Intrepid
Intrepid_CubatureDirectLineGaussDef.hpp
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43 
49 namespace Intrepid {
50 
51 template <class Scalar, class ArrayPoint, class ArrayWeight>
52 CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::CubatureDirectLineGauss(const int degree) {
53  this->degree_ = degree;
54  this->dimension_ = 1;
55  TEUCHOS_TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM),
56  std::out_of_range,
57  ">>> ERROR (CubatureDirectLineGauss): No cubature rule implemented for the desired polynomial degree.");
58 } // end constructor
59 
60 
61 
62 template <class Scalar, class ArrayPoint, class ArrayWeight>
63 const CubatureTemplate * CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::exposeCubatureData() const {
64  return cubature_data_;
65 }
66 
67 
68 
69 template <class Scalar, class ArrayPoint, class ArrayWeight>
70 int CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getMaxAccuracy() const {
71  return INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM;
72 }
73 
74 
75 
76 template <class Scalar, class ArrayPoint, class ArrayWeight>
77 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::getName() const {
78  return cubature_name_;
79 } // end getName
80 
81 
82 
83 template <class Scalar, class ArrayPoint, class ArrayWeight>
84 const char* CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_name_ = "INTREPID_CUBATURE_LINE_GAUSS";
85 
86 
87 //-------------------------------------------------------------------------------------//
88 // Definition of cubature templates //
89 //-------------------------------------------------------------------------------------//
90 
91 /*
92  Cubature templates for lines are defined the reference cell:
93 
94  Line -> (-1,0,0),(1,0,0)
95 */
96 
97 /*
98  This static const member contains templates for Gauss(-Legendre) rules.
99 */
100 
101 template <class Scalar, class ArrayPoint, class ArrayWeight>
102 const CubatureTemplate CubatureDirectLineGauss<Scalar,ArrayPoint,ArrayWeight>::cubature_data_[INTREPID_CUBATURE_LINE_GAUSS_MAX_ENUM+1] =
103 {
104 
105  // Collection of Gauss rules on [-1,1]
106  // The rule with array index i is exact for polynomials up to order i
107  {
108  1,
109  {{0e0, 0.0, 0.0}},
110  {2e0}
111  },
112  {
113  1,
114  {{0e0, 0.0, 0.0}},
115  {2e0}
116  },
117  {
118  2,
119  {{5.773502691896257645091487805019574556476e-1, 0.0, 0.0},
120  {-5.773502691896257645091487805019574556476e-1, 0.0, 0.0}},
121  {1e0,
122  1e0}
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  3,
133  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
134  {0e0, 0.0, 0.0},
135  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
136  {5.555555555555555555555555555555555555556e-1,
137  8.888888888888888888888888888888888888889e-1,
138  5.555555555555555555555555555555555555556e-1}
139  },
140  {
141  3,
142  {{7.745966692414833770358530799564799221666e-1, 0.0, 0.0},
143  {0e0, 0.0, 0.0},
144  {-7.745966692414833770358530799564799221666e-1, 0.0, 0.0}},
145  {5.555555555555555555555555555555555555556e-1,
146  8.888888888888888888888888888888888888889e-1,
147  5.555555555555555555555555555555555555556e-1}
148  },
149  {
150  4,
151  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
152  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
153  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
154  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
155  {3.478548451374538573730639492219994072353e-1,
156  6.521451548625461426269360507780005927647e-1,
157  6.521451548625461426269360507780005927647e-1,
158  3.478548451374538573730639492219994072353e-1}
159  },
160  {
161  4,
162  {{8.611363115940525752239464888928095050957e-1, 0.0, 0.0},
163  {3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
164  {-3.399810435848562648026657591032446872006e-1, 0.0, 0.0},
165  {-8.611363115940525752239464888928095050957e-1, 0.0, 0.0}},
166  {3.478548451374538573730639492219994072353e-1,
167  6.521451548625461426269360507780005927647e-1,
168  6.521451548625461426269360507780005927647e-1,
169  3.478548451374538573730639492219994072353e-1}
170  },
171  {
172  5,
173  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
174  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
175  {0e0, 0.0, 0.0},
176  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
177  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
178  {2.369268850561890875142640407199173626433e-1,
179  4.786286704993664680412915148356381929123e-1,
180  5.688888888888888888888888888888888888889e-1,
181  4.786286704993664680412915148356381929123e-1,
182  2.369268850561890875142640407199173626433e-1}
183  },
184  {
185  5,
186  {{9.061798459386639927976268782993929651257e-1, 0.0, 0.0},
187  {5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
188  {0e0, 0.0, 0.0},
189  {-5.384693101056830910363144207002088049673e-1, 0.0, 0.0},
190  {-9.061798459386639927976268782993929651257e-1, 0.0, 0.0}},
191  {2.369268850561890875142640407199173626433e-1,
192  4.786286704993664680412915148356381929123e-1,
193  5.688888888888888888888888888888888888889e-1,
194  4.786286704993664680412915148356381929123e-1,
195  2.369268850561890875142640407199173626433e-1}
196  },
197  {
198  6,
199  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
200  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
201  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
202  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
203  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
204  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
205  {1.713244923791703450402961421727328935268e-1,
206  3.607615730481386075698335138377161116615e-1,
207  4.679139345726910473898703439895509948117e-1,
208  4.679139345726910473898703439895509948117e-1,
209  3.607615730481386075698335138377161116615e-1,
210  1.713244923791703450402961421727328935268e-1}
211  },
212  {
213  6,
214  {{9.324695142031520278123015544939946091348e-1, 0.0, 0.0},
215  {6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
216  {2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
217  {-2.386191860831969086305017216807119354186e-1, 0.0, 0.0},
218  {-6.612093864662645136613995950199053470064e-1, 0.0, 0.0},
219  {-9.324695142031520278123015544939946091348e-1, 0.0, 0.0}},
220  {1.713244923791703450402961421727328935268e-1,
221  3.607615730481386075698335138377161116615e-1,
222  4.679139345726910473898703439895509948117e-1,
223  4.679139345726910473898703439895509948117e-1,
224  3.607615730481386075698335138377161116615e-1,
225  1.713244923791703450402961421727328935268e-1}
226  },
227  {
228  7,
229  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
230  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
231  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
232  {0e0, 0.0, 0.0},
233  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
234  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
235  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
236  {1.294849661688696932706114326790820183286e-1,
237  2.797053914892766679014677714237795824869e-1,
238  3.818300505051189449503697754889751338784e-1,
239  4.179591836734693877551020408163265306122e-1,
240  3.818300505051189449503697754889751338784e-1,
241  2.797053914892766679014677714237795824869e-1,
242  1.294849661688696932706114326790820183286e-1}
243  },
244  {
245  7,
246  {{9.491079123427585245261896840478512624008e-1, 0.0, 0.0},
247  {7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
248  {4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
249  {0e0, 0.0, 0.0},
250  {-4.058451513773971669066064120769614633474e-1, 0.0, 0.0},
251  {-7.415311855993944398638647732807884070741e-1, 0.0, 0.0},
252  {-9.491079123427585245261896840478512624008e-1, 0.0, 0.0}},
253  {1.294849661688696932706114326790820183286e-1,
254  2.797053914892766679014677714237795824869e-1,
255  3.818300505051189449503697754889751338784e-1,
256  4.179591836734693877551020408163265306122e-1,
257  3.818300505051189449503697754889751338784e-1,
258  2.797053914892766679014677714237795824869e-1,
259  1.294849661688696932706114326790820183286e-1}
260  },
261  {
262  8,
263  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
264  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
265  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
266  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
267  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
268  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
269  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
270  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
271  {1.012285362903762591525313543099621901154e-1,
272  2.223810344533744705443559944262408844301e-1,
273  3.137066458778872873379622019866013132603e-1,
274  3.626837833783619829651504492771956121941e-1,
275  3.626837833783619829651504492771956121941e-1,
276  3.137066458778872873379622019866013132603e-1,
277  2.223810344533744705443559944262408844301e-1,
278  1.012285362903762591525313543099621901154e-1}
279  },
280  {
281  8,
282  {{9.602898564975362316835608685694729904282e-1, 0.0, 0.0},
283  {7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
284  {5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
285  {1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
286  {-1.834346424956498049394761423601839806668e-1, 0.0, 0.0},
287  {-5.25532409916328985817739049189246349042e-1, 0.0, 0.0},
288  {-7.966664774136267395915539364758304368372e-1, 0.0, 0.0},
289  {-9.602898564975362316835608685694729904282e-1, 0.0, 0.0}},
290  {1.012285362903762591525313543099621901154e-1,
291  2.223810344533744705443559944262408844301e-1,
292  3.137066458778872873379622019866013132603e-1,
293  3.626837833783619829651504492771956121941e-1,
294  3.626837833783619829651504492771956121941e-1,
295  3.137066458778872873379622019866013132603e-1,
296  2.223810344533744705443559944262408844301e-1,
297  1.012285362903762591525313543099621901154e-1}
298  },
299  {
300  9,
301  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
302  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
303  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
304  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
305  {0e0, 0.0, 0.0},
306  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
307  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
308  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
309  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
310  {8.127438836157441197189215811052365067566e-2,
311  1.806481606948574040584720312429128095143e-1,
312  2.606106964029354623187428694186328497718e-1,
313  3.123470770400028400686304065844436655988e-1,
314  3.302393550012597631645250692869740488788e-1,
315  3.123470770400028400686304065844436655988e-1,
316  2.606106964029354623187428694186328497718e-1,
317  1.806481606948574040584720312429128095143e-1,
318  8.127438836157441197189215811052365067566e-2}
319  },
320  {
321  9,
322  {{9.681602395076260898355762029036728700494e-1, 0.0, 0.0},
323  {8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
324  {6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
325  {3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
326  {0e0, 0.0, 0.0},
327  {-3.24253423403808929038538014643336608572e-1, 0.0, 0.0},
328  {-6.133714327005903973087020393414741847857e-1, 0.0, 0.0},
329  {-8.360311073266357942994297880697348765441e-1, 0.0, 0.0},
330  {-9.681602395076260898355762029036728700494e-1, 0.0, 0.0}},
331  {8.127438836157441197189215811052365067566e-2,
332  1.806481606948574040584720312429128095143e-1,
333  2.606106964029354623187428694186328497718e-1,
334  3.123470770400028400686304065844436655988e-1,
335  3.302393550012597631645250692869740488788e-1,
336  3.123470770400028400686304065844436655988e-1,
337  2.606106964029354623187428694186328497718e-1,
338  1.806481606948574040584720312429128095143e-1,
339  8.127438836157441197189215811052365067566e-2}
340  },
341  {
342  10,
343  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
344  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
345  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
346  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
347  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
348  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
349  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
350  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
351  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
352  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
353  {6.667134430868813759356880989333179285786e-2,
354  1.494513491505805931457763396576973324026e-1,
355  2.190863625159820439955349342281631924588e-1,
356  2.692667193099963550912269215694693528598e-1,
357  2.95524224714752870173892994651338329421e-1,
358  2.95524224714752870173892994651338329421e-1,
359  2.692667193099963550912269215694693528598e-1,
360  2.190863625159820439955349342281631924588e-1,
361  1.494513491505805931457763396576973324026e-1,
362  6.667134430868813759356880989333179285786e-2}
363  },
364  {
365  10,
366  {{9.739065285171717200779640120844520534283e-1, 0.0, 0.0},
367  {8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
368  {6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
369  {4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
370  {1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
371  {-1.488743389816312108848260011297199846176e-1, 0.0, 0.0},
372  {-4.333953941292471907992659431657841622001e-1, 0.0, 0.0},
373  {-6.794095682990244062343273651148735757693e-1, 0.0, 0.0},
374  {-8.650633666889845107320966884234930485275e-1, 0.0, 0.0},
375  {-9.739065285171717200779640120844520534283e-1, 0.0, 0.0}},
376  {6.667134430868813759356880989333179285786e-2,
377  1.494513491505805931457763396576973324026e-1,
378  2.190863625159820439955349342281631924588e-1,
379  2.692667193099963550912269215694693528598e-1,
380  2.95524224714752870173892994651338329421e-1,
381  2.95524224714752870173892994651338329421e-1,
382  2.692667193099963550912269215694693528598e-1,
383  2.190863625159820439955349342281631924588e-1,
384  1.494513491505805931457763396576973324026e-1,
385  6.667134430868813759356880989333179285786e-2}
386  },
387  {
388  11,
