dlt.h

Go to the documentation of this file.

#ifndef _DLT_CUH_
#define _DLT_CUH_
 
#include <vector>
#include "dg/backend/exceptions.h"
 
namespace dg{
 
template< class real_type>
struct DLT
{
    static std::vector<real_type> abscissas(unsigned n)
    {
        switch( n)
        {
            case(0):
                return {};
            case(1):
                return {0.};
            case(2):
                return {-.57735026918962576451, .57735026918962576451};
            case(3):
                return {-.77459666924148337704, 0., .77459666924148337704};
            case(4):
                return {-.86113631159405257522, -.33998104358485626480, .33998104358485626480, .86113631159405257522};
            case(5):
                return {-.90617984593866399280, -.53846931010568309104, 0., .53846931010568309104, .90617984593866399280};
            case(6):
                return {-.93246951420315202781, -.66120938646626451366, -.23861918608319690863, .23861918608319690863, .66120938646626451366, .93246951420315202781};
            case(7):
                return {-.94910791234275852453, -.74153118559939443986, -.40584515137739716691, 0., .40584515137739716691, .74153118559939443986, .94910791234275852453};
            case(8):
                return {-.96028985649753623168, -.79666647741362673959, -.52553240991632898582, -.18343464249564980494, .18343464249564980494, .52553240991632898582, .79666647741362673959, .96028985649753623168};
            case(9):
                return {-.96816023950762608984, -.83603110732663579430, -.61337143270059039731, -.32425342340380892904, 0., .32425342340380892904, .61337143270059039731, .83603110732663579430, .96816023950762608984};
            case(10):
                return {-.97390652851717172008, -.86506336668898451073, -.67940956829902440623, -.43339539412924719080, -.14887433898163121088, .14887433898163121088, .43339539412924719080, .67940956829902440623, .86506336668898451073, .97390652851717172008};
            case(11):
                return {-.97822865814605699280, -.88706259976809529908, -.73015200557404932409, -.51909612920681181593, -.26954315595234497233, 0., .26954315595234497233, .51909612920681181593, .73015200557404932409, .88706259976809529908, .97822865814605699280};
            case(12):
                return {-.98156063424671925069, -.90411725637047485668, -.76990267419430468704, -.58731795428661744730, -.36783149899818019375, -.12523340851146891547, .12523340851146891547, .36783149899818019375, .58731795428661744730, .76990267419430468704, .90411725637047485668, .98156063424671925069};
            case(13):
                return {-.98418305471858814947, -.91759839922297796521, -.80157809073330991279, -.64234933944034022064, -.44849275103644685288, -.23045831595513479407, 0., .23045831595513479407, .44849275103644685288, .64234933944034022064, .80157809073330991279, .91759839922297796521, .98418305471858814947};
            case(14):
                return {-.98628380869681233884, -.92843488366357351734, -.82720131506976499319, -.68729290481168547015, -.51524863635815409197, -.31911236892788976044, -.10805494870734366207, .10805494870734366207, .31911236892788976044, .51524863635815409197, .68729290481168547015, .82720131506976499319, .92843488366357351734, .98628380869681233884};
            case(15):
                return {-.98799251802048542849, -.93727339240070590431, -.84820658341042721620, -.72441773136017004742, -.57097217260853884754, -.39415134707756336990, -.20119409399743452230, 0., .20119409399743452230, .39415134707756336990, .57097217260853884754, .72441773136017004742, .84820658341042721620, .93727339240070590431, .98799251802048542849};
            case(16):
                return {-.98940093499164993260, -.94457502307323257608, -.86563120238783174388, -.75540440835500303390, -.61787624440264374845, -.45801677765722738634, -.28160355077925891323, -.95012509837637440185e-1, .95012509837637440185e-1, .28160355077925891323, .45801677765722738634, .61787624440264374845, .75540440835500303390, .86563120238783174388, .94457502307323257608, .98940093499164993260};
            case(17):
                return {-.99057547531441733568, -.95067552176876776122, -.88023915372698590212, -.78151400389680140693, -.65767115921669076585, -.51269053708647696789, -.35123176345387631530, -.17848418149584785585, 0., .17848418149584785585, .35123176345387631530, .51269053708647696789, .65767115921669076585, .78151400389680140693, .88023915372698590212, .95067552176876776122, .99057547531441733568};
            case(18):
                return {-.99156516842093094673, -.95582394957139775518, -.89260246649755573921, -.80370495897252311568, -.69168704306035320787, -.55977083107394753461, -.41175116146284264604, -.25188622569150550959, -.84775013041735301242e-1, .84775013041735301242e-1, .25188622569150550959, .41175116146284264604, .55977083107394753461, .69168704306035320787, .80370495897252311568, .89260246649755573921, .95582394957139775518, .99156516842093094673};
            case(19):
                return {-.99240684384358440319, -.96020815213483003085, -.90315590361481790164, -.82271465653714282498, -.72096617733522937862, -.60054530466168102347, -.46457074137596094572, -.31656409996362983199, -.16035864564022537587, 0., .16035864564022537587, .31656409996362983199, .46457074137596094572, .60054530466168102347, .72096617733522937862, .82271465653714282498, .90315590361481790164, .96020815213483003085, .99240684384358440319};
            case(20):
                return {-.99312859918509492479, -.96397192727791379127, -.91223442825132590587, -.83911697182221882339, -.74633190646015079261, -.63605368072651502545, -.51086700195082709800, -.37370608871541956067, -.22778585114164507808, -.76526521133497333755e-1, .76526521133497333755e-1, .22778585114164507808, .37370608871541956067, .51086700195082709800, .63605368072651502545, .74633190646015079261, .83911697182221882339, .91223442825132590587, .96397192727791379127, .99312859918509492479};
            default:
                throw Error( Message(_ping_)<<"n>20 not allowed! You typed: "<<n );
        }
    }
    static std::vector<real_type> weights(unsigned n)
    {
        switch( n)
        {
            case(0):
                return {};
            case(1):
                return {2.};
            case(2):
                return {1.0000000000000000000, 1.0000000000000000000};
            case(3):
                return {.55555555555555555556, .88888888888888888889, .55555555555555555556};
            case(4):
                return {.34785484513745385737, .65214515486254614263, .65214515486254614263, .34785484513745385737};
            case(5):
                return {.23692688505618908751, .47862867049936646804, .56888888888888888889, .47862867049936646804, .23692688505618908751};
            case(6):
                return {.17132449237917034504, .36076157304813860757, .46791393457269104739, .46791393457269104739, .36076157304813860757, .17132449237917034504};
            case(7):
                return {.12948496616886969327, .27970539148927666790, .38183005050511894495, .41795918367346938776, .38183005050511894495, .27970539148927666790, .12948496616886969327};
            case(8):
                return {.10122853629037625915, .22238103445337447054, .31370664587788728734, .36268378337836198297, .36268378337836198297, .31370664587788728734, .22238103445337447054, .10122853629037625915};
            case(9):
                return {.81274388361574411972e-1, .18064816069485740406, .26061069640293546232, .31234707704000284007, .33023935500125976316, .31234707704000284007, .26061069640293546232, .18064816069485740406, .81274388361574411972e-1};
            case(10):
                return {.66671344308688137594e-1, .14945134915058059315, .21908636251598204400, .26926671930999635509, .29552422471475287017, .29552422471475287017, .26926671930999635509, .21908636251598204400, .14945134915058059315, .66671344308688137594e-1, };
            case(11):
                return {.55668567116173666483e-1, .12558036946490462463, .18629021092773425143, .23319376459199047992, .26280454451024666218, .27292508677790063071, .26280454451024666218, .23319376459199047992, .18629021092773425143, .12558036946490462463, .55668567116173666483e-1};
            case(12):
                return {.47175336386511827195e-1, .10693932599531843096, .16007832854334622633, .20316742672306592175, .23349253653835480876, .24914704581340278500, .24914704581340278500, .23349253653835480876, .20316742672306592175, .16007832854334622633, .10693932599531843096, .47175336386511827195e-1};
            case(13):
                return {.40484004765315879520e-1, .92121499837728447914e-1, .13887351021978723846, .17814598076194573828, .20781604753688850231, .22628318026289723841, .23255155323087391019, .22628318026289723841, .20781604753688850231, .17814598076194573828, .13887351021978723846, .92121499837728447914e-1, .40484004765315879520e-1};
            case(14):
                return {.35119460331751863032e-1, .80158087159760209806e-1, .12151857068790318469, .15720316715819353457, .18553839747793781374, .20519846372129560397, .21526385346315779020, .21526385346315779020, .20519846372129560397, .18553839747793781374, .15720316715819353457, .12151857068790318469, .80158087159760209806e-1, .35119460331751863032e-1};
            case(15):
                return {.30753241996117268355e-1, .70366047488108124709e-1, .10715922046717193501, .13957067792615431445, .16626920581699393355, .18616100001556221103, .19843148532711157646, .20257824192556127288, .19843148532711157646, .18616100001556221103, .16626920581699393355, .13957067792615431445, .10715922046717193501, .70366047488108124709e-1, .30753241996117268355e-1};
            case(16):
                return {.27152459411754094852e-1, .62253523938647892863e-1, .95158511682492784810e-1, .12462897125553387205, .14959598881657673208, .16915651939500253819, .18260341504492358887, .18945061045506849629, .18945061045506849629, .18260341504492358887, .16915651939500253819, .14959598881657673208, .12462897125553387205, .95158511682492784810e-1, .62253523938647892863e-1, .27152459411754094852e-1};
            case(17):
                return {.24148302868547931960e-1, .55459529373987201129e-1, .85036148317179180884e-1, .11188384719340397109, .13513636846852547329, .15404576107681028808, .16800410215645004451, .17656270536699264633, .17944647035620652546, .17656270536699264633, .16800410215645004451, .15404576107681028808, .13513636846852547329, .11188384719340397109, .85036148317179180884e-1, .55459529373987201129e-1, .24148302868547931960e-1};
            case(18):
                return {.21616013526483310313e-1, .49714548894969796453e-1, .76425730254889056529e-1, .10094204410628716556, .12255520671147846018, .14064291467065065120, .15468467512626524493, .16427648374583272299, .16914238296314359184, .16914238296314359184, .16427648374583272299, .15468467512626524493, .14064291467065065120, .12255520671147846018, .10094204410628716556, .76425730254889056529e-1, .49714548894969796453e-1, .21616013526483310313e-1};
            case(19):
                return {.19461788229726477036e-1, .44814226765699600333e-1, .69044542737641226581e-1, .91490021622449999464e-1, .11156664554733399472, .12875396253933622768, .14260670217360661178, .15276604206585966678, .15896884339395434765, .16105444984878369598, .15896884339395434765, .15276604206585966678, .14260670217360661178, .12875396253933622768, .11156664554733399472, .91490021622449999464e-1, .69044542737641226581e-1, .44814226765699600333e-1, .19461788229726477036e-1};
            case(20):
                return {.17614007139152118312e-1, .40601429800386941331e-1, .62672048334109063570e-1, .83276741576704748725e-1, .10193011981724043504, .11819453196151841731, .13168863844917662690, .14209610931838205133, .14917298647260374679, .15275338713072585070, .15275338713072585070, .14917298647260374679, .14209610931838205133, .13168863844917662690, .11819453196151841731, .10193011981724043504, .83276741576704748725e-1, .62672048334109063570e-1, .40601429800386941331e-1, .17614007139152118312e-1};
            default:
                throw Error( Message(_ping_)<<"n>20 not allowed! You typed: "<<n );
        }
    }
    static std::vector<real_type> backward(unsigned n)
    {
        switch( n)
        {
            case(0):
                return {};
            case(1):
                return {1.};
            case(2):
                return {1.0000000000000000000, -.57735026918962576451, 1.0000000000000000000, .57735026918962576451};
            case(3):
                return {1.0000000000000000000, -.77459666924148337704, .40000000000000000001, 1.0000000000000000000, 0., -.50000000000000000000, 1.0000000000000000000, .77459666924148337704, .40000000000000000001};
            case(4):
                return {1.0000000000000000000, -.86113631159405257522, .61233362071871381152, -.30474698495520619086, 1.0000000000000000000, -.33998104358485626480, -.32661933500442809725, .41172799967289957387, 1.0000000000000000000, .33998104358485626480, -.32661933500442809725, -.41172799967289957387, 1.0000000000000000000, .86113631159405257522, .61233362071871381152, .30474698495520619086};
            case(5):
                return {1.0000000000000000000, -.90617984593866399280, .73174286977813121333, -.50103117104466202336, .24573545909491200988, 1.0000000000000000000, -.53846931010568309104, -.65076203111464546650e-1, .41738210372666809706, -.34450089119367744197, 1.0000000000000000000, 0., -.50000000000000000000, 0., .37500000000000000000, 1.0000000000000000000, .53846931010568309104, -.65076203111464546650e-1, -.41738210372666809706, -.34450089119367744197, 1.0000000000000000000, .90617984593866399280, .73174286977813121333, .50103117104466202336, .24573545909491200988};
            case(6):
                return {1.0000000000000000000, -.93246951420315202781, .80424909237739351198, -.62824992464368875927, .42200500927062268771, -.20571231105962256243, 1.0000000000000000000, -.66120938646626451366, .15579677912664091270, .26911576974459906981, -.42824586209712069174, .29439571492543739257, 1.0000000000000000000, -.23861918608319690863, -.41459132604948897014, .32396186535393522316, .17566234042980378913, -.33461902074104079971, 1.0000000000000000000, .23861918608319690863, -.41459132604948897014, -.32396186535393522316, .17566234042980378913, .33461902074104079971, 1.0000000000000000000, .66120938646626451366, .15579677912664091270, -.26911576974459906981, -.42824586209712069174, -.29439571492543739257, 1.0000000000000000000, .93246951420315202781, .80424909237739351198, .62824992464368875927, .42200500927062268771, .20571231105962256243};
            case(7):
                return {1.0000000000000000000, -.94910791234275852453, .85120874390744409879, -.71374298160132105529, .54707688669903696127, -.36362861800556101236, .17682772500692664552, 1.0000000000000000000, -.74153118559939443986, .32480274882466534585, .92935178029768938512e-1, -.36420214392803338104, .41177290322881744727, -.25629270346308332938, 1.0000000000000000000, -.40584515137739716691, -.25293456965518636771, .44165054876874131017, -.12397210694529083142, -.26275617769737747746, .29881367709479615096, 1.0000000000000000000, 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 1.0000000000000000000, .40584515137739716691, -.25293456965518636771, -.44165054876874131017, -.12397210694529083142, .26275617769737747746, .29881367709479615096, 1.0000000000000000000, .74153118559939443986, .32480274882466534585, -.92935178029768938512e-1, -.36420214392803338104, -.41177290322881744727, -.25629270346308332938, 1.0000000000000000000, .94910791234275852453, .85120874390744409879, .71374298160132105529, .54707688669903696127, .36362861800556101236, .17682772500692664552};
            case(8):
