#! /usr/bin/env python3 # def patterson_rule_test ( ): #*****************************************************************************80 # ## patterson_rule_test() tests patterson_rule(). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2019 # # Author: # # John Burkardt # import numpy as np import platform print ( '' ) print ( 'patterson_rule_test():' ) print ( ' python version: ' + platform.python_version ( ) ) print ( ' numpy version: ' + np.version.version ) print ( ' Test patterson_rule().' ) order = 7 x, w = patterson_set ( order ) a = 0.0; b = np.pi x, w = rescale ( a, b, x, w ) print ( '' ) print ( ' order = ', order ) print ( ' a = ', a ) print ( ' b = ', b ) print ( '' ) print ( ' i wi xi' ) print ( '' ) for i in range ( 0, order ): print ( ' %2d %14.6g %14.6g' % ( i, w[i], x[i] ) ) # # Terminate. # print ( '' ) print ( 'patterson_rule_test():' ) print ( ' Normal end of execution.' ) return def order_check ( order ): #*****************************************************************************80 # ## order_check() checks the value of ORDER. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 17 December 2009 # # Author: # # John Burkardt # # Input: # # integer ORDER, the requested order. # # Output: # # logical CHECK, is TRUE if the requested order is acceptable. # check = ( order == 1 ) or \ ( order == 3 ) or \ ( order == 7 ) or \ ( order == 15 ) or \ ( order == 31 ) or \ ( order == 63 ) or \ ( order == 127 ) or \ ( order == 255 ) or \ ( order == 511 ) return check def patterson_set ( n ): #*****************************************************************************80 # ## patterson_set() sets abscissas and weights for Gauss-Patterson quadrature. # # Discussion: # # The integration interval is [ -1, 1 ]. # # The weight function is w(x) = 1.0. # # The integral to approximate: # # Integral ( -1 <= X <= 1 ) F(X) dX # # The quadrature rule: # # Sum ( 1 <= I <= N ) W(I) * F ( X(I) ) # # The zeroth rule, of order 1, is the standard Gauss-Legendre rule. # # The first rule, of order 3, is the standard Gauss-Legendre rule. # # The second rule, of order 7, includes the abscissas of the previous # rule. # # Each subsequent rule is nested in a similar way. Rules are available # of orders 1, 3, 7, 15, 31, 63, 127, 255 or 511. # # The data for N = 511 was supplied by Dirk Laurie. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 September 2011 # # Author: # # John Burkardt # # Reference: # # Prem Kythe, Michael Schaeferkotter, # Handbook of Computational Methods for Integration, # Chapman and Hall, 2004, # ISBN: 1-58488-428-2, # LC: QA299.3.K98. # # Thomas Patterson, # The Optimal Addition of Points to Quadrature Formulae, # Mathematics of Computation, # Volume 22, Number 104, October 1968, pages 847-856. # # Input: # # integer N, the order of the rule. # ORDER must be 1, 3, 7, 15, 31, 63, 127, 255 or 511. # # Output: # # real X(N), the abscissas of the rule. # # real W(N), the weights of the rule. # The weights are positive, symmetric and should sum to 2. # import numpy as np x = np.zeros ( n ) w = np.zeros ( n ) if ( n == 1 ): x[0] = 0.0 w[0] = 2.0 elif ( n == 3 ): x[0] = -0.77459666924148337704 x[1] = 0.0 x[2] = 0.77459666924148337704 w[0] = 0.555555555555555555556 w[1] = 0.888888888888888888889 w[2] = 0.555555555555555555556 elif ( n == 7 ): x[0] = -0.96049126870802028342 x[1] = -0.77459666924148337704 x[2] = -0.43424374934680255800 x[3] = 0.0 x[4] = 0.43424374934680255800 x[5] = 0.77459666924148337704 x[6] = 0.96049126870802028342 w[0] = 0.104656226026467265194 w[1] = 0.268488089868333440729 w[2] = 0.401397414775962222905 w[3] = 0.450916538658474142345 w[4] = 0.401397414775962222905 w[5] = 0.268488089868333440729 w[6] = 0.104656226026467265194 elif ( n == 15 ): x[ 0] = -0.99383196321275502221 x[ 1] = -0.96049126870802028342 x[ 2] = -0.88845923287225699889 x[ 3] = -0.77459666924148337704 x[ 4] = -0.62110294673722640294 x[ 5] = -0.43424374934680255800 x[ 6] = -0.22338668642896688163 x[ 7] = 0.0 x[ 8] = 0.22338668642896688163 x[ 9] = 0.43424374934680255800 x[10] = 0.62110294673722640294 x[11] = 0.77459666924148337704 x[12] = 0.88845923287225699889 x[13] = 0.96049126870802028342 x[14] = 0.99383196321275502221 w[ 0] = 0.0170017196299402603390 w[ 1] = 0.0516032829970797396969 w[ 2] = 0.0929271953151245376859 w[ 3] = 0.134415255243784220360 w[ 4] = 0.171511909136391380787 w[ 5] = 0.200628529376989021034 w[ 6] = 0.219156858401587496404 w[ 7] = 0.225510499798206687386 w[ 8] = 0.219156858401587496404 w[ 9] = 0.200628529376989021034 w[10] = 0.171511909136391380787 w[11] = 0.134415255243784220360 w[12] = 0.0929271953151245376859 w[13] = 0.0516032829970797396969 w[14] = 0.0170017196299402603390 elif ( n == 31 ): x[ 0] = -0.99909812496766759766 x[ 1] = -0.99383196321275502221 x[ 2] = -0.98153114955374010687 x[ 3] = -0.96049126870802028342 x[ 4] = -0.92965485742974005667 x[ 5] = -0.88845923287225699889 x[ 6] = -0.83672593816886873550 x[ 7] = -0.77459666924148337704 x[ 8] = -0.70249620649152707861 x[ 9] = -0.62110294673722640294 x[10] = -0.53131974364437562397 x[11] = -0.43424374934680255800 x[12] = -0.33113539325797683309 x[13] = -0.22338668642896688163 x[14] = -0.11248894313318662575 x[15] = 0.0 x[16] = 0.11248894313318662575 x[17] = 0.22338668642896688163 x[18] = 0.33113539325797683309 x[19] = 0.43424374934680255800 x[20] = 0.53131974364437562397 x[21] = 0.62110294673722640294 x[22] = 0.70249620649152707861 x[23] = 0.77459666924148337704 x[24] = 0.83672593816886873550 x[25] = 0.88845923287225699889 x[26] = 0.92965485742974005667 x[27] = 0.96049126870802028342 x[28] = 0.98153114955374010687 x[29] = 0.99383196321275502221 x[30] = 0.99909812496766759766 w[ 0] = 0.00254478079156187441540 w[ 1] = 0.00843456573932110624631 w[ 2] = 0.0164460498543878109338 w[ 3] = 0.0258075980961766535646 w[ 4] = 0.0359571033071293220968 w[ 5] = 0.0464628932617579865414 w[ 6] = 0.0569795094941233574122 w[ 7] = 0.0672077542959907035404 w[ 8] = 0.0768796204990035310427 w[ 9] = 0.0857559200499903511542 w[10] = 0.0936271099812644736167 w[11] = 0.100314278611795578771 w[12] = 0.105669893580234809744 w[13] = 0.109578421055924638237 w[14] = 0.111956873020953456880 w[15] = 0.112755256720768691607 w[16] = 0.111956873020953456880 w[17] = 0.109578421055924638237 w[18] = 0.105669893580234809744 w[19] = 0.100314278611795578771 w[20] = 0.0936271099812644736167 w[21] = 0.0857559200499903511542 w[22] = 0.0768796204990035310427 w[23] = 0.0672077542959907035404 w[24] = 0.0569795094941233574122 w[25] = 0.0464628932617579865414 w[26] = 0.0359571033071293220968 w[27] = 0.0258075980961766535646 w[28] = 0.0164460498543878109338 w[29] = 0.00843456573932110624631 w[30] = 0.00254478079156187441540 elif ( n == 63 ): x[ 0] = -0.99987288812035761194 x[ 1] = -0.99909812496766759766 x[ 2] = -0.99720625937222195908 x[ 3] = -0.99383196321275502221 x[ 4] = -0.98868475754742947994 x[ 5] = -0.98153114955374010687 x[ 6] = -0.97218287474858179658 x[ 7] = -0.96049126870802028342 x[ 8] = -0.94634285837340290515 x[ 9] = -0.92965485742974005667 x[10] = -0.91037115695700429250 x[11] = -0.88845923287225699889 x[12] = -0.86390793819369047715 x[13] = -0.83672593816886873550 x[14] = -0.80694053195021761186 x[15] = -0.77459666924148337704 x[16] = -0.73975604435269475868 x[17] = -0.70249620649152707861 x[18] = -0.66290966002478059546 x[19] = -0.62110294673722640294 x[20] = -0.57719571005204581484 x[21] = -0.53131974364437562397 x[22] = -0.48361802694584102756 x[23] = -0.43424374934680255800 x[24] = -0.38335932419873034692 x[25] = -0.33113539325797683309 x[26] = -0.27774982202182431507 x[27] = -0.22338668642896688163 x[28] = -0.16823525155220746498 x[29] = -0.11248894313318662575 x[30] = -0.056344313046592789972 x[31] = 0.0 x[32] = 0.056344313046592789972 x[33] = 0.11248894313318662575 x[34] = 0.16823525155220746498 x[35] = 0.22338668642896688163 x[36] = 0.27774982202182431507 x[37] = 0.33113539325797683309 x[38] = 0.38335932419873034692 x[39] = 0.43424374934680255800 x[40] = 0.48361802694584102756 x[41] = 0.53131974364437562397 x[42] = 0.57719571005204581484 x[43] = 0.62110294673722640294 x[44] = 0.66290966002478059546 x[45] = 0.70249620649152707861 x[46] = 0.73975604435269475868 x[47] = 0.77459666924148337704 x[48] = 0.80694053195021761186 x[49] = 0.83672593816886873550 x[50] = 0.86390793819369047715 x[51] = 0.88845923287225699889 x[52] = 0.91037115695700429250 x[53] = 0.92965485742974005667 x[54] = 0.94634285837340290515 x[55] = 0.96049126870802028342 x[56] = 0.97218287474858179658 x[57] = 0.98153114955374010687 x[58] = 0.98868475754742947994 x[59] = 0.99383196321275502221 x[60] = 0.99720625937222195908 x[61] = 0.99909812496766759766 x[62] = 0.99987288812035761194 w[ 0] = 0.000363221481845530659694 w[ 1] = 0.00126515655623006801137 w[ 2] = 0.00257904979468568827243 w[ 3] = 0.00421763044155885483908 w[ 4] = 0.00611550682211724633968 w[ 5] = 0.00822300795723592966926 w[ 6] = 0.0104982469096213218983 w[ 7] = 0.0129038001003512656260 w[ 8] = 0.0154067504665594978021 w[ 9] = 0.0179785515681282703329 w[10] = 0.0205942339159127111492 w[11] = 0.0232314466399102694433 w[12] = 0.0258696793272147469108 w[13] = 0.0284897547458335486125 w[14] = 0.0310735511116879648799 w[15] = 0.0336038771482077305417 w[16] = 0.0360644327807825726401 w[17] = 0.0384398102494555320386 w[18] = 0.0407155101169443189339 w[19] = 