389  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
390  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
391  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
392  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
393  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
394  {0e0, 0.0, 0.0},
395  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
396  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
397  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
398  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
399  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
400  {5.566856711617366648275372044254857872852e-2,
401  1.255803694649046246346942992239401001976e-1,
402  1.862902109277342514260976414316558916913e-1,
403  2.331937645919904799185237048431751394318e-1,
404  2.628045445102466621806888698905091953728e-1,
405  2.72925086777900630714483528336342189156e-1,
406  2.628045445102466621806888698905091953728e-1,
407  2.331937645919904799185237048431751394318e-1,
408  1.862902109277342514260976414316558916913e-1,
409  1.255803694649046246346942992239401001976e-1,
410  5.566856711617366648275372044254857872852e-2}
411  },
412  {
413  11,
414  {{9.782286581460569928039380011228573907714e-1, 0.0, 0.0},
415  {8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
416  {7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
417  {5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
418  {2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
419  {0e0, 0.0, 0.0},
420  {-2.695431559523449723315319854008615246796e-1, 0.0, 0.0},
421  {-5.190961292068118159257256694586095544802e-1, 0.0, 0.0},
422  {-7.301520055740493240934162520311534580496e-1, 0.0, 0.0},
423  {-8.870625997680952990751577693039272666317e-1, 0.0, 0.0},
424  {-9.782286581460569928039380011228573907714e-1, 0.0, 0.0}},
425  {5.566856711617366648275372044254857872852e-2,
426  1.255803694649046246346942992239401001976e-1,
427  1.862902109277342514260976414316558916913e-1,
428  2.331937645919904799185237048431751394318e-1,
429  2.628045445102466621806888698905091953728e-1,
430  2.72925086777900630714483528336342189156e-1,
431  2.628045445102466621806888698905091953728e-1,
432  2.331937645919904799185237048431751394318e-1,
433  1.862902109277342514260976414316558916913e-1,
434  1.255803694649046246346942992239401001976e-1,
435  5.566856711617366648275372044254857872852e-2}
436  },
437  {
438  12,
439  { // points
440  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
441  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
442  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
443  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
444  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
445  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
446  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
447  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
448  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
449  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
450  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
451  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
452  },
453  { // weights
454  .04717533638651182719461596148501706031703,
455  .1069393259953184309602547181939962242146,
456  .160078328543346226334652529543359071872,
457  .2031674267230659217490644558097983765065,
458  .2334925365383548087608498989248780562594,
459  .2491470458134027850005624360429512108305,
460  .2491470458134027850005624360429512108305,
461  .2334925365383548087608498989248780562594,
462  .2031674267230659217490644558097983765065,
463  .160078328543346226334652529543359071872,
464  .1069393259953184309602547181939962242146,
465  .04717533638651182719461596148501706031703
466  }
467  },
468  {
469  12,
470  { // points
471  {.9815606342467192506905490901492808229602 ,0.0, 0.0},
472  {.9041172563704748566784658661190961925376 ,0.0, 0.0},
473  {.7699026741943046870368938332128180759849 ,0.0, 0.0},
474  {.5873179542866174472967024189405342803691 ,0.0, 0.0},
475  {.3678314989981801937526915366437175612564 ,0.0, 0.0},
476  {.1252334085114689154724413694638531299834 ,0.0, 0.0},
477  {-.1252334085114689154724413694638531299834 ,0.0, 0.0},
478  {-.3678314989981801937526915366437175612564 ,0.0, 0.0},
479  {-.5873179542866174472967024189405342803691 ,0.0, 0.0},
480  {-.7699026741943046870368938332128180759849 ,0.0, 0.0},
481  {-.9041172563704748566784658661190961925376 ,0.0, 0.0},
482  {-.9815606342467192506905490901492808229602 ,0.0, 0.0}
483  },
484  { // weights
485  .04717533638651182719461596148501706031703,
486  .1069393259953184309602547181939962242146,
487  .160078328543346226334652529543359071872,
488  .2031674267230659217490644558097983765065,
489  .2334925365383548087608498989248780562594,
490  .2491470458134027850005624360429512108305,
491  .2491470458134027850005624360429512108305,
492  .2334925365383548087608498989248780562594,
493  .2031674267230659217490644558097983765065,
494  .160078328543346226334652529543359071872,
495  .1069393259953184309602547181939962242146,
496  .04717533638651182719461596148501706031703
497  }
498  },
499  {
500  13,
501  { // points
502  {.984183054718588149472829448807109611065 ,0.0, 0.0},
503  {.9175983992229779652065478365007195123905 ,0.0, 0.0},
504  {.8015780907333099127942064895828598903056 ,0.0, 0.0},
505  {.6423493394403402206439846069955156500717 ,0.0, 0.0},
506  {.4484927510364468528779128521276398678019 ,0.0, 0.0},
507  {.2304583159551347940655281210979888352115 ,0.0, 0.0},
508  { 0 ,0.0, 0.0},
509  {-.2304583159551347940655281210979888352115 ,0.0, 0.0},
510  {-.4484927510364468528779128521276398678019 ,0.0, 0.0},
511  {-.6423493394403402206439846069955156500717 ,0.0, 0.0},
512  {-.8015780907333099127942064895828598903056 ,0.0, 0.0},
513  {-.9175983992229779652065478365007195123905 ,0.0, 0.0},
514  {-.984183054718588149472829448807109611065 ,0.0, 0.0}
515  },
516  { // weights
517  .04048400476531587952002159220098606004199,
518  .09212149983772844791442177595379712092368,
519  .1388735102197872384636017768688714676219,
520  .1781459807619457382800466919960979955128,
521  .2078160475368885023125232193060527633866,
522  .2262831802628972384120901860397766184348,
523  .2325515532308739101945895152688359481566,
524  .2262831802628972384120901860397766184348,
525  .2078160475368885023125232193060527633866,
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527  .1388735102197872384636017768688714676219,
528  .09212149983772844791442177595379712092368,
529  .04048400476531587952002159220098606004199
530  }
531  },
532  {
533  13,
534  { // points
535  {.984183054718588149472829448807109611065 ,0.0, 0.0},
536  {.9175983992229779652065478365007195123905 ,0.0, 0.0},
537  {.8015780907333099127942064895828598903056 ,0.0, 0.0},
538  {.6423493394403402206439846069955156500717 ,0.0, 0.0},
539  {.4484927510364468528779128521276398678019 ,0.0, 0.0},
540  {.2304583159551347940655281210979888352115 ,0.0, 0.0},
541  { 0 ,0.0, 0.0},
542  {-.2304583159551347940655281210979888352115 ,0.0, 0.0},
543  {-.4484927510364468528779128521276398678019 ,0.0, 0.0},
544  {-.6423493394403402206439846069955156500717 ,0.0, 0.0},
545  {-.8015780907333099127942064895828598903056 ,0.0, 0.0},
546  {-.9175983992229779652065478365007195123905 ,0.0, 0.0},
547  {-.984183054718588149472829448807109611065 ,0.0, 0.0}
548  },
549  { // weights
550  .04048400476531587952002159220098606004199,
551  .09212149983772844791442177595379712092368,
552  .1388735102197872384636017768688714676219,
553  .1781459807619457382800466919960979955128,
554  .2078160475368885023125232193060527633866,
555  .2262831802628972384120901860397766184348,
556  .2325515532308739101945895152688359481566,
557  .2262831802628972384120901860397766184348,
558  .2078160475368885023125232193060527633866,
559  .1781459807619457382800466919960979955128,
560  .1388735102197872384636017768688714676219,
561  .09212149983772844791442177595379712092368,
562  .04048400476531587952002159220098606004199
563  }
564  },
565  {
566  14,
567  { // points
568  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
569  {.928434883663573517336391139377874264477 ,0.0, 0.0},
570  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
571  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
572  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
573  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
574  {.108054948707343662066244650219834747612 ,0.0, 0.0},
575  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
576  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
577  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
578  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
579  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
580  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
581  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
582  },
583  { // weights
584  .03511946033175186303183287613819178061971,
585  .0801580871597602098056332770628543095837,
586  .1215185706879031846894148090724766259567,
587  .1572031671581935345696019386238421566057,
588  .1855383974779378137417165901251570362489,
589  .2051984637212956039659240656612180557103,
590  .215263853463157790195876443316260035275,
591  .215263853463157790195876443316260035275,
592  .2051984637212956039659240656612180557103,
593  .1855383974779378137417165901251570362489,
594  .1572031671581935345696019386238421566057,
595  .1215185706879031846894148090724766259567,
596  .0801580871597602098056332770628543095837,
597  .03511946033175186303183287613819178061971
598  }
599  },
600  {
601  14,
602  { // points
603  {.9862838086968123388415972667040528016761 ,0.0, 0.0},
604  {.928434883663573517336391139377874264477 ,0.0, 0.0},
605  {.8272013150697649931897947426503949610397 ,0.0, 0.0},
606  {.6872929048116854701480198030193341375384 ,0.0, 0.0},
607  {.5152486363581540919652907185511886623089 ,0.0, 0.0},
608  {.3191123689278897604356718241684754668343 ,0.0, 0.0},
609  {.108054948707343662066244650219834747612 ,0.0, 0.0},
610  {-.108054948707343662066244650219834747612 ,0.0, 0.0},
611  {-.3191123689278897604356718241684754668343 ,0.0, 0.0},
612  {-.5152486363581540919652907185511886623089 ,0.0, 0.0},
613  {-.6872929048116854701480198030193341375384 ,0.0, 0.0},
614  {-.8272013150697649931897947426503949610397 ,0.0, 0.0},
615  {-.928434883663573517336391139377874264477 ,0.0, 0.0},
616  {-.9862838086968123388415972667040528016761 ,0.0, 0.0}
617  },
618  { // weights
619  .03511946033175186303183287613819178061971,
620  .0801580871597602098056332770628543095837,
621  .1215185706879031846894148090724766259567,
622  .1572031671581935345696019386238421566057,
623  .1855383974779378137417165901251570362489,
624  .2051984637212956039659240656612180557103,
625  .215263853463157790195876443316260035275,
626  .215263853463157790195876443316260035275,
627  .2051984637212956039659240656612180557103,
628  .1855383974779378137417165901251570362489,
629  .1572031671581935345696019386238421566057,
630  .1215185706879031846894148090724766259567,
631  .0801580871597602098056332770628543095837,
632  .03511946033175186303183287613819178061971
633  }
634  },
635  {
636  15,
637  { // points
638  {.987992518020485428489565718586612581147 ,0.0, 0.0},
639  {.937273392400705904307758947710209471244 ,0.0, 0.0},
640  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
641  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
642  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
643  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
644  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
645  { 0 ,0.0, 0.0},
646  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
647  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
648  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
649  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
650  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
651  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
652  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
653  },
654  { // weights
655  .03075324199611726835462839357720441772175,
656  .07036604748810812470926741645066733846671,
657  .1071592204671719350118695466858693034155,
658  .1395706779261543144478047945110283225209,
659  .1662692058169939335532008604812088111309,
660  .1861610000155622110268005618664228245062,
661  .1984314853271115764561183264438393248187,
662  .2025782419255612728806201999675193148387,
663  .1984314853271115764561183264438393248187,
664  .1861610000155622110268005618664228245062,
665  .1662692058169939335532008604812088111309,
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667  .1071592204671719350118695466858693034155,
668  .07036604748810812470926741645066733846671,
669  .03075324199611726835462839357720441772175
670  }
671  },
672  {
673  15,
674  { // points
675  {.987992518020485428489565718586612581147 ,0.0, 0.0},
676  {.937273392400705904307758947710209471244 ,0.0, 0.0},
677  {.8482065834104272162006483207742168513663 ,0.0, 0.0},
678  {.7244177313601700474161860546139380096309 ,0.0, 0.0},
679  {.5709721726085388475372267372539106412384 ,0.0, 0.0},
680  {.3941513470775633698972073709810454683628 ,0.0, 0.0},
681  {.2011940939974345223006283033945962078128 ,0.0, 0.0},
682  { 0 ,0.0, 0.0},
683  {-.2011940939974345223006283033945962078128 ,0.0, 0.0},
684  {-.3941513470775633698972073709810454683628 ,0.0, 0.0},
685  {-.5709721726085388475372267372539106412384 ,0.0, 0.0},
686  {-.7244177313601700474161860546139380096309 ,0.0, 0.0},
687  {-.8482065834104272162006483207742168513663 ,0.0, 0.0},
688  {-.937273392400705904307758947710209471244 ,0.0, 0.0},
689  {-.987992518020485428489565718586612581147 ,0.0, 0.0}
690  },
691  { // weights
692  .03075324199611726835462839357720441772175,
693  .07036604748810812470926741645066733846671,
694  .1071592204671719350118695466858693034155,
695  .1395706779261543144478047945110283225209,
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697  .1861610000155622110268005618664228245062,
698  .1984314853271115764561183264438393248187,
699  .2025782419255612728806201999675193148387,
700  .1984314853271115764561183264438393248187,
701  .1861610000155622110268005618664228245062,