                return {1.0000000000000000000, -.96028985649753623168, .88323491273808809320, -.77340930834643009705, .63729376446667512056, -.48284868105051651382, .31899212911048349874, -.15501881289034966478, 1.0000000000000000000, -.79666647741362673959, .45201621435195496602, -.69065957093606829988e-1, -.24272272845677845606, .40331707559708017427, -.38679791509661859831, .22657623839999653345, 1.0000000000000000000, -.52553240991632898582, -.85723529191303339177e-1, .42543909474828335763, -.32697591039397435322, -.31045687085550912587e-1, .30239170237287130345, -.26852031408771530434, 1.0000000000000000000, -.18343464249564980494, -.44952759789873972005, .25972131868457243498, .25377239575159905620, -.29156822258958438604, -.11342352322434304154, .28855496859568764271, 1.0000000000000000000, .18343464249564980494, -.44952759789873972005, -.25972131868457243498, .25377239575159905620, .29156822258958438604, -.11342352322434304154, -.28855496859568764271, 1.0000000000000000000, .52553240991632898582, -.85723529191303339177e-1, -.42543909474828335763, -.32697591039397435322, .31045687085550912587e-1, .30239170237287130345, .26852031408771530434, 1.0000000000000000000, .79666647741362673959, .45201621435195496602, .69065957093606829988e-1, -.24272272845677845606, -.40331707559708017427, -.38679791509661859831, -.22657623839999653345, 1.0000000000000000000, .96028985649753623168, .88323491273808809320, .77340930834643009705, .63729376446667512056, .48284868105051651382, .31899212911048349874, .15501881289034966478};
            case(9):
                return {1.0000000000000000000, -.96816023950762608984, .90600137404519587127, -.81648401914464121749, .70385185564224685836, -.57340727072995963395, .43123200800123612775, -.28386832422400701334, .13797828944143667640, 1.0000000000000000000, -.83603110732663579430, .54842201862670122774, -.20680904097355931856, -.10874362879202823797, .32909073428753625869, -.41378547616844158310, .36037764030756310359, -.20285067900653618745, 1.0000000000000000000, -.61337143270059039731, .64336771679762342467e-1, .34314372543281593512, -.41658305611897433234, .18542128240062157922, .13864366442718689660, -.31686407350043643702, .24310311375303873512, 1.0000000000000000000, -.32425342340380892904, -.34228957611636532382, .40114989368782276889, .29087286016160556289e-1, -.33789688867313665423, .17662833698776002963, .18326298197708336391, -.26596913728165218241, 1.0000000000000000000, 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 1.0000000000000000000, .32425342340380892904, -.34228957611636532382, -.40114989368782276889, .29087286016160556289e-1, .33789688867313665423, .17662833698776002963, -.18326298197708336391, -.26596913728165218241, 1.0000000000000000000, .61337143270059039731, .64336771679762342467e-1, -.34314372543281593512, -.41658305611897433234, -.18542128240062157922, .13864366442718689660, .31686407350043643702, .24310311375303873512, 1.0000000000000000000, .83603110732663579430, .54842201862670122774, .20680904097355931856, -.10874362879202823797, -.32909073428753625869, -.41378547616844158310, -.36037764030756310359, -.20285067900653618745, 1.0000000000000000000, .96816023950762608984, .90600137404519587127, .81648401914464121749, .70385185564224685836, .57340727072995963395, .43123200800123612775, .28386832422400701334, .13797828944143667640};
            case(10):
                return {1.0000000000000000000, -.97390652851717172008, .92274088943255291925, -.84850127490206051451, .75407596231954058980, -.64311808493991644516, .51988768420619977502, -.38906823100481328544, .25556594547122784256, -.12430099765556255718, 1.0000000000000000000, -.86506336668898451073, .62250194258092071463, -.32079713257315065471, .18765776238138317556e-1, .22741725203054758027, -.37631042528707037732, .40963103032338160615, -.33514737448347966183, .18351721458256048534, 1.0000000000000000000, -.67940956829902440623, .19239604224440006411, .23508019219316842037, -.42379956249712147495, .33021610628813775084, -.58145665319847555415e-1, -.20967646569634330465, .31798282660714999433, -.22169756095639975783, 1.0000000000000000000, -.43339539412924719080, -.21825264852133173443, .44657975046225583746, -.17501532579202909996, -.22073229538927357449, .32123076511505157766, -.69352195765652122103e-1, -.22472019031770104995, .24561037653348758026, 1.0000000000000000000, -.14887433898163121088, -.46675464678917354251, .21506254183332575029, .29403572102037504054, -.25084390595367278740, -.17656536292520278005, .26382601538929637767, .80850460720979004811e-1, -.25724773603885605693, 1.0000000000000000000, .14887433898163121088, -.46675464678917354251, -.21506254183332575029, .29403572102037504054, .25084390595367278740, -.17656536292520278005, -.26382601538929637767, .80850460720979004811e-1, .25724773603885605693, 1.0000000000000000000, .43339539412924719080, -.21825264852133173443, -.44657975046225583746, -.17501532579202909996, .22073229538927357449, .32123076511505157766, .69352195765652122103e-1, -.22472019031770104995, -.24561037653348758026, 1.0000000000000000000, .67940956829902440623, .19239604224440006411, -.23508019219316842037, -.42379956249712147495, -.33021610628813775084, -.58145665319847555415e-1, .20967646569634330465, .31798282660714999433, .22169756095639975783, 1.0000000000000000000, .86506336668898451073, .62250194258092071463, .32079713257315065471, .18765776238138317556e-1, -.22741725203054758027, -.37631042528707037732, -.40963103032338160615, -.33514737448347966183, -.18351721458256048534, 1.0000000000000000000, .97390652851717172008, .92274088943255291925, .84850127490206051451, .75407596231954058980, .64311808493991644516, .51988768420619977502, .38906823100481328544, .25556594547122784256, .12430099765556255718};
            case(11):
                return {1.0000000000000000000, -.97822865814605699280, .93539696142735285421, -.87290108525425936201, .79277177924387966535, -.69760086468303704964, .59044763989419703586, -.47472874916163770830, .35409569123459934481, -.23230460065179811985, .11308321166471240144, 1.0000000000000000000, -.88706259976809529908, .68032008386099803923, -.41443577059491235677, .13311326328068104303, .11900498117505332970, -.30446331070914362242, .39956918858016944055, -.39817500914666202888, .31199457672845976976, -.16748406042596278988, 1.0000000000000000000, -.73015200557404932409, .29968292686570983285, .12207785357053424637, -.38074912698550859655, .40274624678384007899, -.22183002386091955390, -.44410314580196471569e-1, .25490054636375129356, -.31207688343316282475, .20353027670346685936, 1.0000000000000000000, -.51909612920681181593, -.95808812963757399194e-1, .42895405939351767363, -.31781307599494874069, -.46207279906295353312e-1, .30881860025343557276, -.25810590582919170912, -.19000444019222434002e-1, .24805769051939423233, -.22755459562303754243, 1.0000000000000000000, -.26954315595234497233, -.39101973061887475567, .35535659101930877944, .12564290815848643670, -.34524440759397134247, .65904399730518715195e-1, .26293334384788750151, -.19055113096269641076, -.13670188291261617691, .24150542606172632829, 1.0000000000000000000, 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 0., -.24609375000000000000, 1.0000000000000000000, .26954315595234497233, -.39101973061887475567, -.35535659101930877944, .12564290815848643670, .34524440759397134247, .65904399730518715195e-1, -.26293334384788750151, -.19055113096269641076, .13670188291261617691, .24150542606172632829, 1.0000000000000000000, .51909612920681181593, -.95808812963757399194e-1, -.42895405939351767363, -.31781307599494874069, .46207279906295353312e-1, .30881860025343557276, .25810590582919170912, -.19000444019222434002e-1, -.24805769051939423233, -.22755459562303754243, 1.0000000000000000000, .73015200557404932409, .29968292686570983285, -.12207785357053424637, -.38074912698550859655, -.40274624678384007899, -.22183002386091955390, .44410314580196471569e-1, .25490054636375129356, .31207688343316282475, .20353027670346685936, 1.0000000000000000000, .88706259976809529908, .68032008386099803923, .41443577059491235677, .13311326328068104303, -.11900498117505332970, -.30446331070914362242, -.39956918858016944055, -.39817500914666202888, -.31199457672845976976, -.16748406042596278988, 1.0000000000000000000, .97822865814605699280, .93539696142735285421, .87290108525425936201, .79277177924387966535, .69760086468303704964, .59044763989419703586, .47472874916163770830, .35409569123459934481, .23230460065179811985, .11308321166471240144};
            case(12):
                return {1.0000000000000000000, -.98156063424671925069, .94519191805423264647, -.89189820811916330727, .82314736043800261195, -.74082571484673894480, .64718035694227896075, -.54475051601988938745, .43629030394558757725, -.32468527317797861470, .21286546352414856374, -.10371771048417290210, 1.0000000000000000000, -.90411725637047485668, .72614201990031243672, -.49145104703232548652, .23296988657047647963, .14023067232388513927e-1, -.21738548344081438719, .35298673797546972715, -.40817782900218502906, .38331073521826138431, -.29109986939751313762, .15398630618695745115, 1.0000000000000000000, -.76990267419430468704, .38912519159731250843, .13954240117632991322e-1, -.31064485556808578677, .41933595695372462487, -.33301705720817928987, .11672337941961243659, .12289184638936422361, -.28247088614203358646, .30260001043286677512, -.18797407642662957481, 1.0000000000000000000, -.58731795428661744730, .17413569141125892310e-1, .37449979984975391643, -.39797347543072843916, .12112670153075637389, .20122143751263623208, -.32330181838363991541, .17995804703311127959, .87737831374865407946e-1, -.25986924923939743982, .21161500718202439726, 1.0000000000000000000, -.36783149899818019375, -.29704998251712764468, .42732823324321726467, -.52285886158823287538e-1, -.30724427400652710259, .25076412855413827689, .92051336446518436806e-1, -.28290495199094979418, .11473692244779111233, .17442713386047780003, -.22679317280626205044, 1.0000000000000000000, -.12523340851146891547, -.47647489008889931750, .18293989660091324328, .31726334065955539733, -.21786946246448716312, -.21436446899214918028, .23660135504145943757, .13201192133636643564, -.24153999879715486831, -.61337862254404560506e-1, .23424659352281780539, 1.0000000000000000000, .12523340851146891547, -.47647489008889931750, -.18293989660091324328, .31726334065955539733, .21786946246448716312, -.21436446899214918028, -.23660135504145943757, .13201192133636643564, .24153999879715486831, -.61337862254404560506e-1, -.23424659352281780539, 1.0000000000000000000, .36783149899818019375, -.29704998251712764468, -.42732823324321726467, -.52285886158823287538e-1, .30724427400652710259, .25076412855413827689, -.92051336446518436806e-1, -.28290495199094979418, -.11473692244779111233, .17442713386047780003, .22679317280626205044, 1.0000000000000000000, .58731795428661744730, .17413569141125892310e-1, -.37449979984975391643, -.39797347543072843916, -.12112670153075637389, .20122143751263623208, .32330181838363991541, .17995804703311127959, -.87737831374865407946e-1, -.25986924923939743982, -.21161500718202439726, 1.0000000000000000000, .76990267419430468704, .38912519159731250843, -.13954240117632991322e-1, -.31064485556808578677, -.41933595695372462487, -.33301705720817928987, -.11672337941961243659, .12289184638936422361, .28247088614203358646, .30260001043286677512, .18797407642662957481, 1.0000000000000000000, .90411725637047485668, .72614201990031243672, .49145104703232548652, .23296988657047647963, -.14023067232388513927e-1, -.21738548344081438719, -.35298673797546972715, -.40817782900218502906, -.38331073521826138431, -.29109986939751313762, -.15398630618695745115, 1.0000000000000000000, .98156063424671925069, .94519191805423264647, .89189820811916330727, .82314736043800261195, .74082571484673894480, .64718035694227896075, .54475051601988938745, .43629030394558757725, .32468527317797861470, .21286546352414856374, .10371771048417290210};
            case(13):
                return {1.0000000000000000000, -.98418305471858814947, .95292442779281721332, -.90696475395610377605, .84739052777895620077, -.77560551353947851447, .69329386673261911452, -.60237598589779283012, .50495831265272875804, -.40327846243371863207, .29964719382698605761, -.19638880703556635034, .95781599698468620071e-1, 1.0000000000000000000, -.91759839922297796521, .76298023338485747324, -.55511680183921360357, .31916983027287947279, -.83072064138223915133e-1, -.12622573792619772572, .28630733437613996000, -.38214338876959683613, .40785134174861395370, -.36713405289535943216, .27236368968103682433, -.14247471569000520183, 1.0000000000000000000, -.80157809073330991279, .46379115331548762862, -.85222651467174043075e-1, -.22829629704861227751, .39757327901121940209, -.39401080730621350174, .24576513205244923104, -.24615441080979514716e-1, -.18118785399192739330, .29810270370001984426, -.29146599796736506564, .17453530809000375738, 1.0000000000000000000, -.64234933944034022064, .11891901081916213078, .30092031288258103592, -.42745719547190785060, .25350207456465588527, .57680030963758478629e-1, -.28609599066257535601, .29410541781665200049, -.10253835881393063519, -.13955052663727943144, .26434795898395230017, -.19753584618433634907, 1.0000000000000000000, -.44849275103644685288, -.19828137840163955056, .44720810215538129720, -.20228575223631713893, -.19446383339560771912, .32846676282752813109, -.10690164381793691614, -.19751226936241542880, .26234678982112437090, -.45794161209493619630e-1, -.19928750563854042712, .21328773427315827084, 1.0000000000000000000, -.23045831595513479407, -.42033344691068489541, .31508777449451235729, .18817453887891463693, -.33012971679981355609, -.17330028334972757653e-1, .29038547709868643015, -.11031450276313315507, -.21009940108241733507, .19127944538442885393, .10684302679649932766, -.22253331432094505219, 1.0000000000000000000, 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 0., -.24609375000000000000, 0., .22558593750000000000, 1.0000000000000000000, .23045831595513479407, -.42033344691068489541, -.31508777449451235729, .18817453887891463693, .33012971679981355609, -.17330028334972757653e-1, -.29038547709868643015, -.11031450276313315507, .21009940108241733507, .19127944538442885393, -.10684302679649932766, -.22253331432094505219, 1.0000000000000000000, .44849275103644685288, -.19828137840163955056, -.44720810215538129720, -.20228575223631713893, .19446383339560771912, .32846676282752813109, .10690164381793691614, -.19751226936241542880, -.26234678982112437090, -.45794161209493619630e-1, .19928750563854042712, .21328773427315827084, 1.0000000000000000000, .64234933944034022064, .11891901081916213078, -.30092031288258103592, -.42745719547190785060, -.25350207456465588527, .57680030963758478629e-1, .28609599066257535601, .29410541781665200049, .10253835881393063519, -.13955052663727943144, -.26434795898395230017, -.19753584618433634907, 1.0000000000000000000, .80157809073330991279, .46379115331548762862, .85222651467174043075e-1, -.22829629704861227751, -.39757327901121940209, -.39401080730621350174, -.24576513205244923104, -.24615441080979514716e-1, .18118785399192739330, .29810270370001984426, .29146599796736506564, .17453530809000375738, 1.0000000000000000000, .91759839922297796521, .76298023338485747324, .55511680183921360357, .31916983027287947279, .83072064138223915133e-1, -.12622573792619772572, -.28630733437613996000, -.38214338876959683613, -.40785134174861395370, -.36713405289535943216, -.27236368968103682433, -.14247471569000520183, 1.0000000000000000000, .98418305471858814947, .95292442779281721332, .90696475395610377605, .84739052777895620077, .77560551353947851447, .69329386673261911452, .60237598589779283012, .50495831265272875804, .40327846243371863207, .29964719382698605761, .19638880703556635034, .95781599698468620071e-1};
            case(14):