0.0428779600250077344929 w[20] = 0.0449145316536321974143 w[21] = 0.0468135549906280124026 w[22] = 0.0485643304066731987159 w[23] = 0.0501571393058995374137 w[24] = 0.0515832539520484587768 w[25] = 0.0528349467901165198621 w[26] = 0.0539054993352660639269 w[27] = 0.0547892105279628650322 w[28] = 0.0554814043565593639878 w[29] = 0.0559784365104763194076 w[30] = 0.0562776998312543012726 w[31] = 0.0563776283603847173877 w[32] = 0.0562776998312543012726 w[33] = 0.0559784365104763194076 w[34] = 0.0554814043565593639878 w[35] = 0.0547892105279628650322 w[36] = 0.0539054993352660639269 w[37] = 0.0528349467901165198621 w[38] = 0.0515832539520484587768 w[39] = 0.0501571393058995374137 w[40] = 0.0485643304066731987159 w[41] = 0.0468135549906280124026 w[42] = 0.0449145316536321974143 w[43] = 0.0428779600250077344929 w[44] = 0.0407155101169443189339 w[45] = 0.0384398102494555320386 w[46] = 0.0360644327807825726401 w[47] = 0.0336038771482077305417 w[48] = 0.0310735511116879648799 w[49] = 0.0284897547458335486125 w[50] = 0.0258696793272147469108 w[51] = 0.0232314466399102694433 w[52] = 0.0205942339159127111492 w[53] = 0.0179785515681282703329 w[54] = 0.0154067504665594978021 w[55] = 0.0129038001003512656260 w[56] = 0.0104982469096213218983 w[57] = 0.00822300795723592966926 w[58] = 0.00611550682211724633968 w[59] = 0.00421763044155885483908 w[60] = 0.00257904979468568827243 w[61] = 0.00126515655623006801137 w[62] = 0.000363221481845530659694 elif ( n == 127 ): x[ 0] = -0.99998243035489159858 x[ 1] = -0.99987288812035761194 x[ 2] = -0.99959879967191068325 x[ 3] = -0.99909812496766759766 x[ 4] = -0.99831663531840739253 x[ 5] = -0.99720625937222195908 x[ 6] = -0.99572410469840718851 x[ 7] = -0.99383196321275502221 x[ 8] = -0.99149572117810613240 x[ 9] = -0.98868475754742947994 x[ 10] = -0.98537149959852037111 x[ 11] = -0.98153114955374010687 x[ 12] = -0.97714151463970571416 x[ 13] = -0.97218287474858179658 x[ 14] = -0.96663785155841656709 x[ 15] = -0.96049126870802028342 x[ 16] = -0.95373000642576113641 x[ 17] = -0.94634285837340290515 x[ 18] = -0.93832039777959288365 x[ 19] = -0.92965485742974005667 x[ 20] = -0.92034002547001242073 x[ 21] = -0.91037115695700429250 x[ 22] = -0.89974489977694003664 x[ 23] = -0.88845923287225699889 x[ 24] = -0.87651341448470526974 x[ 25] = -0.86390793819369047715 x[ 26] = -0.85064449476835027976 x[ 27] = -0.83672593816886873550 x[ 28] = -0.82215625436498040737 x[ 29] = -0.80694053195021761186 x[ 30] = -0.79108493379984836143 x[ 31] = -0.77459666924148337704 x[ 32] = -0.75748396638051363793 x[ 33] = -0.73975604435269475868 x[ 34] = -0.72142308537009891548 x[ 35] = -0.70249620649152707861 x[ 36] = -0.68298743109107922809 x[ 37] = -0.66290966002478059546 x[ 38] = -0.64227664250975951377 x[ 39] = -0.62110294673722640294 x[ 40] = -0.59940393024224289297 x[ 41] = -0.57719571005204581484 x[ 42] = -0.55449513263193254887 x[ 43] = -0.53131974364437562397 x[ 44] = -0.50768775753371660215 x[ 45] = -0.48361802694584102756 x[ 46] = -0.45913001198983233287 x[ 47] = -0.43424374934680255800 x[ 48] = -0.40897982122988867241 x[ 49] = -0.38335932419873034692 x[ 50] = -0.35740383783153215238 x[ 51] = -0.33113539325797683309 x[ 52] = -0.30457644155671404334 x[ 53] = -0.27774982202182431507 x[ 54] = -0.25067873030348317661 x[ 55] = -0.22338668642896688163 x[ 56] = -0.19589750271110015392 x[ 57] = -0.16823525155220746498 x[ 58] = -0.14042423315256017459 x[ 59] = -0.11248894313318662575 x[ 60] = -0.084454040083710883710 x[ 61] = -0.056344313046592789972 x[ 62] = -0.028184648949745694339 x[ 63] = 0.0 x[ 64] = 0.028184648949745694339 x[ 65] = 0.056344313046592789972 x[ 66] = 0.084454040083710883710 x[ 67] = 0.11248894313318662575 x[ 68] = 0.14042423315256017459 x[ 69] = 0.16823525155220746498 x[ 70] = 0.19589750271110015392 x[ 71] = 0.22338668642896688163 x[ 72] = 0.25067873030348317661 x[ 73] = 0.27774982202182431507 x[ 74] = 0.30457644155671404334 x[ 75] = 0.33113539325797683309 x[ 76] = 0.35740383783153215238 x[ 77] = 0.38335932419873034692 x[ 78] = 0.40897982122988867241 x[ 79] = 0.43424374934680255800 x[ 80] = 0.45913001198983233287 x[ 81] = 0.48361802694584102756 x[ 82] = 0.50768775753371660215 x[ 83] = 0.53131974364437562397 x[ 84] = 0.55449513263193254887 x[ 85] = 0.57719571005204581484 x[ 86] = 0.59940393024224289297 x[ 87] = 0.62110294673722640294 x[ 88] = 0.64227664250975951377 x[ 89] = 0.66290966002478059546 x[ 90] = 0.68298743109107922809 x[ 91] = 0.70249620649152707861 x[ 92] = 0.72142308537009891548 x[ 93] = 0.73975604435269475868 x[ 94] = 0.75748396638051363793 x[ 95] = 0.77459666924148337704 x[ 96] = 0.79108493379984836143 x[ 97] = 0.80694053195021761186 x[ 98] = 0.82215625436498040737 x[ 99] = 0.83672593816886873550 x[100] = 0.85064449476835027976 x[101] = 0.86390793819369047715 x[102] = 0.87651341448470526974 x[103] = 0.88845923287225699889 x[104] = 0.89974489977694003664 x[105] = 0.91037115695700429250 x[106] = 0.92034002547001242073 x[107] = 0.92965485742974005667 x[108] = 0.93832039777959288365 x[109] = 0.94634285837340290515 x[110] = 0.95373000642576113641 x[111] = 0.96049126870802028342 x[112] = 0.96663785155841656709 x[113] = 0.97218287474858179658 x[114] = 0.97714151463970571416 x[115] = 0.98153114955374010687 x[116] = 0.98537149959852037111 x[117] = 0.98868475754742947994 x[118] = 0.99149572117810613240 x[119] = 0.99383196321275502221 x[120] = 0.99572410469840718851 x[121] = 0.99720625937222195908 x[122] = 0.99831663531840739253 x[123] = 0.99909812496766759766 x[124] = 0.99959879967191068325 x[125] = 0.99987288812035761194 x[126] = 0.99998243035489159858 w[ 0] = 0.0000505360952078625176247 w[ 1] = 0.000180739564445388357820 w[ 2] = 0.000377746646326984660274 w[ 3] = 0.000632607319362633544219 w[ 4] = 0.000938369848542381500794 w[ 5] = 0.00128952408261041739210 w[ 6] = 0.00168114286542146990631 w[ 7] = 0.00210881524572663287933 w[ 8] = 0.00256876494379402037313 w[ 9] = 0.00305775341017553113613 w[ 10] = 0.00357289278351729964938 w[ 11] = 0.00411150397865469304717 w[ 12] = 0.00467105037211432174741 w[ 13] = 0.00524912345480885912513 w[ 14] = 0.00584344987583563950756 w[ 15] = 0.00645190005017573692280 w[ 16] = 0.00707248999543355546805 w[ 17] = 0.00770337523327974184817 w[ 18] = 0.00834283875396815770558 w[ 19] = 0.00898927578406413572328 w[ 20] = 0.00964117772970253669530 w[ 21] = 0.0102971169579563555237 w[ 22] = 0.0109557333878379016480 w[ 23] = 0.0116157233199551347270 w[ 24] = 0.0122758305600827700870 w[ 25] = 0.0129348396636073734547 w[ 26] = 0.0135915710097655467896 w[ 27] = 0.0142448773729167743063 w[ 28] = 0.0148936416648151820348 w[ 29] = 0.0155367755558439824399 w[ 30] = 0.0161732187295777199419 w[ 31] = 0.0168019385741038652709 w[ 32] = 0.0174219301594641737472 w[ 33] = 0.0180322163903912863201 w[ 34] = 0.0186318482561387901863 w[ 35] = 0.0192199051247277660193 w[ 36] = 0.0197954950480974994880 w[ 37] = 0.0203577550584721594669 w[ 38] = 0.0209058514458120238522 w[ 39] = 0.0214389800125038672465 w[ 40] = 0.0219563663053178249393 w[ 41] = 0.0224572658268160987071 w[ 42] = 0.0229409642293877487608 w[ 43] = 0.0234067774953140062013 w[ 44] = 0.0238540521060385400804 w[ 45] = 0.0242821652033365993580 w[ 46] = 0.0246905247444876769091 w[ 47] = 0.0250785696529497687068 w[ 48] = 0.0254457699654647658126 w[ 49] = 0.0257916269760242293884 w[ 50] = 0.0261156733767060976805 w[ 51] = 0.0264174733950582599310 w[ 52] = 0.0266966229274503599062 w[ 53] = 0.0269527496676330319634 w[ 54] = 0.0271855132296247918192 w[ 55] = 0.0273946052639814325161 w[ 56] = 0.0275797495664818730349 w[ 57] = 0.0277407021782796819939 w[ 58] = 0.0278772514766137016085 w[ 59] = 0.0279892182552381597038 w[ 60] = 0.0280764557938172466068 w[ 61] = 0.0281388499156271506363 w[ 62] = 0.0281763190330166021307 w[ 63] = 0.0281888141801923586938 w[ 64] = 0.0281763190330166021307 w[ 65] = 0.0281388499156271506363 w[ 66] = 0.0280764557938172466068 w[ 67] = 0.0279892182552381597038 w[ 68] = 0.0278772514766137016085 w[ 69] = 0.0277407021782796819939 w[ 70] = 0.0275797495664818730349 w[ 71] = 0.0273946052639814325161 w[ 72] = 0.0271855132296247918192 w[ 73] = 0.0269527496676330319634 w[ 74] = 0.0266966229274503599062 w[ 75] = 0.0264174733950582599310 w[ 76] = 0.0261156733767060976805 w[ 77] = 0.0257916269760242293884 w[ 78] = 0.0254457699654647658126 w[ 79] = 0.0250785696529497687068 w[ 80] = 0.0246905247444876769091 w[ 81] = 0.0242821652033365993580 w[ 82] = 0.0238540521060385400804 w[ 83] = 0.0234067774953140062013 w[ 84] = 0.0229409642293877487608 w[ 85] = 0.0224572658268160987071 w[ 86] = 0.0219563663053178249393 w[ 87] = 0.0214389800125038672465 w[ 88] = 0.0209058514458120238522 w[ 89] = 0.0203577550584721594669 w[ 90] = 0.0197954950480974994880 w[ 91] = 0.0192199051247277660193 w[ 92] = 0.0186318482561387901863 w[ 93] = 0.0180322163903912863201 w[ 94] = 0.0174219301594641737472 w[ 95] = 0.0168019385741038652709 w[ 96] = 0.0161732187295777199419 w[ 97] = 0.0155367755558439824399 w[ 98] = 0.0148936416648151820348 w[ 99] = 0.0142448773729167743063 w[100] = 0.0135915710097655467896 w[101] = 0.0129348396636073734547 w[102] = 0.0122758305600827700870 w[103] = 0.0116157233199551347270 w[104] = 0.0109557333878379016480 w[105] = 0.0102971169579563555237 w[106] = 0.00964117772970253669530 w[107] = 0.00898927578406413572328 w[108] = 0.00834283875396815770558 