702  .1662692058169939335532008604812088111309,
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704  .1071592204671719350118695466858693034155,
705  .07036604748810812470926741645066733846671,
706  .03075324199611726835462839357720441772175
707  }
708  },
709  {
710  16,
711  { // points
712  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
713  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
714  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
715  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
716  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
717  {.45801677765722738634241944298357757354 ,0.0, 0.0},
718  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
719  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
720  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
721  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
722  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
723  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
724  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
725  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
726  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
727  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
728  },
729  { // weights
730  .02715245941175409485178057245601810351227,
731  .06225352393864789286284383699437769427499,
732  .09515851168249278480992510760224622635526,
733  .1246289712555338720524762821920164201449,
734  .1495959888165767320815017305474785489705,
735  .1691565193950025381893120790303599622116,
736  .1826034150449235888667636679692199393836,
737  .1894506104550684962853967232082831051469,
738  .1894506104550684962853967232082831051469,
739  .1826034150449235888667636679692199393836,
740  .1691565193950025381893120790303599622116,
741  .1495959888165767320815017305474785489705,
742  .1246289712555338720524762821920164201449,
743  .09515851168249278480992510760224622635526,
744  .06225352393864789286284383699437769427499,
745  .02715245941175409485178057245601810351227
746  }
747  },
748  {
749  16,
750  { // points
751  {.9894009349916499325961541734503326274263 ,0.0, 0.0},
752  {.9445750230732325760779884155346083450911 ,0.0, 0.0},
753  {.8656312023878317438804678977123931323873 ,0.0, 0.0},
754  {.7554044083550030338951011948474422683538 ,0.0, 0.0},
755  {.6178762444026437484466717640487910189919 ,0.0, 0.0},
756  {.45801677765722738634241944298357757354 ,0.0, 0.0},
757  {.2816035507792589132304605014604961064861 ,0.0, 0.0},
758  {.09501250983763744018531933542495806313035 ,0.0, 0.0},
759  {-.09501250983763744018531933542495806313035 ,0.0, 0.0},
760  {-.2816035507792589132304605014604961064861 ,0.0, 0.0},
761  {-.45801677765722738634241944298357757354 ,0.0, 0.0},
762  {-.6178762444026437484466717640487910189919 ,0.0, 0.0},
763  {-.7554044083550030338951011948474422683538 ,0.0, 0.0},
764  {-.8656312023878317438804678977123931323873 ,0.0, 0.0},
765  {-.9445750230732325760779884155346083450911 ,0.0, 0.0},
766  {-.9894009349916499325961541734503326274263 ,0.0, 0.0}
767  },
768  { // weights
769  .02715245941175409485178057245601810351227,
770  .06225352393864789286284383699437769427499,
771  .09515851168249278480992510760224622635526,
772  .1246289712555338720524762821920164201449,
773  .1495959888165767320815017305474785489705,
774  .1691565193950025381893120790303599622116,
775  .1826034150449235888667636679692199393836,
776  .1894506104550684962853967232082831051469,
777  .1894506104550684962853967232082831051469,
778  .1826034150449235888667636679692199393836,
779  .1691565193950025381893120790303599622116,
780  .1495959888165767320815017305474785489705,
781  .1246289712555338720524762821920164201449,
782  .09515851168249278480992510760224622635526,
783  .06225352393864789286284383699437769427499,
784  .02715245941175409485178057245601810351227
785  }
786  },
787  {
788  17,
789  { // points
790  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
791  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
792  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
793  {.781514003896801406925230055520476050224 ,0.0, 0.0},
794  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
795  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
796  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
797  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
798  { 0 ,0.0, 0.0},
799  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
800  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
801  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
802  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
803  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
804  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
805  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
806  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
807  },
808  { // weights
809  .0241483028685479319601100262875653246917,
810  .05545952937398720112944016535824466051285,
811  .08503614831717918088353537019106207385049,
812  .1118838471934039710947883856263559267358,
813  .1351363684685254732863199817023501973721,
814  .1540457610768102880814315948019586119405,
815  .1680041021564500445099706637883231550212,
816  .1765627053669926463252709901131972391509,
817  .1794464703562065254582656442618856214488,
818  .1765627053669926463252709901131972391509,
819  .1680041021564500445099706637883231550212,
820  .1540457610768102880814315948019586119405,
821  .1351363684685254732863199817023501973721,
822  .1118838471934039710947883856263559267358,
823  .08503614831717918088353537019106207385049,
824  .05545952937398720112944016535824466051285,
825  .0241483028685479319601100262875653246917
826  }
827  },
828  {
829  17,
830  { // points
831  {.9905754753144173356754340199406652765078 ,0.0, 0.0},
832  {.9506755217687677612227169578958030214434 ,0.0, 0.0},
833  {.8802391537269859021229556944881556926234 ,0.0, 0.0},
834  {.781514003896801406925230055520476050224 ,0.0, 0.0},
835  {.6576711592166907658503022166430023351478 ,0.0, 0.0},
836  {.5126905370864769678862465686295518745829 ,0.0, 0.0},
837  {.3512317634538763152971855170953460050405 ,0.0, 0.0},
838  {.1784841814958478558506774936540655574754 ,0.0, 0.0},
839  { 0 ,0.0, 0.0},
840  {-.1784841814958478558506774936540655574754 ,0.0, 0.0},
841  {-.3512317634538763152971855170953460050405 ,0.0, 0.0},
842  {-.5126905370864769678862465686295518745829 ,0.0, 0.0},
843  {-.6576711592166907658503022166430023351478 ,0.0, 0.0},
844  {-.781514003896801406925230055520476050224 ,0.0, 0.0},
845  {-.8802391537269859021229556944881556926234 ,0.0, 0.0},
846  {-.9506755217687677612227169578958030214434 ,0.0, 0.0},
847  {-.9905754753144173356754340199406652765078 ,0.0, 0.0}
848  },
849  { // weights
850  .0241483028685479319601100262875653246917,
851  .05545952937398720112944016535824466051285,
852  .08503614831717918088353537019106207385049,
853  .1118838471934039710947883856263559267358,
854  .1351363684685254732863199817023501973721,
855  .1540457610768102880814315948019586119405,
856  .1680041021564500445099706637883231550212,
857  .1765627053669926463252709901131972391509,
858  .1794464703562065254582656442618856214488,
859  .1765627053669926463252709901131972391509,
860  .1680041021564500445099706637883231550212,
861  .1540457610768102880814315948019586119405,
862  .1351363684685254732863199817023501973721,
863  .1118838471934039710947883856263559267358,
864  .08503614831717918088353537019106207385049,
865  .05545952937398720112944016535824466051285,
866  .0241483028685479319601100262875653246917
867  }
868  },
869  {
870  18,
871  { // points
872  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
873  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
874  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
875  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
876  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
877  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
878  {.411751161462842646035931793833051637079 ,0.0, 0.0},
879  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
880  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
881  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
882  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
883  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
884  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
885  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
886  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
887  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
888  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
889  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
890  },
891  { // weights
892  .02161601352648331031334271026645246938769,
893  .04971454889496979645333494620263864168087,
894  .07642573025488905652912967761663652560532,
895  .1009420441062871655628139849248346070628,
896  .1225552067114784601845191268002015552282,
897  .1406429146706506512047313037519472280955,
898  .1546846751262652449254180038363747721932,
899  .1642764837458327229860537764659275904123,
900  .1691423829631435918406564701349866103341,
901  .1691423829631435918406564701349866103341,
902  .1642764837458327229860537764659275904123,
903  .1546846751262652449254180038363747721932,
904  .1406429146706506512047313037519472280955,
905  .1225552067114784601845191268002015552282,
906  .1009420441062871655628139849248346070628,
907  .07642573025488905652912967761663652560532,
908  .04971454889496979645333494620263864168087,
909  .02161601352648331031334271026645246938769
910  }
911  },
912  {
913  18,
914  { // points
915  {.9915651684209309467300160047061507702526 ,0.0, 0.0},
916  {.9558239495713977551811958929297763099728 ,0.0, 0.0},
917  {.8926024664975557392060605911271455154079 ,0.0, 0.0},
918  {.8037049589725231156824174550145907971033 ,0.0, 0.0},
919  {.6916870430603532078748910812888483894523 ,0.0, 0.0},
920  {.5597708310739475346078715485253291369276 ,0.0, 0.0},
921  {.411751161462842646035931793833051637079 ,0.0, 0.0},
922  {.2518862256915055095889728548779112301629 ,0.0, 0.0},
923  {.08477501304173530124226185293578381173332 ,0.0, 0.0},
924  {-.08477501304173530124226185293578381173332 ,0.0, 0.0},
925  {-.2518862256915055095889728548779112301629 ,0.0, 0.0},
926  {-.411751161462842646035931793833051637079 ,0.0, 0.0},
927  {-.5597708310739475346078715485253291369276 ,0.0, 0.0},
928  {-.6916870430603532078748910812888483894523 ,0.0, 0.0},
929  {-.8037049589725231156824174550145907971033 ,0.0, 0.0},
930  {-.8926024664975557392060605911271455154079 ,0.0, 0.0},
931  {-.9558239495713977551811958929297763099728 ,0.0, 0.0},
932  {-.9915651684209309467300160047061507702526 ,0.0, 0.0}
933  },
934  { // weights
935  .02161601352648331031334271026645246938769,
936  .04971454889496979645333494620263864168087,
937  .07642573025488905652912967761663652560532,
938  .1009420441062871655628139849248346070628,
939  .1225552067114784601845191268002015552282,
940  .1406429146706506512047313037519472280955,
941  .1546846751262652449254180038363747721932,
942  .1642764837458327229860537764659275904123,
943  .1691423829631435918406564701349866103341,
944  .1691423829631435918406564701349866103341,
945  .1642764837458327229860537764659275904123,
946  .1546846751262652449254180038363747721932,
947  .1406429146706506512047313037519472280955,
948  .1225552067114784601845191268002015552282,
949  .1009420441062871655628139849248346070628,
950  .07642573025488905652912967761663652560532,
951  .04971454889496979645333494620263864168087,
952  .02161601352648331031334271026645246938769
953  }
954  },
955  {
956  19,
957  { // points
958  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
959  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
960  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
961  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
962  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
963  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
964  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
965  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
966  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
967  { 0 ,0.0, 0.0},
968  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
969  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
970  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
971  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
972  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
973  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
974  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
975  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
976  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
977  },
978  { // weights
979  .01946178822972647703631204146443843575291,
980  .04481422676569960033283815740199421195175,
981  .06904454273764122658070825800601304496185,
982  .09149002162244999946446209412383965266091,
983  .1115666455473339947160239016817659974813,
984  .1287539625393362276755157848568771170558,
985  .1426067021736066117757461094419029724757,
986  .152766042065859666778855400897662998461,
987  .1589688433939543476499564394650472016788,
988  .1610544498487836959791636253209167350399,
989  .1589688433939543476499564394650472016788,
990  .152766042065859666778855400897662998461,
991  .1426067021736066117757461094419029724757,
992  .1287539625393362276755157848568771170558,
993  .1115666455473339947160239016817659974813,
994  .09149002162244999946446209412383965266091,
995  .06904454273764122658070825800601304496185,
996  .04481422676569960033283815740199421195175,
997  .01946178822972647703631204146443843575291
998  }
999  },
1000  {
1001  19,
1002  { // points
1003  {.9924068438435844031890176702532604935893 ,0.0, 0.0},
1004  {.9602081521348300308527788406876515266151 ,0.0, 0.0},
1005  {.9031559036148179016426609285323124878094 ,0.0, 0.0},
1006  {.8227146565371428249789224867127139017745 ,0.0, 0.0},
1007  {.7209661773352293786170958608237816296571 ,0.0, 0.0},
1008  {.6005453046616810234696381649462392798683 ,0.0, 0.0},
1009  {.4645707413759609457172671481041023679763 ,0.0, 0.0},
1010  {.3165640999636298319901173288498449178923 ,0.0, 0.0},
1011  {.1603586456402253758680961157407435495049 ,0.0, 0.0},
