const double Sphere::Gauss2_10[][2] = {
{.491257073594768335536505153897e-1,.153240036697160842128257022849e-3},
{.128289925425591512388138657995,.154552319473657862858532681468e-2},
{.234652320451892103790466872755,.646988906855852922973060656083e-2},
{.360390511345290290671463493833,.171975750465530080791375023239e-1},
{.496192873585126092994469357943,.338545650168141160441010713095e-1},
{.631992149550662282395230433750,.528837887669641582098848389424e-1},
{.757718803867476438888605444635,.674522193814378249705257943166e-1},
{.864049765949771045734236570615,.700695077086663340863724553267e-1},
{.943101849466342079288565140621,.562729364028081262824158321421e-1},
{.989031547543825865749718967010,.274340887100974969604516485853e-1}
} ;
const double Sphere::Gauss2_20[][2] = {
{.142042111593581533199768686408e-1,.374922099333713477252413687678e-5},
{.378512878495018102908391935771e-1,.410391020873202055490740417407e-4},
{.713009850812494546549021628327e-1,.193888309617511810769838525298e-3},
{.113858697085452856312717069635,.607045704267258254152723739783e-3},
{.164621085368438274828481605287,.147744444197148580628385763826e-2},
{.222507407964513246448874054163,.302248917090737937491848598086e-2},
{.286284388984712319257916564646,.543209080612302745001201114180e-2},
{.354592954222632433382679165236,.881355607824335532892527316772e-2},
{.425977341817173128272487803346,.131409192566616517421081337206e-1},
{.498916184517151448629375345863,.182205034182686915518433153096e-1},
{.571854959066743315384574965228,.236822904142460539808664502667e-1},
{.643239129897546894352944933367,.290024047455892851699163572650e-1},
{.711547287818727615228059293348,.335564314534754934790027148453e-1},
{.775323580615694961590618035168,.366974204720181327132542496121e-1},
{.833208746518990569987019298542,.378473903769223407153546955208e-1},
{.883969092344513195053302568433,.365879165532270649866092988735e-1},
{.926522808214714716942433454714,.327346443175731480474796486234e-1},
{.959963099538093219003679850171,.263825644291255847945133896568e-1},
{.983577911866012167097458385744,.179137523257385591017739577255e-1},
{.996869316259256410437849858250,.797579273627665168522730902981e-2}
} ;
const double Sphere::Gauss2_30[][2] = {
{.663211500271097817570325702452e-2,.382608923075889919800716609207e-6},
{.177493240267956088263321828052e-1,.426094552744211642542690366445e-5},
{.336431883896836683181702598759e-1,.206420183064916067816864504749e-4},
{.541642235507796662191580997968e-1,.668049905165764118033976156847e-4},
{.791101848860494046855361442670e-1,.169475219011455575437117744711e-3},
{.108233681317975288648319034737,.364546671821359393848956829907e-3},
{.141245482613304182282994800760,.695261358264572683955917552282e-3},
{.177817601261726064985332074227,.120892191277920989730184745665e-2},
{.217586618271696688264834593661,.195237804481221793873138947333e-2},
{.260157320111423121852313465603,.296667307897631051686161587943e-2},
{.305106637351990915333926252905,.428134886133223033186156472609e-2},
{.351987854466849679129433085440,.590897443386360594206730468508e-2},
{.400335052129502344898162640635,.784047862993814990112827880857e-2},
{.449667739169172944250821201566,.100418264051183570924583835973e-1},
{.499495628737103521028236076305,.124524856098612741754829672065e-1},
{.549323511498440112648910041523,.149859922309779830046969430549e-1},
{.598656177562581454536003223359,.175327493560042250339784002570e-1},
{.647003338314649721384544908742,.199650030227992002266880727219e-1},
{.693884499279487818633411309326,.221437434854455441261790459055e-1},
{.738833735621502524896663558114,.239271005634396089176655721874e-1},
{.781404322848115420369642692426,.251796529404075319969638435637e-1},
{.821173176732691237121658201575,.257819673686486353899011716944e-1},
{.857745058400042785512239065895,.256396348287622814366844391660e-1},
{.890756502937347891125326812655,.246910822719888413400818389227e-1},
{.919879432887674464171597682934,.229135110306361676601618552119e-1},
{.944824421911954230264200984788,.203264418623155075093237305904e-1},
{.965343580434010265050895515566,.169925247346079037433860226042e-1},
{.981233053725386775501700669856,.130155029862658423666781666328e-1},
{.992335232135193209347489299056,.853567610909337999139220296440e-2},
{.998542272166093496407410606509,.372828975288835111552929677766e-2}
} ;
const double Sphere::Gauss2_40[][2] = {
{.382418266735670194784708810536e-2,.734215836527357072782540115202e-7},
{.102507855211380570639395037195e-1,.822877113532537636741171522943e-6},
