325505127856958148694887917310239,
2164  .06120309065707913854210984802390704492406,
2165  .05159482690249792391259438117954259791962,
2166  .04140206251868283610483001011407692153349,
2167  .03074049220209362264440852537461674974712,
2168  .01973208505612270598385980164039563114961,
2169  .008516903878746409654263813302249803002399
2170  }
2171  },
2172  {
2173  30,
2174  { // points
2175  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2176  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2177  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2178  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2179  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2180  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2181  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2182  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2183  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2184  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2185  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2186  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2187  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2188  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2189  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2190  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2191  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2192  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2193  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2194  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2195  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2196  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2197  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2198  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2199  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2200  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2201  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2202  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2203  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2204  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2205  },
2206  { // weights
2207  .007968192496166605615465883474673622450481,
2208  .01846646831109095914230213191204726909621,
2209  .02878470788332336934971917961129204363959,
2210  .0387991925696270495968019364463476920332,
2211  .04840267283059405290293814042280751781527,
2212  .05749315621761906648172168940205612879712,
2213  .06597422988218049512812851511596236123744,
2214  .07375597473770520626824385002219073415377,
2215  .08075589522942021535469493846052973087589,
2216  .08689978720108297980238753071512570257675,
2217  .09212252223778612871763270708761876719691,
2218  .09636873717464425963946862635180986509641,
2219  .09959342058679526706278028210356947652987,
2220  .1017623897484055045964289521685540446327,
2221  .1028526528935588403412856367054150438684,
2222  .1028526528935588403412856367054150438684,
2223  .1017623897484055045964289521685540446327,
2224  .09959342058679526706278028210356947652987,
2225  .09636873717464425963946862635180986509641,
2226  .09212252223778612871763270708761876719691,
2227  .08689978720108297980238753071512570257675,
2228  .08075589522942021535469493846052973087589,
2229  .07375597473770520626824385002219073415377,
2230  .06597422988218049512812851511596236123744,
2231  .05749315621761906648172168940205612879712,
2232  .04840267283059405290293814042280751781527,
2233  .0387991925696270495968019364463476920332,
2234  .02878470788332336934971917961129204363959,
2235  .01846646831109095914230213191204726909621,
2236  .007968192496166605615465883474673622450481
2237  }
2238  },
2239  {
2240  30,
2241  { // points
2242  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2243  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2244  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2245  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2246  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2247  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2248  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2249  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2250  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2251  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2252  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2253  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2254  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2255  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2256  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2257  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2258  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2259  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2260  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2261  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2262  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2263  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2264  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2265  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2266  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2267  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2268  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2269  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2270  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2271  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2272  },
2273  { // weights
2274  .007968192496166605615465883474673622450481,
2275  .01846646831109095914230213191204726909621,
2276  .02878470788332336934971917961129204363959,
2277  .0387991925696270495968019364463476920332,
2278  .04840267283059405290293814042280751781527,
2279  .05749315621761906648172168940205612879712,
2280  .06597422988218049512812851511596236123744,
2281  .07375597473770520626824385002219073415377,
2282  .08075589522942021535469493846052973087589,
2283  .08689978720108297980238753071512570257675,
2284  .09212252223778612871763270708761876719691,
2285  .09636873717464425963946862635180986509641,
2286  .09959342058679526706278028210356947652987,
2287  .1017623897484055045964289521685540446327,
2288  .1028526528935588403412856367054150438684,
2289  .1028526528935588403412856367054150438684,
2290  .1017623897484055045964289521685540446327,
2291  .09959342058679526706278028210356947652987,
2292  .09636873717464425963946862635180986509641,
2293  .09212252223778612871763270708761876719691,
2294  .08689978720108297980238753071512570257675,
2295  .08075589522942021535469493846052973087589,
2296  .07375597473770520626824385002219073415377,
2297  .06597422988218049512812851511596236123744,
2298  .05749315621761906648172168940205612879712,
2299  .04840267283059405290293814042280751781527,
2300  .0387991925696270495968019364463476920332,
2301  .02878470788332336934971917961129204363959,
2302  .01846646831109095914230213191204726909621,
2303  .007968192496166605615465883474673622450481
2304  }
2305  },
2306  {
2307  31,
2308  { // points
2309  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2310  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2311  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2312  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2313  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2314  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2315  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2316  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2317  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2318  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2319  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2320  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2321  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2322  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2323  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2324  {0 ,0.0, 0.0},