w[109] = 0.00770337523327974184817 w[110] = 0.00707248999543355546805 w[111] = 0.00645190005017573692280 w[112] = 0.00584344987583563950756 w[113] = 0.00524912345480885912513 w[114] = 0.00467105037211432174741 w[115] = 0.00411150397865469304717 w[116] = 0.00357289278351729964938 w[117] = 0.00305775341017553113613 w[118] = 0.00256876494379402037313 w[119] = 0.00210881524572663287933 w[120] = 0.00168114286542146990631 w[121] = 0.00128952408261041739210 w[122] = 0.000938369848542381500794 w[123] = 0.000632607319362633544219 w[124] = 0.000377746646326984660274 w[125] = 0.000180739564445388357820 w[126] = 0.0000505360952078625176247 elif ( n == 255 ): x[ 0] = -0.99999759637974846462 x[ 1] = -0.99998243035489159858 x[ 2] = -0.99994399620705437576 x[ 3] = -0.99987288812035761194 x[ 4] = -0.99976049092443204733 x[ 5] = -0.99959879967191068325 x[ 6] = -0.99938033802502358193 x[ 7] = -0.99909812496766759766 x[ 8] = -0.99874561446809511470 x[ 9] = -0.99831663531840739253 x[ 10] = -0.99780535449595727456 x[ 11] = -0.99720625937222195908 x[ 12] = -0.99651414591489027385 x[ 13] = -0.99572410469840718851 x[ 14] = -0.99483150280062100052 x[ 15] = -0.99383196321275502221 x[ 16] = -0.99272134428278861533 x[ 17] = -0.99149572117810613240 x[ 18] = -0.99015137040077015918 x[ 19] = -0.98868475754742947994 x[ 20] = -0.98709252795403406719 x[ 21] = -0.98537149959852037111 x[ 22] = -0.98351865757863272876 x[ 23] = -0.98153114955374010687 x[ 24] = -0.97940628167086268381 x[ 25] = -0.97714151463970571416 x[ 26] = -0.97473445975240266776 x[ 27] = -0.97218287474858179658 x[ 28] = -0.96948465950245923177 x[ 29] = -0.96663785155841656709 x[ 30] = -0.96364062156981213252 x[ 31] = -0.96049126870802028342 x[ 32] = -0.95718821610986096274 x[ 33] = -0.95373000642576113641 x[ 34] = -0.95011529752129487656 x[ 35] = -0.94634285837340290515 x[ 36] = -0.94241156519108305981 x[ 37] = -0.93832039777959288365 x[ 38] = -0.93406843615772578800 x[ 39] = -0.92965485742974005667 x[ 40] = -0.92507893290707565236 x[ 41] = -0.92034002547001242073 x[ 42] = -0.91543758715576504064 x[ 43] = -0.91037115695700429250 x[ 44] = -0.90514035881326159519 x[ 45] = -0.89974489977694003664 x[ 46] = -0.89418456833555902286 x[ 47] = -0.88845923287225699889 x[ 48] = -0.88256884024734190684 x[ 49] = -0.87651341448470526974 x[ 50] = -0.87029305554811390585 x[ 51] = -0.86390793819369047715 x[ 52] = -0.85735831088623215653 x[ 53] = -0.85064449476835027976 x[ 54] = -0.84376688267270860104 x[ 55] = -0.83672593816886873550 x[ 56] = -0.82952219463740140018 x[ 57] = -0.82215625436498040737 x[ 58] = -0.81462878765513741344 x[ 59] = -0.80694053195021761186 x[ 60] = -0.79909229096084140180 x[ 61] = -0.79108493379984836143 x[ 62] = -0.78291939411828301639 x[ 63] = -0.77459666924148337704 x[ 64] = -0.76611781930376009072 x[ 65] = -0.75748396638051363793 x[ 66] = -0.74869629361693660282 x[ 67] = -0.73975604435269475868 x[ 68] = -0.73066452124218126133 x[ 69] = -0.72142308537009891548 x[ 70] = -0.71203315536225203459 x[ 71] = -0.70249620649152707861 x[ 72] = -0.69281376977911470289 x[ 73] = -0.68298743109107922809 x[ 74] = -0.67301883023041847920 x[ 75] = -0.66290966002478059546 x[ 76] = -0.65266166541001749610 x[ 77] = -0.64227664250975951377 x[ 78] = -0.63175643771119423041 x[ 79] = -0.62110294673722640294 x[ 80] = -0.61031811371518640016 x[ 81] = -0.59940393024224289297 x[ 82] = -0.58836243444766254143 x[ 83] = -0.57719571005204581484 x[ 84] = -0.56590588542365442262 x[ 85] = -0.55449513263193254887 x[ 86] = -0.54296566649831149049 x[ 87] = -0.53131974364437562397 x[ 88] = -0.51955966153745702199 x[ 89] = -0.50768775753371660215 x[ 90] = -0.49570640791876146017 x[ 91] = -0.48361802694584102756 x[ 92] = -0.47142506587165887693 x[ 93] = -0.45913001198983233287 x[ 94] = -0.44673538766202847374 x[ 95] = -0.43424374934680255800 x[ 96] = -0.42165768662616330006 x[ 97] = -0.40897982122988867241 x[ 98] = -0.39621280605761593918 x[ 99] = -0.38335932419873034692 x[100] = -0.37042208795007823014 x[101] = -0.35740383783153215238 x[102] = -0.34430734159943802278 x[103] = -0.33113539325797683309 x[104] = -0.31789081206847668318 x[105] = -0.30457644155671404334 x[106] = -0.29119514851824668196 x[107] = -0.27774982202182431507 x[108] = -0.26424337241092676194 x[109] = -0.25067873030348317661 x[110] = -0.23705884558982972721 x[111] = -0.22338668642896688163 x[112] = -0.20966523824318119477 x[113] = -0.19589750271110015392 x[114] = -0.18208649675925219825 x[115] = -0.16823525155220746498 x[116] = -0.15434681148137810869 x[117] = -0.14042423315256017459 x[118] = -0.12647058437230196685 x[119] = -0.11248894313318662575 x[120] = -0.098482396598119202090 x[121] = -0.084454040083710883710 x[122] = -0.070406976042855179063 x[123] = -0.056344313046592789972 x[124] = -0.042269164765363603212 x[125] = -0.028184648949745694339 x[126] = -0.014093886410782462614 x[127] = 0.0 x[128] = 0.014093886410782462614 x[129] = 0.028184648949745694339 x[130] = 0.042269164765363603212 x[131] = 0.056344313046592789972 x[132] = 0.070406976042855179063 x[133] = 0.084454040083710883710 x[134] = 0.098482396598119202090 x[135] = 0.11248894313318662575 x[136] = 0.12647058437230196685 x[137] = 0.14042423315256017459 x[138] = 0.15434681148137810869 x[139] = 0.16823525155220746498 x[140] = 0.18208649675925219825 x[141] = 0.19589750271110015392 x[142] = 0.20966523824318119477 x[143] = 0.22338668642896688163 x[144] = 0.23705884558982972721 x[145] = 0.25067873030348317661 x[146] = 0.26424337241092676194 x[147] = 0.27774982202182431507 x[148] = 0.29119514851824668196 x[149] = 0.30457644155671404334 x[150] = 0.31789081206847668318 x[151] = 0.33113539325797683309 x[152] = 0.34430734159943802278 x[153] = 0.35740383783153215238 x[154] = 0.37042208795007823014 x[155] = 0.38335932419873034692 x[156] = 0.39621280605761593918 x[157] = 0.40897982122988867241 x[158] = 0.42165768662616330006 x[159] = 0.43424374934680255800 x[160] = 0.44673538766202847374 x[161] = 0.45913001198983233287 x[162] = 0.47142506587165887693 x[163] = 0.48361802694584102756 x[164] = 0.49570640791876146017 x[165] = 0.50768775753371660215 x[166] = 0.51955966153745702199 x[167] = 0.53131974364437562397 x[168] = 0.54296566649831149049 x[169] = 0.55449513263193254887 x[170] = 0.56590588542365442262 x[171] = 0.57719571005204581484 x[172] = 0.58836243444766254143 x[173] = 0.59940393024224289297 x[174] = 0.61031811371518640016 x[175] = 0.62110294673722640294 x[176] = 0.63175643771119423041 x[177] = 0.64227664250975951377 x[178] = 0.65266166541001749610 x[179] = 0.66290966002478059546 x[180] = 0.67301883023041847920 x[181] = 0.68298743109107922809 x[182] = 0.69281376977911470289 x[183] = 0.70249620649152707861 x[184] = 0.71203315536225203459 x[185] = 0.72142308537009891548 x[186] = 0.73066452124218126133 x[187] = 0.73975604435269475868 x[188] = 0.74869629361693660282 x[189] = 0.75748396638051363793 x[190] = 0.76611781930376009072 x[191] = 0.77459666924148337704 x[192] = 0.78291939411828301639 x[193] = 0.79108493379984836143 x[194] = 0.79909229096084140180 x[195] = 0.80694053195021761186 x[196] = 0.81462878765513741344 x[197] = 0.82215625436498040737 x[198] = 0.82952219463740140018 x[199] = 0.83672593816886873550 x[200] = 0.84376688267270860104 x[201] = 0.85064449476835027976 x[202] = 0.85735831088623215653 x[203] = 0.86390793819369047715 x[204] = 0.87029305554811390585 x[205] = 0.87651341448470526974 x[206] = 0.88256884024734190684 x[207] = 0.88845923287225699889 x[208] = 0.89418456833555902286 x[209] = 0.89974489977694003664 x[210] = 0.90514035881326159519 x[211] = 0.91037115695700429250 x[212] = 0.91543758715576504064 x[213] = 0.92034002547001242073 x[214] = 0.92507893290707565236 x[215] = 0.92965485742974005667 x[216] = 0.93406843615772578800 x[217] = 0.93832039777959288365 x[218] = 0.94241156519108305981 x[219] = 0.94634285837340290515 x[220] = 0.95011529752129487656 x[221] = 0.95373000642576113641 x[222] = 0.95718821610986096274 x[223] = 0.96049126870802028342 x[224] = 0.96364062156981213252 x[225] = 0.96663785155841656709 x[226] = 0.96948465950245923177 x[227] = 0.97218287474858179658 x[228] = 0.97473445975240266776 x[229] = 0.97714151463970571416 x[230] = 0.97940628167086268381 x[231] = 0.98153114955374010687 x[232] = 0.98351865757863272876 x[233] = 0.98537149959852037111 x[234] = 0.98709252795403406719 x[235] = 0.98868475754742947994 x[236] = 0.99015137040077015918 x[237] = 0.99149572117810613240 x[238] = 0.99272134428278861533 x[239] = 0.99383196321275502221 x[240] = 0.99483150280062100052 x[241] = 0.99572410469840718851 x[242] = 0.99651414591489027385 x[243] = 0.99720625937222195908 x[244] = 0.99780535449595727456 x[245] = 0.99831663531840739253 x[246] = 0.99874561446809511470 x[247] = 0.99909812496766759766 x[248] = 0.99938033802502358193 x[249] = 0.99959879967191068325 x[250] = 0.99976049092443204733 x[251] = 0.99987288812035761194 x[252] = 0.99994399620705437576 x[253] = 0.99998243035489159858 x[254] = 0.99999759637974846462 w[ 0] = 0.69379364324108267170E-05 w[ 1] = 0.25157870384280661489E-04 w[ 2] = 0.53275293669780613125E-04 w[ 3] = 0.90372734658751149261E-04 w[ 4] = 0.13575491094922871973E-03 w[ 5] = 0.18887326450650491366E-03 w[ 6] = 0.24921240048299729402E-03 w[ 7] = 0.31630366082226447689E-03 w[ 8] = 0.38974528447328229322E-03 w[ 9] = 0.46918492424785040975E-03 w[ 10] = 