const double Sphere::Gauss0_10[][2] = {
{.130467357414141399610179939578e-1,.333356721543440687967844049449e-1},
{.674683166555077446339516557883e-1,.747256745752902965728881698313e-1},
{.160295215850487796882836317443,.109543181257991021997767467109},
{.283302302935376404600367028417,.134633359654998177545613460785},
{.425562830509184394557586999435,.147762112357376435086946497325},
{.574437169490815605442413000565,.147762112357376435086946497325},
{.716697697064623595399632971583,.134633359654998177545613460784},
{.839704784149512203117163682557,.109543181257991021997767467131},
{.932531683344492255366048344212,.747256745752902965728881698262e-1},
{.986953264258585860038982006042,.333356721543440687967844049537e-1}
} ;
const double Sphere::Gauss0_20[][2] = {
{.343570040745253760693880576434e-2,.880700356957605915593098128925e-2},
{.180140363610431043661669344014e-1,.203007149001934706655199788236e-1},
{.438827858743370470661237793984e-1,.313360241670545317847532691265e-1},
{.804415140888905883027354691492e-1,.416383707883523743623790744004e-1},
{.126834046769924603692847464822,.509650599086202175183750646127e-1},
{.181973159636742487273581651887,.590972659807592086561886889867e-1},
{.244566499024586450997817974522,.658443192245883134492472499003e-1},
{.313146955642290219663725911488,.710480546591910256646491625341e-1},
{.386107074429177460959751902316,.745864932363018733939143684989e-1},
{.461736739433251333122679795301,.763766935653629253490421659777e-1},
{.538263260566748666877320204699,.763766935653629253490421659782e-1},
{.613892925570822539040248097684,.745864932363018733939143685011e-1},
{.686853044357709780336274088512,.710480546591910256646491625260e-1},
{.755433500975413549002182025478,.658443192245883134492472498097e-1},
{.818026840363257512726418348113,.590972659807592086561886896800e-1},
{.873165953230075396307152535178,.509650599086202175183750686151e-1},
{.919558485911109411697264530851,.416383707883523743623790726408e-1},
{.956117214125662952933876220602,.313360241670545317847532567888e-1},
{.981985963638956895633833065599,.203007149001934706655199749353e-1},
{.996564299592547462393061194236,.880700356957605915593098209281e-2}
} ;
const double Sphere::Gauss0_30[][2] = {
{.155325796267522986418497454065e-2,.398409624808330280773216207310e-2},
{.816593836012639501498370919717e-2,.923323415554547957115087802654e-2},
{.199890675158462438915644872091e-1,.143923539416616846748628951077e-1},
{.368999762853628370603378614598e-1,.193995962848135247983860625633e-1},
{.587197321039736592284417687349e-1,.242013364152970264514639766495e-1},
{.852171188086158012785509401337e-1,.287465781088095332408610738104e-1},
{.116111283947586902541011329513,.329871149410902475640630339525e-1},
{.151074752603342101533853805987,.368779873688526031341216188729e-1},
{.189736908505378569429761221784,.403779476147101076773474725605e-1},
{.231687925928990050367915103344,.434498936005414899011937664819e-1},
{.276483115230955411609695049839,.460612611188930643588163535007e-1},
{.323647637234560943264481396455,.481843685873221298197343130798e-1},
{.372681536916055076780097435091,.497967102933976335313901410581e-1},
{.423065043195708226518102663628,.508811948742027522982144760847e-1},
{.474264078722341152083487393417,.514263264467794201706428183526e-1},
{.525735921277658847916512606583,.514263264467794201706428183526e-1},
{.576934956804291773481897336372,.508811948742027522982144760832e-1},
{.627318463083944923219902564909,.497967102933976335313901410648e-1},
{.676352362765439056735518603545,.481843685873221298197343130798e-1},
{.723516884769044588390304950161,.460612611188930643588163525922e-1},
{.768312074071009949632084896656,.434498936005414899011937711956e-1},
{.810263091494621430570238778216,.403779476147101076773475498157e-1},
{.848925247396657898466146194013,.368779873688526031341222193618e-1},