{.194745604033743002506883631189e-1,.402326273021395685800917950044e-5},
{.314475454325494670237896474260e-1,.131791520888207570727480100659e-4},
{.461021363890960480719067945095e-1,.339401875896988166785790443041e-4},
{.633546976764088761443755613422e-1,.743353697788864963655359236095e-4},
{.831065289265554861323943536824e-1,.144798432045007956536079532853e-3},
{.105244549300301357170927664715,.257969284227432726183939405129e-3},
{.129641983053297638971472164484,.428270434711565358816168096530e-3},
{.156159100047213845003401373439,.671271561081320601575744600012e-3},
{.184644022285522115403080777576,.100286919949645223865526956895e-2},
{.214933596781184557808747669092,.143832108619827335826279464425e-2},
{.246854331576483555820979013034,.199118529446588074373199121206e-2},
{.280223390301430060737495576200,.267222234894058416387565727020e-2},
{.314849639908600139000879579462,.348832348037184561104618836470e-2},
{.350534745743557047254877705520,.444152977989564889199085175548e-2},
{.387074307759989974037480743010,.552820507231234213766985424587e-2},
{.424259031415026157814827448463,.673841988817089370178436528592e-2},
{.461875926562247165995043139253,.805559519642279278901393622404e-2},
{.499709527489342785784304875871,.945644296050923394611228326005e-2},
{.537543127120583224482282410770,.109112266551553185440912201120e-1},
{.575160018319947375869594848582,.123843493121684027237707006165e-1},
{.612344735188204681760956179355,.138352602292641308265988188276e-1},
{.648884287246187109710884472649,.152196550097922750484239852707e-1},
{.684569379436614380791742183996,.164909279494078717755122032569e-1},
{.719195610957772939161521107889,.176018217637624364000020596550e-1},
{.752564646063586711067079929241,.185062080019055722937047649837e-1},
{.784485350125507995402982307206,.191609228445912564795154266609e-1},
{.814774884451461095411188403410,.195275778318371933391809196879e-1},
{.843259753595093482082927169448,.195742637162785578630596981877e-1},
{.869776799164520768005395941810,.192770682270361617526508400018e-1},
{.894174134454589149041293819757,.186213349875048161453187811951e-1},
{.916312014585356933334311577850,.176026009046549753975323641731e-1},
{.936063637249193923068050848563,.162271626144488536978738513889e-1},
{.953315869708445671913030122583,.145122384977372356009922393923e-1},
{.967969898565730363750795944577,.124857109450236409082518183199e-1},
{.979941801024461257687387764941,.101854546677466944184224884515e-1},
{.989163045363521989057803503808,.765829042516365388555884935841e-2},
{.995580989385131945673450605462,.495875600479143167619547030270e-2},
{.999160306802194153093739864860,.215070445532877514987819863515e-2}
} ;
const double Sphere::Gauss2_50[][2] = {
{.248423504086096233037901719068e-2,.201363422662114030102233446462e-7},
{.666406537053075654857309746640e-2,.226363052897815263870338160695e-6},
{.126742857668779893006468657357e-1,.111160010575586337622603198749e-5},
{.204956970987988138379698838836e-1,.366225634219276154715196326889e-5},
{.300998353954127143740494288160e-1,.949870304369855405182874469494e-5},
{.414511696150291773368722628621e-1,.209816573476194359915040433640e-4},
{.545075499911913373466363359391e-1,.412778513975992694655360522783e-4},
{.692204419129185470471667018400e-1,.743799666826858576522737374861e-4},
{.855351309806664984311913226395e-1,.125077635216093417002477832344e-3},
{.103390935829044787343504797856,.198878278296499976942833055684e-3},
{.122721437854033611174998611178,.301878598813881647611666540289e-3},
{.143454730181224411369069763250,.440589590533456085616899444703e-3},
{.165513686126832811229520224770,.621719903114778922824164167187e-3},
{.188816246636468402208260152197,.851924232449482038544047849256e-3},
{.213275725848581779182875654903,.113752502444506102764539240291e-2},
{.238801133749483514894393379446,.148421712578447901172019966207e-2},
{.265297514772260334415112061908,.189676603565368592129513708665e-2},
{.292666301108058561088485383362,.237871106704599034160648334200e-2},
{.320805679431028981559733705049,.293208498647914992964112236853e-2},
{.349610969681727053606088583028,.355716155166782674689255064404e-2},
{.378975014505263353898271199251,.425224180676616005237433470144e-2},
{.408788577898784035393808942736,.501348903726226215023295658295e-2},
{.438940751587377986954776608157,.583482095829188953098532603014e-2},
{.469319367618016843982680960216,.670786605084101737613393920384e-2},
{.499811415637543768081790540368,.762198902153961337890704606099e-2},
