Lfunction data - 32-12e32-1.1-c2e16-0-1

Formats: - HTML - YAML - JSON - 2025-12-21T12:23:02.566862

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '137232135108105863622251405146,336085348293233505420795311872,967183512312438527701439346493,1294866112531013223074433073808,1451746856807591762623942053326,1482017335356797121264211233059,1931714135209384842329762774687,1980087067934388647578926888382,2148553897993950060879227384356,2532196276647501268322839575553,2645876708941299678173130037337,2832029369714542483646938414942,2973939967699396196048717529647,3407109558920056432060070830100,3696337820918772331239153620014,4132723398472477533549245210594', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 6, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3156172308.1058936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -6, -4, 10, 56, 88, -128, -496, -512, 1408, 3584, 2560, -4096, -24576, 0, 65536]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '144.1', 'coefficient_field': '1.1.1.1', 'conductor': 34182189187166852111368841966125056, 'conductor_radical': 6, 'degree': 32, 'euler_factors': [[1, 0, -6, -4, 10, 56, 88, -128, -496, -512, 1408, 3584, 2560, -4096, -24576, 0, 65536], [1], [1, 0, 0, -32, -344, -5664, 512, -145600, 223452, 2255168, 20875776, 67282720, 753060504, -1881828576, 2740220928, -75471830656, -399298967994, -1886795766400, 1712638080000, -29403571500000, 294164259375000, 657057812500000, 5096625000000000, 13764453125000000, 34096069335937500, -555419921875000000, 48828125000000000, -13504028320312500000, -20503997802734375000, -47683715820312500000, 0, 0, 23283064365386962890625], [1, 0, 336, -896, 58376, -263552, 7407024, -39795456, 757778332, -4246975232, 64072810512, -358262212224, 4568044589112, -24788168573056, 279500753010928, -1432888676504064, 14752709956620358, -70211545148699136, 671081307979238128, -2916303244451465344, 26333868015357446712, -101200207605265243776, 886850172071843856912, -2880396592160634675968, 25183194694504055685532, -64803461685446965119744, 591023231480803234095024, -1030441156996143666290048, 11183745963071945007072776, -8411182382532387857861504, 154555476279032626888205136, 0, 1104427674243920646305299201], [1, 32, 512, 8480, 137032, 1636576, 18165248, 219655136, 2263228700, 21867108000, 253620152832, 2916953293728, 33797606438392, 431768458252384, 5293166227138048, 61910274521995104, 703855220885889990, 7491143217161407584, 77497246731528160768, 764904161670051651424, 7244817096612104559352, 75658256120708606202528, 795968684556265691023872, 8304030623946757937028000, 103994747384483599296220700, 1221264393643890740902536416, 12220670499948695842018446848, 133221785980516668883794428896, 1349728568031268563530552995912, 10106613703992673592061925813280, 73835487286527607827290144809472, 558380872604365034193881720121632, 2111377674535255285545615254209921], [1, 0, 0, 3200, 7608, 95360, 5120000, 68335872, 2004669468, 7270355200, 184268595200, 4889456013184, 5354592144136, 669839496880000, 7008632866619392, 70586941744778752, 2398056097119178950, 11929193154867609088, 200173563303516454912, 3233187312095855920000, 4367905310396995202056, 674053031939570500537216, 4293105416369593808691200, 28626124880126031417452800, 1333940359929609046405794588, 7684738295176870566317023488, 97305414527389693126661120000, 306280955401774982827806707840, 4129628261008210861166297506488, 293546656618459573306878771228800, 0, 0, 442779263776840698304313192148785281], [1, 0, 1936, 5888, 1970104, 12118784, 1412088752, 12342981120, 803992020380, 8384758342144, 385156459019152, 4284704575184128, 159049561847732232, 1754956969783214336, 56986337962883453232, 598166401551176027136, 17699896684274407333702, 172870090048289871842304, 4759555932997988897389872, 42360394950173251076989184, 1109491164547107826349538312, 8637938288797125779076873472, 224400717837231097263723382672, 1411807385876012504979853451776, 39123209970216247349866931642780, 173580385880837474525376256750080, 5739055454852175186987568798891952, 14234273794978469606239527330450176, 668749185151602171785786035156550584, 577616721466425684522335197824841472, 54887715035215868918645487860698047376, 0, 2367911594760467245844106297320951247361], [1, 32, 512, -2656, -523448, -8424608, 1945088, 4454446304, 107916937244, -703649376, -30601835632128, -698985761087712, 998616856187896, 253693358084547040, 3161998119961945600, -30474951661580761248, -1910909655870418467642, -11001457549830654810528, 412074756991560712537600, 11935227534935987982742240, 16960072330872362657151736, -4285528014488222255165241312, -67731499355399346164889220608, -562220555870954483221958496, 31127713926547623702996478011164, 463829690679844028766014887069664, 73115806292591152730397659237888, -114321765590792791654590700633616288, -2564247658685593345039959330637191608, -4697012278412155302375467373195101536, 326866782169983241283381922259938632192, 7374931772710246881456304620989865388832, 83198449060887472631428936505541918917761], [1, -128, 11088, -703360, 37418488, -1719054464, 71192321008, -2695787852672, 94963463800604, -3133315670487680, 97608794561723984, -2881444739461007744, 80972669723070041032, -2170372074719910288000, 55638543600337855059568, -1364769401046612538272128, 32076997834145946433448774, -721963013153658032745955712, 15569945679662145697724568688, -321292959541936345484326032000, 6341049546846612329389018049992, -119368202810791358519006027497856, 2139060074082408660121065881078864, -36324015721076064717500264536853120, 582373927212729564239528154295772444, -8745542615130426331486171769039235968, 122177116844122975978330716463342682608, -1560637466328161065379884377642483222656, 17970257449593941260499095894184096342008, -178690474825862624479024292019028921095040, 1490159053679180176208754967727478284501328, -9100076645267374467121862948661887590201472, 37608910510519071039902074217516707306379521], [1, 32, 512, -18368, -1552984, -20596992, 304715776, 25469097376, 491466517980, -9791032230816, -347423504794624, -2649303176415616, 694517140133881240, 20658732330776531008, 190851587110380169728, -11485440538974369182240, -825511918710437437518010, -9659255493277444482263840, 134985701383016796825389568, 12288295772642566683038037568, 347429708091906261612770751640, -1114581009523248128213672338816, -122923572029394124477602295235584, -2913402246673399205822631354830496, 122987763056454027065527520746127580, 5360157068985091075692931429304357536, 53933039619676501706832037612223666176, -3065912485852378435676636899888916259072, -194410148006867402337936613313365933238104, -1933792253116779126640356744769334708731328, 45332941738570348306746760204906215750328832, 2382812750133603932873376583270382965376659232, 62623297589448778360828428329074752308805325441], [1, 0, -7312, 0, 29025544, 0, -80335806576, 0, 171125889681052, 0, -295006946315669072, 0, 423507628633392203064, 0, -514807310246870517530800, 0, 534544428224191949216973638, 0, -475435361966500107220561946800, 0, 361205860749311633126295498919224, 0, -232365992571959154769108053280691792, 0, 124480928883555283432512372945523642012, 0, -53968833982798547907484231483371363928176, 0, 18007814989012006396727795042356541234498824, 0, -4189513653245889742853916344818291077714715792, 0, 529144398052420314716929933900838757437386767361], [1, 96, 4608, 145952, 4040888, 217733344, 12932982272, 602883756192, 21839639792924, 655265530977504, 21703692469355008, 815191556064282016, 35433653736114978312, 1467845464506621375840, 50867428451208042071552, 1465079699916707177725984, 43181875126876200893659590, 2005694109185972126306872096, 95333750573544515336861967872, 