                return {1.0000000000000000000, -.98628380869681233884, .95913362694623547777, -.91910740525832624765, .86702609624466996958, -.80395491659203874455, .73117906791713580423, -.65017449824697722415, .56257440391357048487, -.47013227245187115371, .37468234818151256204, -.27809846156506938145, .18225219974176150992, -.88971407987391225174e-1, 1.0000000000000000000, -.92843488366357351734, .79298699980508993696, -.60810473240889244026, .39328463150249002225, -.17076672204512031546, -.37069926440194714011e-1, .21028878560223916962, -.33363777223302164482, .39818064460156161843, -.40212712584098190969, .35077449374957341707, -.25558674754745692461, .13254595235649819925, 1.0000000000000000000, -.82720131506976499319, .52639302347972291983, -.17425412539678413924, -.14254409466182693429, .35164609292487346604, -.41449712371057776485, .33535239974129773505, -.15744741564912508849, -.52080793353601666209e-1, .22355714551296693113, -.30569582967790304999, .27974393522818021547, -.16282798626566994045, 1.0000000000000000000, -.68729290481168547015, .20855730550672681673, .21929534267209631347, -.42017821201440842970, .34437763283545636552, -.83780046631356589396e-1, -.18824388371770460670, .31589257640251390437, -.24277014220095459034, .32719654083933541127e-1, .17776851944674195197, -.26416951362996817081, .18506335202114389320, 1.0000000000000000000, -.51524863635815409197, -.10177826409659403371, .43090094388321964444, -.31220326847477767712, -.55168600079837537549e-1, .31228289132400990828, -.25153310576939790363, -.30243611633608148209e-1, .25301950002801563185, -.22047985901652093883, -.13141283593040569229e-1, .21508434196348823962, -.20098864956542065621, 1.0000000000000000000, -.31911236892788976044, -.34725094399584556662, .39742836487019360056, .38495670759370070123e-1, -.34005469233723810442, .16686564816795635890, .19258465062701316918, -.26123771229834215626, -.13720672910450565262e-1, .24343297029641128772, -.13582956175006757674, -.14006917743241647991, .21133845512359956768, 1.0000000000000000000, -.10805494870734366207, -.48248619208977999538, .15892833370200033929, .33181190641128682002, -.19167972031156379474, -.23853802770748167427, .21216515834317998072, .16573547055231316679, -.22241848986969335045, -.10349842831965620341, .22354897848433885047, .48575376935918265874e-1, -.21644676833794842458, 1.0000000000000000000, .10805494870734366207, -.48248619208977999538, -.15892833370200033929, .33181190641128682002, .19167972031156379474, -.23853802770748167427, -.21216515834317998072, .16573547055231316679, .22241848986969335045, -.10349842831965620341, -.22354897848433885047, .48575376935918265874e-1, .21644676833794842458, 1.0000000000000000000, .31911236892788976044, -.34725094399584556662, -.39742836487019360056, .38495670759370070123e-1, .34005469233723810442, .16686564816795635890, -.19258465062701316918, -.26123771229834215626, .13720672910450565262e-1, .24343297029641128772, .13582956175006757674, -.14006917743241647991, -.21133845512359956768, 1.0000000000000000000, .51524863635815409197, -.10177826409659403371, -.43090094388321964444, -.31220326847477767712, .55168600079837537549e-1, .31228289132400990828, .25153310576939790363, -.30243611633608148209e-1, -.25301950002801563185, -.22047985901652093883, .13141283593040569229e-1, .21508434196348823962, .20098864956542065621, 1.0000000000000000000, .68729290481168547015, .20855730550672681673, -.21929534267209631347, -.42017821201440842970, -.34437763283545636552, -.83780046631356589396e-1, .18824388371770460670, .31589257640251390437, .24277014220095459034, .32719654083933541127e-1, -.17776851944674195197, -.26416951362996817081, -.18506335202114389320, 1.0000000000000000000, .82720131506976499319, .52639302347972291983, .17425412539678413924, -.14254409466182693429, -.35164609292487346604, -.41449712371057776485, -.33535239974129773505, -.15744741564912508849, .52080793353601666209e-1, .22355714551296693113, .30569582967790304999, .27974393522818021547, .16282798626566994045, 1.0000000000000000000, .92843488366357351734, .79298699980508993696, .60810473240889244026, .39328463150249002225, .17076672204512031546, -.37069926440194714011e-1, -.21028878560223916962, -.33363777223302164482, -.39818064460156161843, -.40212712584098190969, -.35077449374957341707, -.25558674754745692461, -.13254595235649819925, 1.0000000000000000000, .98628380869681233884, .95913362694623547777, .91910740525832624765, .86702609624466996958, .80395491659203874455, .73117906791713580423, .65017449824697722415, .56257440391357048487, .47013227245187115371, .37468234818151256204, .27809846156506938145, .18225219974176150992, .88971407987391225174e-1};
            case(15):
                return {1.0000000000000000000, -.98799251802048542849, .96419382349668883623, -.92903212721349820032, .88313901608076942836, -.82733683069679348786, .76262225071991605351, -.69014643243615667247, .61119211484279829781, -.52714817351704228505, .43948215415518605271, -.34971135882867407136, .25937308683763494403, -.16999464794941811556, .83063768471759834353e-1, 1.0000000000000000000, -.93727339240070590431, .81772211815349144262, -.65253304460421903362, .45701166703195706908, -.24899434026296441924, .47012522449250390815e-1, .13159134548008345353, -.27239295737188993451, .36527584965928210371, -.40533667443248964438, .39321621650110362355, -.33483098471189082315, .24054690192548666878, -.12389777788023574989, 1.0000000000000000000, -.84820658341042721620, .57918161221118503362, -.25330503850603557007, -.58389956932649284467e-1, .29179217338041244481, -.40509178037911378495, .38800952210810334985, -.26263012543957600130, .75880227436778092713e-1, .11407910681676256156, 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            case(16):
                return {1.0000000000000000000, -.98940093499164993260, .96837131524352664402, -.93724518454063179250, .89651622189396953291, -.84682903108622948653, .78896777950213752944, -.72384239668753330238, .65247258806545882316, -.57596995935581177374, .49551858173719833858, -.41235435600443723162, .32774355538335211566, -.24296094086855060522, .15926784969177756389, -.77890656694384388535e-1, 1.0000000000000000000, -.94457502307323257608, .83833296132069678021, -.69006394508875920581, .51193032100436350724, -.31835071452324386978, .12468597727601452861, .54146558418323361481e-1, -.20499801761774507144, .31762662837940415788, -.38554392582131206333, .40649201194568901382, -.38251228765894147861, .31960651386020941708, -.22703094113843247746, .11629958289453816827, 1.0000000000000000000, -.86563120238783174388, .62397606782110498211, -.32313445482346942601, .21519665792279851707e-1, .22497699434421564105, -.37496941605383685621, .40996371116288619083, -.33729684888284324866, 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            case(17):
                return {1.0000000000000000000, -.99057547531441733568, .97185965844157574257, -.94411692162317373522, .90773862585002287954, -.86323698007421742704, .81123701184264784675, -.75246678161964512638, .68774600187741408608, -.61797324811478916163, .54411197187784042047, -.46717554521476346333, .38821158147838685232, -.30828578873543893694, .22846561906655233045, -.14980397963330551187, .73323269513034686642e-1, 1.0000000000000000000, -.95067552176876776122, .85567592153547823816, -.72199990743867475349, .55942142661060358259, -.37969093598605536610, .19558075540342448648, -.19856323009673134549e-1, -.13573893553243980777, .26139924458058376982, -.34999609816085977941, .39758134019567591996, -.40361436875497468314, .37089857176073644484, -.30523760167481490392, .21484637107890643896, -.10957254616064452226, 1.0000000000000000000, -.88023915372698590212, .66223145163100047847, -.38471065177378483023, .95941823734198313049e-1, .15575537190356199190, -.33130514382534143002, 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            case(18):
                return {1.0000000000000000000, -.99156516842093094673, .97480222483844373100, -.94992310813442879278, .91724199810360310177, -.87717090289068774636, .83021387735469632418, -.77695995761081713249, .71807491586093307720, -.65429195690553618592, .58640149317160734477, -.51524014846031207934, .44167915171446998985, -.36661229076312028637, .29094360209116002279, -.21557497611754698274, .14139385819837140706, -.69261223595194679857e-1, 1.0000000000000000000, -.95582394957139775518, .87039913386139887841, -.74936459667061150625, .60065674940664327457, -.43392811446174597460, .25984399651843919973, -.89311115507178319730e-1, -.67302803519824630408e-1, .20089918435285754319, -.30427355535441706634, .37258901240729269438, -.40366411862003732013, .39805597346953996110, -.35893536722624152958, .29176719742498539173, -.20382436353427019045, .10357598299311274681, 1.0000000000000000000, -.89260246649755573921, .69510874479628017374, -.43902465581692900063, .16444880001479465810, 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            case(19):
                return {1.0000000000000000000, -.99240684384358440319, .97730701556137677769, -.95487238873670832477, .92535805209323402843, -.88909908403620171925, .84650631898538438082, -.79806116170227930597, .74430951841110765568, -.68585492517072902080, .62335096451419889830, -.55749307069099147953, .48900983179778836552, -.41865390356009485220, .34719265444216027513, -.27539866505177779628, .20404020642709404444, -.13387182172524989294, .65625134081528870065e-1, 1.0000000000000000000, -.96020815213483003085, .88299954313927734030, -.77296683133288769474, .63661618500295912561, -.48193782605115950172, .31788099972437925535, -.15376972845236929119, -.13003494872241340315e-2, .13904268140548029347, -.25249852620393171551, .33645883586083153931, -.38776150866151243957, .40544523170708771238, -.39075138850660978103, .34697627656401642462, -.27918638139873434456, .19381893380298003695, -.98197762548394464408e-1, 1.0000000000000000000, -.90315590361481790164, .72353587935144736548, 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            case(20):
                return {1.0000000000000000000, -.99312859918509492479, .97945662177902339157, -.95912490512654811380, .93234268724149760308, -.89938521239186956877, .86059058350138391789, -.81635589918410713611, .76713272179854075356, -.71342193090414660220, .65576802382815864605, -.59475293161364673118, .53098942434067618620, -.46511418462116395405, .39778063190624517128, -.32965158306640185161, .26139183647579662224, -.19366076753289830862, .12710502317269298511, -.62351401478136745526e-1, 1.0000000000000000000, -.96397192727791379127, .89386281486984327235, -.79344981576829726780, .66811374803044205690, -.52451736257895846189, .37020856695057091206, -.21317349709171753113, .61367379235892387567e-1, .77747628061715268967e-1, -.19762904995378550238, .29301906354127047499, -.36022582774687192292, .39730468255504633321, -.40412924102765101418, .38234950007800833172, -.33524131897421972241, .26745848649760147354, -.18470467343309454750, .93347457053951225369e-1, 1.0000000000000000000, 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.29495065984622500868, .28512860168314749406, .80385040345188470633e-1, -.15947026001971032498, -.26671954239480537874, -.17897749275058868300, .27280937150560557899e-1, .19965822849580625756, .22005827082885687875, .84010102484257130577e-1, -.10338702832070793137, -.20720895771272593062, -.15870980204403000664, 1.0000000000000000000, .74633190646015079261, .33551697190066490861, -.80209568826167054305e-1, -.35639790965766357118, -.41461638141085631071, -.27031103832989828668, -.19277784999506946127e-1, .20954535973051553295, .31253987476605217950, .25460028934256856714, .78631268934247966131e-1, -.12090396759945480145, -.24611057254910851306, -.24197236336375883258, -.11944074312338750736, .54135617950202451220e-1, .19084443972917103919, .22582554465334795157, .14741105409530103159, 1.0000000000000000000, .83911697182221882339, .55617593860013556826, .21841646778273089118, -.96397265126688541538e-1, -.32033262039527555200, -.41246259946468613131, -.36819443635911611194, -.21839185136736871571, -.18866862439739801907e-1, .16647280772201228226, .28383290443932582724, .30389052353503397941, .22838442642944237848, .87409778471351034983e-1, -.71354542671652845054e-1, -.19795410737591006791, -.25528510617105921980, -.22957069211469879143, -.13328550823254538206, 1.0000000000000000000, .91223442825132590587, .74825747813053520804, .52948743574442903502, .28408606077411339163, .42885604808457328455e-1, -.16501522114355962225, -.31631956938790568606, -.39665718435928862296, -.40231080236166153503, -.34031188714291296346, -.22692914473429351821, -.84821545769476829001e-1, .60670875315477926828e-1, .18550169634900756966, .27053451526215738337, .30424952619937640507, .28414677711099439851, .21666970006201517203, .11571261738705642742, 1.0000000000000000000, .96397192727791379127, .89386281486984327235, .79344981576829726780, .66811374803044205690, .52451736257895846189, .37020856695057091206, .21317349709171753113, .61367379235892387567e-1, -.77747628061715268967e-1, -.19762904995378550238, -.29301906354127047499, -.36022582774687192292, -.39730468255504633321, -.40412924102765101418, -.38234950007800833172, -.33524131897421972241, -.26745848649760147354, -.18470467343309454750, -.93347457053951225369e-1, 1.0000000000000000000, .99312859918509492479, .97945662177902339157, .95912490512654811380, .93234268724149760308, .89938521239186956877, .86059058350138391789, .81635589918410713611, .76713272179854075356, .71342193090414660220, .65576802382815864605, .59475293161364673118, .53098942434067618620, .46511418462116395405, .39778063190624517128, .32965158306640185161, .26139183647579662224, .19366076753289830862, .12710502317269298511, .62351401478136745526e-1};
            default:
                throw Error( Message(_ping_)<<"n>20 not allowed! You typed: "<<n );
        }
    }
    static std::vector<real_type> forward(unsigned n)
    {
        switch( n)
        {
            case(0):
                return {};
            case(1):
                return {1.};
            case(2):
                return {.50000000000000000000, .50000000000000000000, -.86602540378443864675, .86602540378443864675};
            case(3):
                return {.27777777777777777778, .44444444444444444444, .27777777777777777778, -.64549722436790281420, 0., .64549722436790281420, .55555555555555555555, -1.1111111111111111111, .55555555555555555555};
            case(4):
                return {.17392742256872692868, .32607257743127307132, .32607257743127307132, .17392742256872692868, -.44932565746768105384, -.33257548547846420788, .33257548547846420788, .44932565746768105384, .53250804201891149915, -.53250804201891149920, -.53250804201891149920, .53250804201891149915, -.37102700340194730524, .93977247037775304055, -.93977247037775304055, .37102700340194730524};
            case(5):
                return {.11846344252809454376, .23931433524968323402, .28444444444444444444, .23931433524968323402, .11846344252809454376, -.32204755229841746931, -.38659027500089126226, 0., .38659027500089126226, .32204755229841746931, .43342389699652308412, -.77868341440967528540e-1, -.71111111111111111110, -.77868341440967528540e-1, .43342389699652308412, -.41547714135083258686, .69919864488923337625, 0., -.69919864488923337625, .41547714135083258686, .26199601592044532880, -.74199601592044532880, .96000000000000000000, -.74199601592044532880, .26199601592044532880};
            case(6):
                return {.85662246189585172520e-1, .18038078652406930378, .23395696728634552370, .23395696728634552370, .18038078652406930378, .85662246189585172520e-1, -.23963229926985989010, -.35780840756364629484, -.16747986333708268263, .16747986333708268263, .35780840756364629484, .23963229926985989010, .34446891874491355394, .14051372778390095470, -.48498264652881450866, -.48498264652881450866, .14051372778390095470, .34446891874491355394, -.37672109799391199436, .33980319948792779488, .53055194874243867420, -.53055194874243867420, -.33980319948792779488, .37672109799391199436, .32534907297640428362, -.69522592887681074560, .36987685590040646196, .36987685590040646196, -.69522592887681074560, .32534907297640428362, -.19383956497639703850, .58413663668322694185, -.86115096417790722320, .86115096417790722320, -.58413663668322694185, .19383956497639703850};
            case(7):
                return {.64742483084434846635e-1, .13985269574463833395, .19091502525255947248, .20897959183673469388, .19091502525255947248, .13985269574463833395, .64742483084434846635e-1, -.18434280888046294490, -.31111540585437914820, -.23244581197153380567, 0., .23244581197153380567, .31111540585437914820, .18434280888046294490, .27554683851875366443, .22712270004199054418, -.24144504876482584128, -.52244897959183673470, -.24144504876482584128, .22712270004199054418, .27554683851875366443, -.32346645039070334272, .90980646238797506880e-1, .59022407969693697245, 0., -.59022407969693697245, -.90980646238797506880e-1, .32346645039070334272, .31877204474697911646, -.45841186461881008858, -.21301324135265882380, .70530612244897959185, -.21301324135265882380, -.45841186461881008858, .31877204474697911646, -.25896441615265599776, .63346305606260831320, -.55180512530396907690, 0., .55180512530396907690, -.63346305606260831320, .25896441615265599776, .14882745793656058593, -.46596193122691430834, .74162426920872106940, -.84897959183673469390, .74162426920872106940, -.46596193122691430834, .14882745793656058593, };