{.883888716052413097458988670487,.329871149410902475640660513288e-1},
{.914782881191384198721449059866,.287465781088095332408579561304e-1},
{.941280267896026340771558231265,.242013364152970264514639766495e-1},
{.963100023714637162939662138540,.193995962848135247983860625633e-1},
{.980010932484153756108435512791,.143923539416616846748598090577e-1},
{.991834061639873604985016290803,.923323415554547957114894167073e-2},
{.998446742037324770135815025459,.398409624808330280773317978297e-2}
} ;
const double Sphere::Gauss0_40[][2] = {
{.881145144720399825188648789707e-3,.226063854926659562884464246335e-2},
{.463688065027149677347282388931e-2,.524914226557640679846994703179e-2},
{.113700250081128686683148581435e-1,.821052919095394436826588532098e-2},
{.210415903931041720977295002736e-1,.111229245970834786280659849780e-1},
{.335935958606617333195739165774e-1,.139685034900117005969937091614e-1},
{.489505965155628516358733345658e-1,.167300976412739237053551290655e-1},
{.670202483938702480896090958227e-1,.193910839872360088138920116231e-1},
{.876938845833441684018398846670e-1,.219354540928366359945478541065e-1},
{.110847174286740306152514227247,.243479038175361160314845455339e-1},
{.136340872405036448359501774123,.266139234919684121774755086140e-1},
{.164021657692910225810322742519,.287198845496957756833671535755e-1},
{.193723055166009881023693774885,.306531212464644695832681641272e-1},
{.225266437452435898962034347235,.324020067283005190372762975019e-1},
{.258462099156910643545716712878,.339560229076169519128454039932e-1},
{.293110397814197499237560127098,.353058236956433898477417907865e-1},
{.329002954587120763496253759410,.364432911979020295302553438180e-1},
{.365923907496373159429407827596,.373615845289841321000946681385e-1},
{.403651209649314450142241573967,.380551809503131211857790379561e-1},
{.441957964662372395758274357796,.385199090821239827941537671425e-1},
{.480613791246974589033403277988,.387529739892124056318619814791e-1},
{.519386208753025410966596722012,.387529739892124056318619814792e-1},
{.558042035337627604241725642204,.385199090821239827941537671419e-1},
{.596348790350685549857758426033,.380551809503131211857790379655e-1},
{.634076092503626840570592172404,.373615845289841321000946680869e-1},
{.670997045412879236503746240590,.364432911979020295302553438180e-1},
{.706889602185802500762439872902,.353058236956433898477418087813e-1},
{.741537900843089356454283287122,.339560229076169519128450998351e-1},
{.774733562547564101037965652765,.324020067283005190372762975019e-1},
{.806276944833990118976306225115,.306531212464644695832681641272e-1},
{.835978342307089774189677257481,.287198845496957756832857323978e-1},
{.863659127594963551640498225877,.266139234919684121776396920023e-1},
{.889152825713259693847485772753,.243479038175361160309628964894e-1},
{.912306115416655831598160115333,.219354540928366359937705470742e-1},
{.932979751606129751910390904177,.193910839872360088255172019048e-1},
{.951049403484437148364126665434,.167300976412739236888788525341e-1},
{.966406404139338266680426083423,.139685034900117005333606257895e-1},
{.978958409606895827902270499726,.111229245970834786224239110742e-1},
{.988629974991887131331685141856,.821052919095394437200247320222e-2},
{.995363119349728503226527176111,.524914226557640680120937576973e-2},
{.999118854855279600174811351210,.226063854926659562767586048896e-2}
} ;
const double Sphere::Gauss0_50[][2] = {
{.566797789964474907270277512891e-3,.145431127657756986099244236437e-2},
{.298401528395464370744589978965e-2,.337989959787268188781176508918e-2},
{.732295797599705884549518718376e-2,.529527419182551874924329728849e-2},
{.135678074466539631433279476969e-1,.719041138074274631082082566812e-2},
{.216945223785960285011271779217e-1,.905778035674468394767874092642e-2},
{.316716905275610331095625263638e-1,.108901215850622886524320964188e-1},