3766089872615510619356602558560, 124459980725454940457402518361352, 3919917377017695306048158128103584, 142874365875275818372623258034037248, 5905293130321981955930416013149196256, 269446816147411178023745063078939270684, 10182739083597405563517698021971929022368, 299042671345538323243211413530790200591872, 6892279360058368588727890523815164520992736, 175112920437535849046858269928673978179517368, 8658743533427367681727180434867343437927188768, 374249082483169821377980583689543656211184890368, 10673895706655405947217821230645526361523169060704, 152214200233450528559804138174517974884637692126081], [1, 0, -13840, 0, 102706104, 0, -524939980080, 0, 2044068651261084, 0, -6376104819902485008, 0, 16402857938643748508168, 0, -35383360569917421812676272, 0, 64577774780000237359256539206, 0, -99984920347410423778809915042992, 0, 130975594183964147316577669339960328, 0, -143867179257987808259948724187240773648, 0, 130327836327428627758263533192221310642844, 0, -94577272396201366241415571692902103329164080, 0, 52288817022836677339754428612357436314532476344, 0, -19910587654352744331498189290377125594313655706640, 0, 4065214023175683899921868126254722311886802750234881], [1, -160, 12800, -978464, 71106632, -3813053664, 178619596288, -8719368905312, 336417491247900, -9339737479444512, 288453906337733120, -7137460469658328480, -129151507673078938376, 13166699894046358977184, -444909531434654535928320, 28972919499885413370278176, -1725860576868082036875113530, 53570928155288129321644347424, -1521057150978328362086276344320, 83231490187496868731360371674016, -1509548687837068929080749572115976, -154251100701786455099704084452111520, 11526511599283975053699449693148101120, -690069841169201212548904345148858265888, 45959347805131236616846050940888629327900, -2202506774663292515595320792900595941019488, 83425384132219209728594707834387496433868288, -3292903018667363424129999428899641159211808736, 113541085637070176903456488799040510541683196232, -2888848033840853858437622085436880595374137960736, 69875789182349331644715482041701831060558996492800, -1615004177477048927638486578688833570387169806439840, 18663392025969146670022260524972832947786731075670401], [1, 0, -24144, 0, 280869112, 0, -2097883923184, 0, 11327375509374492, 0, -47271044690493269328, 0, 159378111080716584342216, 0, -447837309295947983522369904, 0, 1069451862014464590113083289158, 0, -2185303209262560752182421495520624, 0, 3794997890552929841601714620665202376, 0, -5492492790697802075734747006265493492048, 0, 6422365603496382914720509973369815941845532, 0, -5804149811601969119174985502258382340206124784, 0, 3791862421616779449515053523942013352026525646072, 0, -1590557026786853140797198116121630204596987902319184, 0, 321463340914028260476243062478235279920395730789296641], [1, -160, 12800, -602944, 3948712, 1481707264, -105845942272, 3791430241760, 34861972067036, -14471440004155872, 1098860393015073792, -54880211634179791488, 1349758970889735695512, 17264917459299251320000, -1853658370277165714728448, -16562877726012460012653408, 5168183120809487531686006854, -46525123532369000175543423072, -14626256151162940805916239103488, 382665865430285765535809940280000, 84035575657552168608684076721511832, -9597861385825702742638183560963126912, 539824952603700609723101838569018268672, -19969809540319112647568076276372227283168, 135134383349547902989533848962368780910556, 41282759798405789748356760661092786290812640, -3237364540580026851537576611559091487297923072, 127300919681547610483917934009535941216524510976, 952963638614918140606811320515739527079739471272, -408742302834945234868084424680060517972525248250176, 24374421582918186280531772612807345185963770774540800, -855846877830214815775171865867197907842152901321063840, 15025461748906708859452861070130993269553796873817927041], [1, -128, 8192, -1121408, 136226184, -9279937408, 700645040128, -71627082366848, 5234572115355804, -316007889653226112, 25502997282495045632, -1933332663772110218880, 109616149725595055398840, -6942765907527045516409216, 514753163863417494131859456, -29693308567434592900791332224, 1551148300110104846432558538438, -103362407123239817887654627471744, 6237449912425184470111122629615616, -292849570924032438522237153010435456, 16094987232709893287572215966762387640, -988158714157281547667574057570499850880, 45374866922385004013931376318655031713792, -1957158906943328129915769705443377912815232, 112853068885090981244908191013139679262871964, -5375433217101460040442041576389108558855361408, 183036745352664748592495038226134208339748118528, -8438967281469639479612015154077154543503289931648, 431229904897938978480921955113961460928772736127624, -12357082684872196580104906312376497460537241998284928, 314229004550458559856419523786837759416542508999647232, -17091111950627285107190568160968472508265382403558937728, 464798130469793589516643498190087912509935907396786423681], [1, 32, 512, -38048, -60439624, -1520787552, -16996289024, 2981900088544, 2018049968078364, 40394929489472928, 275088896591278592, -106313082771719258656, -45042859320290008592120, -716503209267746480098016, -1881770414874206829193728, 2374239565266043975563213664, 727531884046275952665257798342, 8834545422354949633070718043744, -26054693962852302758130516085248, -36914513572332223337489820293367776, -8635045530007332393450369640198025720, -75837684012235257272478539035681044256, 730181930507715075956726036306729964032, 398973953764462715268504351165757985497248, 74166754614213041825415492722132736373995804, 407783940373892409492826009414227308146615264, -8648699503302341210543242609413807832983693824, -2879551958378001106630412404894196487561803479392, -425831509637567421889503450998126820687979283360584, -997487686455595834984361408280915341677644012352928, 49946532296737050993800623047445395947956445684982272, 11615690417259910421745757397471519895146620899613689632, 1350687001332003958728623852374735172807518011483204347521], [1, -320, 51200, -6047552, 641735304, -64228593856, 5982745065472, -525110406070976, 43992629224199580, -3502096836597496384, 267198268901850048512, -19906861744922068822080, 1452416951976727517992120, -103061266987555377988785088, 7141615968030041699303675904, -487804437589338070744177941952, 32904927223065445517751311967174, -2189754120338538599570614781422528, 143911567507305501917713988886288384, -9322755475981627749160772086312295872, 589779578533085125858313455047891668920, -36286980158629190964198042997668583993920, 2186408326228342046021326537719503646943232, -128639809544168174813112855549363875062966336, 7253986810986234678621398403276418014374989980, -388684366853248517964353058626632075825057851584, 19879092349412107477898739757007825851172836636672, -958018892490632578339453043786362824676175956705984, 42968599306971490817615113791774729073769303333282184, -1817709519089971127692730265942293218931177568385825088, 69081925909389100925678441059675990896951571900428339200, -1938179783795297962846065761980534519602597539131392591680, 27189028279553414235049966267283185807800188603627566700161], [1, 512, 201744, 56254976, 13334748280, 2640692651520, 463721900725296, 71822582790153728, 10087539873984698908, 1281533895294227735040, 149578753624082666366224, 16008541217716991792554496, 1586531743774045246375645512, 145287048222533985248020993536, 12376373818709017395122609264304, 978084861433718526221159012464128, 72053716823970739027227311635230534, 4930525786487375090680862581831669248, 314504463417785381868306702512137935024, 18611312127350621900343114875330105734656, 1024508475975584611882491175572827888674632, 52111700560049108089321999277072877278429696, 2454539891711673509371207994541047583332275984, 