            case(8):
                return {.50614268145188129575e-1, .11119051722668723527, .15685332293894364367, .18134189168918099148, .18134189168918099148, .15685332293894364367, .11119051722668723527, .50614268145188129575e-1, -.14581310488161158486, -.26574527304235230365, -.24729451442246177792, -.99793155214469291065e-1, .99793155214469291065e-1, .24729451442246177792, .26574527304235230365, .14581310488161158486, .22352144354258714756, .25129958334321499280, -.67230102038547325535e-1, -.40759092484725481484, -.40759092484725481484, -.67230102038547325535e-1, .25129958334321499280, .22352144354258714756, -.27401882283041490455, -.53756356443960321800e-1, .46712075003583032558, .32968848669588295664, -.32968848669588295664, -.46712075003583032558, .53756356443960321800e-1, .27401882283041490455, .29030541733775395146, -.24289619147803757642, -.46158532259653042906, .41417609673681405396, .41417609673681405396, -.46158532259653042906, -.24289619147803757642, .29030541733775395146, -.26882935877865387361, .49329537666193687178, -.53565811005204403310e-1, -.58160886344932168820, .58160886344932168820, .53565811005204403310e-1, -.49329537666193687178, .26882935877865387361, .20989219106703229187, -.55910738314336459945, .61660486350253587505, -.26738967142620356752, -.26738967142620356752, .61660486350253587505, -.55910738314336459945, .20989219106703229187, -.11769245644771356058, .37789693708459212620, -.63177455311900480475, .78490655792181316395, -.78490655792181316395, .63177455311900480475, -.37789693708459212620, .11769245644771356058};
            case(9):
                return {.40637194180787205986e-1, .90324080347428702030e-1, .13030534820146773116, .15617353852000142004, .16511967750062988158, .15617353852000142004, .13030534820146773116, .90324080347428702030e-1, .40637194180787205986e-1, -.11802994695296655162, -.22654122273336252027, -.23977673434465068730, -.15191941353059125124, 0., .15191941353059125124, .23977673434465068730, .22654122273336252027, .11802994695296655162, .18408676882567323211, .24767857237368600964, .41917127179448800064e-1, -.26728287150302068984, -.41279919375157470395, -.26728287150302068984, .41917127179448800064e-1, .24767857237368600964, .18408676882567323211, -.23225733742043254638, -.13075885503429312514, .31299423837970343208, .43854298861904764590, 0., -.43854298861904764590, -.31299423837970343208, .13075885503429312514, .23225733742043254638, .25742308079017251530, -.88399514378539077605e-1, -.48854700164173070642, .40883979447784343565e-1, .55727891156462585030, .40883979447784343565e-1, -.48854700164173070642, -.88399514378539077605e-1, .25742308079017251530, -.25631828865861448586, .32697299717919908166, .26577523243893242908, -.58047608034881012665, 0., .58047608034881012665, -.26577523243893242908, -.32697299717919908166, .25631828865861448586, .22781276499952119007, -.48587230374848570511, .23485814259845643855, .35860074107366252346, -.67079868984630889390, .35860074107366252346, .23485814259845643855, -.48587230374848570511, .22781276499952119007, -.17303418319898450494, .48826168407835635280, -.61933625145014751080, .42931242562632532096, 0., -.42931242562632532096, .61933625145014751080, -.48826168407835635280, .17303418319898450494, .95319859192996895970e-1, -.31147911749498633493, .53851981006966243045, -.70613480220859009905, .76754850088183421515, -.70613480220859009905, .53851981006966243045, -.31147911749498633493, .95319859192996895970e-1};
            case(10):
                return {.33335672154344068797e-1, .74725674575290296575e-1, .10954318125799102200, .13463335965499817754, .14776211235737643508, .14776211235737643508, .13463335965499817754, .10954318125799102200, .74725674575290296575e-1, .33335672154344068797e-1, -.97397486230871337200e-1, -.19392733087861823016, -.22327405646578038461, -.17504843391186786825, -.65993960411201812395e-1, .65993960411201812395e-1, .17504843391186786825, .22327405646578038461, .19392733087861823016, .97397486230871337200e-1, .15380093886765716780, .23258438791893963554, .10537837264449207014, -.14692043662014180792, -.34484326281094706551, -.34484326281094706551, -.14692043662014180792, .10537837264449207014, .23258438791893963554, .15380093886765716780, -.19799752225874642408, -.16780247493343260160, .18026002472505729990, .42087172511036960156, .22244666829167194558, -.22244666829167194558, -.42087172511036960156, -.18026002472505729990, .16780247493343260160, .19799752225874642408, .22623866153420144849, .12620567594914553360e-1, -.41781917062511524765, -.21206611172245439330, .39102605321845363909, .39102605321845363909, -.21206611172245439330, -.41781917062511524765, .12620567594914553360e-1, .22623866153420144849, -.23582650999695321896, .18693298324845622380, .39790215063972452789, -.32689723563879101620, -.40771747957258742706, .40771747957258742706, .32689723563879101620, -.39790215063972452789, -.18693298324845622380, .23582650999695321896, .22530047017112747534, -.36556065493077927679, -.82802995021481062590e-1, .56222890271580475405, -.33916572293467189001, -.33916572293467189001, .56222890271580475405, -.82802995021481062590e-1, -.36556065493077927679, .22530047017112747534, -.19454776491670589876, .45914932601828828098, -.34452940630964207000, -.14005678673071325790, .58475233993128203730, -.58475233993128203730, .14005678673071325790, .34452940630964207000, -.45914932601828828098, .19454776491670589876, .14483086372474501934, -.42574993188706268500, .59215845700324115635, -.51433218148130563870, .20309279264038214806, .20309279264038214806, -.51433218148130563870, .59215845700324115635, -.42574993188706268500, .14483086372474501934, -.78729488819770758190e-1, .26055550546134254061, -.46142366598172683002, .62827965301781860070, -.72221790864882911365, .72221790864882911365, -.62827965301781860070, .46142366598172683002, -.26055550546134254061, .78729488819770758190e-1};
            case(11):
                return {.27834283558086833242e-1, .62790184732452312315e-1, .93145105463867125715e-1, .11659688229599523996, .13140227225512333109, .13646254338895031536, .13140227225512333109, .11659688229599523996, .93145105463867125715e-1, .62790184732452312315e-1, .27834283558086833242e-1, -.81684881566452419050e-1, -.16709647352606434058, -.20403025669154676518, -.18157497083230012268, -.10625574948886560274, 0., .10625574948886560274, .18157497083230012268, .20403025669154676518, .16709647352606434058, .81684881566452419050e-1, .13018052131870875656, .21358711871414757922, .13956998914313460596, -.55855044440271221670e-1, -.25690440549953182588, -.34115635847237578840, -.25690440549953182588, -.55855044440271221670e-1, .13956998914313460596, .21358711871414757922, .13018052131870875656, -.17007603427590149108, -.18215749016773542376, .79596681819409582335e-1, .35010294181446732048, .32686264464540208700, 0., -.32686264464540208700, -.35010294181446732048, -.79596681819409582335e-1, .18215749016773542376, .17007603427590149108, .19859611050290847946, .75223857525601714445e-1, -.31918425829506481372, -.33350412432520105746, .14858787262290202008, .46056108393770731432, .14858787262290202008, -.33350412432520105746, -.31918425829506481372, .75223857525601714445e-1, .19859611050290847946, -.21358942305749637574, .82195792272699692620e-1, .41265225795043184383, -.59263872540976677980e-1, -.49902489605343970330, 0., .49902489605343970330, .59263872540976677980e-1, -.41265225795043184383, -.82195792272699692620e-1, .21358942305749637574, .21365093145523691066, -.24852499780785500822, -.26861095257850766654, .46809471779932983236, .11257984239060125980, -.55437908251761065610, .11257984239060125980, .46809471779932983236, -.26861095257850766654, -.24852499780785500822, .21365093145523691066, -.19820601926011351477, .37633534746517371042, -.62049051528838743620e-1, -.45141515882801246092, .51825058249875105955, 0., -.51825058249875105955, .45141515882801246092, .62049051528838743620e-1, -.37633534746517371042, .19820601926011351477, .16755199790085020919, -.42502520046280156489, .40362655065543242570, -.37661673092975722550e-1, -.42566047701779221320, .63433760403457373155, -.42566047701779221320, -.37661673092975722550e-1, .40362655065543242570, -.42502520046280156489, .16755199790085020919, -.12285461040141517279, .37221374505776186656, -.55230025018412145555, .54953231353801824930, -.34129582268916007405, 0., .34129582268916007405, -.54953231353801824930, .55230025018412145555, -.37221374505776186656, .12285461040141517279, .66099393761829909305e-1, -.22084345697163559506, .39811483086132405752, -.55717528443721414100, .66642159667550293160, -.70523415977961432505, .66642159667550293160, -.55717528443721414100, .39811483086132405752, -.22084345697163559506, .66099393761829909305e-1};
            case(12):
                return {.23587668193255913598e-1, .53469662997659215480e-1, .80039164271673113165e-1, .10158371336153296088, .11674626826917740438, .12457352290670139250, .12457352290670139250, .11674626826917740438, .10158371336153296088, .80039164271673113165e-1, .53469662997659215480e-1, .23587668193255913598e-1, -.69458179656520322690e-1, -.14502853502549265018, -.18486709983911513114, -.17898581616100099648, -.12882886457968561368, -.46802300651663298236e-1, .46802300651663298236e-1, .12882886457968561368, .17898581616100099648, .18486709983911513114, .14502853502549265018, .69458179656520322690e-1, .11147436671005186654, .19413284546254628794, .15572627566251785017, .88446750811668417620e-2, -.17339738474149520930, -.29678077817478763710, -.29678077817478763710, -.17339738474149520930, .88446750811668417620e-2, .15572627566251785017, .19413284546254628794, .11147436671005186654, -.14726459296692032103, -.18394405305265649007, .78182000194311869720e-2, .26630156225322206517, .34922283590044379624, .15952627179834415086, -.15952627179834415086, -.34922283590044379624, -.26630156225322206517, -.78182000194311869720e-2, .18394405305265649007, .14726459296692032103, .17474514130949431825, .11211139191173643730, -.22377379162467767810, -.36384861108283378261, -.54937638829706878920e-1, .35570350831598758408, .35570350831598758408, -.54937638829706878920e-1, -.36384861108283378261, -.22377379162467767810, .11211139191173643730, .17474514130949431825, -.19221786265920149397, .82478954702026470070e-2, .36919629498002251602, .13534950141601142324, -.39456584681068129362, -.29854843120289561917, .29854843120289561917, .39456584681068129362, -.13534950141601142324, -.36919629498002251602, -.82478954702026470070e-2, .19221786265920149397, .19845118176971623163, -.15110587102212645100, -.34650729031301012490, .26573067079623031460, .38058509091808292124, -.34715378214889289157, -.34715378214889289157, .38058509091808292124, .26573067079623031460, -.34650729031301012490, -.15110587102212645100, .19845118176971623163, -.19274091629973136386, .28311122883287104028, .14013662609566782742, -.49263298871919097078, .16119975028982323357, .44211396483020754362, -.44211396483020754362, -.16119975028982323357, .49263298871919097078, -.14013662609566782742, -.28311122883287104028, .19274091629973136386, .17494820573185594904, -.37102722631767105820, .16721473157372820448, .31077371333751833610, -.56147765613684104145, .27956823181140961004, .27956823181140961004, -.56147765613684104145, .31077371333751833610, .16721473157372820448, -.37102722631767105820, .17494820573185594904, -.14551280132821745791, .38941442087460297676, -.42956593949985867220, .16934195955358997847, .25450704304092285940, -.57170028288779797680, .57170028288779797680, -.25450704304092285940, -.16934195955358997847, .42956593949985867220, -.38941442087460297676, .14551280132821745791, .10544099839163595455, -.32686525022230040722, .50861689081657065530, -.55436814985044605570, .42763805622508023892, -.16046254536054038592, -.16046254536054038592, .42763805622508023892, -.55436814985044605570, .50861689081657065530, -.32686525022230040722, .10544099839163595455, -.56268555635291563000e-1, .18937270565563256637, -.34604162358432194398, .49442267934928262057, -.60897690166332891715, .67116123783272482010, -.67116123783272482010, .60897690166332891715, -.49442267934928262057, .34604162358432194398, -.18937270565563256637, .56268555635291563000e-1};
            case(13):
                return {.20242002382657939760e-1, .46060749918864223957e-1, .69436755109893619230e-1, .89072990380972869140e-1, .10390802376844425116, .11314159013144861920, .11627577661543695510, .11314159013144861920, .10390802376844425116, .89072990380972869140e-1, .69436755109893619230e-1, .46060749918864223957e-1, .20242002382657939760e-1, -.59765507215755692470e-1, -.12679581117767917228, -.16697694476311478472, -.17164792959958110272, -.13980598630401020894, -.78223260978539240045e-1, 0., .78223260978539240045e-1, .13980598630401020894, .17164792959958110272, .16697694476311478472, .12679581117767917228, .59765507215755692470e-1, .96445492689375799520e-1, .17571720861488290260, .16102076367451320290, .52962359534050185150e-1, -.10301513089898725501, -.23778597284453864128, -.29068944153859238775, -.23778597284453864128, -.10301513089898725501, .52962359534050185150e-1, .16102076367451320290, .17571720861488290260, .96445492689375799520e-1, -.12851147897396357312, -.17898367329693007836, -.41423090658193861270e-1, .18762710494380640738, .32527957075741543203, .24954672286101899086, 0., -.24954672286101899086, -.32527957075741543203, -.18762710494380640738, .41423090658193861270e-1, .17898367329693007836, .12851147897396357312, .15437592974109060456, .13231081560460897177, -.14266938663594018128, -.34267401594492198706, -.18917201476249979494, .19161329895911252522, .39243074607709972344, .19161329895911252522, -.18917201476249979494, -.34267401594492198706, -.14266938663594018128, .13231081560460897177, .15437592974109060456, -.17269789518375634951, -.42089977286660388886e-1, .30366818254233395456, .24838206634179686772, -.22226987884830948788, -.41086541219213284158, 0., .41086541219213284158, .22226987884830948788, -.24838206634179686772, -.30366818254233395456, .42089977286660388886e-1, .17269789518375634951, .18243752932968955956, -.75582677923254952995e-1, -.35566481518844939688, .66790526961717990830e-1, .44369431858734753769, -.25489710516944423138e-1, -.47237034250021263008, -.25489710516944423138e-1, .44369431858734753769, .66790526961717990830e-1, -.35566481518844939688, -.75582677923254952995e-1, .18243752932968955956, -.18289944212698571981, .19781295792954031352, .25597699933314876371, -.38225138136483717708, -.16661907820079925788, .49282011945037109432, 0., -.49282011945037109432, .16661907820079925788, .38225138136483717708, -.25597699933314876371, -.19781295792954031352, .18289944212698571981, .17376324525361096297, -.29923078807548302005, -.29056678022453823756e-1, .44534643388696905559, -.34889286285097683580, -.21217969037207644942, .54050068036082022095, -.21217969037207644942, -.34889286285097683580, .44534643388696905559, -.29056678022453823756e-1, -.29923078807548302005, .17376324525361096297, -.15510010835170129704, .35693283447076656586, -.23904083628396784502, -.17353456671796577358, .51793879297386034980, -.45164862615846419553, 0., .45164862615846419553, -.51793879297386034980, .17353456671796577358, .23904083628396784502, -.35693283447076656586, .15510010835170129704, .12737464343945496282, -.35511986573935663410, .43468497312272458510, -.26103383705326386788, -.99925996619652646060e-1, .45447487281537307582, -.60090957993055895155, .45447487281537307582, -.99925996619652646060e-1, -.26103383705326386788, .43468497312272458510, -.35511986573935663410, .12737464343945496282, -.91431962098649541820e-1, .28854134333967968429, -.46548442184557562752, .54156405377957005690, -.47627413007079880772, .27803296876289690032, 0., -.27803296876289690032, .47627413007079880772, -.54156405377957005690, .46548442184557562752, -.28854134333967968429, .91431962098649541820e-1, .48470284232779770298e-1, -.16406230622896526190, .30297913614688563850, -.43987771317686819640, .55405767405932377835, -.62944432598732976005, .65575450190834806220, -.62944432598732976005, .55405767405932377835, -.43987771317686819640, .30297913614688563850, -.16406230622896526190, .48470284232779770298e-1};
            case(14):