0.55429531493037471492E-03 w[ 11] = 0.64476204130572477933E-03 w[ 12] = 0.74028280424450333046E-03 w[ 13] = 0.84057143271072246365E-03 w[ 14] = 0.94536151685852538246E-03 w[ 15] = 0.10544076228633167722E-02 w[ 16] = 0.11674841174299594077E-02 w[ 17] = 0.12843824718970101768E-02 w[ 18] = 0.14049079956551446427E-02 w[ 19] = 0.15288767050877655684E-02 w[ 20] = 0.16561127281544526052E-02 w[ 21] = 0.17864463917586498247E-02 w[ 22] = 0.19197129710138724125E-02 w[ 23] = 0.20557519893273465236E-02 w[ 24] = 0.21944069253638388388E-02 w[ 25] = 0.23355251860571608737E-02 w[ 26] = 0.24789582266575679307E-02 w[ 27] = 0.26245617274044295626E-02 w[ 28] = 0.27721957645934509940E-02 w[ 29] = 0.29217249379178197538E-02 w[ 30] = 0.30730184347025783234E-02 w[ 31] = 0.32259500250878684614E-02 w[ 32] = 0.33803979910869203823E-02 w[ 33] = 0.35362449977167777340E-02 w[ 34] = 0.36933779170256508183E-02 w[ 35] = 0.38516876166398709241E-02 w[ 36] = 0.40110687240750233989E-02 w[ 37] = 0.41714193769840788528E-02 w[ 38] = 0.43326409680929828545E-02 w[ 39] = 0.44946378920320678616E-02 w[ 40] = 0.46573172997568547773E-02 w[ 41] = 0.48205888648512683476E-02 w[ 42] = 0.49843645647655386012E-02 w[ 43] = 0.51485584789781777618E-02 w[ 44] = 0.53130866051870565663E-02 w[ 45] = 0.54778666939189508240E-02 w[ 46] = 0.56428181013844441585E-02 w[ 47] = 0.58078616599775673635E-02 w[ 48] = 0.59729195655081658049E-02 w[ 49] = 0.61379152800413850435E-02 w[ 50] = 0.63027734490857587172E-02 w[ 51] = 0.64674198318036867274E-02 w[ 52] = 0.66317812429018878941E-02 w[ 53] = 0.67957855048827733948E-02 w[ 54] = 0.69593614093904229394E-02 w[ 55] = 0.71224386864583871532E-02 w[ 56] = 0.72849479805538070639E-02 w[ 57] = 0.74468208324075910174E-02 w[ 58] = 0.76079896657190565832E-02 w[ 59] = 0.77683877779219912200E-02 w[ 60] = 0.79279493342948491103E-02 w[ 61] = 0.80866093647888599710E-02 w[ 62] = 0.82443037630328680306E-02 w[ 63] = 0.84009692870519326354E-02 w[ 64] = 0.85565435613076896192E-02 w[ 65] = 0.87109650797320868736E-02 w[ 66] = 0.88641732094824942641E-02 w[ 67] = 0.90161081951956431600E-02 w[ 68] = 0.91667111635607884067E-02 w[ 69] = 0.93159241280693950932E-02 w[ 70] = 0.94636899938300652943E-02 w[ 71] = 0.96099525623638830097E-02 w[ 72] = 0.97546565363174114611E-02 w[ 73] = 0.98977475240487497440E-02 w[ 74] = 0.10039172044056840798E-01 w[ 75] = 0.10178877529236079733E-01 w[ 76] = 0.10316812330947621682E-01 w[ 77] = 0.10452925722906011926E-01 w[ 78] = 0.10587167904885197931E-01 w[ 79] = 0.10719490006251933623E-01 w[ 80] = 0.10849844089337314099E-01 w[ 81] = 0.10978183152658912470E-01 w[ 82] = 0.11104461134006926537E-01 w[ 83] = 0.11228632913408049354E-01 w[ 84] = 0.11350654315980596602E-01 w[ 85] = 0.11470482114693874380E-01 w[ 86] = 0.11588074033043952568E-01 w[ 87] = 0.11703388747657003101E-01 w[ 88] = 0.11816385890830235763E-01 w[ 89] = 0.11927026053019270040E-01 w[ 90] = 0.12035270785279562630E-01 w[ 91] = 0.12141082601668299679E-01 w[ 92] = 0.12244424981611985899E-01 w[ 93] = 0.12345262372243838455E-01 w[ 94] = 0.12443560190714035263E-01 w[ 95] = 0.12539284826474884353E-01 w[ 96] = 0.12632403643542078765E-01 w[ 97] = 0.12722884982732382906E-01 w[ 98] = 0.12810698163877361967E-01 w[ 99] = 0.12895813488012114694E-01 w[100] = 0.12978202239537399286E-01 w[101] = 0.13057836688353048840E-01 w[102] = 0.13134690091960152836E-01 w[103] = 0.13208736697529129966E-01 w[104] = 0.13279951743930530650E-01 w[105] = 0.13348311463725179953E-01 w[106] = 0.13413793085110098513E-01 w[107] = 0.13476374833816515982E-01 w[108] = 0.13536035934956213614E-01 w[109] = 0.13592756614812395910E-01 w[110] = 0.13646518102571291428E-01 w[111] = 0.13697302631990716258E-01 w[112] = 0.13745093443001896632E-01 w[113] = 0.13789874783240936517E-01 w[114] = 0.13831631909506428676E-01 w[115] = 0.13870351089139840997E-01 w[116] = 0.13906019601325461264E-01 w[117] = 0.13938625738306850804E-01 w[118] = 0.13968158806516938516E-01 w[119] = 0.13994609127619079852E-01 w[120] = 0.14017968039456608810E-01 w[121] = 0.14038227896908623303E-01 w[122] = 0.14055382072649964277E-01 w[123] = 0.14069424957813575318E-01 w[124] = 0.14080351962553661325E-01 w[125] = 0.14088159516508301065E-01 w[126] = 0.14092845069160408355E-01 w[127] = 0.14094407090096179347E-01 w[128] = 0.14092845069160408355E-01 w[129] = 0.14088159516508301065E-01 w[130] = 0.14080351962553661325E-01 w[131] = 0.14069424957813575318E-01 w[132] = 0.14055382072649964277E-01 w[133] = 0.14038227896908623303E-01 w[134] = 0.14017968039456608810E-01 w[135] = 0.13994609127619079852E-01 w[136] = 0.13968158806516938516E-01 w[137] = 0.13938625738306850804E-01 w[138] = 0.13906019601325461264E-01 w[139] = 0.13870351089139840997E-01 w[140] = 0.13831631909506428676E-01 w[141] = 0.13789874783240936517E-01 w[142] = 0.13745093443001896632E-01 w[143] = 0.13697302631990716258E-01 w[144] = 0.13646518102571291428E-01 w[145] = 0.13592756614812395910E-01 w[146] = 0.13536035934956213614E-01 w[147] = 0.13476374833816515982E-01 w[148] = 0.13413793085110098513E-01 w[149] = 0.13348311463725179953E-01 w[150] = 0.13279951743930530650E-01 w[151] = 0.13208736697529129966E-01 w[152] = 0.13134690091960152836E-01 w[153] = 0.13057836688353048840E-01 w[154] = 0.12978202239537399286E-01 w[155] = 0.12895813488012114694E-01 w[156] = 0.12810698163877361967E-01 w[157] = 0.12722884982732382906E-01 w[158] = 0.12632403643542078765E-01 w[159] = 0.12539284826474884353E-01 w[160] = 0.12443560190714035263E-01 w[161] = 0.12345262372243838455E-01 w[162] = 0.12244424981611985899E-01 w[163] = 0.12141082601668299679E-01 w[164] = 0.12035270785279562630E-01 w[165] = 0.11927026053019270040E-01 w[166] = 0.11816385890830235763E-01 w[167] = 0.11703388747657003101E-01 w[168] = 0.11588074033043952568E-01 w[169] = 0.11470482114693874380E-01 w[170] = 0.11350654315980596602E-01 w[171] = 0.11228632913408049354E-01 w[172] = 0.11104461134006926537E-01 w[173] = 0.10978183152658912470E-01 w[174] = 0.10849844089337314099E-01 w[175] = 0.10719490006251933623E-01 w[176] = 0.10587167904885197931E-01 w[177] = 0.10452925722906011926E-01 w[178] = 0.10316812330947621682E-01 w[179] = 0.10178877529236079733E-01 w[180] = 0.10039172044056840798E-01 w[181] = 0.98977475240487497440E-02 w[182] = 0.97546565363174114611E-02 w[183] = 0.96099525623638830097E-02 w[184] = 0.94636899938300652943E-02 w[185] = 0.93159241280693950932E-02 w[186] = 0.91667111635607884067E-02 w[187] = 0.90161081951956431600E-02 w[188] = 0.88641732094824942641E-02 w[189] = 0.87109650797320868736E-02 w[190] = 0.85565435613076896192E-02 w[191] = 0.84009692870519326354E-02 w[192] = 0.82443037630328680306E-02 w[193] = 0.80866093647888599710E-02 w[194] = 0.79279493342948491103E-02 w[195] = 0.77683877779219912200E-02 w[196] = 0.76079896657190565832E-02 w[197] = 0.74468208324075910174E-02 w[198] = 0.72849479805538070639E-02 w[199] = 0.71224386864583871532E-02 w[200] = 0.69593614093904229394E-02 w[201] = 0.67957855048827733948E-02 w[202] = 0.66317812429018878941E-02 w[203] = 0.64674198318036867274E-02 w[204] = 0.63027734490857587172E-02 w[205] = 0.61379152800413850435E-02 w[206] = 0.59729195655081658049E-02 w[207] = 0.58078616599775673635E-02 w[208] = 0.56428181013844441585E-02 w[209] = 0.54778666939189508240E-02 w[210] = 0.53130866051870565663E-02 w[211] = 0.51485584789781777618E-02 w[212] = 0.49843645647655386012E-02 w[213] = 0.48205888648512683476E-02 w[214] = 0.46573172997568547773E-02 w[215] = 0.44946378920320678616E-02 w[216] = 0.43326409680929828545E-02 w[217] = 0.41714193769840788528E-02 w[218] = 0.40110687240750233989E-02 w[219] = 0.38516876166398709241E-02 w[220] = 0.36933779170256508183E-02 w[221] = 0.35362449977167777340E-02 w[222] = 0.33803979910869203823E-02 w[223] = 0.32259500250878684614E-02 w[224] = 0.30730184347025783234E-02 w[225] = 0.29217249379178197538E-02 w[226] = 0.27721957645934509940E-02 w[227] = 0.26245617274044295626E-02 w[228] = 0.24789582266575679307E-02 w[229] = 0.23355251860571608737E-02 w[230] = 0.21944069253638388388E-02 w[231] = 0.20557519893273465236E-02 w[232] = 0.19197129710138724125E-02 w[233] = 0.17864463917586498247E-02 w[234] = 0.16561127281544526052E-02 w[235] = 0.15288767050877655684E-02 w[236] = 0.14049079956551446427E-02 w[237] = 0.12843824718970101768E-02 w[238] = 0.11674841174299594077E-02 w[239] = 0.10544076228633167722E-02 w[240] = 0.94536151685852538246E-03 w[241] = 0.84057143271072246365E-03 w[242] = 0.74028280424450333046E-03 w[243] = 0.64476204130572477933E-03 w[244] = 0.55429531493037471492E-03 w[245] = 0.46918492424785040975E-03 w[246] = 0.38974528447328229322E-03 w[247] = 0.31630366082226447689E-03 w[248] = 0.24921240048299729402E-03 w[249] = 0.18887326450650491366E-03 w[250] = 0.13575491094922871973E-03 w[251] = 0.90372734658751149261E-04 w[252] = 0.53275293669780613125E-04 w[253] = 0.25157870384280661489E-04 w[254] = 0.69379364324108267170E-05 elif ( n == 511 ): x[ 0] = -0.999999672956734384381 x[ 1] = -0.999997596379748464620 x[ 2] = -0.999992298136257588028 x[ 3] = -0.999982430354891598580 x[ 4] = -0.999966730098486276883 x[ 5] = -0.999943996207054375764 x[ 6] = -0.999913081144678282800 x[ 7] = -0.999872888120357611938 x[ 8] = -0.999822363679787739196 x[ 9] = -0.999760490924432047330 x[ 10] = -0.999686286448317731776 x[ 11] = -0.999598799671910683252 x[ 12] = -0.999497112467187190535 x[ 13] = -0.999380338025023581928 x[ 