106010035366148777339882216535449070953122890240, 4206480150543226281850122017273336437534576419868, 150977175246556526942047920988592870127626993796608, 4913880397730004169580778918976381755746333068635696, 141059236459363619022541067101954605123253307829880320, 3590750182213011563828951429702436558585007321663490680, 76362125884101120380762701527162791348105186250614391296, 1380493580719140793947133005500035837291045700832090848784, 17661208699576971984550711347705748353167829652837357363712, 173887017684702179246328390437079448141248104062408434512641], [1, 0, -42768, 0, 946714744, 0, -14391245893936, 0, 167549428359087132, 0, -1579092364147683166224, 0, 12431125925178146870479176, 0, -83211218053743713189923429296, 0, 477990969232323851403899754270022, 0, -2363052224193764919402324316694268336, 0, 10025206955966061014687204222669908157256, 0, -36164449193556131500267145282734319906866704, 0, 108970441980869065421050966224100320962219969052, 0, -265800379188431140047017281295855916748245432633136, 0, 496555485216069339122503522948341872374586239474154104, 0, -637028737809508333054430813890192766263583467389141953808, 0, 422991386556309150149363832086603107763045099853453376062721], [1, 0, -62928, 0, 1905826568, 0, -37296559235888, 0, 534425714020543644, 0, -6018997282533146289808, 0, 55719824438563216525904696, 0, -436059000346206004998920193136, 0, 2929869749724252435562307026190662, 0, -16984533384263751937394346435182844016, 0, 84533036542191154857672699133007751110456, 0, -355671644320424164978230065489486786554653328, 0, 1230044452883634612617334624119049598764934791324, 0, -3343571340248160653599764615720802038541919305783088, 0, 6654777933452895172349946037478306278263205573396627208, 0, -8558595187601530498590654945696182392611530339877340985808, 0, 5297450670659957549009604563595170759963655420038456036451841], [1, -160, 12800, -895904, 107479624, -16432771168, 1654826188288, -174484645067104, 18280323695716892, -1483531366054758688, 116856254345162512896, -11468497917913001109536, 1366230707693329274647800, -120877910851657649855602144, 8917938316345038560246232576, -740834868592221092687137649376, 61671226222619243489644185991366, -5103611409731811107521691266551264, 423230379275302386749543544632464896, -39519869305905648816355633895676903136, 3077150810247510247335822671565904759800, -177945686049722700149588984619570812389664, 12490765931265373648548534148890056555936256, -1092420964995984155570123865099443669485982752, 92732797115079963555989346760985188617375111452, -6097655398787066900299546229255953304728456253536, 398395324232612542964619385367707223114795175321088, -27253911408269568727273654526441134649933673775027552, 1228005623141667205092173933789916062915231195411813704, -70516683301185795495827033999423698173733099523983446176, 6940592652953801409733220519656103964265418760877550604800, -597671784827484223895651951998886252622805873046068076455840, 25733505785478367615107164358252046214490685371339768616901761], [1, 0, -81008, 0, 3201135736, 0, -82544801381712, 0, 1567286911309649436, 0, -23398814610877335886704, 0, 285472189102998157435756872, 0, -2909237845695713148204132464336, 0, 25036289222433160823905054207568710, 0, -182532102040961247011492396273293216976, 0, 1123786623962130138494850058387671580450632, 0, -5779282663689345401733205072037200452228284784, 0, 24287824330763877053282311203215947422818373613596, 0, -80258282135852284438470158204153476259290072689548112, 0, 195282914984273870762746216186288257723995687838973651576, 0, -310061680192030639259528238560452122383480734622957208603248, 0, 240148684864128390378794468324923219083866317778128398613374721], [1, 0, 76432, 232448, 3001425784, 15854050304, 80617465349552, 544041740544000, 1656877944527714588, 12587985920266725376, 27565039357597995290512, 219887145530657392067584, 383075562467330745780676680, 3057500955957496305351185408, 4527285108585971726697834270768, 34760406346449901605547724599296, 45918202346304448047444859096398406, 327060663313747124206598540754776064, 400797295545123003650887772248250357808, 2546812701356249824375486900748568876032, 3002329282466308061593796633144617581969480, 16215008630836305420474016198078687363695616, 19125791988807964639819181701421754384507950992, 82178938689134700072609891665117992389902854144, 101774333076789378439170915781420889182014115160348, 314429610823518326108472943591141428233498716416000, 438393215981794447500496057730173963289731501423570352, 811182150430481310014960264370535857788000427494644736, 1444938062707497296192209251533763360274177986531711702904, 1052909161983592131070078841986050854282537568980502612992, 3257495192144822749974924435877391012865527232082177311543952, 0, 3773075507922571775273744352333525624409237957166570157859261441], [1, 0, 0, 316576, 94347688, -10165950816, 50110181888, -95966947676224, -24684689773322532, -553387914666269248, 16564665762724968960, -23439598109674748509088, -798510982499682603704424, 267963536767021511443393632, 2484244011827450709496648704, 1154684179264511558830767366272, 347396034378977267774676403885638, 11778933312677282411632657903340672, 258511428052613263637955772294370304, 284448693904505275477597853127164372832, -8646729719174478255326922662658549963624, -2589189868269337221246949557314950907197088, 18665479997208570343654042957639403401320960, -6361051378262183172324870661946577443530896448, -2894474008476441337028587863216738131516047773732, -114790622212269585900076661506073519303080171599424, 611439448397186036306203284959657558837224381157888, -1265372021012301646622284767648640881384585322282706016, 119796528462478724354813393585753818206635629135459678888, 4100470631671215059413064570914387761967290278047295414176, 0, 0, 13749406785310970541622913505711040449564178320493809360964963201], [1, -384, 177552, -48439040, 13508011016, -2925272135168, 621299082072432, -112843018023165312, 19842318872420897692, -3117726164431724180096, 472413192982418185858896, -65420247696005314218160128, 8729612070327318039569803320, -1077418665480003815183400123136, 128155386863090850481376592216496, -14183180915928620656809320982232704, 1513135716149715532902515096994155590, -150469366337086736548090086300506756736, 14424001696336701604718209546744367532976, -1286494231839608971647420596349242185394944, 110584113928108525547118016987881617606654520, -8791934241941109592490782169393567808170422272, 673548252984447632546202252759189678917953843536, -47158405612313629909197732681937998332544076356224, 3184109686122520747605451438750372445582961970898332, -192107684612726946052786601004384636824800568359978368, 11221352522208136236725145460001156478576541698616421232, -560512391004086045656976949176861759064433561329178138112, 27459005183326996205282559658070192592927406066607747071496, -1044632106722068259331676208932956179837586877220870363836160, 40622613468250218912871108242482862499577384200942269150582672, -932068788936829570038712273251150447705902068640814346403961216, 25750827556851106532658069028441289322166445432839581773436522241], [1, 0, 0, -532480, 349087368, 4980826112, 141767475200, -222431357190144, 31725670810718364, 2357680121343361024, 81355328670025121792, -30846780023722675232768, -6121450460200569859450184, 376879759434784990616756224, 20008556661831013854808637440, 370180407965890365933569081344, -1647983076192989199391339643473722, 4238195490801478799573432412307456, 2622713623818701225513788126988861440, 565594893981331356337948731558580658176, -105177915812423663794263827853377190182984, -6068028519167871058115720837027800173535232, 183227786947773905482561486693363587473211392, 60793587081344754772556537669795548394134552576, 