                return {.17559730165875931516e-1, .40079043579880104903e-1, .60759285343951592345e-1, .78601583579096767285e-1, .92769198738968906870e-1, .10259923186064780198, .10763192673157889510, .10763192673157889510, .10259923186064780198, .92769198738968906870e-1, .78601583579096767285e-1, .60759285343951592345e-1, .40079043579880104903e-1, .17559730165875931516e-1, -.51956632643065266115e-1, -.11163234649029983481, -.15078048221764756684, -.16206693210262768262, -.14339760943887695234, -.98222051787699428335e-1, -.34890486966759986034e-1, .34890486966759986034e-1, .98222051787699428335e-1, .14339760943887695234, .16206693210262768262, .15078048221764756684, .11163234649029983481, .51956632643065266115e-1, .84210638410969016620e-1, .15891080261733287918, .15991631958334947616, .81964672399091031780e-1, -.47209440046420978007e-1, -.17813840058429292008, -.25965459238002850564, -.25965459238002850564, -.17813840058429292008, -.47209440046420978007e-1, .81964672399091031780e-1, .15991631958334947616, .15891080261733287918, .84210638410969016620e-1, -.11297494620856210320, -.17060579249943130802, -.74112892891407506515e-1, .12065872843883210932, .27982034709938184080, .28543091468720588838, .11974033938009934938, -.11974033938009934938, -.28543091468720588838, -.27982034709938184080, -.12065872843883210932, .74112892891407506515e-1, .17060579249943130802, .11297494620856210320, .13702269867146261972, .14186224696756847023, -.77947895894878706935e-1, -.29724005564789369079, -.26066562354083084726, .35546636248845926976e-1, .32142199319572622806, .32142199319572622806, .35546636248845926976e-1, -.26066562354083084726, -.29724005564789369079, -.77947895894878706935e-1, .14186224696756847023, .13702269867146261972, -.15528954540974040310, -.75285835843236147325e-1, .23502341830118914527, .29775490019096385034, -.56297415074528588655e-1, -.38378285246850500262, -.22693943373754146228, .22693943373754146228, .38378285246850500262, .56297415074528588655e-1, -.29775490019096385034, -.23502341830118914527, .75285835843236147325e-1, .15528954540974040310, .16691099276230048919, -.19314453564893678154e-1, -.32739913717911656948, -.85608176388217593905e-1, .37661303690421975422, .22256373523749864964, -.33376599777179105149, -.33376599777179105149, .22256373523749864964, .37661303690421975422, -.85608176388217593905e-1, -.32739913717911656948, -.19314453564893678154e-1, .16691099276230048919, -.17125333124926040876, .12642260103768311446, .30563658219990640863, -.22194401038936397603, -.35001787017827041012, .29638555833724162865, .34253617166680473614, -.34253617166680473614, -.29638555833724162865, .35001787017827041012, .22194401038936397603, -.30563658219990640863, -.12642260103768311446, .17125333124926040876, .16793713042616350389, -.22732200782476357704, -.16262867171957998978, .42210416468401293374, -.47696485509780568534e-1, -.45564740645232778177, .30325327639627547948, .30325327639627547948, -.45564740645232778177, -.47696485509780568534e-1, .42210416468401293374, -.16262867171957998978, -.22732200782476357704, .16793713042616350389, -.15685252108397355757, .30321528874536405874, -.60123443901906363145e-1, -.36256023483163324962, .44597590937573708997, -.26746879523245109989e-1, -.45484728150266189074, .45484728150266189074, .26746879523245109989e-1, -.44597590937573708997, .36256023483163324962, .60123443901906363145e-1, -.30321528874536405874, .15685252108397355757, .13816573957166683728, -.33845428262588554578, .28524662029293496801, .54008149128306179230e-1, -.42952853703991300964, .52449675100132151090, -.23393444032843093998, -.23393444032843093998, .52449675100132151090, -.42952853703991300964, .54008149128306179230e-1, .28524662029293496801, -.33845428262588554578, .13816573957166683728, -.11231668072644025410, .32335024309908929228, -.42719878330868195118, .32137640419758366074, -.28039446034542435090e-1, -.32052820008908331074, .55340316728235031785, -.55340316728235031785, .32052820008908331074, .28039446034542435090e-1, -.32137640419758366074, .42719878330868195118, -.32335024309908929228, .11231668072644025410, .80007486240066381040e-1, -.25609180983485851505, .42492603959422284284, -.51910355261588214560, .49883005163127975844, -.35927475029796787484, .13070653528313955306, .13070653528313955306, -.35927475029796787484, .49883005163127975844, -.51910355261588214560, .42492603959422284284, -.25609180983485851505, .80007486240066381040e-1, -.42182475751889509408e-1, .14343250502248569218, -.26711942614641551112, .39274935834557920612, -.50343001134691010775, .58544540527402716675, -.62900773319800157730, .62900773319800157730, -.58544540527402716675, .50343001134691010775, -.39274935834557920612, .26711942614641551112, -.14343250502248569218, .42182475751889509408e-1};
            case(15):
                return {.15376620998058634178e-1, .35183023744054062354e-1, .53579610233585967505e-1, .69785338963077157225e-1, .83134602908496966775e-1, .93080500007781105515e-1, .99215742663555788230e-1, .10128912096278063644, .99215742663555788230e-1, .93080500007781105515e-1, .83134602908496966775e-1, .69785338963077157225e-1, .53579610233585967505e-1, .35183023744054062354e-1, .15376620998058634178e-1, -.45575959495555859288e-1, -.98928336058512408600e-1, -.13633973441007694682, -.15166121080149850758, -.14240263452483799746, -.11006341339416021142, -.59884864366430153570e-1, 0., .59884864366430153570e-1, .11006341339416021142, .14240263452483799746, .15166121080149850758, .13633973441007694682, .98928336058512408600e-1, .45575959495555859288e-1, .74130214962888130275e-1, .14384968349516235422, .15516162518367614494, .10020182825270227130, -.45666532216762307938e-2, -.12424714338629531752, -.21791815408298155688, -.25322280240695159110, -.21791815408298155688, -.12424714338629531752, -.45666532216762307938e-2, .10020182825270227130, .15516162518367614494, .14384968349516235422, .74130214962888130275e-1, -.99997624406275096835e-1, -.16070659921463088770, -.95003896633498096885e-1, .66545483122303967815e-1, .22759921705442971584, .28547817168660442059, .19545653980363524230, 0., -.19545653980363524230, -.28547817168660442059, -.22759921705442971584, -.66545483122303967815e-1, .95003896633498096885e-1, .16070659921463088770, .99997624406275096835e-1, .12221724544985160888, .14471147099245567226, -.28156600206064975601e-1, -.24373760595153139900, -.28622886190326990867, -.85439969774410168695e-1, .20570892976827684684, .34185078324938464798, .20570892976827684684, -.85439969774410168695e-1, -.28622886190326990867, -.24373760595153139900, -.28156600206064975601e-1, .14471147099245567226, .12221724544985160888, -.13993809371695555524, -.96364111641676489450e-1, .17197522010826781318, .30479207702892341760, .73418443305911730540e-1, -.28479903020814684046, -.33676912075020135697, 0., .33676912075020135697, .28479903020814684046, -.73418443305911730540e-1, -.30479207702892341760, -.17197522010826781318, .96364111641676489450e-1, .13993809371695555524, .15244519308208576794, .21502555016798064855e-1, -.28216057612005021448, -.18500517510293604460, .25370831699804987220, .34606123776812695470, -.10080802468642623280, -.41148705391129633553, -.10080802468642623280, .34606123776812695470, .25370831699804987220, -.18500517510293604460, -.28216057612005021448, .21502555016798064855e-1, .15244519308208576794, -.15918180187099591729, .69446721488066960435e-1, .31184098442208202422, -.69062559848567751880e-1, -.39622888411422604414, .40595191136665513174e-1, .43708762902082404033, 0., -.43708762902082404033, -.40595191136665513174e-1, .39622888411422604414, .69062559848567751880e-1, -.31184098442208202422, -.69446721488066960435e-1, .15918180187099591729, .15976718161797382088, -.16292133407778126336, 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            case(16):
                return {.13576229705877047426e-1, .31126761969323946432e-1, .47579255841246392405e-1, .62314485627766936025e-1, .74797994408288366040e-1, .84578259697501269095e-1, .91301707522461794435e-1, .94725305227534248145e-1, .94725305227534248145e-1, .91301707522461794435e-1, .84578259697501269095e-1, .74797994408288366040e-1, .62314485627766936025e-1, .47579255841246392405e-1, .31126761969323946432e-1, .13576229705877047426e-1, -.40297003093968489856e-1, -.88204685716107554880e-1, -.12355826532772914480, -.14121791144276886637, -.13864771162152948877, -.11621478589951702436, -.77132655091603846295e-1, -.27000266984412920974e-1, .27000266984412920974e-1, .77132655091603846295e-1, .11621478589951702436, .13864771162152948877, .14121791144276886637, .12355826532772914480, .88204685716107554880e-1, .40297003093968489856e-1, .65734157081641966515e-1, .13047295269033893761, .14844158484837632164, .11090536803696773090, .27172832358607645842e-1, -.78374844859199739375e-1, 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.10954179147129811000, -.12646419992395141032, -.10900149605102133014, .11774661769527886490, .28673879574294529361, .16152203654857205786, -.16447783221146653922, -.34805003127899844752, -.17787032786934122042, .17787032786934122042, .34805003127899844752, .16447783221146653922, -.16152203654857205786, -.28673879574294529361, -.11774661769527886490, .10900149605102133014, .12646419992395141032, .13924570146573803338, .50453919562579504690e-1, -.23192995512788745835, -.23959819842067113232, .12327693233144715706, .36401331460651631036, .10836995418974235480, -.31383166860746476963, -.31383166860746476963, .10836995418974235480, .36401331460651631036, .12327693233144715706, -.23959819842067113232, -.23192995512788745835, .50453919562579504690e-1, .13924570146573803338, -.14740575972423791000, .25281105530178674779e-1, .29258652448568702464, .52694048195870830080e-1, -.35201317927912986078, -.16501933751603285803, .34141737366237718391, .27179595715446729278, -.27179595715446729278, 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            case(17):
                return {.12074151434273965980e-1, .27729764686993600564e-1, .42518074158589590442e-1, .55941923596701985545e-1, .67568184234262736645e-1, .77022880538405144040e-1, .84002051078225022255e-1, .88281352683496323165e-1, .89723235178103262730e-1, .88281352683496323165e-1, .84002051078225022255e-1, .77022880538405144040e-1, .67568184234262736645e-1, .55941923596701985545e-1, .42518074158589590442e-1, .27729764686993600564e-1, .12074151434273965980e-1, -.35881074888072562966e-1, -.79086025536998376775e-1, -.11227822084637438779, -.13115819008724256633, -.13331293815454350932, -.11846670597354746276, -.88512565601842700695e-1, -.47270474925180338689e-1, 0., .47270474925180338689e-1, .88512565601842700695e-1, .11846670597354746276, .13331293815454350932, .13115819008724256633, .11227822084637438779, .79086025536998376775e-1, .35881074888072562966e-1, .58671903444426792205e-1, .11863845976252605712, .14078402985298656865, .11640009670559180274, .50269725851047242290e-1, 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            case(18):
                return {.10808006763241655156e-1, .24857274447484898226e-1, .38212865127444528264e-1, .50471022053143582780e-1, .61277603355739230090e-1, .70321457335325325600e-1, .77342337563132622465e-1, .82138241872916361495e-1, .84571191481571795920e-1, .84571191481571795920e-1, .82138241872916361495e-1, .77342337563132622465e-1, .70321457335325325600e-1, .61277603355739230090e-1, .50471022053143582780e-1, .38212865127444528264e-1, .24857274447484898226e-1, .10808006763241655156e-1, -.32150529139464817617e-1, -.71277534713925598080e-1, -.10232669299408626169, -.12169143212556921776, -.12715477281286933522, -.11809170184477860470, -.95537391965613300795e-1, -.62068475190914636525e-1, -.21508571582416027238e-1, .21508571582416027238e-1, .62068475190914636525e-1, .95537391965613300795e-1, .11809170184477860470, .12715477281286933522, .12169143212556921776, .10232669299408626169, .71277534713925598080e-1, .32150529139464817617e-1, .52678345194384562055e-1, .10817875074622968888, 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            case(19):
                return {.97308941148632385180e-2, .22407113382849800166e-1, .34522271368820613290e-1, .45745010811224999732e-1, .55783322773666997360e-1, .64376981269668113840e-1, .71303351086803305890e-1, .76383021032929833390e-1, .79484421696977173825e-1, .80527224924391847990e-1, .79484421696977173825e-1, .76383021032929833390e-1, .71303351086803305890e-1, .64376981269668113840e-1, .55783322773666997360e-1, .45745010811224999732e-1, .34522271368820613290e-1, .22407113382849800166e-1, .97308941148632385180e-2, -.28971017748922609256e-1, -.64546478808065480700e-1, -.93536979578829412450e-1, -.11290527257353458278, -.12065366693756381996, -.11598388148937651078, -.99376352030959927340e-1, -.72540366917377319285e-1, -.38238042638471411842e-1, 0., .38238042638471411842e-1, .72540366917377319285e-1, .99376352030959927340e-1, .11598388148937651078, .12065366693756381996, .11290527257353458278, .93536979578829412450e-1, .64546478808065480700e-1, .28971017748922609256e-1, 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.23192241373182424886, -.20641618035282752246, -.11881302521873335516, .12738100687379637132, -.12477283893527210104, .17339863952729196093, .11527526502019042159, -.32506050821605097915, .55504067612071859240e-1, .35260068659676064435, -.27060940055360995632, -.22755407320876915952, .41550960979271537882, 0., -.41550960979271537882, .22755407320876915952, .27060940055360995632, -.35260068659676064435, -.55504067612071859240e-1, .32506050821605097915, -.11527526502019042159, -.17339863952729196093, .12477283893527210104, .11896257235878402417, -.21721540225208510218, .83567187363493310755e-2, .30406015681903176887, -.30061447796774610155, -.82942395978365781150e-1, .41517541647376953594, -.27904602983056528500, -.19380917746970116070, .45414523822105754116, -.19380917746970116070, -.27904602983056528500, .41517541647376953594, -.82942395978365781150e-1, -.30061447796774610155, .30406015681903176887, .83567187363493310755e-2, -.21721540225208510218, .11896257235878402417, -.10999467377057111808, .24529114648970612666, -.14058907558723880878, -.16731268737646547479, .38999262543337873693, -.27862942670343084634, -.10735789368456185091, .43004731755719045946, -.38570257098455495675, 0., .38570257098455495675, -.43004731755719045946, .10735789368456185091, .27862942670343084634, -.38999262543337873693, .16731268737646547479, .14058907558723880878, -.24529114648970612666, .10999467377057111808, .97976353777213939970e-1, -.25391270933643433084, .25401588827617325338, -.42382840077369990392e-1, -.25862192502341045832, .43595211113043404076, -.34389003777414916136, .18573243652945050494e-1, .33687956510222436068, -.48917929945525340862, .33687956510222436068, .18573243652945050494e-1, -.34389003777414916136, .43595211113043404076, -.25862192502341045832, -.42382840077369990392e-1, .25401588827617325338, -.25391270933643433084, .97976353777213939970e-1, -.83076132718799640755e-1, .24101683987399794306, -.32347034715808991466, .25135566837724596710, -.32572191274890116378e-1, -.24249125008339168500, .44521849862260472132, -.47299204831623518612, .30167624144353761864, 0., -.30167624144353761864, .47299204831623518612, -.44521849862260472132, .24249125008339168500, .32572191274890116378e-1, -.25135566837724596710, .32347034715808991466, -.24101683987399794306, .83076132718799640755e-1, .65521290249257362495e-1, -.20644010979731663183, .33156053960174730182, -.38129815704119137372, .32433515699040812444, -.16472257233143268874, -.59732744176891964605e-1, .28900874454347424660, -.45916291660524234765, .52186153713437594240, -.45916291660524234765, .28900874454347424660, -.59732744176891964605e-1, -.16472257233143268874, .32433515699040812444, -.38129815704119137372, .33156053960174730182, -.20644010979731663183, .65521290249257362495e-1, -.45594238276028918748e-1, .15200229889132517249, -.27279086780265678798, .37875687383936367688, -.44681252154321677965, .46134146804534618498, -.41596492739281136278, .31424880748716539704, -.16897407700449885702, 0., .16897407700449885702, -.31424880748716539704, .41596492739281136278, -.46134146804534618498, .44681252154321677965, -.37875687383936367688, .27279086780265678798, -.15200229889132517249, .45594238276028918748e-1, .23627875547779228189e-1, -.81412150776469350535e-1, .15533580164509645419, -.23676404432003361798, .31872410109858546316, -.39507648229300996080, .46047846054277308606, -.51052432174254323525, .54191623745061862305, -.55261095430559338005, .54191623745061862305, -.51052432174254323525, .46047846054277308606, -.39507648229300996080, .31872410109858546316, -.23676404432003361798, .15533580164509645419, -.81412150776469350535e-1, .23627875547779228189e-1};