1012  { 0 ,0.0, 0.0},
1013  {-.1603586456402253758680961157407435495049 ,0.0, 0.0},
1014  {-.3165640999636298319901173288498449178923 ,0.0, 0.0},
1015  {-.4645707413759609457172671481041023679763 ,0.0, 0.0},
1016  {-.6005453046616810234696381649462392798683 ,0.0, 0.0},
1017  {-.7209661773352293786170958608237816296571 ,0.0, 0.0},
1018  {-.8227146565371428249789224867127139017745 ,0.0, 0.0},
1019  {-.9031559036148179016426609285323124878094 ,0.0, 0.0},
1020  {-.9602081521348300308527788406876515266151 ,0.0, 0.0},
1021  {-.9924068438435844031890176702532604935893 ,0.0, 0.0}
1022  },
1023  { // weights
1024  .01946178822972647703631204146443843575291,
1025  .04481422676569960033283815740199421195175,
1026  .06904454273764122658070825800601304496185,
1027  .09149002162244999946446209412383965266091,
1028  .1115666455473339947160239016817659974813,
1029  .1287539625393362276755157848568771170558,
1030  .1426067021736066117757461094419029724757,
1031  .152766042065859666778855400897662998461,
1032  .1589688433939543476499564394650472016788,
1033  .1610544498487836959791636253209167350399,
1034  .1589688433939543476499564394650472016788,
1035  .152766042065859666778855400897662998461,
1036  .1426067021736066117757461094419029724757,
1037  .1287539625393362276755157848568771170558,
1038  .1115666455473339947160239016817659974813,
1039  .09149002162244999946446209412383965266091,
1040  .06904454273764122658070825800601304496185,
1041  .04481422676569960033283815740199421195175,
1042  .01946178822972647703631204146443843575291
1043  }
1044  },
1045  {
1046  20,
1047  { // points
1048  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1049  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1050  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1051  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1052  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1053  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1054  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1055  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1056  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1057  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1058  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1059  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1060  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1061  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1062  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1063  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1064  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1065  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1066  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1067  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1068  },
1069  { // weights
1070  .01761400713915211831186196235185281636214,
1071  .04060142980038694133103995227493210987909,
1072  .0626720483341090635695065351870416063516,
1073  .08327674157670474872475814322204620610018,
1074  .1019301198172404350367501354803498761667,
1075  .118194531961518417312377377711382287005,
1076  .1316886384491766268984944997481631349161,
1077  .1420961093183820513292983250671649330345,
1078  .1491729864726037467878287370019694366927,
1079  .1527533871307258506980843319550975934919,
1080  .1527533871307258506980843319550975934919,
1081  .1491729864726037467878287370019694366927,
1082  .1420961093183820513292983250671649330345,
1083  .1316886384491766268984944997481631349161,
1084  .118194531961518417312377377711382287005,
1085  .1019301198172404350367501354803498761667,
1086  .08327674157670474872475814322204620610018,
1087  .0626720483341090635695065351870416063516,
1088  .04060142980038694133103995227493210987909,
1089  .01761400713915211831186196235185281636214
1090  }
1091  },
1092  {
1093  20,
1094  { // points
1095  {.9931285991850949247861223884713202782226 ,0.0, 0.0},
1096  {.9639719272779137912676661311972772219121 ,0.0, 0.0},
1097  {.9122344282513259058677524412032981130492 ,0.0, 0.0},
1098  {.8391169718222188233945290617015206853296 ,0.0, 0.0},
1099  {.7463319064601507926143050703556415903107 ,0.0, 0.0},
1100  {.6360536807265150254528366962262859367434 ,0.0, 0.0},
1101  {.5108670019508270980043640509552509984255 ,0.0, 0.0},
1102  {.3737060887154195606725481770249272373957 ,0.0, 0.0},
1103  {.2277858511416450780804961953685746247431 ,0.0, 0.0},
1104  {.0765265211334973337546404093988382110048 ,0.0, 0.0},
1105  {-.0765265211334973337546404093988382110048 ,0.0, 0.0},
1106  {-.2277858511416450780804961953685746247431 ,0.0, 0.0},
1107  {-.3737060887154195606725481770249272373957 ,0.0, 0.0},
1108  {-.5108670019508270980043640509552509984255 ,0.0, 0.0},
1109  {-.6360536807265150254528366962262859367434 ,0.0, 0.0},
1110  {-.7463319064601507926143050703556415903107 ,0.0, 0.0},
1111  {-.8391169718222188233945290617015206853296 ,0.0, 0.0},
1112  {-.9122344282513259058677524412032981130492 ,0.0, 0.0},
1113  {-.9639719272779137912676661311972772219121 ,0.0, 0.0},
1114  {-.9931285991850949247861223884713202782226 ,0.0, 0.0}
1115  },
1116  { // weights
1117  .01761400713915211831186196235185281636214,
1118  .04060142980038694133103995227493210987909,
1119  .0626720483341090635695065351870416063516,
1120  .08327674157670474872475814322204620610018,
1121  .1019301198172404350367501354803498761667,
1122  .118194531961518417312377377711382287005,
1123  .1316886384491766268984944997481631349161,
1124  .1420961093183820513292983250671649330345,
1125  .1491729864726037467878287370019694366927,
1126  .1527533871307258506980843319550975934919,
1127  .1527533871307258506980843319550975934919,
1128  .1491729864726037467878287370019694366927,
1129  .1420961093183820513292983250671649330345,
1130  .1316886384491766268984944997481631349161,
1131  .118194531961518417312377377711382287005,
1132  .1019301198172404350367501354803498761667,
1133  .08327674157670474872475814322204620610018,
1134  .0626720483341090635695065351870416063516,
1135  .04060142980038694133103995227493210987909,
1136  .01761400713915211831186196235185281636214
1137  }
1138  },
1139  {
1140  21,
1141  { // points
1142  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1143  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1144  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1145  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1146  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1147  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1148  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1149  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1150  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1151  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1152  {0 ,0.0, 0.0},
1153  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1154  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1155  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1156  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1157  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1158  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1159  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1160  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1161  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1162  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1163  },
1164  { // weights
1165  .01601722825777433332422461685847101526589,
1166  .03695378977085249379995066829932966618894,
1167  .05713442542685720828363582647244795749129,
1168  .07610011362837930201705165330018317922615,
1169  .09344442345603386155328974111393208848353,
1170  .1087972991671483776634745780701056420337,
1171  .1218314160537285341953671771257335983563,
1172  .132268938633337461781052574496775604329,
1173  .1398873947910731547221334238675831108928,
1174  .1445244039899700590638271665537525436099,
1175  .1460811336496904271919851476833711882448,
1176  .1445244039899700590638271665537525436099,
1177  .1398873947910731547221334238675831108928,
1178  .132268938633337461781052574496775604329,
1179  .1218314160537285341953671771257335983563,
1180  .1087972991671483776634745780701056420337,
1181  .09344442345603386155328974111393208848353,
1182  .07610011362837930201705165330018317922615,
1183  .05713442542685720828363582647244795749129,
1184  .03695378977085249379995066829932966618894,
1185  .01601722825777433332422461685847101526589
1186  }
1187  },
1188  {
1189  21,
1190  { // points
1191  {.9937521706203895002602420359379409291933 ,0.0, 0.0},
1192  {.9672268385663062943166222149076951614247 ,0.0, 0.0},
1193  {.9200993341504008287901871337149688941591 ,0.0, 0.0},
1194  {.8533633645833172836472506385875676702761 ,0.0, 0.0},
1195  {.768439963475677908615877851306228034821 ,0.0, 0.0},
1196  {.667138804197412319305966669990339162597 ,0.0, 0.0},
1197  {.5516188358872198070590187967243132866221 ,0.0, 0.0},
1198  {.4243421202074387835736688885437880520964 ,0.0, 0.0},
1199  {.288021316802401096600792516064600319909 ,0.0, 0.0},
1200  {.1455618541608950909370309823386863301163 ,0.0, 0.0},
1201  {0 ,0.0, 0.0},
1202  {-.1455618541608950909370309823386863301163 ,0.0, 0.0},
1203  {-.288021316802401096600792516064600319909 ,0.0, 0.0},
1204  {-.4243421202074387835736688885437880520964 ,0.0, 0.0},
1205  {-.5516188358872198070590187967243132866221 ,0.0, 0.0},
1206  {-.667138804197412319305966669990339162597 ,0.0, 0.0},
1207  {-.768439963475677908615877851306228034821 ,0.0, 0.0},
1208  {-.8533633645833172836472506385875676702761 ,0.0, 0.0},
1209  {-.9200993341504008287901871337149688941591 ,0.0, 0.0},
1210  {-.9672268385663062943166222149076951614247 ,0.0, 0.0},
1211  {-.9937521706203895002602420359379409291933 ,0.0, 0.0}
1212  },
1213  { // weights
1214  .01601722825777433332422461685847101526589,
1215  .03695378977085249379995066829932966618894,
1216  .05713442542685720828363582647244795749129,
1217  .07610011362837930201705165330018317922615,
1218  .09344442345603386155328974111393208848353,
1219  .1087972991671483776634745780701056420337,
1220  .1218314160537285341953671771257335983563,
1221  .132268938633337461781052574496775604329,
1222  .1398873947910731547221334238675831108928,
1223  .1445244039899700590638271665537525436099,
1224  .1460811336496904271919851476833711882448,
1225  .1445244039899700590638271665537525436099,
1226  .1398873947910731547221334238675831108928,
1227  .132268938633337461781052574496775604329,
1228  .1218314160537285341953671771257335983563,
1229  .1087972991671483776634745780701056420337,
1230  .09344442345603386155328974111393208848353,
1231  .07610011362837930201705165330018317922615,
1232  .05713442542685720828363582647244795749129,
1233  .03695378977085249379995066829932966618894,
1234  .01601722825777433332422461685847101526589
1235  }
1236  },
1237  {
1238  22,
1239  { // points
1240  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1241  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1242  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1243  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1244  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1245  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1246  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1247  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1248  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1249  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1250  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1251  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1252  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1253  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1254  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1255  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1256  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1257  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1258  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1259  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1260  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1261  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1262  },
1263  { // weights
1264  .01462799529827220068499109804718544519021,
1265  .03377490158481415479330224686591290134917,
1266  .05229333515268328594031205127321125611215,
1267  .06979646842452048809496141893021765739878,
1268  .08594160621706772741444368137270286618914,
1269  .1004141444428809649320788378305362823508,
1270  .1129322960805392183934006074217843191143,
1271  .1232523768105124242855609861548144719594,
1272  .1311735047870623707329649925303074458757,
1273  .1365414983460151713525738312315173965864,
1274  .1392518728556319933754102483418099578739,
1275  .1392518728556319933754102483418099578739,
1276  .1365414983460151713525738312315173965864,
1277  .1311735047870623707329649925303074458757,
1278  .1232523768105124242855609861548144719594,
1279  .1129322960805392183934006074217843191143,
1280  .1004141444428809649320788378305362823508,
1281  .08594160621706772741444368137270286618914,
1282  .06979646842452048809496141893021765739878,
1283  .05229333515268328594031205127321125611215,
1284  .03377490158481415479330224686591290134917,
1285  .01462799529827220068499109804718544519021
1286  }
1287  },
1288  {
1289  22,
1290  { // points
1291  {.9942945854823992920730314211612989803931 ,0.0, 0.0},
1292  {.970060497835428727123950986765268710806 ,0.0, 0.0},
1293  {.9269567721871740005206929392590531966353 ,0.0, 0.0},
1294  {.8658125777203001365364256370193787290848 ,0.0, 0.0},
1295  {.7878168059792081620042779554083515213882 ,0.0, 0.0},
1296  {.6944872631866827800506898357622567712673 ,0.0, 0.0},
1297  {.5876404035069115929588769276386473488776 ,0.0, 0.0},
1298  {.4693558379867570264063307109664063460953 ,0.0, 0.0},
1299  {.3419358208920842251581474204273796195592 ,0.0, 0.0},
1300  {.2078604266882212854788465339195457342157 ,0.0, 0.0},
1301  {.0697392733197222212138417961186280818223 ,0.0, 0.0},
1302  {-.0697392733197222212138417961186280818223 ,0.0, 0.0},
1303  {-.2078604266882212854788465339195457342157 ,0.0, 0.0},
1304  {-.3419358208920842251581474204273796195592 ,0.0, 0.0},
1305  {-.4693558379867570264063307109664063460953 ,0.0, 0.0},
1306  {-.5876404035069115929588769276386473488776 ,0.0, 0.0},