9365937526632244919534008110950022684606143255964, -751802923301959725447018647565297703502532319789056, 5485953960673347235254949646773511384077157217075200, 2206706067872326758882054550243666995985127245741580288, 1770699229287654917044257489332947556116043683949087244168, -30922992854675208478518299130938964870189750325063681515520, 0, 0, 87152707983437572386914428735274683878049343856532228222877116801], [1, 512, 131072, 23221120, 3129092536, 339671142272, 33385414991872, 3530546904697088, 450129432181098524, 60290271496335416576, 7074696994735888441344, 676007164680463342638208, 51312358155789112360441608, 3553558994712477847404533888, 337558945072969988445988995072, 44485396891836996339175221559296, 5441798310899826307854357720392902, 528531000471915353505740807345995776, 47649199915600454377227054370601582592, 5959674183912329130807900867730740679808, 1022430879182524273954634889799558783528968, 160035480542854022737184746358432661710305408, 19898751078878917081083346902995975269349105664, 2014736297387157879939338193348280755679643899136, 178715153182654240562424274691226956247884013504284, 16654014888334886837324730984807940094474831433429248, 1871055792671942536020819912051581928207993643391721472, 226173441507699103228932458681270157298845638024502031232, 24754511313572059176801350383109989693567339313675143399096, 2182589739555426513643719049625234734271274108495420073217920, 146369931176329492855648378873211982531466834977410379247910912, 6793051376195198064913899958564967048657646352994580921267302912, 157633287891748336346175869936934323252151359999860577979642238081], [1, -224, 138864, -28917152, 9742621560, -1833167748192, 450719766589776, -76118329449976608, 15248343366190105372, -2319900147384255486816, 398712225999823001446768, -54960419728452946699392800, 8331971495446962250042671176, -1044608702666008545805372874464, 141976320942318002594714818993872, -16209064157146065162887066440749216, 1993740436444401096922491317886892102, -206973540222598106064904951381926739104, 23148864454133983545859403784543504771792, -2174824919306110262710067511399072941476576, 221500812375328976574273213709299133156711496, -18656684854664437961101977232333138158723687200, 1728227353925081241807331382692551921069769610608, -128400732486733742400982586462813866603115050461024, 10776500631325522549940839255547706979002653380372252, -686912202017549037312384061023622973056579775906041632, 51936834277096230515032039996062425809918277470078602576, -2697292001400760325166163832090430116516695114078361598048, 183045255635915879922840548954007449709554751869542160951160, -6937373042480217317764433977448777352192006703207810635159968, 425388836553238470013702641077992188713468185445597505363794544, -8761961142444547566594027691548375574092850978150441714928458976, 499470901017296553026067587470451820114248277410727635080006663681]], 'euler_factors_factorization': [[[[1, 0, -6, -4, 10, 56, 88, -128, -496, -512, 1408, 3584, 2560, -4096, -24576, 0, 65536], 1]], [1], [[[1, 0, 0, -32, -344, -5664, 512, -145600, 223452, 2255168, 20875776, 67282720, 753060504, -1881828576, 2740220928, -75471830656, -399298967994, -1886795766400, 1712638080000, -29403571500000, 294164259375000, 657057812500000, 5096625000000000, 13764453125000000, 34096069335937500, -555419921875000000, 48828125000000000, -13504028320312500000, -20503997802734375000, -47683715820312500000, 0, 0, 23283064365386962890625], 1]], [[[1, 0, 168, -448, 15076, -56512, 1070392, -3649664, 60103046, -178833536, 2570011192, -6648580288, 86910139876, -126548911552, 2325336249768, 0, 33232930569601], 2]], [[[1, 32, 512, 8480, 137032, 1636576, 18165248, 219655136, 2263228700, 21867108000, 253620152832, 2916953293728, 33797606438392, 431768458252384, 5293166227138048, 61910274521995104, 703855220885889990, 7491143217161407584, 77497246731528160768, 764904161670051651424, 7244817096612104559352, 75658256120708606202528, 795968684556265691023872, 8304030623946757937028000, 103994747384483599296220700, 1221264393643890740902536416, 12220670499948695842018446848, 133221785980516668883794428896, 1349728568031268563530552995912, 10106613703992673592061925813280, 73835487286527607827290144809472, 558380872604365034193881720121632, 2111377674535255285545615254209921], 1]], [[[1, 0, 0, 3200, 7608, 95360, 5120000, 68335872, 2004669468, 7270355200, 184268595200, 4889456013184, 5354592144136, 669839496880000, 7008632866619392, 70586941744778752, 2398056097119178950, 11929193154867609088, 200173563303516454912, 3233187312095855920000, 4367905310396995202056, 674053031939570500537216, 4293105416369593808691200, 28626124880126031417452800, 1333940359929609046405794588, 7684738295176870566317023488, 97305414527389693126661120000, 306280955401774982827806707840, 4129628261008210861166297506488, 293546656618459573306878771228800, 0, 0, 442779263776840698304313192148785281], 1]], [[[1, 0, 968, 2944, 516540, 3209600, 201700088, 1543904000, 63894476806, 446188256000, 16846193049848, 77471941462400, 3603257748574140, 5935086042921856, 563978325638408648, 0, 48661191875666868481], 2]], [[[1, 32, 512, -2656, -523448, -8424608, 1945088, 4454446304, 107916937244, -703649376, -30601835632128, -698985761087712, 998616856187896, 253693358084547040, 3161998119961945600, -30474951661580761248, -1910909655870418467642, -11001457549830654810528, 412074756991560712537600, 11935227534935987982742240, 16960072330872362657151736, -4285528014488222255165241312, -67731499355399346164889220608, -562220555870954483221958496, 31127713926547623702996478011164, 463829690679844028766014887069664, 73115806292591152730397659237888, -114321765590792791654590700633616288, -2564247658685593345039959330637191608, -4697012278412155302375467373195101536, 326866782169983241283381922259938632192, 7374931772710246881456304620989865388832, 83198449060887472631428936505541918917761], 1]], [[[1, -64, 3496, -127936, 4410332, -130001728, 3673719192, -94049622208, 2261818535238, -49752250148032, 1028057252408472, -19244921376016192, 345377444336323292, -5299942138629398464, 76613527014343042216, -741941524770479987776, 6132610415680998648961], 2]], [[[1, 32, 512, -18368, -1552984, -20596992, 304715776, 25469097376, 491466517980, -9791032230816, -347423504794624, -2649303176415616, 694517140133881240, 20658732330776531008, 190851587110380169728, -11485440538974369182240, -825511918710437437518010, -9659255493277444482263840, 134985701383016796825389568, 12288295772642566683038037568, 347429708091906261612770751640, -1114581009523248128213672338816, -122923572029394124477602295235584, -2913402246673399205822631354830496, 122987763056454027065527520746127580, 5360157068985091075692931429304357536, 53933039619676501706832037612223666176, -3065912485852378435676636899888916259072, -194410148006867402337936613313365933238104, -1933792253116779126640356744769334708731328, 45332941738570348306746760204906215750328832, 2382812750133603932873376583270382965376659232, 62623297589448778360828428329074752308805325441], 1]], [[[1, 0, -7312, 0, 29025544, 0, -80335806576, 0, 171125889681052, 0, -295006946315669072, 0, 423507628633392203064, 0, -514807310246870517530800, 0, 534544428224191949216973638, 0, -475435361966500107220561946800, 0, 361205860749311633126295498919224, 0, -232365992571959154769108053280691792, 0, 124480928883555283432512372945523642012, 0, -53968833982798547907484231483371363928176, 0, 18007814989012006396727795042356541234498824, 0, -4189513653245889742853916344818291077714715792, 0, 529144398052420314716929933900838757437386767361], 1]], [[[1, 96, 4608, 145952, 4040888, 217733344, 12932982272, 602883756192, 21839639792924, 