            case(20):
                return {.88070035695760591560e-2, .20300714900193470666e-1, .31336024167054531785e-1, .41638370788352374362e-1, .50965059908620217520e-1, .59097265980759208655e-1, .65844319224588313450e-1, .71048054659191025665e-1, .74586493236301873395e-1, .76376693565362925350e-1, .76376693565362925350e-1, .74586493236301873395e-1, .71048054659191025665e-1, .65844319224588313450e-1, .59097265980759208655e-1, .50965059908620217520e-1, .41638370788352374362e-1, .31336024167054531785e-1, .20300714900193470666e-1, .88070035695760591560e-2, -.26239461354213606950e-1, -.58707957802376883700e-1, -.85757400269108165725e-1, -.10481839082259893608, -.11411055097336897646, -.11276710064380726667, -.10091306987327592036, -.79653271852576858490e-1, -.50969243536504727945e-1, -.17534527962709187194e-1, .17534527962709187194e-1, .50969243536504727945e-1, .79653271852576858490e-1, .10091306987327592036, .11276710064380726667, .11411055097336897646, .10481839082259893608, .85757400269108165725e-1, .58707957802376883700e-1, .26239461354213606950e-1, .43130389821263835469e-1, .90730270822785525570e-1, .11723707208938864538, .11579129977496174300, .85498212866381165985e-1, .31571658621479413790e-1, -.35727904401933781481e-1, -.10320285495444626601, -.15744105178823337974, -.18758709285164690197, -.18758709285164690197, -.15744105178823337974, -.10320285495444626601, -.35727904401933781481e-1, .31571658621479413790e-1, .85498212866381165985e-1, .11579129977496174300, .11723707208938864538, .90730270822785525570e-1, .43130389821263835469e-1, -.59129115241831658225e-1, -.11275318948266265590, -.11614421757847413240, -.63661541102736986035e-1, .28615198363291403784e-1, .12855919398708987664, .19956437042107754870, .21389600517679826232, .16296545924685066653, .60771836845896574380e-1, -.60771836845896574380e-1, -.16296545924685066653, -.21389600517679826232, -.19956437042107754870, -.12855919398708987664, -.28615198363291403784e-1, .63661541102736986035e-1, .11614421757847413240, .11275318948266265590, .59129115241831658225e-1, .73900308371436042270e-1, .12206868047699131016, .80119148993468457195e-1, -.36124425614953504908e-1, -.16347456735308855914, -.22660547332412300152, -.18115674518713485780, -.40528184656064970200e-1, .12902266177134091762, .24277859652212816632, .24277859652212816632, .12902266177134091762, -.40528184656064970200e-1, -.18115674518713485780, -.22660547332412300152, -.16347456735308855914, -.36124425614953504908e-1, .80119148993468457195e-1, .12206868047699131016, .73900308371436042270e-1, -.87129776535550291455e-1, -.11712885181708527516, -.14782507835662257670e-1, .14671941265985312716, .23244043589469583958, .15547586739636862025, -.47277515561841594404e-1, -.23557745046418402236, -.26952784407510375840, -.11727268368079519872, .11727268368079519872, .26952784407510375840, .23557745046418402236, .47277515561841594404e-1, -.15547586739636862025, -.23244043589469583958, -.14671941265985312716, .14782507835662257670e-1, .11712885181708527516, .87129776535550291455e-1, .98529916430923012965e-1, .97701481426545450685e-1, -.67221972449923619560e-1, -.22326551848689754500, -.17909343741177982716, .58502019122960714845e-1, .27038951084131243680, .23953016911368789400, -.22283358869663088342e-1, -.27278880971716542919, -.27278880971716542919, -.22283358869663088342e-1, .23953016911368789400, .27038951084131243680, .58502019122960714845e-1, -.17909343741177982716, -.22326551848689754500, -.67221972449923619560e-1, .97701481426545450685e-1, .98529916430923012965e-1, -.10784473977238357539, -.64913615831042693535e-1, .14868296506277543170, .22996524694993931510, .14737402011080575198e-1, -.26146166394199191495, -.24074002071738737010, .83534804000277633305e-1, .32590933187946483326, .18180535067816802583, -.18180535067816802583, -.32590933187946483326, -.83534804000277633305e-1, .24074002071738737010, .26146166394199191495, -.14737402011080575198e-1, -.22996524694993931510, -.14868296506277543170, .64913615831042693535e-1, .10784473977238357539, .11485439052671188784, .21178628390678367912e-1, -.21130420495701404312, -.15458917503461706432, .18155136080806467579, .28645545381064555912, -.48042466135759005584e-1, -.34041490251735633358, -.13225745607350377594, .28256837118214973192, .28256837118214973192, -.13225745607350377594, -.34041490251735633358, -.48042466135759005584e-1, .28645545381064555912, .18155136080806467579, -.15458917503461706432, -.21130420495701404312, .21178628390678367912e-1, .11485439052671188784, -.11937908034964661140, .29988316197496100147e-1, .23952959948397037998, .14926122863695763157e-1, -.30264365538440568086, -.90260186092919598530e-1, .32286908653152735076, .17451125550826214062, -.30334963661660809935, -.25034997048389792261, .25034997048389792261, .30334963661660809935, -.17451125550826214062, -.32286908653152735076, .90260186092919598530e-1, .30264365538440568086, -.14926122863695763157e-1, -.23952959948397037998, -.29988316197496100147e-1, .11937908034964661140, .12128237786003705967, -.84252230981265754750e-1, -.22394445191677135544, .14556478637625199354, .27249009898101701890, -.19790938382051869871, -.29296872251053843496, .24150784463627780184, .29214655760977506032, -.27391687623426469036, -.27391687623426469036, .29214655760977506032, .24150784463627780184, -.29296872251053843496, -.19790938382051869871, .27249009898101701890, .14556478637625199354, -.22394445191677135544, -.84252230981265754750e-1, .12128237786003705967, -.12047379740995588894, .13681541879327915846, .16355431476286525862, -.27182181349053161609, -.92171288634269834140e-1, .36253510200096049472, -.42368185502164264818e-1, -.38075659711306876044, .19468632523465129776, .31933419122653763868, -.31933419122653763868, -.19468632523465129776, .38075659711306876044, .42368185502164264818e-1, -.36253510200096049472, .92171288634269834140e-1, .27182181349053161609, -.16355431476286525862, -.13681541879327915846, .12047379740995588894, .11691064388938679908, -.18282104571938623512, -.66449250202981199870e-1, .31633765745045671430, -.15404694879740229158, -.26442701234127356156, .36480065611441002554, .32889478259426256812e-1, -.41119987400704597714, .24800569535440946955, .24800569535440946955, -.41119987400704597714, .32889478259426256812e-1, .36480065611441002554, -.26442701234127356156, -.15404694879740229158, .31633765745045671430, -.66449250202981199870e-1, -.18282104571938623512, .11691064388938679908, -.11059908167391432680, .21777036540467038113, -.51331968408298550995e-1, -.25675799660876624828, .33866208200097371868, -.43530177572758418036e-1, -.34115429887656486570, .38706497502547501722, -.16428380009755962780e-1, -.38545232469659013674, .38545232469659013674, .16428380009755962780e-1, -.38706497502547501722, .34115429887656486570, .43530177572758418036e-1, -.33866208200097371868, .25675799660876624828, .51331968408298550995e-1, -.21777036540467038113, .11059908167391432680, .10159440790808912848, -.23791926264308348886, .16857368355484126563, .10554842222901780065, -.35763194385686727514, .34217840760525193921, -.31924582284556919735e-1, -.33505578079440720228, .45067260880034801209, -.20603596051863326009, -.20603596051863326009, .45067260880034801209, -.33505578079440720228, -.31924582284556919735e-1, .34217840760525193921, -.35763194385686727514, .10554842222901780065, .16857368355484126563, -.23791926264308348886, .10159440790808912848, -.90000522732248196400e-1, .24062101399276959775, -.26280175935659775192, .92103694061063377130e-1, .18870644349322044028, -.40315010703560590516, .39928834371188505376, -.15600847562879205442, -.19455274400282302328, .44563819287270795874, -.44563819287270795874, .19455274400282302328, .15600847562879205442, -.39928834371188505376, .40315010703560590516, -.18870644349322044028, -.92103694061063377130e-1, .26280175935659775192, -.24062101399276959775, .90000522732248196400e-1, .75968601617712619030e-1, -.22458606849559499506, .31462102669135214866, -.27200205522585028094, .91047825396734050215e-1, .16383732326223845898, -.38665795593816451922, .47768743984024482215, -.38937970378035676850, .14946356663168446474, .14946356663168446474, -.38937970378035676850, .47768743984024482215, -.38665795593816451922, .16383732326223845898, .91047825396734050215e-1, -.27200205522585028094, .31462102669135214866, -.22458606849559499506, .75968601617712619030e-1, -.59694987483217617555e-1, .19003594687087683468, -.31164105960892722805, .37203795676230633364, -.34042394064084918304, .21384617490702065910, -.17610179385184979307e-1, -.20175276721936800810, .38934310208750808798, -.49709210356060489846, .49709210356060489846, -.38934310208750808798, .20175276721936800810, .17610179385184979307e-1, -.21384617490702065910, .34042394064084918304, -.37203795676230633364, .31164105960892722805, -.19003594687087683468, .59694987483217617555e-1, .41418332533339328916e-1, -.13873656589564788807, .25121397742423527596, -.35368113521518890436, .42584085924972273094, -.45308286683915950872, .42793355453058783578, -.35085285124816942976, .23002220531294430754, -.80075509852663748050e-1, -.80075509852663748050e-1, .23002220531294430754, -.35085285124816942976, .42793355453058783578, -.45308286683915950872, .42584085924972273094, -.35368113521518890436, .25121397742423527596, -.13873656589564788807, .41418332533339328916e-1, -.21416031600054791272e-1, .73905784380102391835e-1, -.14141296162008345011, .21644186508752798419, -.29299971492323503666, .36579330002083763032, -.43015043504117463788, .48211063670381045319, -.51855508252321620900, .53732818115559507200, -.53732818115559507200, .51855508252321620900, -.48211063670381045319, .43015043504117463788, -.36579330002083763032, .29299971492323503666, -.21644186508752798419, .14141296162008345011, -.73905784380102391835e-1, .21416031600054791272e-1};
            default:
                throw Error( Message(_ping_)<<"n>20 not allowed! You typed: "<<n );
        }
    }
    static std::vector<real_type> backwardEQ(unsigned n)
    {
        switch( n)
        {
            case(0):
                return {};
            case(1):
                return {1.};
            case(2):
                return {1., -.50000000000000000000, 1., .50000000000000000000};
            case(3):
                return {1., -.66666666666666666667, .16666666666666666667, 1., 0., -.50000000000000000000, 1., .66666666666666666667, .16666666666666666667};
            case(4):
                return {1., -.75000000000000000000, .34375000000000000000, .70312500000000000000e-1, 1., -.25000000000000000000, -.40625000000000000000, .33593750000000000000, 1., .25000000000000000000, -.40625000000000000000, -.33593750000000000000, 1., .75000000000000000000, .34375000000000000000, -.70312500000000000000e-1};
            case(5):
                return {1., -.80000000000000000000, .46000000000000000000, -.80000000000000000000e-1, -.23300000000000000000, 1., -.40000000000000000000, -.26000000000000000000, .44000000000000000000, -.11300000000000000000, 1., 0., -.50000000000000000000, 0., .37500000000000000000, 1., .40000000000000000000, -.26000000000000000000, -.44000000000000000000, -.11300000000000000000, 1., .80000000000000000000, .46000000000000000000, .80000000000000000000e-1, -.23300000000000000000};
            case(6):
                return {1., -.83333333333333333333, .54166666666666666667, -.19675925925925925926, -.11930941358024691358, .33637152777777777778, 1., -.50000000000000000000, -.12500000000000000000, .43750000000000000000, -.28906250000000000000, -.89843750000000000000e-1, 1., -.16666666666666666667, -.45833333333333333333, .23842592592592592593, .27420910493827160494, -.27300347222222222222, 1., .16666666666666666667, -.45833333333333333333, -.23842592592592592593, .27420910493827160494, .27300347222222222222, 1., .50000000000000000000, -.12500000000000000000, -.43750000000000000000, -.28906250000000000000, .89843750000000000000e-1, 1., .83333333333333333333, .54166666666666666667, .19675925925925925926, -.11930941358024691358, -.33637152777777777778};
            case(7):
                return {1., -.85714285714285714286, .60204081632653061224, -.28862973760932944606, -.18586005830903790087e-1, .25957934194085797584, -.39242205628607127982, 1., -.57142857142857142857, -.10204081632653061224e-1, .39067055393586005831, -.38301749271137026239, .81424406497292794669e-1, .23387948473850181472, 1., -.28571428571428571429, -.37755102040816326531, .37026239067055393586, .98032069970845481050e-1, -.34662640566430653894, .99872820848456000476e-1, 1., 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 1., .28571428571428571429, -.37755102040816326531, -.37026239067055393586, .98032069970845481050e-1, .34662640566430653894, .99872820848456000476e-1, 1., .57142857142857142857, -.10204081632653061224e-1, -.39067055393586005831, -.38301749271137026239, -.81424406497292794669e-1, .23387948473850181472, 1., .85714285714285714286, .60204081632653061224, .28862973760932944606, -.18586005830903790087e-1, -.25957934194085797584, -.39242205628607127982};
            case(8):
                return {1., -.87500000000000000000, .64843750000000000000, -.36230468750000000000, .68450927734375000000e-1, .18203353881835937500, -.34905457496643066406, .41118493676185607910, 1., -.62500000000000000000, .85937500000000000000e-1, .32714843750000000000, -.42227172851562500000, .21333694458007812500, .10744452476501464844, -.30757263302803039551, 1., -.37500000000000000000, -.28906250000000000000, .43066406250000000000, -.65826416015625000000e-1, -.30009841918945312500, .26117300987243652344, .75338870286941528320e-1, 1., -.12500000000000000000, -.47656250000000000000, .18261718750000000000, .31747436523437500000, -.21752548217773437500, -.21471238136291503906, .23629435896873474121, 1., .12500000000000000000, -.47656250000000000000, -.18261718750000000000, .31747436523437500000, .21752548217773437500, -.21471238136291503906, -.23629435896873474121, 1., .37500000000000000000, -.28906250000000000000, -.43066406250000000000, -.65826416015625000000e-1, .30009841918945312500, .26117300987243652344, -.75338870286941528320e-1, 1., .62500000000000000000, .85937500000000000000e-1, -.32714843750000000000, -.42227172851562500000, -.21333694458007812500, .10744452476501464844, .30757263302803039551, 1., .87500000000000000000, .64843750000000000000, .36230468750000000000, .68450927734375000000e-1, -.18203353881835937500, -.34905457496643066406, -.41118493676185607910};
            case(9):
                return {1., -.88888888888888888889, .68518518518518518519, -.42249657064471879287, .14332799878067367779, .10867245846669714982, -.29653585722591971639, .39637168879831753039, -.40115060625784946547, 1., -.66666666666666666667, .16666666666666666667, .25925925925925925926, -.42746913580246913580, .30555555555555555556, -.17232510288065843621e-1, -.24056927297668038409, .31579003772290809328, 1., -.44444444444444444444, -.20370370370370370370, .44718792866941015089, -.19503505563176345069, -.20172229843011736016, .32689553026582442830, -.96913705692008457508e-1, -.20527216757258932684, 1., -.22222222222222222222, -.42592592592592592593, .30589849108367626886, .20048392013412589544, -.32491236092059137327, -.34698230847826945983e-1, .29281621415484817067, -.91645803906004826709e-1, 1., 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 1., .22222222222222222222, -.42592592592592592593, -.30589849108367626886, .20048392013412589544, .32491236092059137327, -.34698230847826945983e-1, -.29281621415484817067, -.91645803906004826709e-1, 1., .44444444444444444444, -.20370370370370370370, -.44718792866941015089, -.19503505563176345069, .20172229843011736016, .32689553026582442830, .96913705692008457508e-1, -.20527216757258932684, 1., .66666666666666666667, .16666666666666666667, -.25925925925925925926, -.42746913580246913580, -.30555555555555555556, -.17232510288065843621e-1, .24056927297668038409, .31579003772290809328, 1., .88888888888888888889, .68518518518518518519, .42249657064471879287, .14332799878067367779, -.10867245846669714982, -.29653585722591971639, -.39637168879831753039, -.40115060625784946547};
            case(10):