2325  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2326  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2327  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2328  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2329  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2330  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2331  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2332  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2333  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2334  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2335  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2336  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2337  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2338  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2339  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2340  },
2341  { // weights
2342  .007470831579248775858696875032212407022151,
2343  .01731862079031058246315799608682114136627,
2344  .02700901918497942180060870809193215614236,
2345  .03643227391238546402439201046780344232715,
2346  .04549370752720110290231585789462967726355,
2347  .05410308242491685371166625908662004272039,
2348  .06217478656102842691034354368669666715873,
2349  .06962858323541036616775612625512571051509,
2350  .07639038659877661642635767490133064492576,
2351  .08239299176158926390382336743196177061577,
2352  .08757674060847787612619806969533309222926,
2353  .09189011389364147821536287160715012549731,
2354  .09529024291231951280720419748759668454132,
2355  .09774333538632872509347401097899670383573,
2356  .09922501122667230787487551442861501401754,
2357  .09972054479342645142753383373434943964325,
2358  .09922501122667230787487551442861501401754,
2359  .09774333538632872509347401097899670383573,
2360  .09529024291231951280720419748759668454132,
2361  .09189011389364147821536287160715012549731,
2362  .08757674060847787612619806969533309222926,
2363  .08239299176158926390382336743196177061577,
2364  .07639038659877661642635767490133064492576,
2365  .06962858323541036616775612625512571051509,
2366  .06217478656102842691034354368669666715873,
2367  .05410308242491685371166625908662004272039,
2368  .04549370752720110290231585789462967726355,
2369  .03643227391238546402439201046780344232715,
2370  .02700901918497942180060870809193215614236,
2371  .01731862079031058246315799608682114136627,
2372  .007470831579248775858696875032212407022151
2373  }
2374  },
2375  {
2376  31,
2377  { // points
2378  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2379  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2380  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2381  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2382  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2383  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2384  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2385  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2386  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2387  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2388  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2389  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2390  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2391  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2392  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2393  {0 ,0.0, 0.0},
2394  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2395  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2396  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2397  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2398  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2399  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2400  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2401  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2402  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2403  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2404  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2405  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2406  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2407  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2408  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2409  },
2410  { // weights
2411  .007470831579248775858696875032212407022151,
2412  .01731862079031058246315799608682114136627,
2413  .02700901918497942180060870809193215614236,
2414  .03643227391238546402439201046780344232715,
2415  .04549370752720110290231585789462967726355,
2416  .05410308242491685371166625908662004272039,
2417  .06217478656102842691034354368669666715873,
2418  .06962858323541036616775612625512571051509,
2419  .07639038659877661642635767490133064492576,
2420  .08239299176158926390382336743196177061577,
2421  .08757674060847787612619806969533309222926,
2422  .09189011389364147821536287160715012549731,
2423  .09529024291231951280720419748759668454132,
2424  .09774333538632872509347401097899670383573,
2425  .09922501122667230787487551442861501401754,
2426  .09972054479342645142753383373434943964325,
2427  .09922501122667230787487551442861501401754,
2428  .09774333538632872509347401097899670383573,
2429  .09529024291231951280720419748759668454132,
2430  .09189011389364147821536287160715012549731,
2431  .08757674060847787612619806969533309222926,
2432  .08239299176158926390382336743196177061577,
2433  .07639038659877661642635767490133064492576,
2434  .06962858323541036616775612625512571051509,
2435  .06217478656102842691034354368669666715873,
2436  .05410308242491685371166625908662004272039,
2437  .04549370752720110290231585789462967726355,
2438  .03643227391238546402439201046780344232715,
2439  .02700901918497942180060870809193215614236,
2440  .01731862079031058246315799608682114136627,
2441  .007470831579248775858696875032212407022151
2442  }
2443  } // end Gauss
2444  };
2445 
2446 } // end namespace Intrepid2
Intrepid2::CubatureDirect::CubatureData::points_
Kokkos::DynRankView< pointValueType, ExecSpaceType > points_
Array with the (X,Y,Z) coordinates of the cubature points.
Definition: Intrepid2_CubatureDirect.hpp:109
Intrepid2::Parameters::MaxDimension
static constexpr ordinal_type MaxDimension
The maximum ambient space dimension.
Definition: Intrepid2_Types.hpp:135
Intrepid2::CubatureDirectLineGauss::CubatureDirectLineGauss
CubatureDirectLineGauss(const ordinal_type degree=0)
Constructor.
Definition: Intrepid2_CubatureDirectLineGaussDef.hpp:53
Intrepid2::CubatureDirect::CubatureDataStatic::numPoints_
ordinal_type numPoints_
Number of cubature points stored in the template.
Definition: Intrepid2_CubatureDirect.hpp:87
Intrepid2::CubatureDirectLineGauss
Defines Gauss integration rules on a line.
Definition: Intrepid2_CubatureDirectLineGauss.hpp:63
Intrepid2::CubatureDirect::cubatureData_
CubatureData cubatureData_
Cubature data on device.
Definition: Intrepid2_CubatureDirect.hpp:127
Intrepid2::CubatureDirect::degree_
ordinal_type degree_
The degree of polynomials that are integrated exactly by this cubature rule.
Definition: Intrepid2_CubatureDirect.hpp:119
Intrepid2::CubatureDirectLineGauss::cubatureDataStatic_
static const CubatureDataStatic cubatureDataStatic_[cubatureDataStaticSize]
Complete set of data defining line Gauss(-Legendre) rules.
Definition: Intrepid2_CubatureDirectLineGauss.hpp:78
Intrepid2::CubatureDirect
Defines direct cubature (integration) rules in Intrepid.
Definition: Intrepid2_CubatureDirect.hpp:76
Intrepid2::CubatureDirect::CubatureDataStatic
Cubature data is defined on the host space and is static.
Definition: Intrepid2_CubatureDirect.hpp:83
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:127
Intrepid2::CubatureDirect::CubatureData::numPoints_
ordinal_type numPoints_
Number of cubature points stored in the template.
Definition: Intrepid2_CubatureDirect.hpp:105
Intrepid2::CubatureDirect::CubatureData::weights_
Kokkos::DynRankView< weightValueType, ExecSpaceType > weights_
Array with the associated cubature weights.
Definition: Intrepid2_CubatureDirect.hpp:113
Generated by   doxygen 1.8.5