14] = -0.999247618943342473599 x[ 15] = -0.999098124967667597662 x[ 16] = -0.998931050830810562236 x[ 17] = -0.998745614468095114704 x[ 18] = -0.998541055697167906027 x[ 19] = -0.998316635318407392531 x[ 20] = -0.998071634524930323302 x[ 21] = -0.997805354495957274562 x[ 22] = -0.997517116063472399965 x[ 23] = -0.997206259372221959076 x[ 24] = -0.996872143485260161299 x[ 25] = -0.996514145914890273849 x[ 26] = -0.996131662079315037786 x[ 27] = -0.995724104698407188509 x[ 28] = -0.995290903148810302261 x[ 29] = -0.994831502800621000519 x[ 30] = -0.994345364356723405931 x[ 31] = -0.993831963212755022209 x[ 32] = -0.993290788851684966211 x[ 33] = -0.992721344282788615328 x[ 34] = -0.992123145530863117683 x[ 35] = -0.991495721178106132399 x[ 36] = -0.990838611958294243677 x[ 37] = -0.990151370400770159181 x[ 38] = -0.989433560520240838716 x[ 39] = -0.988684757547429479939 x[ 40] = -0.987904547695124280467 x[ 41] = -0.987092527954034067190 x[ 42] = -0.986248305913007552681 x[ 43] = -0.985371499598520371114 x[ 44] = -0.984461737328814534596 x[ 45] = -0.983518657578632728762 x[ 46] = -0.982541908851080604251 x[ 47] = -0.981531149553740106867 x[ 48] = -0.980486047876721339416 x[ 49] = -0.979406281670862683806 x[ 50] = -0.978291538324758539526 x[ 51] = -0.977141514639705714156 x[ 52] = -0.975955916702011753129 x[ 53] = -0.974734459752402667761 x[ 54] = -0.973476868052506926773 x[ 55] = -0.972182874748581796578 x[ 56] = -0.970852221732792443256 x[ 57] = -0.969484659502459231771 x[ 58] = -0.968079947017759947964 x[ 59] = -0.966637851558416567092 x[ 60] = -0.965158148579915665979 x[ 61] = -0.963640621569812132521 x[ 62] = -0.962085061904651475741 x[ 63] = -0.960491268708020283423 x[ 64] = -0.958859048710200221356 x[ 65] = -0.957188216109860962736 x[ 66] = -0.955478592438183697574 x[ 67] = -0.953730006425761136415 x[ 68] = -0.951942293872573589498 x[ 69] = -0.950115297521294876558 x[ 70] = -0.948248866934137357063 x[ 71] = -0.946342858373402905148 x[ 72] = -0.944397134685866648591 x[ 73] = -0.942411565191083059813 x[ 74] = -0.940386025573669721370 x[ 75] = -0.938320397779592883655 x[ 76] = -0.936214569916450806625 x[ 77] = -0.934068436157725787999 x[ 78] = -0.931881896650953639345 x[ 79] = -0.929654857429740056670 x[ 80] = -0.927387230329536696843 x[ 81] = -0.925078932907075652364 x[ 82] = -0.922729888363349241523 x[ 83] = -0.920340025470012420730 x[ 84] = -0.917909278499077501636 x[ 85] = -0.915437587155765040644 x[ 86] = -0.912924896514370590080 x[ 87] = -0.910371156957004292498 x[ 88] = -0.907776324115058903624 x[ 89] = -0.905140358813261595189 x[ 90] = -0.902463227016165675048 x[ 91] = -0.899744899776940036639 x[ 92] = -0.896985353188316590376 x[ 93] = -0.894184568335559022859 x[ 94] = -0.891342531251319871666 x[ 95] = -0.888459232872256998890 x[ 96] = -0.885534668997285008926 x[ 97] = -0.882568840247341906842 x[ 98] = -0.879561752026556262568 x[ 99] = -0.876513414484705269742 x[100] = -0.873423842480859310192 x[101] = -0.870293055548113905851 x[102] = -0.867121077859315215614 x[103] = -0.863907938193690477146 x[104] = -0.860653669904299969802 x[105] = -0.857358310886232156525 x[106] = -0.854021903545468625813 x[107] = -0.850644494768350279758 x[108] = -0.847226135891580884381 x[109] = -0.843766882672708601038 x[110] = -0.840266795261030442350 x[111] = -0.836725938168868735503 x[112] = -0.833144380243172624728 x[113] = -0.829522194637401400178 x[114] = -0.825859458783650001088 x[115] = -0.822156254364980407373 x[116] = -0.818412667287925807395 x[117] = -0.814628787655137413436 x[118] = -0.810804709738146594361 x[119] = -0.806940531950217611856 x[120] = -0.803036356819268687782 x[121] = -0.799092290960841401800 x[122] = -0.795108445051100526780 x[123] = -0.791084933799848361435 x[124] = -0.787021875923539422170 x[125] = -0.782919394118283016385 x[126] = -0.778777615032822744702 x[127] = -0.774596669241483377036 x[128] = -0.770376691217076824278 x[129] = -0.766117819303760090717 x[130] = -0.761820195689839149173 x[131] = -0.757483966380513637926 x[132] = -0.753109281170558142523 x[133] = -0.748696293616936602823 x[134] = -0.744245161011347082309 x[135] = -0.739756044352694758677 x[136] = -0.735229108319491547663 x[137] = -0.730664521242181261329 x[138] = -0.726062455075389632685 x[139] = -0.721423085370098915485 x[140] = -0.716746591245747095767 x[141] = -0.712033155362252034587 x[142] = -0.707282963891961103412 x[143] = -0.702496206491527078610 x[144] = -0.697673076273711232906 x[145] = -0.692813769779114702895 x[146] = -0.687918486947839325756 x[147] = -0.682987431091079228087 x[148] = -0.678020808862644517838 x[149] = -0.673018830230418479199 x[150] = -0.667981708447749702165 x[151] = -0.662909660024780595461 x[152] = -0.657802904699713735422 x[153] = -0.652661665410017496101 x[154] = -0.647486168263572388782 x[155] = -0.642276642509759513774 x[156] = -0.637033320510492495071 x[157] = -0.631756437711194230414 x[158] = -0.626446232611719746542 x[159] = -0.621102946737226402941 x[160] = -0.615726824608992638014 x[161] = -0.610318113715186400156 x[162] = -0.604877064481584353319 x[163] = -0.599403930242242892974 x[164] = -0.593898967210121954393 x[165] = -0.588362434447662541434 x[166] = -0.582794593837318850840 x[167] = -0.577195710052045814844 x[168] = -0.571566050525742833992 x[169] = -0.565905885423654422623 x[170] = -0.560215487612728441818 x[171] = -0.554495132631932548866 x[172] = -0.548745098662529448608 x[173] = -0.542965666498311490492 x[174] = -0.537157119515795115982 x[175] = -0.531319743644375623972 x[176] = -0.525453827336442687395 x[177] = -0.519559661537457021993 x[178] = -0.513637539655988578507 x[179] = -0.507687757533716602155 x[180] = -0.501710613415391878251 x[181] = -0.495706407918761460170 x[182] = -0.489675444004456155436 x[183] = -0.483618026945841027562 x[184] = -0.477534464298829155284 x[185] = -0.471425065871658876934 x[186] = -0.465290143694634735858 x[187] = -0.459130011989832332874 x[188] = -0.452944987140767283784 x[189] = -0.446735387662028473742 x[190] = -0.440501534168875795783 x[191] = -0.434243749346802558002 x[192] = -0.427962357921062742583 x[193] = -0.421657686626163300056 x[194] = -0.415330064175321663764 x[195] = -0.408979821229888672409 x[196] = -0.402607290368737092671 x[197] = -0.396212806057615939183 x[198] = -0.389796704618470795479 x[199] = -0.383359324198730346916 x[200] = -0.376901004740559344802 x[201] = -0.370422087950078230138 x[202] = -0.363922917266549655269 x[203] = -0.357403837831532152376 x[204] = -0.350865196458001209011 x[205] = -0.344307341599438022777 x[206] = -0.337730623318886219621 x[207] = -0.331135393257976833093 x[208] = -0.324522004605921855207 x[209] = -0.317890812068476683182 x[210] = -0.311242171836871800300 x[211] = -0.304576441556714043335 x[212] = -0.297893980296857823437 x[213] = -0.291195148518246681964 x[214] = -0.284480308042725577496 x[215] = -0.277749822021824315065 x[216] = -0.271004054905512543536 x[217] = -0.264243372410926761945 x[218] = -0.257468141491069790481 x[219] = -0.250678730303483176613 x[220] = -0.243875508178893021593 x[221] = -0.237058845589829727213 x[222] = -0.230229114119222177156 x[223] = -0.223386686428966881628 x[224] = -0.216531936228472628081 x[225] = -0.209665238243181194766 x[226] = -0.202786968183064697557 x[227] = -0.195897502711100153915 x[228] = -0.188997219411721861059 x[229] = -0.182086496759252198246 x[230] = -0.175165714086311475707 x[231] = -0.168235251552207464982 x[232] = -0.161295490111305257361 x[233] = -0.154346811481378108692 x[234] = -0.147389598111939940054 x[235] = -0.140424233152560174594 x[236] = -0.133451100421161601344 x[237] = -0.126470584372301966851 x[238] = -0.119483070065440005133 x[239] = -0.112488943133186625746 x[240] = -0.105488589749541988533 x[241] = -0.984823965981192020903E-01 x[242] = -0.914707508403553909095E-01 x[243] = -0.844540400837108837102E-01 x[244] = -0.774326523498572825675E-01 x[245] = -0.704069760428551790633E-01 x[246] = -0.633773999173222898797E-01 x[247] = -0.563443130465927899720E-01 x[248] = -0.493081047908686267156E-01 x[249] = -0.422691647653636032124E-01 x[250] = -0.352278828084410232603E-01 x[251] = -0.281846489497456943394E-01 x[252] = -0.211398533783310883350E-01 x[253] = -0.140938864107824626142E-01 x[254] = -0.704713845933674648514E-02 x[255] = +0.000000000000000000000 x[256] = +0.704713845933674648514E-02 x[257] = +0.140938864107824626142E-01 x[258] = +0.211398533783310883350E-01 x[259] = +0.281846489497456943394E-01 x[260] = +0.352278828084410232603E-01 x[261] = +0.422691647653636032124E-01 x[262] = +0.493081047908686267156E-01 x[263] = +0.563443130465927899720E-01 x[264] = +0.633773999173222898797E-01 x[265] = +0.704069760428551790633E-01 x[266] = +0.774326523498572825675E-01 x[267] = +0.844540400837108837102E-01 x[268] = +0.914707508403553909095E-01 x[269] = +0.984823965981192020903E-01 x[270] = +0.105488589749541988533 x[271] = +0.112488943133186625746 x[272] = +0.119483070065440005133 x[273] = +0.126470584372301966851 x[274] = +0.133451100421161601344 x[275] = +0.140424233152560174594 x[276] = +0.147389598111939940054 x[277] = +0.154346811481378108692 x[278] = +0.161295490111305257361 x[279] = +0.168235251552207464982 x[280] = +0.175165714086311475707 x[281] = +0.182086496759252198246 x[282] = +0.188997219411721861059 x[283] = +0.195897502711100153915 