                return {1., -.90000000000000000000, .71500000000000000000, -.47250000000000000000, .20793750000000000000, .41141250000000000000e-1, -.24116431250000000000, .36782499375000000000, -.40968590351562500000, .36951048597656250000, 1., -.70000000000000000000, .23500000000000000000, .19250000000000000000, -.41206250000000000000, .36519875000000000000, -.12528631250000000000, -.15015529375000000000, .30670434648437500000, -.27205993035156250000, 1., -.50000000000000000000, -.12500000000000000000, .43750000000000000000, -.28906250000000000000, -.89843750000000000000e-1, .32324218750000000000, -.22314453125000000000, -.73638916015625000000e-1, .26789855957031250000, 1., -.30000000000000000000, -.36500000000000000000, .38250000000000000000, .72937500000000000000e-1, -.34538625000000000000, .12918118750000000000, .22407298125000000000, -.23907459101562500000, -.63700381757812500000e-1, 1., -.10000000000000000000, -.48500000000000000000, .14750000000000000000, .33793750000000000000, -.17882875000000000000, -.24882931250000000000, .19949294375000000000, .18032072148437500000, -.21138764183593750000, 1., .10000000000000000000, -.48500000000000000000, -.14750000000000000000, .33793750000000000000, .17882875000000000000, -.24882931250000000000, -.19949294375000000000, .18032072148437500000, .21138764183593750000, 1., .30000000000000000000, -.36500000000000000000, -.38250000000000000000, .72937500000000000000e-1, .34538625000000000000, .12918118750000000000, -.22407298125000000000, -.23907459101562500000, .63700381757812500000e-1, 1., .50000000000000000000, -.12500000000000000000, -.43750000000000000000, -.28906250000000000000, .89843750000000000000e-1, .32324218750000000000, .22314453125000000000, -.73638916015625000000e-1, -.26789855957031250000, 1., .70000000000000000000, .23500000000000000000, -.19250000000000000000, -.41206250000000000000, -.36519875000000000000, -.12528631250000000000, .15015529375000000000, .30670434648437500000, .27205993035156250000, 1., .90000000000000000000, .71500000000000000000, .47250000000000000000, .20793750000000000000, -.41141250000000000000e-1, -.24116431250000000000, -.36782499375000000000, -.40968590351562500000, -.36951048597656250000};
            case(11):
                return {1., -.90909090909090909091, .73966942148760330579, -.51465063861758076634, .26401031350317601257, -.20296365747496134765e-1, -.18618131834015311920, .33172898082538507000, -.40253847285927239003, .39635747548931737519, -.32233283209002122431, 1., -.72727272727272727273, .29338842975206611570, .12922614575507137491, -.38451096236595860938, .39997888867501598872, -.21287938292838914381, -.55313647116864731161e-1, .26169716067624695242, -.31033548389581302209, .19329976950195573698, 1., -.54545454545454545455, -.53719008264462809917e-1, .41247182569496619083, -.35343385014684789290, .17030319588204978547e-1, .27749788886750159887, -.29569917434398251034, .59608957365463668380e-1, .20142842112114309834, -.26240115260901105800, 1., -.36363636363636363636, -.30165289256198347107, .42524417731029301277, -.44370261594153404822e-1, -.31115298880478854524, .24441054386498686751, .10164609065112632306, -.28316337859854054752, .10414397744850142225, .18289301995608551013, 1., -.18181818181818181818, -.45041322314049586777, .25770097670924117205, .25581415203879516426, -.28988177658008953685, -.11655120117229945794, .28782504525669734206, .38601265064333863545e-2, -.25717018468493031553, .85366495399004061282e-1, 1., 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 0., -.24609375000000000000, 1., .18181818181818181818, -.45041322314049586777, -.25770097670924117205, .25581415203879516426, .28988177658008953685, -.11655120117229945794, -.28782504525669734206, .38601265064333863545e-2, .25717018468493031553, .85366495399004061282e-1, 1., .36363636363636363636, -.30165289256198347107, -.42524417731029301277, -.44370261594153404822e-1, .31115298880478854524, .24441054386498686751, -.10164609065112632306, -.28316337859854054752, -.10414397744850142225, .18289301995608551013, 1., .54545454545454545455, -.53719008264462809917e-1, -.41247182569496619083, -.35343385014684789290, -.17030319588204978547e-1, .27749788886750159887, .29569917434398251034, .59608957365463668380e-1, -.20142842112114309834, -.26240115260901105800, 1., .72727272727272727273, .29338842975206611570, -.12922614575507137491, -.38451096236595860938, -.39997888867501598872, -.21287938292838914381, .55313647116864731161e-1, .26169716067624695242, .31033548389581302209, .19329976950195573698, 1., .90909090909090909091, .73966942148760330579, .51465063861758076634, .26401031350317601257, .20296365747496134765e-1, -.18618131834015311920, -.33172898082538507000, -.40253847285927239003, -.39635747548931737519, -.32233283209002122431};
            case(12):
                return {1., -.91666666666666666667, .76041666666666666667, -.55063657407407407407, .31300033757716049383, -.75941297743055555556e-1, -.13321004482944315844, .29186678390607585305, -.38508724561280510880, .40733429328343771716, -.36286203975046275946, .26470466657836644982, 1., -.75000000000000000000, .34375000000000000000, .70312500000000000000e-1, -.35009765625000000000, .41638183593750000000, -.28077697753906250000, .34183502197265625000e-1, .19760930538177490234, -.31033185124397277832, .26437451317906379700, -.96416370011866092682e-1, 1., -.58333333333333333333, .10416666666666666667e-1, .37876157407407407407, -.39446494020061728395, .11117892795138888889, .20982109666361239712, -.32260241201058009688, .16925292855591113348, .10026604680428022607, -.26345583757506393737, .20224304929561190654, 1., -.41666666666666666667, -.23958333333333333333, .44415509259259259259, -.14417558834876543210, -.24719238281250000000, .30897383827240869342, -.27207713395316250857e-1, -.24909608239826678576, .22023247675743552659, .49835763392136981965e-1, -.23985342702323216892, 1., -.25000000000000000000, -.40625000000000000000, .33593750000000000000, .15771484375000000000, -.33972167968750000000, .24276733398437500000e-1, .27991867065429687500, -.15245401859283447266, -.17682442069053649902, .22120021656155586243, .55176642723381519318e-1, 1., -.83333333333333333333e-1, -.48958333333333333333, .12355324074074074074, .34916931905864197531, -.15121799045138888889, -.26787168400768389918, .17107175243571298440, .20765776218864325797, -.18475064991699427674, -.15763979973292150502, .19303419533659594556, 1., .83333333333333333333e-1, -.48958333333333333333, -.12355324074074074074, .34916931905864197531, .15121799045138888889, -.26787168400768389918, -.17107175243571298440, .20765776218864325797, .18475064991699427674, -.15763979973292150502, -.19303419533659594556, 1., .25000000000000000000, -.40625000000000000000, -.33593750000000000000, .15771484375000000000, .33972167968750000000, .24276733398437500000e-1, -.27991867065429687500, -.15245401859283447266, .17682442069053649902, .22120021656155586243, -.55176642723381519318e-1, 1., .41666666666666666667, -.23958333333333333333, -.44415509259259259259, -.14417558834876543210, .24719238281250000000, .30897383827240869342, .27207713395316250857e-1, -.24909608239826678576, -.22023247675743552659, .49835763392136981965e-1, .23985342702323216892, 1., .58333333333333333333, .10416666666666666667e-1, -.37876157407407407407, -.39446494020061728395, -.11117892795138888889, .20982109666361239712, .32260241201058009688, .16925292855591113348, -.10026604680428022607, -.26345583757506393737, -.20224304929561190654, 1., .75000000000000000000, .34375000000000000000, -.70312500000000000000e-1, -.35009765625000000000, -.41638183593750000000, -.28077697753906250000, -.34183502197265625000e-1, .19760930538177490234, .31033185124397277832, .26437451317906379700, .96416370011866092682e-1, 1., .91666666666666666667, .76041666666666666667, .55063657407407407407, .31300033757716049383, .75941297743055555556e-1, -.13321004482944315844, -.29186678390607585305, -.38508724561280510880, -.40733429328343771716, -.36286203975046275946, -.26470466657836644982};
            case(13):
                return {1., -.92307692307692307692, .77810650887573964497, -.58170232134729176149, .35609309898112811176, -.12630052276773329958, -.83004902928622201541e-1, .25055171024998088799, -.36101790075473018749, .40675447767493116151, -.38846866555062209913, .31479735399311690899, -.20085288800231606862, 1., -.76923076923076923077, .38757396449704142012, .15930814747382794720e-1, -.31212580091733482721, .41942953408763429421, -.33139835500016677685, .11391519221083742903, .12567280262874579171, -.28385945672490493343, .30176599130898984400, -.18509880280174983144, -.37167443127120927062e-2, 1., -.61538461538461538462, .68047337278106508876e-1, .34046426945835229859, -.41768933160603620321, .19029984405846595546, .13337718304163268114, -.31554521838340816883, .24738560143481159881, -.70746930193156229064e-2, -.21437509253028447984, .25828479466852324190, -.10813310248190766597, 1., -.46153846153846153846, -.18047337278106508876, .44651797906235776058, -.22529410734918245159, -.17004697099056540253, .33163098798813046052, -.13850058599791290685, -.17032083814526644510, .27159646525299247618, -.84880453660345909287e-1, -.17211610714465340792, .23006363884225407257, 1., -.30769230769230769231, -.35798816568047337278, .38871187983614019117, .59184727425510311264e-1, -.34374873751996401764, .14458893805410572492, .21201952470048017230, -.24883427735531183948, -.43840168450331049871e-1, .24958048655997419238, -.10675202078667689284, -.16582579272885920108, 1., -.15384615384615384615, -.46449704142011834320, .22166590805644060082, .28869349812681628795, -.25727861823411699116, -.16801215098836519116, .26852800162591890419, .69550631645804473754e-1, -.25890285166711895849, .13083726621472284564e-1, .23152345593443096959, -.80263153075989495474e-1, 1., 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 0., -.24609375000000000000, 0., .22558593750000000000, 1., .15384615384615384615, -.46449704142011834320, -.22166590805644060082, .28869349812681628795, .25727861823411699116, -.16801215098836519116, -.26852800162591890419, .69550631645804473754e-1, .25890285166711895849, .13083726621472284564e-1, -.23152345593443096959, -.80263153075989495474e-1, 1., .30769230769230769231, -.35798816568047337278, -.38871187983614019117, .59184727425510311264e-1, .34374873751996401764, .14458893805410572492, -.21201952470048017230, -.24883427735531183948, .43840168450331049871e-1, .24958048655997419238, .10675202078667689284, -.16582579272885920108, 1., .46153846153846153846, -.18047337278106508876, -.44651797906235776058, -.22529410734918245159, .17004697099056540253, .33163098798813046052, .13850058599791290685, -.17032083814526644510, -.27159646525299247618, -.84880453660345909287e-1, .17211610714465340792, .23006363884225407257, 1., .61538461538461538462, .68047337278106508876e-1, -.34046426945835229859, -.41768933160603620321, -.19029984405846595546, .13337718304163268114, .31554521838340816883, .24738560143481159881, .70746930193156229064e-2, -.21437509253028447984, -.25828479466852324190, -.10813310248190766597, 1., .76923076923076923077, .38757396449704142012, -.15930814747382794720e-1, -.31212580091733482721, -.41942953408763429421, -.33139835500016677685, -.11391519221083742903, .12567280262874579171, .28385945672490493343, .30176599130898984400, .18509880280174983144, -.37167443127120927062e-2, 1., .92307692307692307692, .77810650887573964497, .58170232134729176149, .35609309898112811176, .12630052276773329958, -.83004902928622201541e-1, -.25055171024998088799, -.36101790075473018749, -.40675447767493116151, -.38846866555062209913, -.31479735399311690899, -.20085288800231606862};
            case(14):
                return {1., -.92857142857142857143, .79336734693877551020, -.60878279883381924198, .39424653790087463557, -.17192868856726364015, -.35850656999315761290e-1, .20919153951565825950, -.33284808767518228567, .39785694405128222278, -.40237004381138386451, .35160421943719664820, -.25693258848076596831, .13425045269670276266, 1., -.78571428571428571429, .42602040816326530612, -.34074344023323615160e-1, -.27266308309037900875, .41288297844648063307, -.36752886399640030939, .18239242206102929659, .52884634210512467711e-1, -.24061411006508819587, .31160632209342044290, -.24866938308095957719, .88845120935095385850e-1, .95296967584889988237e-1, 1., -.64285714285714285714, .11989795918367346939, .30010932944606413994, -.42754646501457725948, .25464487453144523115, .56171547290563455703e-1, -.28532898462895228300, .29477322580744053166, -.10431315293726782261, -.13788483785331935231, .26405244003568086203, -.19895589320223070347, .22212420027885904427e-2, 1., -.50000000000000000000, -.12500000000000000000, .43750000000000000000, -.28906250000000000000, -.89843750000000000000e-1, .32324218750000000000, -.22314453125000000000, -.73638916015625000000e-1, .26789855957031250000, -.18822860717773437500, -.63871383666992187500e-1, .23375296592712402344, -.16580426692962646484, 1., -.35714285714285714286, -.30867346938775510204, .42182944606413994169, -.32138301749271137026e-1, -.31680322001249479384, .23421259789447849110, .11620052671335164041, -.28274887586750236749, .87453932197161250085e-1, .19513024857553556819, -.21254692602619356929, -.33375963021548910903e-1, .21912021401150622805, 1., -.21428571428571428571, -.43112244897959183673, .29682944606413994169, .21203079446064139942, -.31924686328613077884, -.51273918140506931636e-1, .29404509513790567098, -.73278440209250677625e-1, -.23171309686328294120, .16029092848266223592, .14507470822371357731, -.20651760627241798313, -.48811706105233693694e-1, 1., -.71428571428571428571e-1, -.49234693877551020408, .10623177842565597668, .35598123177842565598, -.13075443825489379425, -.27952842147245195454, .14915553359747912374, .22461118125301879187, -.16288737971602366127, -.18004391873768513008, .17263087956970584617, .14140626937797783078, -.17877551924263751607, 1., .71428571428571428571e-1, -.49234693877551020408, -.10623177842565597668, .35598123177842565598, .13075443825489379425, -.27952842147245195454, -.14915553359747912374, .22461118125301879187, .16288737971602366127, -.18004391873768513008, -.17263087956970584617, .14140626937797783078, .17877551924263751607, 1., .21428571428571428571, -.43112244897959183673, -.29682944606413994169, .21203079446064139942, .31924686328613077884, -.51273918140506931636e-1, -.29404509513790567098, -.73278440209250677625e-1, .23171309686328294120, .16029092848266223592, -.14507470822371357731, -.20651760627241798313, .48811706105233693694e-1, 1., .35714285714285714286, -.30867346938775510204, -.42182944606413994169, -.32138301749271137026e-1, .31680322001249479384, .23421259789447849110, -.11620052671335164041, -.28274887586750236749, -.87453932197161250085e-1, .19513024857553556819, .21254692602619356929, -.33375963021548910903e-1, -.21912021401150622805, 1., .50000000000000000000, -.12500000000000000000, -.43750000000000000000, -.28906250000000000000, .89843750000000000000e-1, .32324218750000000000, .22314453125000000000, -.73638916015625000000e-1, -.26789855957031250000, -.18822860717773437500, .63871383666992187500e-1, .23375296592712402344, .16580426692962646484, 1., .64285714285714285714, .11989795918367346939, -.30010932944606413994, -.42754646501457725948, -.25464487453144523115, .56171547290563455703e-1, .28532898462895228300, .29477322580744053166, .10431315293726782261, -.13788483785331935231, -.26405244003568086203, -.19895589320223070347, -.22212420027885904427e-2, 1., .78571428571428571429, .42602040816326530612, .34074344023323615160e-1, -.27266308309037900875, -.41288297844648063307, -.36752886399640030939, -.18239242206102929659, .52884634210512467711e-1, .24061411006508819587, .31160632209342044290, .24866938308095957719, .88845120935095385850e-1, -.95296967584889988237e-1, 1., .92857142857142857143, .79336734693877551020, .60878279883381924198, .39424653790087463557, .17192868856726364015, -.35850656999315761290e-1, -.20919153951565825950, -.33284808767518228567, -.39785694405128222278, -.40237004381138386451, -.35160421943719664820, -.25693258848076596831, -.13425045269670276266};
            case(15):