1307  {-.6944872631866827800506898357622567712673 ,0.0, 0.0},
1308  {-.7878168059792081620042779554083515213882 ,0.0, 0.0},
1309  {-.8658125777203001365364256370193787290848 ,0.0, 0.0},
1310  {-.9269567721871740005206929392590531966353 ,0.0, 0.0},
1311  {-.970060497835428727123950986765268710806 ,0.0, 0.0},
1312  {-.9942945854823992920730314211612989803931 ,0.0, 0.0}
1313  },
1314  { // weights
1315  .01462799529827220068499109804718544519021,
1316  .03377490158481415479330224686591290134917,
1317  .05229333515268328594031205127321125611215,
1318  .06979646842452048809496141893021765739878,
1319  .08594160621706772741444368137270286618914,
1320  .1004141444428809649320788378305362823508,
1321  .1129322960805392183934006074217843191143,
1322  .1232523768105124242855609861548144719594,
1323  .1311735047870623707329649925303074458757,
1324  .1365414983460151713525738312315173965864,
1325  .1392518728556319933754102483418099578739,
1326  .1392518728556319933754102483418099578739,
1327  .1365414983460151713525738312315173965864,
1328  .1311735047870623707329649925303074458757,
1329  .1232523768105124242855609861548144719594,
1330  .1129322960805392183934006074217843191143,
1331  .1004141444428809649320788378305362823508,
1332  .08594160621706772741444368137270286618914,
1333  .06979646842452048809496141893021765739878,
1334  .05229333515268328594031205127321125611215,
1335  .03377490158481415479330224686591290134917,
1336  .01462799529827220068499109804718544519021
1337  }
1338  },
1339  {
1340  23,
1341  { // points
1342  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1343  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1344  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1345  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1346  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1347  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1348  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1349  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1350  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1351  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1352  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1353  {0 ,0.0, 0.0},
1354  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1355  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1356  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1357  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1358  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1359  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1360  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1361  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1362  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1363  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1364  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1365  },
1366  { // weights
1367  .01341185948714177208130949345861506497662,
1368  .03098800585697944431069421964188450538377,
1369  .04803767173108466857164107163203399656122,
1370  .06423242140852585212716961515891099803916,
1371  .07928141177671895492289252474204322691371,
1372  .09291576606003514747701861736976464860346,
1373  .1048920914645414100740861850147438548585,
1374  .1149966402224113649416435129339613014914,
1375  .1230490843067295304675784006720096548159,
1376  .1289057221880821499785953393997936532597,
1377  .132462039404696617371642464703316925805,
1378  .1336545721861061753514571105458443385832,
1379  .132462039404696617371642464703316925805,
1380  .1289057221880821499785953393997936532597,
1381  .1230490843067295304675784006720096548159,
1382  .1149966402224113649416435129339613014914,
1383  .1048920914645414100740861850147438548585,
1384  .09291576606003514747701861736976464860346,
1385  .07928141177671895492289252474204322691371,
1386  .06423242140852585212716961515891099803916,
1387  .04803767173108466857164107163203399656122,
1388  .03098800585697944431069421964188450538377,
1389  .01341185948714177208130949345861506497662
1390  }
1391  },
1392  {
1393  23,
1394  { // points
1395  {.9947693349975521235239257154455743605736 ,0.0, 0.0},
1396  {.9725424712181152319560240768207773751816 ,0.0, 0.0},
1397  {.9329710868260161023491969890384229782357 ,0.0, 0.0},
1398  {.8767523582704416673781568859341456716389 ,0.0, 0.0},
1399  {.8048884016188398921511184069967785579414 ,0.0, 0.0},
1400  {.7186613631319501944616244837486188483299 ,0.0, 0.0},
1401  {.6196098757636461563850973116495956533872 ,0.0, 0.0},
1402  {.5095014778460075496897930478668464305448 ,0.0, 0.0},
1403  {.3903010380302908314214888728806054585781 ,0.0, 0.0},
1404  {.264135680970344930533869538283309602979 ,0.0, 0.0},
1405  {.1332568242984661109317426822417661370104 ,0.0, 0.0},
1406  {0 ,0.0, 0.0},
1407  {-.1332568242984661109317426822417661370104 ,0.0, 0.0},
1408  {-.264135680970344930533869538283309602979 ,0.0, 0.0},
1409  {-.3903010380302908314214888728806054585781 ,0.0, 0.0},
1410  {-.5095014778460075496897930478668464305448 ,0.0, 0.0},
1411  {-.6196098757636461563850973116495956533872 ,0.0, 0.0},
1412  {-.7186613631319501944616244837486188483299 ,0.0, 0.0},
1413  {-.8048884016188398921511184069967785579414 ,0.0, 0.0},
1414  {-.8767523582704416673781568859341456716389 ,0.0, 0.0},
1415  {-.9329710868260161023491969890384229782357 ,0.0, 0.0},
1416  {-.9725424712181152319560240768207773751816 ,0.0, 0.0},
1417  {-.9947693349975521235239257154455743605736 ,0.0, 0.0}
1418  },
1419  { // weights
1420  .01341185948714177208130949345861506497662,
1421  .03098800585697944431069421964188450538377,
1422  .04803767173108466857164107163203399656122,
1423  .06423242140852585212716961515891099803916,
1424  .07928141177671895492289252474204322691371,
1425  .09291576606003514747701861736976464860346,
1426  .1048920914645414100740861850147438548585,
1427  .1149966402224113649416435129339613014914,
1428  .1230490843067295304675784006720096548159,
1429  .1289057221880821499785953393997936532597,
1430  .132462039404696617371642464703316925805,
1431  .1336545721861061753514571105458443385832,
1432  .132462039404696617371642464703316925805,
1433  .1289057221880821499785953393997936532597,
1434  .1230490843067295304675784006720096548159,
1435  .1149966402224113649416435129339613014914,
1436  .1048920914645414100740861850147438548585,
1437  .09291576606003514747701861736976464860346,
1438  .07928141177671895492289252474204322691371,
1439  .06423242140852585212716961515891099803916,
1440  .04803767173108466857164107163203399656122,
1441  .03098800585697944431069421964188450538377,
1442  .01341185948714177208130949345861506497662
1443  }
1444  },
1445  {
1446  24,
1447  { // points
1448  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1449  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1450  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1451  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1452  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1453  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1454  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1455  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1456  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1457  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1458  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1459  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1460  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1461  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1462  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1463  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1464  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1465  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1466  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1467  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1468  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1469  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1470  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1471  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1472  },
1473  { // weights
1474  .01234122979998719954680566707003729157591,
1475  .0285313886289336631813078159518782864492,
1476  .04427743881741980616860274821133822885931,
1477  .0592985849154367807463677585001085845412,
1478  .07334648141108030573403361525311651811934,
1479  .08619016153195327591718520298374266718508,
1480  .09761865210411388826988066446424715442792,
1481  .1074442701159656347825773424466062227946,
1482  .1155056680537256013533444839067835598623,
1483  .121670472927803391204463153476262425607,
1484  .1258374563468282961213753825111836887264,
1485  .1279381953467521569740561652246953718517,
1486  .1279381953467521569740561652246953718517,
1487  .1258374563468282961213753825111836887264,
1488  .121670472927803391204463153476262425607,
1489  .1155056680537256013533444839067835598623,
1490  .1074442701159656347825773424466062227946,
1491  .09761865210411388826988066446424715442792,
1492  .08619016153195327591718520298374266718508,
1493  .07334648141108030573403361525311651811934,
1494  .0592985849154367807463677585001085845412,
1495  .04427743881741980616860274821133822885931,
1496  .0285313886289336631813078159518782864492,
1497  .01234122979998719954680566707003729157591
1498  }
1499  },
1500  {
1501  24,
1502  { // points
1503  {.9951872199970213601799974097007368118746 ,0.0, 0.0},
1504  {.9747285559713094981983919930081690617412 ,0.0, 0.0},
1505  {.9382745520027327585236490017087214496548 ,0.0, 0.0},
1506  {.8864155270044010342131543419821967550873 ,0.0, 0.0},
1507  {.8200019859739029219539498726697452080761 ,0.0, 0.0},
1508  {.7401241915785543642438281030999784255233 ,0.0, 0.0},
1509  {.6480936519369755692524957869107476266697 ,0.0, 0.0},
1510  {.5454214713888395356583756172183723700108 ,0.0, 0.0},
1511  {.4337935076260451384870842319133497124524 ,0.0, 0.0},
1512  {.3150426796961633743867932913198102407865 ,0.0, 0.0},
1513  {.1911188674736163091586398207570696318404 ,0.0, 0.0},
1514  {.064056892862605626085043082624745038591 ,0.0, 0.0},
1515  {-.064056892862605626085043082624745038591 ,0.0, 0.0},
1516  {-.1911188674736163091586398207570696318404 ,0.0, 0.0},
1517  {-.3150426796961633743867932913198102407865 ,0.0, 0.0},
1518  {-.4337935076260451384870842319133497124524 ,0.0, 0.0},
1519  {-.5454214713888395356583756172183723700108 ,0.0, 0.0},
1520  {-.6480936519369755692524957869107476266697 ,0.0, 0.0},
1521  {-.7401241915785543642438281030999784255233 ,0.0, 0.0},
1522  {-.8200019859739029219539498726697452080761 ,0.0, 0.0},
1523  {-.8864155270044010342131543419821967550873 ,0.0, 0.0},
1524  {-.9382745520027327585236490017087214496548 ,0.0, 0.0},
1525  {-.9747285559713094981983919930081690617412 ,0.0, 0.0},
1526  {-.9951872199970213601799974097007368118746 ,0.0, 0.0}
1527  },
1528  { // weights
1529  .01234122979998719954680566707003729157591,
1530  .0285313886289336631813078159518782864492,
1531  .04427743881741980616860274821133822885931,
1532  .0592985849154367807463677585001085845412,
1533  .07334648141108030573403361525311651811934,
1534  .08619016153195327591718520298374266718508,
1535  .09761865210411388826988066446424715442792,
1536  .1074442701159656347825773424466062227946,
1537  .1155056680537256013533444839067835598623,
1538  .121670472927803391204463153476262425607,
1539  .1258374563468282961213753825111836887264,
1540  .1279381953467521569740561652246953718517,
1541  .1279381953467521569740561652246953718517,
1542  .1258374563468282961213753825111836887264,
1543  .121670472927803391204463153476262425607,
1544  .1155056680537256013533444839067835598623,
1545  .1074442701159656347825773424466062227946,
1546  .09761865210411388826988066446424715442792,
1547  .08619016153195327591718520298374266718508,
1548  .07334648141108030573403361525311651811934,
1549  .0592985849154367807463677585001085845412,
1550  .04427743881741980616860274821133822885931,
1551  .0285313886289336631813078159518782864492,
1552  .01234122979998719954680566707003729157591
1553  }
1554  },
1555  {
1556  25,
1557  { // points
1558  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1559  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1560  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1561  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1562  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1563  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1564  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1565  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1566  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1567  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1568  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1569  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1570  {0 ,0.0, 0.0},
1571  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1572  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1573  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1574  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1575  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1576  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1577  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1578  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1579  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1580  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1581  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1582  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1583  },
1584  { // weights
1585  .01139379850102628794790296411323477360332,
1586  .02635498661503213726190181529529914493596,
1587  .04093915670130631265562348771164595366085,
1588  .05490469597583519192593689154047332416011,
1589  .06803833381235691720718718565670796855471,
1590  .08014070033500101801323495966911130229023,
1591  .09102826198296364981149722070289165338099,
1592  .1005359490670506442022068903926858269885,
1593  .1085196244742636531160939570501166193401,
1594  .1148582591457116483393255458695558086409,
1595  .1194557635357847722281781265129010473902,
1596  .1222424429903100416889595189458515058351,
1597  .1231760537267154512039028730790501424382,
1598  .1222424429903100416889595189458515058351,