{.434607216721040534551321786142e-1,.126803367850061762392766920195e-1},
{.570160102381934756812295087666e-1,.144214967902676036569328150985e-1},
{.722851152850269576943186780326e-1,.161068641117890080990731978521e-1},
{.892089645703320258218729445630e-1,.177299178075730724883122160219e-1},
{.107722083549800368047347401830,.192843783062938369059520328343e-1},
{.127752848886965730869731873659,.207642315450738488579396130056e-1},
{.149223765646588874455226871058,.221637521694016377601020334921e-1},
{.172051767157280319609187567998,.234775256519742164829893049011e-1},
{.196148536407524880409809101804,.247004692247331574586908358497e-1},
{.221420847742674972842238545187,.258278515347905692446903729980e-1},
{.247770927546267899174270434075,.268553109444981232617414934871e-1},
{.275096832512980605426434266111,.277788724031062588117834305072e-1},
{.303292844051217436302885373088,.285949628238641918615145302405e-1},
{.332249877290281321581505871354,.293004249066112229175612142594e-1},
{.361855903110234004836177360739,.298925293521327287547882021417e-1},
{.391996381561979121576357733691,.303689854208851080158750077647e-1},
{.422554705000927048964185689529,.307279497951583318782033930439e-1},
{.453412649219956929572774811180,.309680337103416216920437548902e-1},
{.484450830836405561943835505167,.310883083276736311605165536803e-1},
{.515549169163594438056164494833,.310883083276736311605165536805e-1},
{.546587350780043070427225188820,.309680337103416216920437548902e-1},
{.577445294999072951035814310471,.307279497951583318782033930391e-1},
{.608003618438020878423642266309,.303689854208851080158750075895e-1},
{.638144096889765995163822639261,.298925293521327287547882026652e-1},
{.667750122709718678418494128646,.293004249066112229175611943298e-1},
{.696707155948782563697114626912,.285949628238641918615148514665e-1},
{.724903167487019394573565733889,.277788724031062588117832183838e-1},
{.752229072453732100825729565925,.268553109444981232617414934871e-1},
{.778579152257325027157761454813,.258278515347905692449314594589e-1},
{.803851463592475119590190898196,.247004692247331574598892557823e-1},
{.827948232842719680390812432002,.234775256519742164790436829862e-1},
{.850776234353411125544773128942,.221637521694016377186528578655e-1},
{.872247151113034269130268126341,.207642315450738490779894252940e-1},
{.892277916450199631952652598170,.192843783062938369059520328343e-1},
{.910791035429667974178127055437,.177299178075730790393150820853e-1},
{.927714884714973042305681321967,.161068641117890167969720710867e-1},
{.942983989761806524318770491233,.144214967902676064848336347615e-1},
{.956539278327895946544867821386,.126803367850062043328879393037e-1},
{.968328309472438966890437473636,.108901215850624080975131153531e-1},
{.978305477621403971498872822078,.905778035674463871584050596406e-2},
{.986432192553346036856672052303,.719041138074279189516987674941e-2},
{.992677042024002941154504812816,.529527419182547645099917083650e-2},
{.997015984716045356292554100210,.337989959787269895005765928322e-2},
{.999433202210035525092729722487,.145431127657757117915589737365e-2}
} ;
const double Sphere::Gauss0_60[][2] = {
{.394938386281988982885207101175e-3,.101340598442775369838380166347e-2},
{.207973744058091306162664331128e-2,.235636496347971019460758745309e-2},
{.510605238888914131636050649195e-2,.369496558175585907121861767941e-2},
{.946639912370090719071160008661e-2,.502377859083168996023291546804e-2},
{.151491056174736331392279505431e-1,.633908323874862571520340490253e-2},
{.221388720800019463013840770852e-1,.763730929872759404013925577377e-2},
{.304168619417883752522904941951e-1,.891495050689882856934473579695e-2},
{.399607619111862235716715687401e-1,.101685603646520795997792372518e-1},
{.507448445949770290311053352137e-1,.113947584720241663209123111510e-1},