655265530977504, 21703692469355008, 815191556064282016, 35433653736114978312, 1467845464506621375840, 50867428451208042071552, 1465079699916707177725984, 43181875126876200893659590, 2005694109185972126306872096, 95333750573544515336861967872, 3766089872615510619356602558560, 124459980725454940457402518361352, 3919917377017695306048158128103584, 142874365875275818372623258034037248, 5905293130321981955930416013149196256, 269446816147411178023745063078939270684, 10182739083597405563517698021971929022368, 299042671345538323243211413530790200591872, 6892279360058368588727890523815164520992736, 175112920437535849046858269928673978179517368, 8658743533427367681727180434867343437927188768, 374249082483169821377980583689543656211184890368, 10673895706655405947217821230645526361523169060704, 152214200233450528559804138174517974884637692126081], 1]], [[[1, 0, -13840, 0, 102706104, 0, -524939980080, 0, 2044068651261084, 0, -6376104819902485008, 0, 16402857938643748508168, 0, -35383360569917421812676272, 0, 64577774780000237359256539206, 0, -99984920347410423778809915042992, 0, 130975594183964147316577669339960328, 0, -143867179257987808259948724187240773648, 0, 130327836327428627758263533192221310642844, 0, -94577272396201366241415571692902103329164080, 0, 52288817022836677339754428612357436314532476344, 0, -19910587654352744331498189290377125594313655706640, 0, 4065214023175683899921868126254722311886802750234881], 1]], [[[1, -160, 12800, -978464, 71106632, -3813053664, 178619596288, -8719368905312, 336417491247900, -9339737479444512, 288453906337733120, -7137460469658328480, -129151507673078938376, 13166699894046358977184, -444909531434654535928320, 28972919499885413370278176, -1725860576868082036875113530, 53570928155288129321644347424, -1521057150978328362086276344320, 83231490187496868731360371674016, -1509548687837068929080749572115976, -154251100701786455099704084452111520, 11526511599283975053699449693148101120, -690069841169201212548904345148858265888, 45959347805131236616846050940888629327900, -2202506774663292515595320792900595941019488, 83425384132219209728594707834387496433868288, -3292903018667363424129999428899641159211808736, 113541085637070176903456488799040510541683196232, -2888848033840853858437622085436880595374137960736, 69875789182349331644715482041701831060558996492800, -1615004177477048927638486578688833570387169806439840, 18663392025969146670022260524972832947786731075670401], 1]], [[[1, 0, -24144, 0, 280869112, 0, -2097883923184, 0, 11327375509374492, 0, -47271044690493269328, 0, 159378111080716584342216, 0, -447837309295947983522369904, 0, 1069451862014464590113083289158, 0, -2185303209262560752182421495520624, 0, 3794997890552929841601714620665202376, 0, -5492492790697802075734747006265493492048, 0, 6422365603496382914720509973369815941845532, 0, -5804149811601969119174985502258382340206124784, 0, 3791862421616779449515053523942013352026525646072, 0, -1590557026786853140797198116121630204596987902319184, 0, 321463340914028260476243062478235279920395730789296641], 1]], [[[1, -160, 12800, -602944, 3948712, 1481707264, -105845942272, 3791430241760, 34861972067036, -14471440004155872, 1098860393015073792, -54880211634179791488, 1349758970889735695512, 17264917459299251320000, -1853658370277165714728448, -16562877726012460012653408, 5168183120809487531686006854, -46525123532369000175543423072, -14626256151162940805916239103488, 382665865430285765535809940280000, 84035575657552168608684076721511832, -9597861385825702742638183560963126912, 539824952603700609723101838569018268672, -19969809540319112647568076276372227283168, 135134383349547902989533848962368780910556, 41282759798405789748356760661092786290812640, -3237364540580026851537576611559091487297923072, 127300919681547610483917934009535941216524510976, 952963638614918140606811320515739527079739471272, -408742302834945234868084424680060517972525248250176, 24374421582918186280531772612807345185963770774540800, -855846877830214815775171865867197907842152901321063840, 15025461748906708859452861070130993269553796873817927041], 1]], [[[1, -128, 8192, -1121408, 136226184, -9279937408, 700645040128, -71627082366848, 5234572115355804, -316007889653226112, 25502997282495045632, -1933332663772110218880, 109616149725595055398840, -6942765907527045516409216, 514753163863417494131859456, -29693308567434592900791332224, 1551148300110104846432558538438, -103362407123239817887654627471744, 6237449912425184470111122629615616, -292849570924032438522237153010435456, 16094987232709893287572215966762387640, -988158714157281547667574057570499850880, 45374866922385004013931376318655031713792, -1957158906943328129915769705443377912815232, 112853068885090981244908191013139679262871964, -5375433217101460040442041576389108558855361408, 183036745352664748592495038226134208339748118528, -8438967281469639479612015154077154543503289931648, 431229904897938978480921955113961460928772736127624, -12357082684872196580104906312376497460537241998284928, 314229004550458559856419523786837759416542508999647232, -17091111950627285107190568160968472508265382403558937728, 464798130469793589516643498190087912509935907396786423681], 1]], [[[1, 32, 512, -38048, -60439624, -1520787552, -16996289024, 2981900088544, 2018049968078364, 40394929489472928, 275088896591278592, -106313082771719258656, -45042859320290008592120, -716503209267746480098016, -1881770414874206829193728, 2374239565266043975563213664, 727531884046275952665257798342, 8834545422354949633070718043744, -26054693962852302758130516085248, -36914513572332223337489820293367776, -8635045530007332393450369640198025720, -75837684012235257272478539035681044256, 730181930507715075956726036306729964032, 398973953764462715268504351165757985497248, 74166754614213041825415492722132736373995804, 407783940373892409492826009414227308146615264, -8648699503302341210543242609413807832983693824, -2879551958378001106630412404894196487561803479392, -425831509637567421889503450998126820687979283360584, -997487686455595834984361408280915341677644012352928, 49946532296737050993800623047445395947956445684982272, 11615690417259910421745757397471519895146620899613689632, 1350687001332003958728623852374735172807518011483204347521], 1]], [[[1, -320, 51200, -6047552, 641735304, -64228593856, 5982745065472, -525110406070976, 43992629224199580, -3502096836597496384, 267198268901850048512, -19906861744922068822080, 1452416951976727517992120, -103061266987555377988785088, 7141615968030041699303675904, -487804437589338070744177941952, 32904927223065445517751311967174, -2189754120338538599570614781422528, 143911567507305501917713988886288384, -9322755475981627749160772086312295872, 589779578533085125858313455047891668920, -36286980158629190964198042997668583993920, 2186408326228342046021326537719503646943232, -128639809544168174813112855549363875062966336, 7253986810986234678621398403276418014374989980, -388684366853248517964353058626632075825057851584, 19879092349412107477898739757007825851172836636672, -958018892490632578339453043786362824676175956705984, 42968599306971490817615113791774729073769303333282184, -1817709519089971127692730265942293218931177568385825088, 69081925909389100925678441059675990896951571900428339200, -1938179783795297962846065761980534519602597539131392591680, 27189028279553414235049966267283185807800188603627566700161], 1]], [[[1, 256, 68104, 10692864, 1610923548, 179723087616, 18972832358712, 1588998739085056, 125568612540426694, 8010142643727767296, 482131563566066914872, 23022578550768359022336, 1040259569687950170080028, 34807876577825722338449664, 1117565033368601801486349064, 21176629938066004205493473536, 416997623116370028124580469121], 