1599  .1194557635357847722281781265129010473902,
1600  .1148582591457116483393255458695558086409,
1601  .1085196244742636531160939570501166193401,
1602  .1005359490670506442022068903926858269885,
1603  .09102826198296364981149722070289165338099,
1604  .08014070033500101801323495966911130229023,
1605  .06803833381235691720718718565670796855471,
1606  .05490469597583519192593689154047332416011,
1607  .04093915670130631265562348771164595366085,
1608  .02635498661503213726190181529529914493596,
1609  .01139379850102628794790296411323477360332
1610  }
1611  },
1612  {
1613  25,
1614  { // points
1615  {.9955569697904980979087849468939016172576 ,0.0, 0.0},
1616  {.9766639214595175114983153864795940677454 ,0.0, 0.0},
1617  {.9429745712289743394140111696584705319052 ,0.0, 0.0},
1618  {.8949919978782753688510420067828049541746 ,0.0, 0.0},
1619  {.833442628760834001421021108693569569461 ,0.0, 0.0},
1620  {.7592592630373576305772828652043609763875 ,0.0, 0.0},
1621  {.6735663684734683644851206332476221758834 ,0.0, 0.0},
1622  {.5776629302412229677236898416126540673957 ,0.0, 0.0},
1623  {.4730027314457149605221821150091920413318 ,0.0, 0.0},
1624  {.3611723058093878377358217301276406674221 ,0.0, 0.0},
1625  {.2438668837209884320451903627974515864056 ,0.0, 0.0},
1626  {.1228646926107103963873598188080368055322 ,0.0, 0.0},
1627  {0 ,0.0, 0.0},
1628  {-.1228646926107103963873598188080368055322 ,0.0, 0.0},
1629  {-.2438668837209884320451903627974515864056 ,0.0, 0.0},
1630  {-.3611723058093878377358217301276406674221 ,0.0, 0.0},
1631  {-.4730027314457149605221821150091920413318 ,0.0, 0.0},
1632  {-.5776629302412229677236898416126540673957 ,0.0, 0.0},
1633  {-.6735663684734683644851206332476221758834 ,0.0, 0.0},
1634  {-.7592592630373576305772828652043609763875 ,0.0, 0.0},
1635  {-.833442628760834001421021108693569569461 ,0.0, 0.0},
1636  {-.8949919978782753688510420067828049541746 ,0.0, 0.0},
1637  {-.9429745712289743394140111696584705319052 ,0.0, 0.0},
1638  {-.9766639214595175114983153864795940677454 ,0.0, 0.0},
1639  {-.9955569697904980979087849468939016172576 ,0.0, 0.0}
1640  },
1641  { // weights
1642  .01139379850102628794790296411323477360332,
1643  .02635498661503213726190181529529914493596,
1644  .04093915670130631265562348771164595366085,
1645  .05490469597583519192593689154047332416011,
1646  .06803833381235691720718718565670796855471,
1647  .08014070033500101801323495966911130229023,
1648  .09102826198296364981149722070289165338099,
1649  .1005359490670506442022068903926858269885,
1650  .1085196244742636531160939570501166193401,
1651  .1148582591457116483393255458695558086409,
1652  .1194557635357847722281781265129010473902,
1653  .1222424429903100416889595189458515058351,
1654  .1231760537267154512039028730790501424382,
1655  .1222424429903100416889595189458515058351,
1656  .1194557635357847722281781265129010473902,
1657  .1148582591457116483393255458695558086409,
1658  .1085196244742636531160939570501166193401,
1659  .1005359490670506442022068903926858269885,
1660  .09102826198296364981149722070289165338099,
1661  .08014070033500101801323495966911130229023,
1662  .06803833381235691720718718565670796855471,
1663  .05490469597583519192593689154047332416011,
1664  .04093915670130631265562348771164595366085,
1665  .02635498661503213726190181529529914493596,
1666  .01139379850102628794790296411323477360332
1667  }
1668  },
1669  {
1670  26,
1671  { // points
1672  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1673  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1674  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1675  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1676  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1677  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1678  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1679  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1680  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1681  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1682  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1683  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1684  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1685  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1686  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1687  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1688  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1689  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1690  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1691  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1692  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1693  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1694  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1695  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1696  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1697  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1698  },
1699  { // weights
1700  .01055137261734300715565118768525197790435,
1701  .0244178510926319087896158275197884002405,
1702  .03796238329436276395030314124885049469077,
1703  .05097582529714781199831990072407337952588,
1704  .06327404632957483553945368990704509572222,
1705  .07468414976565974588707579610284833863875,
1706  .08504589431348523921044776507998169658392,
1707  .09421380035591414846366488306730319854917,
1708  .1020591610944254232384140702534307923272,
1709  .1084718405285765906565794267279975822894,
1710  .113361816546319666549440718442598145246,
1711  .116660443485296582044662507540362213632,
1712  .1183214152792622765163710857004686846499,
1713  .1183214152792622765163710857004686846499,
1714  .116660443485296582044662507540362213632,
1715  .113361816546319666549440718442598145246,
1716  .1084718405285765906565794267279975822894,
1717  .1020591610944254232384140702534307923272,
1718  .09421380035591414846366488306730319854917,
1719  .08504589431348523921044776507998169658392,
1720  .07468414976565974588707579610284833863875,
1721  .06327404632957483553945368990704509572222,
1722  .05097582529714781199831990072407337952588,
1723  .03796238329436276395030314124885049469077,
1724  .0244178510926319087896158275197884002405,
1725  .01055137261734300715565118768525197790435
1726  }
1727  },
1728  {
1729  26,
1730  { // points
1731  {.9958857011456169290032169593229060259569 ,0.0, 0.0},
1732  {.9783854459564709911005803543119263054469 ,0.0, 0.0},
1733  {.9471590666617142501359152835180367545207 ,0.0, 0.0},
1734  {.9026378619843070742176655992312102513411 ,0.0, 0.0},
1735  {.8454459427884980187975070614678381615721 ,0.0, 0.0},
1736  {.7763859488206788561929672472422838669762 ,0.0, 0.0},
1737  {.6964272604199572648638139137294246978608 ,0.0, 0.0},
1738  {.6066922930176180632319787469168870544353 ,0.0, 0.0},
1739  {.5084407148245057176957030647255691753763 ,0.0, 0.0},
1740  {.4030517551234863064810773770988831036599 ,0.0, 0.0},
1741  {.2920048394859568951428353820778302968847 ,0.0, 0.0},
1742  {.1768588203568901839690577484183447499774 ,0.0, 0.0},
1743  {.05923009342931320709371857519840336079023 ,0.0, 0.0},
1744  {-.05923009342931320709371857519840336079023 ,0.0, 0.0},
1745  {-.1768588203568901839690577484183447499774 ,0.0, 0.0},
1746  {-.2920048394859568951428353820778302968847 ,0.0, 0.0},
1747  {-.4030517551234863064810773770988831036599 ,0.0, 0.0},
1748  {-.5084407148245057176957030647255691753763 ,0.0, 0.0},
1749  {-.6066922930176180632319787469168870544353 ,0.0, 0.0},
1750  {-.6964272604199572648638139137294246978608 ,0.0, 0.0},
1751  {-.7763859488206788561929672472422838669762 ,0.0, 0.0},
1752  {-.8454459427884980187975070614678381615721 ,0.0, 0.0},
1753  {-.9026378619843070742176655992312102513411 ,0.0, 0.0},
1754  {-.9471590666617142501359152835180367545207 ,0.0, 0.0},
1755  {-.9783854459564709911005803543119263054469 ,0.0, 0.0},
1756  {-.9958857011456169290032169593229060259569 ,0.0, 0.0}
1757  },
1758  { // weights
1759  .01055137261734300715565118768525197790435,
1760  .0244178510926319087896158275197884002405,
1761  .03796238329436276395030314124885049469077,
1762  .05097582529714781199831990072407337952588,
1763  .06327404632957483553945368990704509572222,
1764  .07468414976565974588707579610284833863875,
1765  .08504589431348523921044776507998169658392,
1766  .09421380035591414846366488306730319854917,
1767  .1020591610944254232384140702534307923272,
1768  .1084718405285765906565794267279975822894,
1769  .113361816546319666549440718442598145246,
1770  .116660443485296582044662507540362213632,
1771  .1183214152792622765163710857004686846499,
1772  .1183214152792622765163710857004686846499,
1773  .116660443485296582044662507540362213632,
1774  .113361816546319666549440718442598145246,
1775  .1084718405285765906565794267279975822894,
1776  .1020591610944254232384140702534307923272,
1777  .09421380035591414846366488306730319854917,
1778  .08504589431348523921044776507998169658392,
1779  .07468414976565974588707579610284833863875,
1780  .06327404632957483553945368990704509572222,
1781  .05097582529714781199831990072407337952588,
1782  .03796238329436276395030314124885049469077,
1783  .0244178510926319087896158275197884002405,
1784  .01055137261734300715565118768525197790435
1785  }
1786  },
1787  {
1788  27,
1789  { // points
1790  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1791  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1792  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1793  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1794  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1795  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1796  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1797  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1798  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1799  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1800  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1801  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1802  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1803  {0 ,0.0, 0.0},
1804  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1805  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1806  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1807  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1808  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1809  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1810  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1811  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1812  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1813  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1814  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1815  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1816  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1817  },
1818  { // weights
1819  .009798996051294360261150055091259098098226,
1820  .02268623159618062319603420644676148881277,
1821  .03529705375741971102257828930471164113614,
1822  .04744941252061506270409671011418471822473,
1823  .05898353685983359911030083371953163316524,
1824  .06974882376624559298432288835666727613282,
1825  .07960486777305777126307495900984240297615,
1826  .08842315854375695019432280285374911105654,
1827  .09608872737002850756565264655810585916021,
1828  .1025016378177457986712477115326638093244,
1829  .107578285788533187212162984426657404819,
1830  .1112524883568451926721630960428486748329,
1831  .1134763461089651486203699480920992579205,
1832  .1142208673789569890450457369018352486807,
1833  .1134763461089651486203699480920992579205,
1834  .1112524883568451926721630960428486748329,
1835  .107578285788533187212162984426657404819,
1836  .1025016378177457986712477115326638093244,
1837  .09608872737002850756565264655810585916021,
1838  .08842315854375695019432280285374911105654,
1839  .07960486777305777126307495900984240297615,
1840  .06974882376624559298432288835666727613282,
1841  .05898353685983359911030083371953163316524,
1842  .04744941252061506270409671011418471822473,
1843  .03529705375741971102257828930471164113614,
1844  .02268623159618062319603420644676148881277,
1845  .009798996051294360261150055091259098098226
1846  }
1847  },
1848  {
1849  27,
1850  { // points
1851  {.9961792628889885669388872083812299902607 ,0.0, 0.0},
1852  {.9799234759615012228558733556610471845676 ,0.0, 0.0},
1853  {.9509005578147050068519080306438828930926 ,0.0, 0.0},
1854  {.909482320677491104300645018209689254948 ,0.0, 0.0},
1855  {.8562079080182944903027372227068427977643 ,0.0, 0.0},
1856  {.7917716390705082271443973441072707329194 ,0.0, 0.0},
1857  {.7170134737394236992948162116423395497507 ,0.0, 0.0},
1858  {.6329079719464951409277346376344886121031 ,0.0, 0.0},
1859  {.5405515645794568949003009415599828209592 ,0.0, 0.0},
1860  {.4411482517500268805859741556892814524477 ,0.0, 0.0},
1861  {.33599390363850889973031903420728454179 ,0.0, 0.0},
1862  {.2264593654395368588572391073602301711794 ,0.0, 0.0},
1863  {.1139725856095299669328949838699766271733 ,0.0, 0.0},
1864  {0 ,0.0, 0.0},
1865  {-.1139725856095299669328949838699766271733 ,0.0, 0.0},
1866  {-.2264593654395368588572391073602301711794 ,0.0, 0.0},
1867  {-.33599390363850889973031903420728454179 ,0.0, 0.0},
1868  {-.4411482517500268805859741556892814524477 ,0.0, 0.0},
1869  {-.5405515645794568949003009415599828209592 ,0.0, 0.0},
1870  {-.6329079719464951409277346376344886121031 ,0.0, 0.0},
1871  {-.7170134737394236992948162116423395497507 ,0.0, 0.0},
1872  {-.7917716390705082271443973441072707329194 ,0.0, 0.0},
1873  {-.8562079080182944903027372227068427977643 ,0.0, 0.0},
1874  {-.909482320677491104300645018209689254948 ,0.0, 0.0},
1875  {-.9509005578147050068519080306438828930926 ,0.0, 0.0},
1876  {-.9799234759615012228558733556610471845676 ,0.0, 0.0},
1877  {-.9961792628889885669388872083812299902607 ,0.0, 0.0}
1878  },
1879  { // weights
1880  .009798996051294360261150055091259098098226,
1881  .02268623159618062319603420644676148881277,
1882  .03529705375741971102257828930471164113614,
1883  .04744941252061506270409671011418471822473,
1884  .05898353685983359911030083371953163316524,
1885  .06974882376624559298432288835666727613282,
1886  .07960486777305777126307495900984240297615,
1887  .08842315854375695019432280285374911105654,