                return {1., -.93333333333333333333, .80666666666666666667, -.63259259259259259259, .42823456790123456790, -.21336000000000000000, .82205267489711934156e-2, .16863108696844993141, -.30229736310013717421, .38304475541939744958, -.40719840615360802046, .37733101876515842775, -.30173806126130939088, .19327557981399881956, -.67710701065410583677e-1, 1., -.80000000000000000000, .46000000000000000000, -.80000000000000000000e-1, -.23300000000000000000, .39952000000000000000, -.39179600000000000000, .23965120000000000000, -.16655300000000000000e-1, -.18785528000000000000, .30052979560000000000, -.28821343328000000000, .16644161839600000000, .99791408800000000000e-2, -.16994932015400000000, 1., -.66666666666666666667, .16666666666666666667, .25925925925925925926, -.42746913580246913580, .30555555555555555556, -.17232510288065843621e-1, -.24056927297668038409, .31579003772290809328, -.18382217522735355383, -.51369611995969449102e-1, .23249057456519162052, -.24998247872588396454, 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-.19327557981399881956, -.67710701065410583677e-1};
            case(16):
                return {1., -.93750000000000000000, .81835937500000000000, -.65368652343750000000, .45868492126464843750, -.25108158588409423828, .49309041351079940796e-1, .12936222483403980732, -.27053994702328054700, .36409251189013502881, -.40505383448335052776, .39396111340814665702, -.33659952737885887389, .24319369708032653635, -.12714618581575714934, .34716778494217325814e-2, 1., -.81250000000000000000, .49023437500000000000, -.12219238281250000000, -.19393348693847656250, .38138163089752197266, -.40648848190903663635, .28646354353986680508, -.80731882941108779050e-1, -.13073324613276327000, .27447814336445119920, -.30690462362075598968, .22633504807532619715, -.70351936967768577197e-1, -.99929286267772671482e-1, .22263406168221024350, 1., -.68750000000000000000, .20898437500000000000, .21887207031250000000, -.42006874084472656250, .34473741054534912109, -.84455493837594985962e-1, -.18765764101408421993, .31580098497761355247, -.24329587597924273723, .33584351518033628281e-1, 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            case(17):
                return {1., -.94117647058823529412, .82871972318339100346, -.67250152656218196621, .48610978077369763293, -.28552593676687159341, .87580720639265702358e-1, .91654249220618793589e-1, -.23837592330162594884, .34230897545122942585, -.39759066042367632522, .40319751912110290310, -.36287859577126664472, .28461151315747360026, -.17964707570831372617, .61249815675211184629e-1, .56728293127629605135e-1, 1., -.82352941176470588235, .51730103806228373702, -.16100142479136983513, -.15594431340620921684, .35996565147053541307, -.41352395771504578609, .32390641894238420954, -.13831615448389879014, -.72758354307165623823e-1, .23832996401025041664, -.30855662666735543551, .26856632606358638394, -.14050978408196708387, -.26220418811214424993e-1, .17288948489749499023, -.25127878547298951245, 1., -.70588235294117647059, .24740484429065743945, .17952371259922654183, -.40731821936997880772, .37391476747306242812, -.14445784960780433191, -.13112505666752009992, .29994848752560539325, 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-.35294117647058823529, -.31314878892733564014, .41949928760431508243, -.24240909471869350223e-1, -.32019932288955859639, .22738855505705649148, .12541196336373588653, -.28195819672445553142, .76494830381871788480e-1, .20246584373710772012, -.20596159077964586512, -.46266731623764775866e-1, .22152115050955870074, -.10782133904914493300, -.13318086598715197033, .19215471518802288381, 1., -.23529411764705882353, -.41695501730103806228, .32037451658864237737, .18079734438045521486, -.33287260618498905171, -.70723490215605390916e-2, .28840981495789942275, -.12105131885226662657, -.20256369380601431953, .19950407360972871852, .94532009432113486437e-1, -.22551081682732211331, .14780777188149593205e-1, .20269565790973962595, -.10600204426787999919, -.14170271793296501735, 1., -.11764705882352941176, -.47923875432525951557, .17239975575005088541, .32393499838364004262, -.20651780425775271735, -.22540277616606709648, .22626292617318085444, .14731648954828352094, -.23385959872022376416, 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.20256369380601431953, .19950407360972871852, -.94532009432113486437e-1, -.22551081682732211331, -.14780777188149593205e-1, .20269565790973962595, .10600204426787999919, -.14170271793296501735, 1., .35294117647058823529, -.31314878892733564014, -.41949928760431508243, -.24240909471869350223e-1, .32019932288955859639, .22738855505705649148, -.12541196336373588653, -.28195819672445553142, -.76494830381871788480e-1, .20246584373710772012, .20596159077964586512, -.46266731623764775866e-1, -.22152115050955870074, -.10782133904914493300, .13318086598715197033, .19215471518802288381, 1., .47058823529411764706, -.16782006920415224913, -.44534907388560960716, -.24089300894385843081, .15222871035604289728, .33207874776038962333, .15973833034255584289, -.14962331869396811786, -.27498813247691018734, -.11121075515478368495, .15007794467952445334, .23730761291655415932, .76224533342478929331e-1, -.15117850106127319527, -.20868569090872692739, -.48542402848307401463e-1, 1., .58823529411764705882, .19031141868512110727e-1, -.37349888052106655811, -.39875749811424671639, -.12341471711587857087, .19920361232317968723, .32340143485573927369, .18238959824928314906, -.84812832928120299876e-1, -.25894145169695987520, -.21368729015284022894, -.35589473912831176233e-2, .19322384770750510090, .22250826157352918587, .72706353340930391720e-1, -.12573763663809382707, 1., .70588235294117647059, .24740484429065743945, -.17952371259922654183, -.40731821936997880772, -.37391476747306242812, -.14445784960780433191, .13112505666752009992, .29994848752560539325, .28337571077412265774, .11010319685342553411, -.10923992098683217766, -.24872311766645223486, -.23679634126073260731, -.91404225059627818760e-1, .96270034899230900436e-1, .21735489107617275274, 1., .82352941176470588235, .51730103806228373702, .16100142479136983513, -.15594431340620921684, -.35996565147053541307, -.41352395771504578609, -.32390641894238420954, -.13831615448389879014, .72758354307165623823e-1, .23832996401025041664, .30855662666735543551, .26856632606358638394, .14050978408196708387, -.26220418811214424993e-1, -.17288948489749499023, -.25127878547298951245, 1., .94117647058823529412, .82871972318339100346, .67250152656218196621, .48610978077369763293, .28552593676687159341, .87580720639265702358e-1, -.91654249220618793589e-1, -.23837592330162594884, -.34230897545122942585, -.39759066042367632522, -.40319751912110290310, -.36287859577126664472, -.28461151315747360026, -.17964707570831372617, -.61249815675211184629e-1, .56728293127629605135e-1};
            case(18):
                return {1., -.94444444444444444444, .83796296296296296296, -.68938614540466392318, .51092987921048620637, -.31707187833409541228, .12322918629196373633, .55635814996494593630e-1, -.20634729372842744551, .31865932424703895228, -.38610388970993519675, .40646671849484774661, -.38185146652276990725, .31833359862089785178, -.22524555000263474472, .11417033073641729814, .22518548702064755354e-2, -.11158282952377128967, 1., -.83333333333333333333, .54166666666666666667, -.19675925925925925926, -.11930941358024691358, .33637152777777777778, -.41447643389917695473, .35313317151063100137, -.18910370082358110425, -.16232919676035077859e-1, .19589545356161186710, -.29689465823344153598, .29463591335804713067, -.19811633047369359928, .44810754428820948930e-1, .11271347075123583049, -.22399537359411915761, .25626219069520609096, 1., -.72222222222222222222, .28240740740740740741, .14154663923182441701, -.39070478014022252705, .39467890279682975156, -.19699678599376506517, 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-.45833333333333333333, .23842592592592592593, .27420910493827160494, -.27300347222222222222, -.14508985982510288066, .27891174232681755830, .39793707869834533608e-1, -.26044919750878573833, .46661242128264403557e-1, .22192523887626654280, -.11366558992527195999, -.16842278783281271900, .15968251530544233681, .10574134704553822921, -.18384800141564057728, -.40041032055446381899e-1, 1., -.55555555555555555556e-1, -.49537037037037037037, .82904663923182441701e-1, .36346760211857948483, -.10267049135040390184, -.29243248875757139551, .11817488428327023445, .24356854388336765498, -.13060400359758125861, -.20542571133750842330, .14051848780632476485, .17334428530222776954, -.14822906196034975831, -.14508086542774545476, .15392988411634354549, .11944446964543271831, -.15775645138498764969, 1., .55555555555555555556e-1, -.49537037037037037037, -.82904663923182441701e-1, .36346760211857948483, .10267049135040390184, -.29243248875757139551, -.11817488428327023445, .24356854388336765498, 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            case(19):
                return {1., -.94736842105263157895, .84626038781163434903, -.70462166496573844584, .53349325895289324054, -.34604906750497455877, .15645487513561495426, .21347014389723311299e-1, -.17481705446225054584, .29385539460941943690, -.37160436128092949516, .40494700281531892899, -.39466117393784110577, .34522109971714891411, -.26427121992438954561, .16182724307287625142, -.49283894592808973012e-1, -.61674453579027400818e-1, .16015673598907766315, 1., -.84210526315789473684, .56371191135734072022, -.22977110365942557224, -.84173886019904696864e-1, .31140677331560652462, -.41062344676891054501, .37525793060115977109, -.23321700607903449063, .37402457322345592078e-1, .15005137375537809424, -.27523315058876890985, .30668886974470586461, -.24260076746414183966, .10921571698333430893, .48616531456823193006e-1, -.18171144389090322952, .25128240498923422450, -.23984020589827316546, 1., -.73684210526315789474, .31440443213296398892, .10511736404723720659, -.37134939879221307387, 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1., 0., -.50000000000000000000, 0., .37500000000000000000, 0., -.31250000000000000000, 0., .27343750000000000000, 0., -.24609375000000000000, 0., .22558593750000000000, 0., -.20947265625000000000, 0., .19638061523437500000, 0., -.18547058105468750000, 1., .10526315789473684211, -.48337950138504155125, -.15497885989211255285, .33398588869023411423, .18726462471815545340, -.24218278668221772699, -.20785653888426603450, .17088562146188800431, .21873862596557093211, -.11004933412258501745, -.22096847352443563557, .56297197585509778120e-1, .21536709248116118954, -.85548301114218457168e-2, -.20275026928579418761, -.33330230638039518429e-1, .18401327133365580439, .69142086226440557777e-1, 1., .21052631578947368421, -.43351800554016620499, -.29246245808426884385, .21738917749249929021, .31634902320141480611, -.59058024920396325451e-1, -.29424666120918719414, -.64474226040385002390e-1, .23591371422836417162, .15239228912769217080, -.15321843740030167589, -.20151791521278692052, 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.36653465802365448186e-1, 1., .52631578947368421053, -.84487534626038781163e-1, -.42498906546143752734, -.32807164616600547878, .29186534948723778815e-1, .30155548447482575573, .26973645110957020647, .23262383637085885387e-2, -.23745309968903047562, -.23954671421636820531, -.24826416480964271513e-1, .19454029596754023009, .21981982570665956044, .42480826454194152201e-1, -.16193906654826364540, -.20496100713620744556, -.56989647443579903512e-1, .13525154590567847570, 1., .63157894736842105263, .98337950138504155125e-1, -.31753899985420615250, -.42471762033747439016, -.22880567376344806892, .88998464870920368140e-1, .30050832578117787433, .27799146587355005538, .64520429938392832739e-1, -.17276780336012365055, -.26696826858873587636, -.16480162819397043382, .46268327044698986499e-1, .20938699295636529616, .21248876685938664090, .63718843023446450682e-1, -.12186973154169889895, -.20984348989499047114, 1., .73684210526315789474, .31440443213296398892, -.10511736404723720659, 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-.29385539460941943690, -.37160436128092949516, -.40494700281531892899, -.39466117393784110577, -.34522109971714891411, -.26427121992438954561, -.16182724307287625142, -.49283894592808973012e-1, .61674453579027400818e-1, .16015673598907766315};
            case(20):
                return {1., -.95000000000000000000, .85375000000000000000, -.71843750000000000000, .55408984375000000000, -.37274363281250000000, .18745362402343750000, -.11227208544921875000e-1, -.14402345579986572266, .26842183105857849121, -.35488029484085502625, .39960396104447935104, -.40230527546437237763, .36611559690346859664, -.29720689139550918532, .20416210008651451351, -.97154404788450915195e-1, -.12988412427429177931e-1, .11574942192309365136, -.20183161878436929698, 1., -.85000000000000000000, .58375000000000000000, -.26031250000000000000, -.50597656250000000000e-1, .28566441406250000000, -.40299566503906250000, .39130223061523437500, -.27101672313385009766, .87308200484695434570e-1, .10291230703768196106, -.24636969867905248642, .30704101931341454482, -.27447579048164840311, .16483472431996012633, -.14700992516262631373e-1, -.13032185699974259739, .22886729230017540935, -.25518502094081079291, .20557671827291274046, 1., -.75000000000000000000, .34375000000000000000, .70312500000000000000e-1, -.35009765625000000000, .41638183593750000000, -.28077697753906250000, .34183502197265625000e-1, .19760930538177490234, -.31033185124397277832, .26437451317906379700, -.96416370011866092682e-1, -.10374477185541763902, .23863160864857491106, -.24882914578665804584, .13807942665198424947, .32630657321327305453e-1, -.17746350559615287068, .22798310263535825904, -.16485199986318105347, 1., -.65000000000000000000, .13375000000000000000, .28843750000000000000, -.42841015625000000000, .27048988281250000000, .34674686523437500000e-1, -.27370577114257812500, .30323855787200927734, -.12901554392723083496, -.11358050533467826843, .25822993973551515579, -.21759600336370755219, .33628905987235834897e-1, .15989719597515780544, -.23232445519686842140, .14267998953684572561, .38629735740267878127e-1, -.18357701723430397571, .19577326427158888471, 1., -.55000000000000000000, -.46250000000000000000e-1, .40906250000000000000, -.35903515625000000000, .28194804687500000000e-1, .27076620214843750000, -.30073531049804687500, .73212862071228027344e-1, .19126024706871032715, -.26575853405090751648, .10517350887280714035, .13274158227658102965, -.23748298944435960323, .12864155883237048017, .84861932589648352428e-1, -.21103245832119135072, .14543812924089702216, .43770433531832515870e-1, -.18466392887941779457, 1., -.45000000000000000000, -.19625000000000000000, .44718750000000000000, -.20497265625000000000, -.19172214843750000000, .32898131933593750000, -.11060111821289062500, -.19453896092681884766, .26367022186592102051, -.50352974861225509644e-1, -.19644241874732992172, .21558847979236210799, -.52354902073934349418e-2, -.19564564509149122638, .17509816875649790623, .30754076388701412738e-1, -.19166286673389308699, .13865949180282733909, .60065845404894756318e-1, 1., -.35000000000000000000, -.31625000000000000000, .41781250000000000000, -.18722656250000000000e-1, -.32245472656250000000, .22251066308593750000, .13175783461914062500, -.28116290916900634766, 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-.14196346508179371231, .13323443467019258980, .14654425050085395118, -.11158516394537664511, -.14969626643759567972, 1., .15000000000000000000, -.46625000000000000000, -.21656250000000000000, .29283984375000000000, .25231675781250000000, -.17464609472656250000, -.26492291879882812500, .78305761973571777344e-1, .25767367149147033691, .29618105988544464111e-2, -.23340063741166471481, -.69817676304803514719e-1, .19530702790745872289, .12133023249911810850, -.14710079195555055656, -.15649826063000510722, .92879193010016683781e-1, .17489367744514857848, -.36903450755775036710e-1, 1., .25000000000000000000, -.40625000000000000000, -.33593750000000000000, .15771484375000000000, .33972167968750000000, .24276733398437500000e-1, -.27991867065429687500, -.15245401859283447266, .17682442069053649902, .22120021656155586243, -.55176642723381519318e-1, -.22920567315304651856, -.59262749578920193017e-1, .18426072795227810275, .14437125145059326314, -.10281460753387960949, -.18577414913905876404, 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.11227208544921875000e-1, -.14402345579986572266, -.26842183105857849121, -.35488029484085502625, -.39960396104447935104, -.40230527546437237763, -.36611559690346859664, -.29720689139550918532, -.20416210008651451351, -.97154404788450915195e-1, .12988412427429177931e-1, .11574942192309365136, .20183161878436929698};
            default:
                throw Error( Message(_ping_)<<"n>20 not allowed! You typed: "<<n );
        }
    }
};
 
} //namespace dg
#endif//_DLT_CUH_