{.530303463303011653763504742529,.856438820507725910150318289163e-2},
{.560682078260831991302442585900,.952026542330552012573918538223e-2},
{.590834250125237820920697322930,.104730664371984055241519373375e-1},
{.620647810886487390000071486026,.114047877556509158808252870147e-1},
{.650011852185025916717678000433,.122963432778866350412108316024e-1},
{.678817137899451867893276577717,.131279821213008398362410905361e-1},
{.706956510513554274081816955730,.138797470965766031875291193270e-1},
{.734325289750833546991793935448,.145319617025250964040814293256e-1},
{.760821661993707128143328633017,.150657322806926601758105194496e-1},
{.786347059038934434376771248571,.154634511395190994364312933086e-1},
{.810806524780562656044678217745,.157092860621302342938013369248e-1},
{.834109068456782402917353274611,.157896416691977063652389654493e-1},
{.856168003147390742518582837191,.156935786226025299484122046883e-1},
{.876901268264042844612438267971,.154131776160231716584820257220e-1},
{.896231734836229953089669172641,.149438364797405538045068044675e-1},
{.914087492462416004312633661708,.142844904901634253489104227842e-1},
{.930402116869424268832375785210,.134377480694410883265681497058e-1},
{.945114917108081905076916792014,.124099364285284955403979255649e-1},
{.958171161521450946300724149963,.112110542900399769270214764498e-1},
{.969522281792985453438785834876,.985463159506968223696402768741e-2},
{.979126054760130737003541379553,.835749916791716219762797462748e-2},
{.986946762898335777900775372951,.673947560788911124751286153242e-2},
{.992955340010064117462681862658,.502299085414965334889433371233e-2},
{.997129548049691870942274093338,.323275552250685325591156424502e-2},
{.999454789878689811437940168357,.139740597968450069659097767394e-2}
} ;
const double Sphere::Gauss2_60[][2] = {
{.174241754050518364279071979523e-2,.694971323093340205896175985972e-8},
{.467606176688816650055527532125e-2,.782560941585013896320898708362e-7},
{.889869712591309395685796796307e-2,.385221664244703822063443983547e-6},
{.144015211870506964939608538278e-1,.127316813409095235907994554583e-5},
{.211706204268167486962975536800e-1,.331515588086238462899358729309e-5},
{.291884728627370213641234161760e-1,.735720050894232891683026626649e-5},
{.384342153104206047477990890185e-1,.145531480309028618067830140544e-4},
{.488837518017038467941173276513e-1,.263876536619945856663975217463e-4},
{.605098336028127909321001728919e-1,.446860394569613915567613792118e-4},
{.732821367972458944024387564254e-1,.716101725345659780293265828126e-4},
{.871673441863034364697233482976e-1,.109639899228384218612959221713e-3},
{.102129233528124412531331052552,.161539981250349213277781003535e-3},
{.118128772709531327169810089772,.230312897471823317122915036316e-3},
{.135124221940803959841696953320,.319138288600253690352166475108e-3},
{.153071242857974235835788774280,.431300221297566612705938609568e-3},
{.171923014320430351331092555058,.570103822874053155759266832906e-3},
{.191630354638490958791098932419,.738783177878290157693987702646e-3},
{.212141849931677624714104993362,.940402674750341849958641011523e-3},
{.233403988293723356193046345251,.117775423627912743240053896787e-2},
{.255361299420595834262754373595,.145325305517262412611780611536e-2},
{.277956499341019967867153373271,.176883458024781956942365795195e-2},
{.301130639874222006554144622673,.212585555571687095882205940164e-2},
{.324823262426431033409094798018,.252500190353277635109371808583e-2},
{.348972555725837994895507631462,.296620615617552669005605059731e-2},
{.373515517085117306098447594563,.344857699571221744401356508921e-2},
{.398388116771210098517787037231,.397034323722934690979946609192e-2},
{.423525465053830375832502952548,.452881431520629943467347929734e-2},
{.448861981497080330637862978772,.512035899599045613194932695189e-2},
{.474331566052651082209285839461,.574040365555007644845282937020e-2},
{.499867771508345536933176294251,.638345103764825610518614890582e-2},
{.525403976842097032301866043304,.704311995305583882443530184204e-2},
{.550873561029276188417753736356,.771220590576790360632260589992e-2},
{.576210076849882577077608291410,.838276214834107601303168887705e-2},
{.601347424242208856666718089225,.904620018667586295797645755629e-2},
{.626220022750741834207884693677,.969340828613003452205462687302e-2},
{.650762982618423734849663713321,.103148860868535383747503784661e-1},
{.674912274076931222369973464656,.109008930272965690993839361956e-1},
{.698604894393330030138264648312,.114416079108496646073109548578e-1},