1888  .09608872737002850756565264655810585916021,
1889  .1025016378177457986712477115326638093244,
1890  .107578285788533187212162984426657404819,
1891  .1112524883568451926721630960428486748329,
1892  .1134763461089651486203699480920992579205,
1893  .1142208673789569890450457369018352486807,
1894  .1134763461089651486203699480920992579205,
1895  .1112524883568451926721630960428486748329,
1896  .107578285788533187212162984426657404819,
1897  .1025016378177457986712477115326638093244,
1898  .09608872737002850756565264655810585916021,
1899  .08842315854375695019432280285374911105654,
1900  .07960486777305777126307495900984240297615,
1901  .06974882376624559298432288835666727613282,
1902  .05898353685983359911030083371953163316524,
1903  .04744941252061506270409671011418471822473,
1904  .03529705375741971102257828930471164113614,
1905  .02268623159618062319603420644676148881277,
1906  .009798996051294360261150055091259098098226
1907  }
1908  },
1909  {
1910  28,
1911  { // points
1912  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1913  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1914  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1915  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1916  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1917  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1918  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1919  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1920  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1921  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1922  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1923  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1924  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1925  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1926  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1927  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1928  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1929  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
1930  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
1931  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
1932  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
1933  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
1934  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
1935  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
1936  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
1937  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
1938  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
1939  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
1940  },
1941  { // weights
1942  .009124282593094517738816153922951706240344,
1943  .02113211259277125975150038099326543445137,
1944  .03290142778230437997763081917053204598153,
1945  .04427293475900422783958787765320739061499,
1946  .05510734567571674543148291822694559121906,
1947  .06527292396699959579339756677550463635364,
1948  .07464621423456877902393188717302203802164,
1949  .08311341722890121839039649824433247986113,
1950  .09057174439303284094218603133678412982286,
1951  .09693065799792991585048900609544060176503,
1952  .1021129675780607698142166385057121350466,
1953  .1060557659228464179104164369968108287899,
1954  .1087111922582941352535715193036733678753,
1955  .1100470130164751962823762656018176139566,
1956  .1100470130164751962823762656018176139566,
1957  .1087111922582941352535715193036733678753,
1958  .1060557659228464179104164369968108287899,
1959  .1021129675780607698142166385057121350466,
1960  .09693065799792991585048900609544060176503,
1961  .09057174439303284094218603133678412982286,
1962  .08311341722890121839039649824433247986113,
1963  .07464621423456877902393188717302203802164,
1964  .06527292396699959579339756677550463635364,
1965  .05510734567571674543148291822694559121906,
1966  .04427293475900422783958787765320739061499,
1967  .03290142778230437997763081917053204598153,
1968  .02113211259277125975150038099326543445137,
1969  .009124282593094517738816153922951706240344
1970  }
1971  },
1972  {
1973  28,
1974  { // points
1975  {.9964424975739544499504363904833109917501 ,0.0, 0.0},
1976  {.9813031653708727536945599458078302764442 ,0.0, 0.0},
1977  {.9542592806289381972541018397052155890034 ,0.0, 0.0},
1978  {.9156330263921320738696894233299271463525 ,0.0, 0.0},
1979  {.8658925225743950489422545673796868043419 ,0.0, 0.0},
1980  {.8056413709171791714478859554252776586717 ,0.0, 0.0},
1981  {.7356108780136317720281445102925343680161 ,0.0, 0.0},
1982  {.6566510940388649612198981765067428215696 ,0.0, 0.0},
1983  {.5697204718114017193080032833564309331247 ,0.0, 0.0},
1984  {.4758742249551182610344118476674340426272 ,0.0, 0.0},
1985  {.3762515160890787102213572095560869828717 ,0.0, 0.0},
1986  {.2720616276351780776768263561257697348248 ,0.0, 0.0},
1987  {.1645692821333807712814717778911654571457 ,0.0, 0.0},
1988  {.0550792898840342704265165273418799778508 ,0.0, 0.0},
1989  {-.0550792898840342704265165273418799778508 ,0.0, 0.0},
1990  {-.1645692821333807712814717778911654571457 ,0.0, 0.0},
1991  {-.2720616276351780776768263561257697348248 ,0.0, 0.0},
1992  {-.3762515160890787102213572095560869828717 ,0.0, 0.0},
1993  {-.4758742249551182610344118476674340426272 ,0.0, 0.0},
1994  {-.5697204718114017193080032833564309331247 ,0.0, 0.0},
1995  {-.6566510940388649612198981765067428215696 ,0.0, 0.0},
1996  {-.7356108780136317720281445102925343680161 ,0.0, 0.0},
1997  {-.8056413709171791714478859554252776586717 ,0.0, 0.0},
1998  {-.8658925225743950489422545673796868043419 ,0.0, 0.0},
1999  {-.9156330263921320738696894233299271463525 ,0.0, 0.0},
2000  {-.9542592806289381972541018397052155890034 ,0.0, 0.0},
2001  {-.9813031653708727536945599458078302764442 ,0.0, 0.0},
2002  {-.9964424975739544499504363904833109917501 ,0.0, 0.0}
2003  },
2004  { // weights
2005  .009124282593094517738816153922951706240344,
2006  .02113211259277125975150038099326543445137,
2007  .03290142778230437997763081917053204598153,
2008  .04427293475900422783958787765320739061499,
2009  .05510734567571674543148291822694559121906,
2010  .06527292396699959579339756677550463635364,
2011  .07464621423456877902393188717302203802164,
2012  .08311341722890121839039649824433247986113,
2013  .09057174439303284094218603133678412982286,
2014  .09693065799792991585048900609544060176503,
2015  .1021129675780607698142166385057121350466,
2016  .1060557659228464179104164369968108287899,
2017  .1087111922582941352535715193036733678753,
2018  .1100470130164751962823762656018176139566,
2019  .1100470130164751962823762656018176139566,
2020  .1087111922582941352535715193036733678753,
2021  .1060557659228464179104164369968108287899,
2022  .1021129675780607698142166385057121350466,
2023  .09693065799792991585048900609544060176503,
2024  .09057174439303284094218603133678412982286,
2025  .08311341722890121839039649824433247986113,
2026  .07464621423456877902393188717302203802164,
2027  .06527292396699959579339756677550463635364,
2028  .05510734567571674543148291822694559121906,
2029  .04427293475900422783958787765320739061499,
2030  .03290142778230437997763081917053204598153,
2031  .02113211259277125975150038099326543445137,
2032  .009124282593094517738816153922951706240344
2033  }
2034  },
2035  {
2036  29,
2037  { // points
2038  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2039  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2040  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2041  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2042  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2043  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2044  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2045  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2046  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2047  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2048  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2049  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2050  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2051  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2052  {0 ,0.0, 0.0},
2053  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2054  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2055  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2056  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2057  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2058  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2059  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2060  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2061  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2062  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2063  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2064  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2065  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2066  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2067  },
2068  { // weights
2069  .008516903878746409654263813302249803002399,
2070  .01973208505612270598385980164039563114961,
2071  .03074049220209362264440852537461674974712,
2072  .04140206251868283610483001011407692153349,
2073  .05159482690249792391259438117954259791962,
2074  .06120309065707913854210984802390704492406,
2075  .07011793325505127856958148694887917310239,
2076  .07823832713576378382814488865968033136688,
2077  .0854722573661725275453448492972080713817,
2078  .09173775713925876334796641107711080689823,
2079  .09696383409440860630190007488268875917636,
2080  .1010912737599149661218205469074973636476,
2081  .1040733100777293739133284712851200689107,
2082  .1058761550973209414065913278521878930748,
2083  .1064793817183142442465111269096775683302,
2084  .1058761550973209414065913278521878930748,
2085  .1040733100777293739133284712851200689107,
2086  .1010912737599149661218205469074973636476,
2087  .09696383409440860630190007488268875917636,
2088  .09173775713925876334796641107711080689823,
2089  .0854722573661725275453448492972080713817,
2090  .07823832713576378382814488865968033136688,
2091  .07011793325505127856958148694887917310239,
2092  .06120309065707913854210984802390704492406,
2093  .05159482690249792391259438117954259791962,
2094  .04140206251868283610483001011407692153349,
2095  .03074049220209362264440852537461674974712,
2096  .01973208505612270598385980164039563114961,
2097  .008516903878746409654263813302249803002399
2098  }
2099  },
2100  {
2101  29,
2102  { // points
2103  {.9966794422605965861631915325493538856518 ,0.0, 0.0},
2104  {.9825455052614131748709260157863769561068 ,0.0, 0.0},
2105  {.9572855957780877257982080369808235637376 ,0.0, 0.0},
2106  {.9211802329530587850937534360831064254088 ,0.0, 0.0},
2107  {.8746378049201027904177934212565785469106 ,0.0, 0.0},
2108  {.81818548761525244498957221457878497563 ,0.0, 0.0},
2109  {.7524628517344771339126100772121381902126 ,0.0, 0.0},
2110  {.6782145376026865151561850053919859263883 ,0.0, 0.0},
2111  {.5962817971382278203795862111889897800782 ,0.0, 0.0},
2112  {.5075929551242276421026279196275201533512 ,0.0, 0.0},
2113  {.4131528881740086638907065860316168233234 ,0.0, 0.0},
2114  {.3140316378676399349481959231910474482584 ,0.0, 0.0},
2115  {.2113522861660010745063757289029374990567 ,0.0, 0.0},
2116  {.1062782301326792301709823924303769809172 ,0.0, 0.0},
2117  {0 ,0.0, 0.0},
2118  {-.1062782301326792301709823924303769809172 ,0.0, 0.0},
2119  {-.2113522861660010745063757289029374990567 ,0.0, 0.0},
2120  {-.3140316378676399349481959231910474482584 ,0.0, 0.0},
2121  {-.4131528881740086638907065860316168233234 ,0.0, 0.0},
2122  {-.5075929551242276421026279196275201533512 ,0.0, 0.0},
2123  {-.5962817971382278203795862111889897800782 ,0.0, 0.0},
2124  {-.6782145376026865151561850053919859263883 ,0.0, 0.0},
2125  {-.7524628517344771339126100772121381902126 ,0.0, 0.0},
2126  {-.81818548761525244498957221457878497563 ,0.0, 0.0},
2127  {-.8746378049201027904177934212565785469106 ,0.0, 0.0},
2128  {-.9211802329530587850937534360831064254088 ,0.0, 0.0},
2129  {-.9572855957780877257982080369808235637376 ,0.0, 0.0},
2130  {-.9825455052614131748709260157863769561068 ,0.0, 0.0},
2131  {-.9966794422605965861631915325493538856518 ,0.0, 0.0}
2132  },
2133  { // weights
2134  .008516903878746409654263813302249803002399,
2135  .01973208505612270598385980164039563114961,
2136  .03074049220209362264440852537461674974712,
2137  .04140206251868283610483001011407692153349,
2138  .05159482690249792391259438117954259791962,
2139  .06120309065707913854210984802390704492406,
2140  .07011793325505127856958148694887917310239,
2141  .07823832713576378382814488865968033136688,
2142  .0854722573661725275453448492972080713817,
2143  .09173775713925876334796641107711080689823,
2144  .09696383409440860630190007488268875917636,
2145  .1010912737599149661218205469074973636476,
2146  .1040733100777293739133284712851200689107,
2147  .1058761550973209414065913278521878930748,
2148  .1064793817183142442465111269096775683302,
2149  .1058761550973209414065913278521878930748,
2150  .1040733100777293739133284712851200689107,
2151  .1010912737599149661218205469074973636476,
2152  .09696383409440860630190007488268875917636,
2153  .09173775713925876334796641107711080689823,
2154  .0854722573661725275453448492972080713817,
2155  .07823832713576378382814488865968033136688,
2156  .07011793325505127856958148694887917310239,
2157  .06120309065707913854210984802390704492406,
2158  .05159482690249792391259438117954259791962,
2159  .04140206251868283610483001011407692153349,
2160  .03074049220209362264440852537461674974712,
2161  .01973208505612270598385980164039563114961,
2162  .008516903878746409654263813302249803002399
2163  }
2164  },
2165  {
2166  30,
2167  { // points