2]], [[[1, 0, -42768, 0, 946714744, 0, -14391245893936, 0, 167549428359087132, 0, -1579092364147683166224, 0, 12431125925178146870479176, 0, -83211218053743713189923429296, 0, 477990969232323851403899754270022, 0, -2363052224193764919402324316694268336, 0, 10025206955966061014687204222669908157256, 0, -36164449193556131500267145282734319906866704, 0, 108970441980869065421050966224100320962219969052, 0, -265800379188431140047017281295855916748245432633136, 0, 496555485216069339122503522948341872374586239474154104, 0, -637028737809508333054430813890192766263583467389141953808, 0, 422991386556309150149363832086603107763045099853453376062721], 1]], [[[1, 0, -62928, 0, 1905826568, 0, -37296559235888, 0, 534425714020543644, 0, -6018997282533146289808, 0, 55719824438563216525904696, 0, -436059000346206004998920193136, 0, 2929869749724252435562307026190662, 0, -16984533384263751937394346435182844016, 0, 84533036542191154857672699133007751110456, 0, -355671644320424164978230065489486786554653328, 0, 1230044452883634612617334624119049598764934791324, 0, -3343571340248160653599764615720802038541919305783088, 0, 6654777933452895172349946037478306278263205573396627208, 0, -8558595187601530498590654945696182392611530339877340985808, 0, 5297450670659957549009604563595170759963655420038456036451841], 1]], [[[1, -160, 12800, -895904, 107479624, -16432771168, 1654826188288, -174484645067104, 18280323695716892, -1483531366054758688, 116856254345162512896, -11468497917913001109536, 1366230707693329274647800, -120877910851657649855602144, 8917938316345038560246232576, -740834868592221092687137649376, 61671226222619243489644185991366, -5103611409731811107521691266551264, 423230379275302386749543544632464896, -39519869305905648816355633895676903136, 3077150810247510247335822671565904759800, -177945686049722700149588984619570812389664, 12490765931265373648548534148890056555936256, -1092420964995984155570123865099443669485982752, 92732797115079963555989346760985188617375111452, -6097655398787066900299546229255953304728456253536, 398395324232612542964619385367707223114795175321088, -27253911408269568727273654526441134649933673775027552, 1228005623141667205092173933789916062915231195411813704, -70516683301185795495827033999423698173733099523983446176, 6940592652953801409733220519656103964265418760877550604800, -597671784827484223895651951998886252622805873046068076455840, 25733505785478367615107164358252046214490685371339768616901761], 1]], [[[1, 0, -81008, 0, 3201135736, 0, -82544801381712, 0, 1567286911309649436, 0, -23398814610877335886704, 0, 285472189102998157435756872, 0, -2909237845695713148204132464336, 0, 25036289222433160823905054207568710, 0, -182532102040961247011492396273293216976, 0, 1123786623962130138494850058387671580450632, 0, -5779282663689345401733205072037200452228284784, 0, 24287824330763877053282311203215947422818373613596, 0, -80258282135852284438470158204153476259290072689548112, 0, 195282914984273870762746216186288257723995687838973651576, 0, -310061680192030639259528238560452122383480734622957208603248, 0, 240148684864128390378794468324923219083866317778128398613374721], 1]], [[[1, 0, 38216, 116224, 770481564, 3485408768, 10857255215864, 49274039499776, 116292098553803590, 463619437653392384, 961184997893939713784, 2903247929478075817472, 6038598093541702516847004, 8570638172423614214718976, 26515879667801658619275286856, 0, 61425365346268570446197767595521], 2]], [[[1, 0, 0, 316576, 94347688, -10165950816, 50110181888, -95966947676224, -24684689773322532, -553387914666269248, 16564665762724968960, -23439598109674748509088, -798510982499682603704424, 267963536767021511443393632, 2484244011827450709496648704, 1154684179264511558830767366272, 347396034378977267774676403885638, 11778933312677282411632657903340672, 258511428052613263637955772294370304, 284448693904505275477597853127164372832, -8646729719174478255326922662658549963624, -2589189868269337221246949557314950907197088, 18665479997208570343654042957639403401320960, -6361051378262183172324870661946577443530896448, -2894474008476441337028587863216738131516047773732, -114790622212269585900076661506073519303080171599424, 611439448397186036306203284959657558837224381157888, -1265372021012301646622284767648640881384585322282706016, 119796528462478724354813393585753818206635629135459678888, 4100470631671215059413064570914387761967290278047295414176, 0, 0, 13749406785310970541622913505711040449564178320493809360964963201], 1]], [[[1, -192, 70344, -10713472, 2222879716, -282214687744, 42708829099672, -4554544233047744, 548280798241747334, -48319159768403516096, 4806916341646520411032, -336979096014937830040576, 28158775187522009622850276, -1439801050044462855975584128, 100293723824307611738582927304, -2904172271721813586993179872448, 160470643909878751793805444097921], 2]], [[[1, 0, 0, -532480, 349087368, 4980826112, 141767475200, -222431357190144, 31725670810718364, 2357680121343361024, 81355328670025121792, -30846780023722675232768, -6121450460200569859450184, 376879759434784990616756224, 20008556661831013854808637440, 370180407965890365933569081344, -1647983076192989199391339643473722, 4238195490801478799573432412307456, 2622713623818701225513788126988861440, 565594893981331356337948731558580658176, -105177915812423663794263827853377190182984, -6068028519167871058115720837027800173535232, 183227786947773905482561486693363587473211392, 60793587081344754772556537669795548394134552576, 9365937526632244919534008110950022684606143255964, -751802923301959725447018647565297703502532319789056, 5485953960673347235254949646773511384077157217075200, 2206706067872326758882054550243666995985127245741580288, 1770699229287654917044257489332947556116043683949087244168, -30922992854675208478518299130938964870189750325063681515520, 0, 0, 87152707983437572386914428735274683878049343856532228222877116801], 1]], [[[1, 512, 131072, 23221120, 3129092536, 339671142272, 33385414991872, 3530546904697088, 450129432181098524, 60290271496335416576, 7074696994735888441344, 676007164680463342638208, 51312358155789112360441608, 3553558994712477847404533888, 337558945072969988445988995072, 44485396891836996339175221559296, 5441798310899826307854357720392902, 528531000471915353505740807345995776, 47649199915600454377227054370601582592, 5959674183912329130807900867730740679808, 1022430879182524273954634889799558783528968, 160035480542854022737184746358432661710305408, 19898751078878917081083346902995975269349105664, 2014736297387157879939338193348280755679643899136, 178715153182654240562424274691226956247884013504284, 16654014888334886837324730984807940094474831433429248, 1871055792671942536020819912051581928207993643391721472, 226173441507699103228932458681270157298845638024502031232, 24754511313572059176801350383109989693567339313675143399096, 2182589739555426513643719049625234734271274108495420073217920, 146369931176329492855648378873211982531466834977410379247910912, 6793051376195198064913899958564967048657646352994580921267302912, 157633287891748336346175869936934323252151359999860577979642238081], 1]], [[[1, -112, 63160, -7384656, 2049636508, -220609712240, 43929981559560, -4069436828617936, 664145380373427782, -51962638864622424784, 7162667562064922321160, -459298777040635159234160, 54488442722616178601831068, -2506771244339348470683556944, 273768479008106934391462603960, -6198922852230936571681343110768, 706732552679793116819634555191041], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '32-12e32-1.1-c2e16-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/144/3/m/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.8470122286213644, 0.8408877337410651, 0.824290583281787, 