{.721779032237317223137539965615,.119272966404580167975857046235e-1},
{.744374228940256165197744987651,.123484848975686676654199723382e-1},
{.766331536225323654473741820185,.126961323613163954367553343066e-1},
{.787593669997304504848550153441,.129618049563140033934186673949e-1},
{.808105159790864270509542355635,.131378415860312594064012733000e-1},
{.827812493487482894405020291994,.132175118550504098970978005468e-1},
{.846664256923618217722096713656,.131951614072391329641792220107e-1},
{.864611268026069122488030982117,.130663417060846189157493087985e-1},
{.881606705124913147060926955940,.128279213543662895041378394215e-1},
{.897606229109813377104643166256,.124781763876452159461018747464e-1},
{.912568099111983016279240920328,.120168573728762431861190347174e-1},
{.926453281411833184084773276103,.114452315916882262013293664852e-1},
{.939225551291747761981231052378,.107660990784007391341636228485e-1},
{.950851587575649519411672613264,.998378180593796586115409116355e-2},
{.961301059625044010095679136502,.910408586155454046453279255516e-2},
{.970546706603706738192745720267,.813423702296950961964406659170e-2},
{.978564408907806224935561246245,.708279076845794739042981948708e-2},
{.985333251886480062359231354221,.595951851341779309518125941602e-2},
{.990835582794460959421391039169,.477527359489047628697497260605e-2},
{.995057065825715959096632121549,.354184762928420443337408076649e-2},
{.997986767658383959795422649573,.227188967836856627943375115219e-2},
{.999617697744363863906331550970,.980236106401048223913882624065e-3}
} ;
const double Sphere::Gauss2_70[][2]={
{.128928397458930161185602646491e-2,.281592864823660948777162179155e-8},
{.346088652408477583780604686769e-2,.317406823854088331184976076272e-7},
{.658860446779290491508167881425e-2,.156476497846910565439117264841e-6},
{.106680377743994205037581439660e-1,.518158404438104860753281915846e-6},
{.156916393092645646852485996711e-1,.135244063208953962707047320583e-5},
{.216498140004041233372428617373e-1,.300998714918436502153900728940e-5},
{.285311011927168057136868274206e-1,.597377046029238361976083413884e-5},
{.363222366845172344188508595123e-1,.108726490157154462886554109416e-4},
{.450081910097233740171724531579e-1,.184907663734427971752594720449e-4},
{.545722032467686004621899452158e-1,.297724032977543576545889612583e-4},
{.649958154313983989911583696774e-1,.458220090184312034070915891243e-4},
{.762589091586750416008367984942e-1,.678992357934718737435398050630e-4},
{.883397449128645209636216204497e-1,.974089055199010657359109361059e-4},
{.101215004299318018528477478624,.135885946807381729410742643439e-3},
{.114859835208513251960307851886,.184975448273035173897670297337e-3},
{.129247899878554111893843665464,.246408076353051794369347764377e-3},
{.144351425790492090382886579115,.321971214227713595900715810947e-3},
{.160141259312694935039039833015,.413476271290363185187069869965e-3},
{.176586921998761739320949684575,.522722704660084349683764607726e-3},
{.193656669434959324202030377760,.651459374195339828688554517136e-3},
{.211317552526358321297245731854,.801343922689259570340458218913e-3},
{.229535481105070192142580432947,.973900930869086580458074599224e-3},
{.248275289738874764342060251420,.117047964148221219492993062939e-2},
{.267500805613899958597418193713,.139221207717671834060044142786e-2},
{.287174918360776033041756893570,.163997239235378586213210639159e-2},
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{.999717165737763046972467132947,.725365124399770652082639971623e-3} } ;
const double Sphere::Gauss2_80[][2]={
{.992392729427889142569667633317e-3,.128431379209266589707987028103e-8},
{.266437224307540587544281111915e-2,.144857962058174906553934786829e-7},
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{.821738741886322796132736378163e-2,.237026376439377600682338165082e-6},
{.120916845503124295807418761130e-1,.619541459505582905958536520804e-6},
{.166906905905373359195641616010e-1,.138196218169777125941227406688e-5},
{.220076037197295574134893372241e-1,.274742173791986823553756690468e-5},
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{.977841664033485816339664973493,.542204113328351586725809646000e-2},
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{.991631594455243601485813266657,.332081741769756274829669841860e-2},
{.994775224117718617446918850082,.271566939922982105526033565326e-2},
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{.998853407379547517322954312060,.128768897294335884377223063904e-2},
{.999782319074225900069247726781,.554473945568171940300750259384e-3} } ;