2168  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2169  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2170  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2171  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2172  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2173  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2174  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2175  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2176  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2177  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2178  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2179  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2180  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2181  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2182  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2183  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2184  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2185  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2186  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2187  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2188  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2189  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2190  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2191  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2192  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2193  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2194  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2195  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2196  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2197  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2198  },
2199  { // weights
2200  .007968192496166605615465883474673622450481,
2201  .01846646831109095914230213191204726909621,
2202  .02878470788332336934971917961129204363959,
2203  .0387991925696270495968019364463476920332,
2204  .04840267283059405290293814042280751781527,
2205  .05749315621761906648172168940205612879712,
2206  .06597422988218049512812851511596236123744,
2207  .07375597473770520626824385002219073415377,
2208  .08075589522942021535469493846052973087589,
2209  .08689978720108297980238753071512570257675,
2210  .09212252223778612871763270708761876719691,
2211  .09636873717464425963946862635180986509641,
2212  .09959342058679526706278028210356947652987,
2213  .1017623897484055045964289521685540446327,
2214  .1028526528935588403412856367054150438684,
2215  .1028526528935588403412856367054150438684,
2216  .1017623897484055045964289521685540446327,
2217  .09959342058679526706278028210356947652987,
2218  .09636873717464425963946862635180986509641,
2219  .09212252223778612871763270708761876719691,
2220  .08689978720108297980238753071512570257675,
2221  .08075589522942021535469493846052973087589,
2222  .07375597473770520626824385002219073415377,
2223  .06597422988218049512812851511596236123744,
2224  .05749315621761906648172168940205612879712,
2225  .04840267283059405290293814042280751781527,
2226  .0387991925696270495968019364463476920332,
2227  .02878470788332336934971917961129204363959,
2228  .01846646831109095914230213191204726909621,
2229  .007968192496166605615465883474673622450481
2230  }
2231  },
2232  {
2233  30,
2234  { // points
2235  {.9968934840746495402716300509186952833409 ,0.0, 0.0},
2236  {.9836681232797472099700325816056628019403 ,0.0, 0.0},
2237  {.9600218649683075122168710255817976629304 ,0.0, 0.0},
2238  {.9262000474292743258793242770804740040865 ,0.0, 0.0},
2239  {.8825605357920526815431164625302255900567 ,0.0, 0.0},
2240  {.8295657623827683974428981197325019164391 ,0.0, 0.0},
2241  {.7677774321048261949179773409745031316949 ,0.0, 0.0},
2242  {.6978504947933157969322923880266400683824 ,0.0, 0.0},
2243  {.6205261829892428611404775564311892992074 ,0.0, 0.0},
2244  {.5366241481420198992641697933110727941642 ,0.0, 0.0},
2245  {.4470337695380891767806099003228540001624 ,0.0, 0.0},
2246  {.3527047255308781134710372070893738606536 ,0.0, 0.0},
2247  {.2546369261678898464398051298178051078828 ,0.0, 0.0},
2248  {.1538699136085835469637946727432559204186 ,0.0, 0.0},
2249  {.05147184255531769583302521316672257374914 ,0.0, 0.0},
2250  {-.05147184255531769583302521316672257374914 ,0.0, 0.0},
2251  {-.1538699136085835469637946727432559204186 ,0.0, 0.0},
2252  {-.2546369261678898464398051298178051078828 ,0.0, 0.0},
2253  {-.3527047255308781134710372070893738606536 ,0.0, 0.0},
2254  {-.4470337695380891767806099003228540001624 ,0.0, 0.0},
2255  {-.5366241481420198992641697933110727941642 ,0.0, 0.0},
2256  {-.6205261829892428611404775564311892992074 ,0.0, 0.0},
2257  {-.6978504947933157969322923880266400683824 ,0.0, 0.0},
2258  {-.7677774321048261949179773409745031316949 ,0.0, 0.0},
2259  {-.8295657623827683974428981197325019164391 ,0.0, 0.0},
2260  {-.8825605357920526815431164625302255900567 ,0.0, 0.0},
2261  {-.9262000474292743258793242770804740040865 ,0.0, 0.0},
2262  {-.9600218649683075122168710255817976629304 ,0.0, 0.0},
2263  {-.9836681232797472099700325816056628019403 ,0.0, 0.0},
2264  {-.9968934840746495402716300509186952833409 ,0.0, 0.0}
2265  },
2266  { // weights
2267  .007968192496166605615465883474673622450481,
2268  .01846646831109095914230213191204726909621,
2269  .02878470788332336934971917961129204363959,
2270  .0387991925696270495968019364463476920332,
2271  .04840267283059405290293814042280751781527,
2272  .05749315621761906648172168940205612879712,
2273  .06597422988218049512812851511596236123744,
2274  .07375597473770520626824385002219073415377,
2275  .08075589522942021535469493846052973087589,
2276  .08689978720108297980238753071512570257675,
2277  .09212252223778612871763270708761876719691,
2278  .09636873717464425963946862635180986509641,
2279  .09959342058679526706278028210356947652987,
2280  .1017623897484055045964289521685540446327,
2281  .1028526528935588403412856367054150438684,
2282  .1028526528935588403412856367054150438684,
2283  .1017623897484055045964289521685540446327,
2284  .09959342058679526706278028210356947652987,
2285  .09636873717464425963946862635180986509641,
2286  .09212252223778612871763270708761876719691,
2287  .08689978720108297980238753071512570257675,
2288  .08075589522942021535469493846052973087589,
2289  .07375597473770520626824385002219073415377,
2290  .06597422988218049512812851511596236123744,
2291  .05749315621761906648172168940205612879712,
2292  .04840267283059405290293814042280751781527,
2293  .0387991925696270495968019364463476920332,
2294  .02878470788332336934971917961129204363959,
2295  .01846646831109095914230213191204726909621,
2296  .007968192496166605615465883474673622450481
2297  }
2298  },
2299  {
2300  31,
2301  { // points
2302  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2303  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2304  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2305  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2306  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2307  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2308  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2309  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2310  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2311  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2312  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2313  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2314  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2315  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2316  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2317  {0 ,0.0, 0.0},
2318  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2319  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2320  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2321  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2322  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2323  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2324  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2325  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2326  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2327  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2328  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2329  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2330  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2331  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2332  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2333  },
2334  { // weights
2335  .007470831579248775858696875032212407022151,
2336  .01731862079031058246315799608682114136627,
2337  .02700901918497942180060870809193215614236,
2338  .03643227391238546402439201046780344232715,
2339  .04549370752720110290231585789462967726355,
2340  .05410308242491685371166625908662004272039,
2341  .06217478656102842691034354368669666715873,
2342  .06962858323541036616775612625512571051509,
2343  .07639038659877661642635767490133064492576,
2344  .08239299176158926390382336743196177061577,
2345  .08757674060847787612619806969533309222926,
2346  .09189011389364147821536287160715012549731,
2347  .09529024291231951280720419748759668454132,
2348  .09774333538632872509347401097899670383573,
2349  .09922501122667230787487551442861501401754,
2350  .09972054479342645142753383373434943964325,
2351  .09922501122667230787487551442861501401754,
2352  .09774333538632872509347401097899670383573,
2353  .09529024291231951280720419748759668454132,
2354  .09189011389364147821536287160715012549731,
2355  .08757674060847787612619806969533309222926,
2356  .08239299176158926390382336743196177061577,
2357  .07639038659877661642635767490133064492576,
2358  .06962858323541036616775612625512571051509,
2359  .06217478656102842691034354368669666715873,
2360  .05410308242491685371166625908662004272039,
2361  .04549370752720110290231585789462967726355,
2362  .03643227391238546402439201046780344232715,
2363  .02700901918497942180060870809193215614236,
2364  .01731862079031058246315799608682114136627,
2365  .007470831579248775858696875032212407022151
2366  }
2367  },
2368  {
2369  31,
2370  { // points
2371  {.9970874818194770740556265542231025082514 ,0.0, 0.0},
2372  {.9846859096651524840024651667346847109385 ,0.0, 0.0},
2373  {.9625039250929496617890524041058583018972 ,0.0, 0.0},
2374  {.9307569978966481649569457597292635128134 ,0.0, 0.0},
2375  {.8897600299482710433741920089821592615436 ,0.0, 0.0},
2376  {.8399203201462673400869045359401783560547 ,0.0, 0.0},
2377  {.7817331484166249404063600201946844910954 ,0.0, 0.0},
2378  {.7157767845868532839059708653664859558902 ,0.0, 0.0},
2379  {.6427067229242603461844182032325014539917 ,0.0, 0.0},
2380  {.5632491614071492627209449235951614279486 ,0.0, 0.0},
2381  {.4781937820449024804405940393564857484395 ,0.0, 0.0},
2382  {.3883859016082329430613514612875201019851 ,0.0, 0.0},
2383  {.2947180699817016166179038976717043387529 ,0.0, 0.0},
2384  {.1981211993355706287724129960328339377748 ,0.0, 0.0},
2385  {.099555312152341520325174790118940733839 ,0.0, 0.0},
2386  {0 ,0.0, 0.0},
2387  {-.099555312152341520325174790118940733839 ,0.0, 0.0},
2388  {-.1981211993355706287724129960328339377748 ,0.0, 0.0},
2389  {-.2947180699817016166179038976717043387529 ,0.0, 0.0},
2390  {-.3883859016082329430613514612875201019851 ,0.0, 0.0},
2391  {-.4781937820449024804405940393564857484395 ,0.0, 0.0},
2392  {-.5632491614071492627209449235951614279486 ,0.0, 0.0},
2393  {-.6427067229242603461844182032325014539917 ,0.0, 0.0},
2394  {-.7157767845868532839059708653664859558902 ,0.0, 0.0},
2395  {-.7817331484166249404063600201946844910954 ,0.0, 0.0},
2396  {-.8399203201462673400869045359401783560547 ,0.0, 0.0},
2397  {-.8897600299482710433741920089821592615436 ,0.0, 0.0},
2398  {-.9307569978966481649569457597292635128134 ,0.0, 0.0},
2399  {-.9625039250929496617890524041058583018972 ,0.0, 0.0},
2400  {-.9846859096651524840024651667346847109385 ,0.0, 0.0},
2401  {-.9970874818194770740556265542231025082514 ,0.0, 0.0}
2402  },
2403  { // weights
2404  .007470831579248775858696875032212407022151,
2405  .01731862079031058246315799608682114136627,
2406  .02700901918497942180060870809193215614236,
2407  .03643227391238546402439201046780344232715,
2408  .04549370752720110290231585789462967726355,
2409  .05410308242491685371166625908662004272039,
2410  .06217478656102842691034354368669666715873,
2411  .06962858323541036616775612625512571051509,
2412  .07639038659877661642635767490133064492576,
2413  .08239299176158926390382336743196177061577,
2414  .08757674060847787612619806969533309222926,
2415  .09189011389364147821536287160715012549731,
2416  .09529024291231951280720419748759668454132,
2417  .09774333538632872509347401097899670383573,
2418  .09922501122667230787487551442861501401754,
2419  .09972054479342645142753383373434943964325,
2420  .09922501122667230787487551442861501401754,
2421  .09774333538632872509347401097899670383573,
2422  .09529024291231951280720419748759668454132,
2423  .09189011389364147821536287160715012549731,
2424  .08757674060847787612619806969533309222926,
2425  .08239299176158926390382336743196177061577,
2426  .07639038659877661642635767490133064492576,
2427  .06962858323541036616775612625512571051509,
2428  .06217478656102842691034354368669666715873,
2429  .05410308242491685371166625908662004272039,
2430  .04549370752720110290231585789462967726355,
2431  .03643227391238546402439201046780344232715,
2432  .02700901918497942180060870809193215614236,
2433  .01731862079031058246315799608682114136627,
2434  .007470831579248775858696875032212407022151
2435  }
2436  } // end Gauss
2437 
2438 };
2439 
2440 } // end namespace Intrepid
Intrepid::CubatureDirectLineGauss::getMaxAccuracy
int getMaxAccuracy() const
Returns maximum cubature accuracy.
Definition: Intrepid_CubatureDirectLineGaussDef.hpp:70
Intrepid::CubatureDirectLineGauss::CubatureDirectLineGauss
CubatureDirectLineGauss(const int degree=0)
Constructor.
Definition: Intrepid_CubatureDirectLineGaussDef.hpp:52
Intrepid::CubatureDirectLineGauss::exposeCubatureData
const CubatureTemplate * exposeCubatureData() const
Exposes cubature data.
Definition: Intrepid_CubatureDirectLineGaussDef.hpp:63
Intrepid::CubatureDirectLineGauss
Defines Gauss integration rules on a line.
Definition: Intrepid_CubatureDirectLineGauss.hpp:71
Intrepid::CubatureDirectLineGauss::getName
const char * getName() const
Returns cubature name.
Definition: Intrepid_CubatureDirectLineGaussDef.hpp:77
Intrepid::CubatureTemplate
Template for the cubature rules used by Intrepid. Cubature template consists of cubature points and c...
Definition: Intrepid_Types.hpp:506
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