{.627400386765508424353459500438e-1,.125902388107408144932200231614e-1},
{.759140076070351837547422525028e-1,.137517783749551216016458387814e-1},
{.902312369189271203157409457401e-1,.148762457503957860827551910562e-1},
{.105653130033867972715027600111,.159606095096481394864583158929e-1},
{.122138112346707156565578966699,.170019463624731958302437066549e-1},
{.139641743322134800281989469493,.179974490255422413548821304406e-1},
{.158116836309322281388534880388,.189444337846217282417770686490e-1},
{.177513585755261466093276051790,.198403477261903978599721790809e-1},
{.197779701475744818277895611844,.206827756177923776334054765153e-1},
{.218860549623027730410863706257,.214694464179678209439476207232e-1},
{.240699299970715126291055325758,.221982393978935566646268144054e-1},
{.263237079119146444445918473124,.228671898580572433233141074768e-1},
{.286413129208460805346273573235,.234744944244561024234776368610e-1},
{.310164971711601011422523664739,.240185159099855904818370077568e-1},
{.334428575865775902873823517325,.244977877278784176947379985131e-1},
{.359138531288369154154652569830,.249110178452750905055796209583e-1},
{.384228224311985330994827684327,.252570922662546872991193669573e-1},
{.409630017563287291379561529369,.255350780349278137022745603956e-1},
{.435275432301527498426777917675,.257442257504904669975221985852e-1},
{.461095333025231715290357246459,.258839715874550937719018215143e-1},
{.487020113849376100705414807300,.259539388156103198664324691810e-1},
{.512979886150623899294585192700,.259539388156103198664324691810e-1},
{.538904666974768284709642753541,.258839715874550937719018215147e-1},
{.564724567698472501573222082325,.257442257504904669975221985852e-1},
{.590369982436712708620438470631,.255350780349278137022745604134e-1},
{.615771775688014669005172315673,.252570922662546872991193677268e-1},
{.640861468711630845845347430170,.249110178452750905055796209583e-1},
{.665571424134224097126176482675,.244977877278784176947379985131e-1},
{.689835028288398988577476335261,.240185159099855904818321336038e-1},
{.713586870791539194653726426765,.234744944244561024234776368610e-1},
{.736762920880853555554081526876,.228671898580572433237080831789e-1},
{.759300700029284873708944674242,.221982393978935566672977007765e-1},
{.781139450376972269589136293743,.214694464179678209722676846342e-1},
{.802220298524255181722104388156,.206827756177923777868430031241e-1},
{.822486414244738533906723948210,.198403477261903978599721790809e-1},
{.841883163690677718611465119612,.189444337846217063135076737443e-1},
{.860358256677865199718010530507,.179974490255422247366365392611e-1},
{.877861887653292843434421033301,.170019463624731405503046956043e-1},
{.894346869966132027284972399889,.159606095096478820303821404550e-1},
{.909768763081072879684259054260,.148762457503957860827551910562e-1},
{.924085992392964816245257747497,.137517783749546534329103217577e-1},
{.937259961323449157564654049956,.125902388107566784421229905876e-1},
{.949255155405022970968894664786,.113947584720694077858816101155e-1},
{.960039238088813776428328431260,.101685603646520795997792372518e-1},
{.969583138058211624747709505805,.891495050689882856934473579695e-2},
{.977861127919998053698615922915,.763730929872759404013925577377e-2},
{.984850894382526366860772049457,.633908323849011108025039272241e-2},
{.990533600876299092809288399913,.502377859118510564718329612335e-2},
{.994893947611110858683639493508,.369496558183092587249295501953e-2},
{.997920262559419086938373356689,.235636496356113923571996415931e-2},
{.999605061613718011017114792899,.101340598443997726310863308691e-2}
} ;
const double Sphere::Gauss0_70[][2]={
{.290857013212078971628709057395e-3,.746360594653686213939765457726e-3},
{.153187401915992169509325208292e-2,.173594698007457305258126810507e-2},
{.376197239415500945052895712030e-2,.272355416121033081125607190194e-2},