x[284] = +0.202786968183064697557 x[285] = +0.209665238243181194766 x[286] = +0.216531936228472628081 x[287] = +0.223386686428966881628 x[288] = +0.230229114119222177156 x[289] = +0.237058845589829727213 x[290] = +0.243875508178893021593 x[291] = +0.250678730303483176613 x[292] = +0.257468141491069790481 x[293] = +0.264243372410926761945 x[294] = +0.271004054905512543536 x[295] = +0.277749822021824315065 x[296] = +0.284480308042725577496 x[297] = +0.291195148518246681964 x[298] = +0.297893980296857823437 x[299] = +0.304576441556714043335 x[300] = +0.311242171836871800300 x[301] = +0.317890812068476683182 x[302] = +0.324522004605921855207 x[303] = +0.331135393257976833093 x[304] = +0.337730623318886219621 x[305] = +0.344307341599438022777 x[306] = +0.350865196458001209011 x[307] = +0.357403837831532152376 x[308] = +0.363922917266549655269 x[309] = +0.370422087950078230138 x[310] = +0.376901004740559344802 x[311] = +0.383359324198730346916 x[312] = +0.389796704618470795479 x[313] = +0.396212806057615939183 x[314] = +0.402607290368737092671 x[315] = +0.408979821229888672409 x[316] = +0.415330064175321663764 x[317] = +0.421657686626163300056 x[318] = +0.427962357921062742583 x[319] = +0.434243749346802558002 x[320] = +0.440501534168875795783 x[321] = +0.446735387662028473742 x[322] = +0.452944987140767283784 x[323] = +0.459130011989832332874 x[324] = +0.465290143694634735858 x[325] = +0.471425065871658876934 x[326] = +0.477534464298829155284 x[327] = +0.483618026945841027562 x[328] = +0.489675444004456155436 x[329] = +0.495706407918761460170 x[330] = +0.501710613415391878251 x[331] = +0.507687757533716602155 x[332] = +0.513637539655988578507 x[333] = +0.519559661537457021993 x[334] = +0.525453827336442687395 x[335] = +0.531319743644375623972 x[336] = +0.537157119515795115982 x[337] = +0.542965666498311490492 x[338] = +0.548745098662529448608 x[339] = +0.554495132631932548866 x[340] = +0.560215487612728441818 x[341] = +0.565905885423654422623 x[342] = +0.571566050525742833992 x[343] = +0.577195710052045814844 x[344] = +0.582794593837318850840 x[345] = +0.588362434447662541434 x[346] = +0.593898967210121954393 x[347] = +0.599403930242242892974 x[348] = +0.604877064481584353319 x[349] = +0.610318113715186400156 x[350] = +0.615726824608992638014 x[351] = +0.621102946737226402941 x[352] = +0.626446232611719746542 x[353] = +0.631756437711194230414 x[354] = +0.637033320510492495071 x[355] = +0.642276642509759513774 x[356] = +0.647486168263572388782 x[357] = +0.652661665410017496101 x[358] = +0.657802904699713735422 x[359] = +0.662909660024780595461 x[360] = +0.667981708447749702165 x[361] = +0.673018830230418479199 x[362] = +0.678020808862644517838 x[363] = +0.682987431091079228087 x[364] = +0.687918486947839325756 x[365] = +0.692813769779114702895 x[366] = +0.697673076273711232906 x[367] = +0.702496206491527078610 x[368] = +0.707282963891961103412 x[369] = +0.712033155362252034587 x[370] = +0.716746591245747095767 x[371] = +0.721423085370098915485 x[372] = +0.726062455075389632685 x[373] = +0.730664521242181261329 x[374] = +0.735229108319491547663 x[375] = +0.739756044352694758677 x[376] = +0.744245161011347082309 x[377] = +0.748696293616936602823 x[378] = +0.753109281170558142523 x[379] = +0.757483966380513637926 x[380] = +0.761820195689839149173 x[381] = +0.766117819303760090717 x[382] = +0.770376691217076824278 x[383] = +0.774596669241483377036 x[384] = +0.778777615032822744702 x[385] = +0.782919394118283016385 x[386] = +0.787021875923539422170 x[387] = +0.791084933799848361435 x[388] = +0.795108445051100526780 x[389] = +0.799092290960841401800 x[390] = +0.803036356819268687782 x[391] = +0.806940531950217611856 x[392] = +0.810804709738146594361 x[393] = +0.814628787655137413436 x[394] = +0.818412667287925807395 x[395] = +0.822156254364980407373 x[396] = +0.825859458783650001088 x[397] = +0.829522194637401400178 x[398] = +0.833144380243172624728 x[399] = +0.836725938168868735503 x[400] = +0.840266795261030442350 x[401] = +0.843766882672708601038 x[402] = +0.847226135891580884381 x[403] = +0.850644494768350279758 x[404] = +0.854021903545468625813 x[405] = +0.857358310886232156525 x[406] = +0.860653669904299969802 x[407] = +0.863907938193690477146 x[408] = +0.867121077859315215614 x[409] = +0.870293055548113905851 x[410] = +0.873423842480859310192 x[411] = +0.876513414484705269742 x[412] = +0.879561752026556262568 x[413] = +0.882568840247341906842 x[414] = +0.885534668997285008926 x[415] = +0.888459232872256998890 x[416] = +0.891342531251319871666 x[417] = +0.894184568335559022859 x[418] = +0.896985353188316590376 x[419] = +0.899744899776940036639 x[420] = +0.902463227016165675048 x[421] = +0.905140358813261595189 x[422] = +0.907776324115058903624 x[423] = +0.910371156957004292498 x[424] = +0.912924896514370590080 x[425] = +0.915437587155765040644 x[426] = +0.917909278499077501636 x[427] = +0.920340025470012420730 x[428] = +0.922729888363349241523 x[429] = +0.925078932907075652364 x[430] = +0.927387230329536696843 x[431] = +0.929654857429740056670 x[432] = +0.931881896650953639345 x[433] = +0.934068436157725787999 x[434] = +0.936214569916450806625 x[435] = +0.938320397779592883655 x[436] = +0.940386025573669721370 x[437] = +0.942411565191083059813 x[438] = +0.944397134685866648591 x[439] = +0.946342858373402905148 x[440] = +0.948248866934137357063 x[441] = +0.950115297521294876558 x[442] = +0.951942293872573589498 x[443] = +0.953730006425761136415 x[444] = +0.955478592438183697574 x[445] = +0.957188216109860962736 x[446] = +0.958859048710200221356 x[447] = +0.960491268708020283423 x[448] = +0.962085061904651475741 x[449] = +0.963640621569812132521 x[450] = +0.965158148579915665979 x[451] = +0.966637851558416567092 x[452] = +0.968079947017759947964 x[453] = +0.969484659502459231771 x[454] = +0.970852221732792443256 x[455] = +0.972182874748581796578 x[456] = +0.973476868052506926773 x[457] = +0.974734459752402667761 x[458] = +0.975955916702011753129 x[459] = +0.977141514639705714156 x[460] = +0.978291538324758539526 x[461] = +0.979406281670862683806 x[462] = +0.980486047876721339416 x[463] = +0.981531149553740106867 x[464] = +0.982541908851080604251 x[465] = +0.983518657578632728762 x[466] = +0.984461737328814534596 x[467] = +0.985371499598520371114 x[468] = +0.986248305913007552681 x[469] = +0.987092527954034067190 x[470] = +0.987904547695124280467 x[471] = +0.988684757547429479939 x[472] = +0.989433560520240838716 x[473] = +0.990151370400770159181 x[474] = +0.990838611958294243677 x[475] = +0.991495721178106132399 x[476] = +0.992123145530863117683 x[477] = +0.992721344282788615328 x[478] = +0.993290788851684966211 x[479] = +0.993831963212755022209 x[480] = +0.994345364356723405931 x[481] = +0.994831502800621000519 x[482] = +0.995290903148810302261 x[483] = +0.995724104698407188509 x[484] = +0.996131662079315037786 x[485] = +0.996514145914890273849 x[486] = +0.996872143485260161299 x[487] = +0.997206259372221959076 x[488] = +0.997517116063472399965 x[489] = +0.997805354495957274562 x[490] = +0.998071634524930323302 x[491] = +0.998316635318407392531 x[492] = +0.998541055697167906027 x[493] = +0.998745614468095114704 x[494] = +0.998931050830810562236 x[495] = +0.999098124967667597662 x[496] = +0.999247618943342473599 x[497] = +0.999380338025023581928 x[498] = +0.999497112467187190535 x[499] = +0.999598799671910683252 x[500] = +0.999686286448317731776 x[501] = +0.999760490924432047330 x[502] = +0.999822363679787739196 x[503] = +0.999872888120357611938 x[504] = +0.999913081144678282800 x[505] = +0.999943996207054375764 x[506] = +0.999966730098486276883 x[507] = +0.999982430354891598580 x[508] = +0.999992298136257588028 x[509] = +0.999997596379748464620 x[510] = +0.999999672956734384381 w[ 0] = 0.945715933950007048827E-06 w[ 1] = 0.345456507169149134898E-05 w[ 2] = 0.736624069102321668857E-05 w[ 3] = 0.125792781889592743525E-04 w[ 4] = 0.190213681905875816679E-04 w[ 5] = 0.266376412339000901358E-04 w[ 6] = 0.353751372055189588628E-04 w[ 7] = 0.451863674126296143105E-04 w[ 8] = 0.560319507856164252140E-04 w[ 9] = 0.678774554733972416227E-04 w[ 10] = 0.806899228014035293851E-04 w[ 11] = 0.944366322532705527066E-04 w[ 12] = 0.109085545645741522051E-03 w[ 13] = 0.124606200241498368482E-03 w[ 14] = 0.140970302204104791413E-03 w[ 15] = 0.158151830411132242924E-03 w[ 16] = 0.176126765545083195474E-03 w[ 17] = 0.194872642236641146532E-03 w[ 18] = 0.214368090034216937149E-03 w[ 19] = 0.234592462123925204879E-03 w[ 20] = 0.255525589595236862014E-03 w[ 21] = 0.277147657465187357459E-03 w[ 22] = 0.299439176850911730874E-03 w[ 23] = 0.322381020652862389664E-03 w[ 24] = 0.345954492129903871350E-03 w[ 25] = 0.370141402122251665232E-03 w[ 26] = 0.394924138246873704434E-03 w[ 27] = 0.420285716355361231823E-03 w[ 28] = 0.446209810101403247488E-03 w[ 29] = 0.472680758429262691232E-03 w[ 30] = 0.499683553312800484519E-03 w[ 31] = 0.527203811431658386125E-03 w[ 32] = 0.555227733977307579715E-03 w[ 33] = 0.583742058714979703847E-03 w[ 34] = 0.612734008012225209294E-03 w[ 35] = 0.642191235948505088403E-03 w[ 36] = 0.672101776960108194646E-03 w[ 37] = 0.702453997827572321358E-03 w[ 38] = 0.733236554224767912055E-03 w[ 39] = 0.764438352543882784191E-03 w[ 40] = 0.796048517297550871506E-03 w[ 41] = 0.828056364077226302608E-03 w[ 42] = 0.860451377808527848128E-03 w[ 43] = 