0.797399777454091, 0.7605098198956944, 0.7140301811850321, 0.6584841614160748, 0.5945070775386131, 0.5228437050584627, 0.4443449084784031, 0.35996340060863885, 0.2707485776416631, 0.1778403847166326, 0.08246217562660456, -0.014087459631897786, -0.11044391459919643, -0.2051868362375327, -0.29685027611352455, -0.38393179977751213, -0.4649086854802452, -0.538250823414409, -0.6024324598276398, -0.655944022851053, -0.6973039513791897, -0.7250704485537074, -0.7378530820825235, -0.7343241547586992, -0.7132297701170695, -0.6734005201674534, -0.6137617245550738, -0.5333431533037184, -0.43128816847553286, -0.3068622236119182, -0.1594633296205796, 0.011359254616008643, 0.20589932685430204, 0.4242878362311187, 0.6664860080740391, 0.932279453617457, 1.2212733443633554, 1.5328887267569822, 1.8663600479985742, 2.220733958174814, 2.594869447465573, 2.987439369966403, 3.3969333976758755, 3.8216624394468783, 4.259764550217376, 4.709212345651788, 5.167822065867013, 5.6332648300972865, 6.103079038149702, 6.574684103266023, 7.04539564651386, 7.512442025381167, 7.972982113340102, 8.424124233260255, 8.862946133837635, 9.286515884792687, 9.691913553613583, 10.0762535142171, 10.436707226210354, 10.770526312604142, 11.075065753997096, 11.347807008560222, 11.586375757134746, 11.788549116455131, 11.952293332661174, 12.075790637359033, 12.15745989663786, 12.19597591329633, 12.190287153018499, 12.139631670234538, 12.043551016909273, 11.901901927584198, 11.714865586695133, 11.482954299511965, 11.207015405983933, 10.888232297279679, 10.528122417811469, 10.128532160919795, 9.691629321230463, 9.219895015500395, 8.716108789580328, 8.183329936999105, 7.624876002821786, 7.044298175157412, 6.445353714818708, 5.831975612901558, 5.208239705009864, 4.57832950901504, 3.9464990901033508, 3.3170342919081346, 2.6942127052202447, 2.082262775587473, 1.485322477526925, 0.9073980055687616, 0.35232538650350825, -0.17626269336702535, -0.6749839914036921, -1.14074633769798, -1.5707821596558063, -1.9626799616868515, -2.314412283971543, -2.6243596914656386, -2.891330378736967, -3.1145750178110543, -3.2937965247253014, -3.429154475638369, -3.521263964682321, -3.5711887627359773, -3.5804287082823576, -3.5509013377234897, -3.4849178719758074, -3.3851548513284624, -3.2546207877298254, -3.0966158628553204, -2.914686781428026, -2.7125775961353664, -2.4941771180842114, -2.263463599247897, -2.024447438381754, -1.781112718030283, -1.5373584261964854, -1.2969402507622334, -1.0634138567244535, -0.840080564775277, -0.629936343901749, -0.4356250098992865, -0.25939716856545353, -0.10307561596448335, 0.031977407595696616, 0.14488312393536185, 0.23526020162063763, 0.3032302411199306, 0.34941445452247655, 0.3749213769932353, 0.3813255989507551, 0.37063766613084326, 0.3452654567082581, 0.3079675077603704, 0.26179892467815796, 0.2100506636502222, 0.15618312598420492, 0.1037551406895931, 0.05634972571374004, 0.01749771903827884, -0.009401113066671527, -0.021155550838973834, -0.014857713062336034, 0.012046143200348497, 0.061690346931079276, 0.13573153706405855, 0.23529877374155939, 0.3609533057189808, 0.5126591135192896, 0.6897651701231824, 0.8910001568324137, 1.1144801443835353, 1.3577295019621978, 1.6177150336010386, 1.8908921560671355, 2.1732617167888795, 2.4604443926562363, 2.7477642005629597, 3.030340201739009, 3.303185570665637, 3.561312101453251, 3.7998380341131526, 4.014096931353428, 4.199745228401445, 4.352866018206575, 4.470066625661854, 4.548567569688654, 4.586280612565907, 4.581873752008988, 4.534821222240879, 4.445438530692059, 4.314903901463666, 4.145250781053479, 3.9393418396727653, 3.700824299572384, 3.434065544998544, 3.1440698397555296, 2.836377455223187, 2.5169479769641327, 2.1920300002517688, 1.8680198324763704, 1.5513121822665734, 1.2481461207045674, 0.9644498394845196, 0.7056878956729157, 0.47671471568063056, 0.28163913371882526, 0.1237028238160906, 0.005168627152796724, -0.0727655665504079, -0.11002773013395174, -0.10770652175709552, -0.06805824423143307, 0.005515205041665174, 0.1085178578404256, 0.23544041777795024, 0.37986922707683757, 0.534621719814364, 0.6919058968672123, 0.8435006654972061, 0.9809532480488021, 1.0957892979743002, 1.1797309842369157, 1.2249192738137598, 1.2241341370462433, 1.1710045769162865, 1.0602038664755111, 0.887624732493017, 0.6505293887976614, 0.3476698146307226, -0.020625697952014972, -0.4524029500356555, -0.9440715550202096, -1.4904353786800661, -2.0847640883893566, -2.718905138294547, -3.3834344407233763, -4.067842911132206, -4.760755356885695, -5.450180178006162, -6.123781930507451, -6.769165921337611, -7.374170047871119, -7.927156738357393, -8.417297362283861, -8.834841519738296, -9.17136386990446, -9.419981619199518, -9.575536451631232, -9.634735534086627, -9.59624724803646, -9.460748461711185, -9.230921433473602, -8.911399794032278, -8.508672923343076, -8.030958510537904, -7.487977257286407, -6.89070443547781, -6.251097236840047, -5.581796839445289, -4.895813361368051, -4.206202427634006, -3.5257423800132766, -2.8666211968695796, -2.2401419567898007, -1.6564551779765484, -1.1243256066620286, -0.6509400316038509, -0.24176149538116504, 0.09956610879891498, 0.37125972528823553, 0.5733875591011791, 0.7078130292225138, 0.7780779875750569, 0.7892370933586873, 0.7476512133922459, 0.660746911800131, 0.5367501341800907, 0.3844029669293547, 0.21267283397112424, 0.030463662577785388, -0.1536616004329024, -0.33173820809153787, -0.49662842431803206, -0.6422148310279446, -0.7635523277914787, -0.8569745767462442, -0.9201538090976052, -0.9521115935406892, -0.9531780823167354, -0.9249045995171532, -0.869934413365901, -0.7918376654274548, -0.6949176801143991, -0.5839968472753367, -0.4641909220726749, -0.34068089456410744, -0.21849153395760934, -0.10228531047052529, 0.0038203442203678805, 0.09640553082164828, 0.17286454883756672, 0.2314828724861678, 0.2714731994501702, 0.2929678818570514, 0.29696809976213606, 0.2852543295568135, 0.26026311254091744, 0.2249364589558398, 0.18255137374447497, 0.13653781035133597, 0.09029381119342467, 0.04700665642856, 0.009488511095742188, -0.019965653763567227, -0.03969115946573133, -0.04873241056993116, -0.04688368310001895, -0.034690176453103516, -0.013409793306804871, 0.01506415208655617, 0.04831499890882679, 0.08354322458557494, 0.11772818564214313, 0.14780280349922387, 0.17083215632538662, 0.1841866443225726, 0.1857005578528243, 0.1738074965247641, 0.14764514225274036, 0.10712333886460956, 0.05295121385706658, -0.013378884269199351, -0.08965066000017437, -0.17302384188503647, -0.2601705248730985, -0.34744402113388606, -0.4310686938134298, -0.507341195761016, -0.5728326732948463, -0.6245807844672816, -0.6602605663851597, -0.6783239513285737, -0.6780990588000747, -0.6598422339626175, -0.6247380887224737, -0.5748454317989422, -0.512989829335611, -0.4426064826850118, -0.3675399994034038, -0.29181087099068204, -0.2193601101027422, -0.15378106804455371, -0.0980594238623405, -0.05433562421879973, -0.02370407888361326, -0.0060629964576546114, -2.6852702954740444e-05, -0.00291086521277631, -0.010793598185270755, -0.01866007042831369, -0.02062364999209367, -0.01022077609165946, 0.019231643967188697, 0.07423024779010812, 0.1606481895914894, 0.28328693971429036, 0.4454382872316868, 0.6484843702321349, 0.8915565088260285, 1.1712741812511922, 1.4815836298059328, 1.8137116616999192, 2.1562456612676133, 2.4953455018226003, 2.815087154103328, 3.097931586855671, 3.3253063229632875, 3.478281045147319, 3.538313232898983, 3.4880352381685715, 3.312050725615682, 2.9977064019548068, 2.5357995327145737, 1.9211823575245486, 1.1532428239607924, 