{.697722096480067003644933034133e-2,.370588337453331620883644696720e-2},
{.111712970212037998030461859319e-1,.468088045258601806491883799597e-2},
{.163358881675067808056908821380e-1,.564659269225376022693891117331e-2},
{.224607454428535786798363226857e-1,.660109483946496392708308713841e-2},
{.295337104980923222385922921290e-1,.754249371162631074142596733090e-2},
{.375407415510327798638670174076e-1,.846891808400367948814932521537e-2},
{.464659418695385752818236378530e-1,.937852819033434711371275045909e-2},
{.562915915683259144378132550030e-1,.102695190415515984571046124030e-1},
{.669981828930706853099827402897e-1,.111401202230118031891160982007e-1},
{.785644590005098788407032349013e-1,.119886039285061733290419099351e-1},
{.909674561872794054863840064467e-1,.128132854463869576340261976382e-1},
{.104182549496053620946161912758,.136125274084675022938440478509e-1},
{.118183501614050215537452471752,.143847429781129098233633824016e-1},
{.132942514969528679346174160531,.151283989901240708163475736356e-1},
{.148430286924235701468526319889,.158420189806667597565909317000e-1},
{.164616067952961297176859402494,.165241861196849292989388655977e-1},
{.181467722695110951860570177656,.171735460249530939894451707466e-1},
{.198951793757322256331616708898,.177888094506463232422348672040e-1},
{.217033568140595856813520321265,.183687548468363479520180180867e-1},
{.235677146160144436367459621670,.189122307846114086974020015747e-1},
{.254845512721181705365110929324,.194181582420367018993001454783e-1},
{.274500610809176067134180148059,.198855327463882837432985705738e-1},
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{.943708408431674085562186744997,.102695189289622354731699093270e-1},
{.953534058130461424718176362147,.937852899403635818541953753169e-2},
{.962459258448967220136132982592,.846891811229361655788776995959e-2},
{.970466289501907677761407707871,.754249487222279749498175109539e-2},
{.977539254557146421320163677314,.660109592921473942563278563274e-2},
{.983664111832493219194309117862,.564659339533230818127917409533e-2},
{.988828702978796200196953814068,.468088054212851552627698115141e-2},
{.993022779035199329963550669659,.370588077922149725799303150821e-2},
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{.998468125980840078304906747917,.173594718554365913766046663598e-2},
{.999709142986787921028371290943,.746360634580001122675388535606e-3} } ;
const double Sphere::Gauss0_80[][2]={
{.223088674184685059959750452716e-3,.572347879584698924701887018271e-3},
{.117506780088115555025289590844e-2,.133261824549431729803007138666e-2},
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{.857571363068546479085598614544e-2,.358995999480610194101793559104e-2},
{.125454297071361033071773849654e-1,.435466201554396187704271338770e-2},
{.172574554781003742738634221643e-1,.507929388603473728929233311200e-2},
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{.288786193450636626238669977500e-1,.654099833088933631515087319866e-2},
{.357700614137771020234770204623e-1,.724769265320370811053477877049e-2},
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{.606387161608930856481133281804e-1,.931368336481594672918622460676e-2},
{.702842966684444515114039382542e-1,.997542326532832047343958502701e-2},
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{.977295383171817452746740758511,.581523987928314880702985597321e-2},
{.982742544521899625726136577836,.508243675409358779738667761410e-2},
{.987454570292863896692822615035,.434170140099697767128638228169e-2},
{.991424286369314535209144013855,.360071931056142540197198818823e-2},
{.994645651249877765513251583568,.285385098690565648413790227226e-2},
{.997113770482844138946031751832,.208371333491691899992751966377e-2},
{.998824932199118844449747104092,.132487681472124123939238711225e-2},
{.999776911325815314940040249547,.572226846106074980087783233009e-3} } ;