0.893223195879324912340E-03 w[ 44] = 0.926361595613111283368E-03 w[ 45] = 0.959856485506936206261E-03 w[ 46] = 0.993697899638760857945E-03 w[ 47] = 0.102787599466367326179E-02 w[ 48] = 0.106238104885340071375E-02 w[ 49] = 0.109720346268191941940E-02 w[ 50] = 0.113233376051597664917E-02 w[ 51] = 0.116776259302858043685E-02 w[ 52] = 0.120348074001265964881E-02 w[ 53] = 0.123947911332878396534E-02 w[ 54] = 0.127574875977346947345E-02 w[ 55] = 0.131228086370221478128E-02 w[ 56] = 0.134906674928353113127E-02 w[ 57] = 0.138609788229672549700E-02 w[ 58] = 0.142336587141720519900E-02 w[ 59] = 0.146086246895890987689E-02 w[ 60] = 0.149857957106456636214E-02 w[ 61] = 0.153650921735128916170E-02 w[ 62] = 0.157464359003212166189E-02 w[ 63] = 0.161297501254393423070E-02 w[ 64] = 0.165149594771914570655E-02 w[ 65] = 0.169019899554346019117E-02 w[ 66] = 0.172907689054461607168E-02 w[ 67] = 0.176812249885838886701E-02 w[ 68] = 0.180732881501808930079E-02 w[ 69] = 0.184668895851282540913E-02 w[ 70] = 0.188619617015808475394E-02 w[ 71] = 0.192584380831993546204E-02 w[ 72] = 0.196562534503150547732E-02 w[ 73] = 0.200553436203751169944E-02 w[ 74] = 0.204556454679958293446E-02 w[ 75] = 0.208570968849203942640E-02 w[ 76] = 0.212596367401472533045E-02 w[ 77] = 0.216632048404649142727E-02 w[ 78] = 0.220677418916003329194E-02 w[ 79] = 0.224731894601603393082E-02 w[ 80] = 0.228794899365195972378E-02 w[ 81] = 0.232865864987842738864E-02 w[ 82] = 0.236944230779380495146E-02 w[ 83] = 0.241029443242563417382E-02 w[ 84] = 0.245120955750556483923E-02 w[ 85] = 0.249218228238276930060E-02 w[ 86] = 0.253320726907925325750E-02 w[ 87] = 0.257427923948908888092E-02 w[ 88] = 0.261539297272236109225E-02 w[ 89] = 0.265654330259352828314E-02 w[ 90] = 0.269772511525294586667E-02 w[ 91] = 0.273893334695947541201E-02 w[ 92] = 0.278016298199139435045E-02 w[ 93] = 0.282140905069222207923E-02 w[ 94] = 0.286266662764757868253E-02 w[ 95] = 0.290393082998878368175E-02 w[ 96] = 0.294519681581857582284E-02 w[ 97] = 0.298645978275408290247E-02 w[ 98] = 0.302771496658198544480E-02 w[ 99] = 0.306895764002069252174E-02 w[100] = 0.311018311158427546158E-02 w[101] = 0.315138672454287935858E-02 w[102] = 0.319256385597434736790E-02 w[103] = 0.323370991590184336368E-02 w[104] = 0.327482034651233969564E-02 w[105] = 0.331589062145094394706E-02 w[106] = 0.335691624518616761342E-02 w[107] = 0.339789275244138669739E-02 w[108] = 0.343881570768790591876E-02 w[109] = 0.347968070469521146972E-02 w[110] = 0.352048336613417922682E-02 w[111] = 0.356121934322919357659E-02 w[112] = 0.360188431545532431869E-02 w[113] = 0.364247399027690353194E-02 w[114] = 0.368298410292403911967E-02 w[115] = 0.372341041620379550870E-02 w[116] = 0.376374872034296338241E-02 w[117] = 0.380399483285952829161E-02 w[118] = 0.384414459846013158917E-02 w[119] = 0.388419388896099560998E-02 w[120] = 0.392413860322995774660E-02 w[121] = 0.396397466714742455513E-02 w[122] = 0.400369803358421688562E-02 w[123] = 0.404330468239442998549E-02 w[124] = 0.408279062042157838350E-02 w[125] = 0.412215188151643401528E-02 w[126] = 0.416138452656509745764E-02 w[127] = 0.420048464352596631772E-02 w[128] = 0.423944834747438184434E-02 w[129] = 0.427827178065384480959E-02 w[130] = 0.431695111253279479928E-02 w[131] = 0.435548253986604343679E-02 w[132] = 0.439386228676004195260E-02 w[133] = 0.443208660474124713206E-02 w[134] = 0.447015177282692726900E-02 w[135] = 0.450805409759782158001E-02 w[136] = 0.454578991327213285488E-02 w[137] = 0.458335558178039420335E-02 w[138] = 0.462074749284080687482E-02 w[139] = 0.465796206403469754658E-02 w[140] = 0.469499574088179046532E-02 w[141] = 0.473184499691503264714E-02 w[142] = 0.476850633375474925263E-02 w[143] = 0.480497628118194150483E-02 w[144] = 0.484125139721057135214E-02 w[145] = 0.487732826815870573054E-02 w[146] = 0.491320350871841897367E-02 w[147] = 0.494887376202437487201E-02 w[148] = 0.498433569972103029914E-02 w[149] = 0.501958602202842039909E-02 w[150] = 0.505462145780650125058E-02 w[151] = 0.508943876461803986674E-02 w[152] = 0.512403472879005351831E-02 w[153] = 0.515840616547381084096E-02 w[154] = 0.519254991870341614863E-02 w[155] = 0.522646286145300596306E-02 w[156] = 0.526014189569259311205E-02 w[157] = 0.529358395244259896547E-02 w[158] = 0.532678599182711857974E-02 w[159] = 0.535974500312596681161E-02 w[160] = 0.539245800482555593606E-02 w[161] = 0.542492204466865704951E-02 w[162] = 0.545713419970309863995E-02 w[163] = 0.548909157632945623482E-02 w[164] = 0.552079131034778706457E-02 w[165] = 0.555223056700346326850E-02 w[166] = 0.558340654103215637610E-02 w[167] = 0.561431645670402467678E-02 w[168] = 0.564495756786715368885E-02 w[169] = 0.567532715799029830087E-02 w[170] = 0.570542254020497332312E-02 w[171] = 0.573524105734693719020E-02 w[172] = 0.576478008199711142954E-02 w[173] = 0.579403701652197628421E-02 w[174] = 0.582300929311348057702E-02 w[175] = 0.585169437382850155033E-02 w[176] = 0.588008975062788803205E-02 w[177] = 0.590819294541511788161E-02 w[178] = 0.593600151007459827614E-02 w[179] = 0.596351302650963502011E-02 w[180] = 0.599072510668009471472E-02 w[181] = 0.601763539263978131522E-02 w[182] = 0.604424155657354634589E-02 w[183] = 0.607054130083414983949E-02 w[184] = 0.609653235797888692923E-02 w[185] = 0.612221249080599294931E-02 w[186] = 0.614757949239083790214E-02 w[187] = 0.617263118612191922727E-02 w[188] = 0.619736542573665996342E-02 w[189] = 0.622178009535701763157E-02 w[190] = 0.624587310952490748541E-02 w[191] = 0.626964241323744217671E-02 w[192] = 0.629308598198198836688E-02 w[193] = 0.631620182177103938227E-02 w[194] = 0.633898796917690165912E-02 w[195] = 0.636144249136619145314E-02 w[196] = 0.638356348613413709795E-02 w[197] = 0.640534908193868098342E-02 w[198] = 0.642679743793437438922E-02 w[199] = 0.644790674400605734710E-02 w[200] = 0.646867522080231481688E-02 w[201] = 0.648910111976869964292E-02 w[202] = 0.650918272318071200827E-02 w[203] = 0.652891834417652442012E-02 w[204] = 0.654830632678944064054E-02 w[205] = 0.656734504598007641819E-02 w[206] = 0.658603290766824937794E-02 w[207] = 0.660436834876456498276E-02 w[208] = 0.662234983720168509457E-02 w[209] = 0.663997587196526532519E-02 w[210] = 0.665724498312454708217E-02 w[211] = 0.667415573186258997654E-02 w[212] = 0.669070671050613006584E-02 w[213] = 0.670689654255504925648E-02 w[214] = 0.672272388271144108036E-02 w[215] = 0.673818741690825799086E-02 w[216] = 0.675328586233752529078E-02 w[217] = 0.676801796747810680683E-02 w[218] = 0.678238251212300746082E-02 w[219] = 0.679637830740619795480E-02 w[220] = 0.681000419582894688374E-02 w[221] = 0.682325905128564571420E-02 w[222] = 0.683614177908911221841E-02 w[223] = 0.684865131599535812903E-02 w[224] = 0.686078663022780697951E-02 w[225] = 0.687254672150094831613E-02 w[226] = 0.688393062104341470995E-02 w[227] = 0.689493739162046825872E-02 w[228] = 0.690556612755588354803E-02 w[229] = 0.691581595475321433825E-02 w[230] = 0.692568603071643155621E-02 w[231] = 0.693517554456992049848E-02 w[232] = 0.694428371707782549438E-02 w[233] = 0.695300980066273063177E-02 w[234] = 0.696135307942366551493E-02 w[235] = 0.696931286915342540213E-02 w[236] = 0.697688851735519545845E-02 w[237] = 0.698407940325846925786E-02 w[238] = 0.699088493783425207545E-02 w[239] = 0.699730456380953992594E-02 w[240] = 0.700333775568106572820E-02 w[241] = 0.700898401972830440494E-02 w[242] = 0.701424289402572916425E-02 w[243] = 0.701911394845431165171E-02 w[244] = 0.702359678471225911031E-02 w[245] = 0.702769103632498213858E-02 w[246] = 0.703139636865428709508E-02 w[247] = 0.703471247890678765907E-02 w[248] = 0.703763909614153052319E-02 w[249] = 0.704017598127683066242E-02 w[250] = 0.704232292709631209597E-02 w[251] = 0.704407975825415053266E-02 w[252] = 0.704544633127951476780E-02 w[253] = 0.704642253458020417748E-02 w[254] = 0.704700828844548013730E-02 w[255] = 0.704720354504808967346E-02 w[256] = 0.704700828844548013730E-02 w[257] = 0.704642253458020417748E-02 w[258] = 0.704544633127951476780E-02 w[259] = 0.704407975825415053266E-02 w[260] = 0.704232292709631209597E-02 w[261] = 0.704017598127683066242E-02 w[262] = 0.703763909614153052319E-02 w[263] = 0.703471247890678765907E-02 w[264] = 0.703139636865428709508E-02 w[265] = 0.702769103632498213858E-02 w[266] = 0.702359678471225911031E-02 w[267] = 0.701911394845431165171E-02 w[268] = 0.701424289402572916425E-02 w[269] = 0.700898401972830440494E-02 w[270] = 0.700333775568106572820E-02 w[271] = 0.699730456380953992594E-02 w[272] = 0.699088493783425207545E-02 w[273] = 0.698407940325846925786E-02 w[274] = 0.697688851735519545845E-02 w[275] = 0.696931286915342540213E-02 w[276] = 0.696135307942366551493E-02 w[277] = 0.695300980066273063177E-02 w[278] = 0.694428371707782549438E-02 w[279] = 0.693517554456992049848E-02 w[280] = 0.692568603071643155621E-02 w[281] = 0.691581595475321433825E-02 w[282] = 0.690556612755588354803E-02 w[283] = 0.689493739162046825872E-02 w[284] = 0.688393062104341470995E-02 w[285] = 0.687254672150094831613E-02 w[286] = 0.686078663022780697951E-02 w[287] = 0.684865131599535812903E-02 w[288] = 0.683614177908911221841E-02 w[289] = 0.682325905128564571420E-02 w[290] = 0.681000419582894688374E-02 w[291] = 0.679637830740619795480E-02 w[292] = 0.678238251212300746082E-02 w[293] = 0.676801796747810680683E-02 w[294] = 0.675328586233752529078E-02 w[295] = 0.673818741690825799086E-02 w[296] = 0.672272388271144108036E-02 w[297] = 0.670689654255504925648E-02 w[298] = 0.669070671050613006584E-02 w[299] = 0.667415573186258997654E-02 w[300] = 0.665724498312454708217E-02 w[301] = 0.663997587196526532519E-02 w[302] = 0.662234983720168509457E-02 w[303] = 0.660436834876456498276E-02 w[304] = 0.658603290766824937794E-02 w[305] = 0.656734504598007641819E-02 w[306] = 0.654830632678944064054E-02 w[307] = 0.652891834417652442012E-02 w[308] = 0.650918272318071200827E-02 w[309] = 0.648910111976869964292E-02 w[310] = 0.646867522080231481688E-02 w[311] = 0.644790674400605734710E-02 w[312] = 0.642679743793437438922E-02 w[313] = 0.640534908193868098342E-02 w[314] = 0.638356348613413709795E-02 w[315] = 0.636144249136619145314E-02 w[316] = 0.633898796917690165912E-02 w[317] = 0.631620182177103938227E-02 w[318] = 0.629308598198198836688E-02 w[319] = 0.626964241323744217671E-02 w[320] = 0.624587310952490748541E-02 w[321] = 0.622178009535701763157E-02 w[322] = 0.619736542573665996342E-02 w[323] = 0.617263118612191922727E-02 w[324] = 0.614757949239083790214E-02 w[325] = 0.612221249080599294931E-02 w[326] = 0.609653235797888692923E-02 w[327] = 0.607054130083414983949E-02 w[328] = 0.604424155657354634589E-02 w[329] = 0.601763539263978131522E-02 w[330] = 0.599072510668009471472E-02 w[331] = 0.596351302650963502011E-02 w[332] = 0.593600151007459827614E-02 w[333] = 0.590819294541511788161E-02 w[334] = 0.588008975062788803205E-02 w[335] = 0.585169437382850155033E-02 w[336] = 0.582300929311348057702E-02 w[337] = 0.579403701652197628421E-02 w[338] = 0.576478008199711142954E-02 w[339] = 0.573524105734693719020E-02 w[340] = 0.570542254020497332312E-02 w[341] = 0.567532715799029830087E-02 w[342] = 0.564495756786715368885E-02 w[343] = 0.561431645670402467678E-02 w[344] = 0.558340654103215637610E-02 w[345] = 0.555223056700346326850E-02 w[346] = 0.552079131034778706457E-02 w[347] = 0.548909157632945623482E-02 w[348] = 0.545713419970309863995E-02 w[349] = 0.542492204466865704951E-02 w[350] = 0.539245800482555593606E-02 w[351] = 0.535974500312596681161E-02 w[352] = 0.532678599182711857974E-02 w[353] = 0.529358395244259896547E-02 w[354] = 0.526014189569259311205E-02 w[355] = 0.522646286145300596306E-02 w[356] = 0.519254991870341614863E-02 w[357] = 0.515840616547381084096E-02 w[358] = 0.512403472879005351831E-02 w[359] = 0.508943876461803986674E-02 w[360] = 0.505462145780650125058E-02 w[361] = 0.501958602202842039909E-02 w[362] = 0.498433569972103029914E-02 w[363] = 0.494887376202437487201E-02 w[364] = 0.491320350871841897367E-02 w[365] = 0.487732826815870573054E-02 w[366] = 0.484125139721057135214E-02 w[367] = 0.480497628118194150483E-02 w[368] = 0.476850633375474925263E-02 w[369] = 0.473184499691503264714E-02 w[370] = 0.469499574088179046532E-02 w[371] = 0.465796206403469754658E-02 w[372] = 0.462074749284080687482E-02 w[373] = 0.458335558178039420335E-02 w[374] = 0.454578991327213285488E-02 w[375] = 0.450805409759782158001E-02 w[376] = 0.447015177282692726900E-02 w[377] = 0.443208660474124713206E-02 w[378] = 0.439386228676004195260E-02 w[379] = 0.435548253986604343679E-02 w[380] = 0.431695111253279479928E-02 w[381] = 0.427827178065384480959E-02 w[382] = 0.423944834747438184434E-02 w[383] = 0.420048464352596631772E-02 w[384] = 0.416138452656509745764E-02 w[385] = 0.412215188151643401528E-02 w[386] = 0.408279062042157838350E-02 w[387] = 0.404330468239442998549E-02 w[388] = 0.400369803358421688562E-02 w[389] = 0.396397466714742455513E-02 w[390] = 0.392413860322995774660E-02 w[391] = 0.388419388896099560998E-02 w[392] = 0.384414459846013158917E-02 w[393] = 0.380399483285952829161E-02 w[394] = 0.376374872034296338241E-02 w[395] = 0.372341041620379550870E-02 w[396] = 0.368298410292403911967E-02 w[397] = 0.364247399027690353194E-02 w[398] = 0.360188431545532431869E-02 w[399] = 0.356121934322919357659E-02 w[400] = 0.352048336613417922682E-02 w[401] = 0.347968070469521146972E-02 w[402] = 0.343881570768790591876E-02 w[403] = 0.339789275244138669739E-02 w[404] = 0.335691624518616761342E-02 w[405] = 0.331589062145094394706E-02 w[406] = 0.327482034651233969564E-02 w[407] = 0.323370991590184336368E-02 w[408] = 0.319256385597434736790E-02 w[409] = 0.315138672454287935858E-02 w[410] = 0.311018311158427546158E-02 w[411] = 0.306895764002069252174E-02 w[412] = 0.302771496658198544480E-02 w[413] = 0.298645978275408290247E-02 w[414] = 0.294519681581857582284E-02 w[415] = 0.290393082998878368175E-02 w[416] = 0.286266662764757868253E-02 w[417] = 0.282140905069222207923E-02 w[418] = 0.278016298199139435045E-02 w[419] = 0.273893334695947541201E-02 w[420] = 0.269772511525294586667E-02 w[421] = 0.265654330259352828314E-02 w[422] = 0.261539297272236109225E-02 w[423] = 0.257427923948908888092E-02 w[424] = 0.253320726907925325750E-02 w[425] = 0.249218228238276930060E-02 w[426] = 0.245120955750556483923E-02 w[427] = 0.241029443242563417382E-02 w[428] = 0.236944230779380495146E-02 w[429] = 0.232865864987842738864E-02 w[430] = 0.228794899365195972378E-02 w[431] = 0.224731894601603393082E-02 w[432] = 0.220677418916003329194E-02 w[433] = 0.216632048404649142727E-02 w[434] = 0.212596367401472533045E-02 w[435] = 0.208570968849203942640E-02 w[436] = 0.204556454679958293446E-02 w[437] = 0.200553436203751169944E-02 w[438] = 0.196562534503150547732E-02 w[439] = 0.192584380831993546204E-02 w[440] = 0.188619617015808475394E-02 w[441] = 0.184668895851282540913E-02 w[442] = 0.180732881501808930079E-02 w[443] = 0.176812249885838886701E-02 w[444] = 0.172907689054461607168E-02 w[445] = 0.169019899554346019117E-02 w[446] = 0.165149594771914570655E-02 w[447] = 0.161297501254393423070E-02 w[448] = 0.157464359003212166189E-02 w[449] = 0.153650921735128916170E-02 w[450] = 0.149857957106456636214E-02 w[451] = 0.146086246895890987689E-02 w[452] = 0.142336587141720519900E-02 w[453] = 0.138609788229672549700E-02 w[454] = 0.134906674928353113127E-02 w[455] = 0.131228086370221478128E-02 w[456] = 0.127574875977346947345E-02 w[457] = 0.123947911332878396534E-02 w[458] = 0.120348074001265964881E-02 w[459] = 0.116776259302858043685E-02 w[460] = 0.113233376051597664917E-02 w[461] = 0.109720346268191941940E-02 w[462] = 0.106238104885340071375E-02 w[463] = 0.102787599466367326179E-02 w[464] = 0.993697899638760857945E-03 w[465] = 0.959856485506936206261E-03 w[466] = 0.926361595613111283368E-03 w[467] = 0.893223195879324912340E-03 w[468] = 0.860451377808527848128E-03 w[469] = 0.828056364077226302608E-03 w[470] = 0.796048517297550871506E-03 w[471] = 0.764438352543882784191E-03 w[472] = 0.733236554224767912055E-03 w[473] = 0.702453997827572321358E-03 w[474] = 0.672101776960108194646E-03 w[475] = 0.642191235948505088403E-03 w[476] = 0.612734008012225209294E-03 w[477] = 0.583742058714979703847E-03 w[478] = 0.555227733977307579715E-03 w[479] = 0.527203811431658386125E-03 w[480] = 0.499683553312800484519E-03 w[481] = 0.472680758429262691232E-03 w[482] = 0.446209810101403247488E-03 w[483] = 0.420285716355361231823E-03 w[484] = 0.394924138246873704434E-03 w[485] = 0.370141402122251665232E-03 w[486] = 0.345954492129903871350E-03 w[487] = 0.322381020652862389664E-03 w[488] = 0.299439176850911730874E-03 w[489] = 0.277147657465187357459E-03 w[490] = 0.255525589595236862014E-03 w[491] = 0.234592462123925204879E-03 w[492] = 0.214368090034216937149E-03 w[493] = 0.194872642236641146532E-03 w[494] = 0.176126765545083195474E-03 w[495] = 0.158151830411132242924E-03 w[496] = 0.140970302204104791413E-03 w[497] = 0.124606200241498368482E-03 w[498] = 0.109085545645741522051E-03 w[499] = 0.944366322532705527066E-04 w[500] = 0.806899228014035293851E-04 w[501] = 0.678774554733972416227E-04 w[502] = 0.560319507856164252140E-04 w[503] = 0.451863674126296143105E-04 w[504] = 0.353751372055189588628E-04 w[505] = 0.266376412339000901358E-04 w[506] = 0.190213681905875816679E-04 w[507] = 0.125792781889592743525E-04 w[508] = 0.736624069102321668857E-05 w[509] = 0.345456507169149134898E-05 w[510] = 0.945715933950007048827E-06 else: print ( '' ) print ( 'patterson_set(): Fatal error!' ) print ( ' Illegal input value of N.' ) print ( ' N must be 1, 3, 7, 15, 31, 63, 127, 255, or 511.' ) raise Exception ( 'patterson_set(): Fatal error!' ) return x, w def rescale ( a, b, x, w ): #*****************************************************************************80 # ## rescale() rescales a quadrature rule from [-1,+1] to [A,B]. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 21 October 2009 # # Author: # # John Burkardt. # # Reference: # # Andreas Glaser, Xiangtao Liu, Vladimir Rokhlin, # A fast algorithm for the calculation of the roots of special functions, # SIAM Journal on Scientific Computing, # Volume 29, Number 4, pages 1420-1438, 2007. # # Input: # # real A, B, the endpoints of the new interval. # # integer N, the order. # # real X(N), the abscissas for [-1,+1]. # # real W(N), the weights for [-1,+1]. # # Output: # # real X(N), the abscissas for [A,B]. # # real W(N), the weights for [A,B]. # x = 0.5 * ( ( x + 1.0 ) * b - ( x - 1.0 ) * a ) w = 0.5 * ( b - a ) * w return x, w def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 21 August 2019 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return if ( __name__ == '__main__' ): timestamp ( ) patterson_rule_test ( ) timestamp ( )