0.23623277869886541, -0.8205783116830981, -2.002938335794164, -3.2918427329367153, -4.663958166830221, -6.092229466734788, -7.546651339740102, -8.995178644536427, -10.404742249545533, -11.742332017889456, -12.976104559004378, -14.076471286643576, -15.017154910822677, -15.776216065825373, -16.336737603857962, -16.68736615085723, -16.82267519811466, -16.743305248283175, -16.45587517988507, -15.97266900248484, -15.311112059810169, -14.493060027617913, -13.543932296373864, -12.491728120035301, -11.365968911474669, -10.196613016578585, -9.012990045592117, -7.84280033301387, -6.711241467750073, -5.640296470900975, -4.64806069852141, -3.748339506396226, -2.950477296193807, -2.2593905923319917, -1.675793403542095, -1.1965938604194062, -0.8154331565718203, -0.5233315735126767, -0.3094021625214573, -0.1615907030238448, -0.06740094467748951, -0.014566826256411767, 0.008361824858371473, 0.011546969217654647, 0.003522186824335794, -0.00900552086091049, -0.021212084546393544, -0.030078996751569078, -0.03419850937938865, -0.03348640201851328, -0.028832745517749253, -0.021724131144773423, -0.0138714775901901, -0.006875721678351815, -0.0019595571106093747, 0.00021282356087688297, -0.00038610379089169523, -0.003176208330534836, -0.007101479531934147, -0.010850796762735208, -0.013145421535153386, -0.013063989522534498, -0.010370704278890414, -0.005809867169611368, -0.0013307732226041803, -0.00021061491983167732, -0.007049497997258282, -0.027620689266480935, -0.06857026188512842, -0.13697269526068911, -0.23976190747646356, -0.38306974226487267, -0.5715151607081048, -0.8074963861291294, -1.090544192011056, -1.4167967267062267, -1.778658499220099, -2.1647079331313206, -2.559861017160001, -2.9458310246488386, -3.3018931323035576, -3.6059367656029595, -3.835769304131368, -3.9706133518426956, -3.9927200868648964, -3.889004697522987, -3.6525979436470117, -3.284201635422499, -2.793136213139253, -2.1979762178337823, -1.5266844420859997, -0.8161776771425746, -0.11129350702168628, 0.5368557252195156, 1.0731696858429853, 1.4413055222669886, 1.5867927187890078, 1.460382362452316, 1.0214559776982708, 0.24129892479137052, -0.8939670423255935, -2.380996697943912, -4.197571600717063, -6.3018545109954225, -8.632677991833173, -11.110949810334754, -13.642201617636484, -16.120245019137986, -18.431878079972833, -20.462578946109783, -22.102577108367942, -23.253223008602816, -23.833356258843637, -23.785294358237053, -23.08008755534853, -21.72169845962169, -19.74979740755376, -17.24091593228743, -14.307769403906008, -11.096643399058069, -7.782833065735853, -4.564226299528192, -1.6532249431417834, 0.7327019289319502, 2.3814443208049707, 3.0972833520925964, 2.7119829230770343, 1.0951207441080033, -1.8367718945466864, -6.112758548976311, -11.70220174581268, -18.512006358075695, -26.386678180063154, -35.11134688862019, -44.41776235750618, -53.99312624040151, -63.491474112840564, -72.54718479183931, -80.79007015061082, -87.8613977281893, -93.43026646601967, -97.20985270400509, -98.9715402893162, -98.55698187566914, -95.88751049241337, -90.97027532110728, -83.90072199274356, -74.8612041715662, -64.11569407455748, -52.0007460783703, -38.91305040542652, -25.29408377610162, -11.612512064075222, 1.6548814559375506, 14.042886205135641, 25.117275030146235, 34.49304132324305, 41.85071298876116, 46.94984343779574, 49.63879957213448, 49.860594707065616, 47.65454349508356, 43.153684760676875, 36.57812114436942, 28.22461914288368, 18.452989653422605, 7.669918583696795, -3.688967987709301, -15.17794485819412, -26.360044631470906, -36.82505401058568, -46.205830467137574, -54.19248234153952, -60.54419147867911, -65.09597240441386, -67.76197285120801, -68.53527046866317, -67.48410307680935, -64.74486621968606, -60.512360444807925, -55.027889072729735, -48.565889855348885, -41.41982757804311, -33.88807829969134, -26.260500745624398, -18.806319688443473, -11.763845164973798, -5.33242681468456, 0.3330795045454245, 5.125362415473909, 8.985273089190386, 11.899664771954418, 13.897064890317381, 15.041657715201998, 15.426051290349315, 15.163333471857344, 14.378921437433712, 13.202678848485569, 11.761718636339998, 10.174232195737137, 8.544593696700371, 6.959887967455071, 5.487908808780403, 4.176578237892285, 3.0546649344937866, 2.1335820068916678, 1.4099312509898634, 0.868680785341387, 0.4866139021919646, 0.23574709196682322, 0.08647318080583313, 0.010235598143552986, -0.01840069965094964, -0.02035237572327112, -0.011302831732045814, -0.001620061059279682, 0.003189435230218707, 0.0016220391183935415, -0.0049348045598208885, -0.013411194412878075, -0.020213367455662785, -0.02220802466950495, -0.017438612861888813, -0.005519086530214777, 0.012306235204975572, 0.03340856360138871, 0.05426386157795432, 0.07109723257410629, 0.08057930446040121, 0.08046824103209535, 0.07009962582480637, 0.05064578357835337, 0.025094061095987687, -0.0020726725950642676, -0.02547390735794925, -0.03965342298908638, -0.04004075847356012, -0.023944730575859205, 0.008541874426614892, 0.05384375074703093, 0.10451453799746983, 0.14923846078227587, 0.17326855042217879, 0.15930747370558676, 0.0887934663786113, -0.056488936127559876, -0.2925918284114154, -0.6315288114651564, -1.0795085258536565, -1.6354483481752735, -2.2899297750819336, -3.0247323105811255, -3.8130662503304715, -4.6206145003286565, -5.407195364319582, -6.1290535839991005, -6.741666763642084, -7.202876098718973, -7.476126182491501, -7.533576609915892, -7.35884342459313, -6.949142237890853, -6.316636762790719, -5.488844806710629, -4.50801539737413, -3.4294614948756355, -2.3189076634258923, -1.248985660199754, -0.29509393508430903, 0.4691716409526114, 0.9768248932095707, 1.171927544529377, 1.0134470040622605, 0.47829502941191165, -0.43667270122124924, -1.7138487346163551, -3.3153313343719977, -5.184635874422598, -7.24956362287067, -9.426052467523089, -11.622767038881015, -13.746135307236203, -15.70550873947976, -17.418115687683596, -18.81354404910538, -19.837584811577585, -20.45476336579425, -20.64966837900772, -20.427064761904717, -19.810791508072786, -18.84156104853446, -17.57384828941224, -16.07211330880972, -14.406638048383149, -12.649272072001567, -10.869375102840117, -9.130215821758402, -7.486040125323163, -5.979961846329634, -4.642759962314251, -3.4926175824177514, -2.535726539279373, -1.767483051824202, -1.1743917559000507, -0.7363781829346986, -0.42925354556366185, -0.22711876721532392, -0.10451960244442675, -0.03820416782290747, -0.00838398948186017, 0.0005452245607126721, -0.00018825081120116605, -0.003456448402760128, -0.005590358431297667, -0.005502367523989912, -0.0037143378674373393, -0.001429902517623815, 0.0002285913556643884, 0.0007291677448182837, 0.0003344559438458198, -5.523914528753736e-06, 0.0009656991617941573, 0.004232674963161772, 0.009837297701398292, 0.01623652832802236, 0.01981024316582508, 0.01462651231650749, -0.007456686061043766, -0.056313751313244446, -0.1427047277329739, -0.27711526726966046, -0.468384585546771, -0.7222631982514066, -1.0400748597419092, -1.4176289186677957, -1.8445487589785643, -2.304146790488198, -2.773926186702386, -3.2267329557765367, -3.6325163152339526, -3.9605885730479873, -4.182214446812166, -4.273310484886669, -4.2170037219121435, -4.0057892813828815, -3.6430418603841233, -3.1436762398872924, -2.533815156977, -1.8494074773632918, -1.1338134020789634, -0.43448039951875866, 0.20098272700476624, 0.7290545426889785, 1.1145215958164354, 1.3342874544066077, 1.3803947034923698, 1.261926559608808, 1.0055293612750047, 0.6543997252771854, 0.2657033607559183, -0.09347306259670075, -0.35140096613871324, -0.43786057027904096, -0.29070344732459, 0.13769226212982463, 0.8746656139881698, 1.9228708061053497, 3.257536205434586, 4.825732497081979, 6.547853494124074, 8.321330312755736, 10.02642033308637, 11.533737546990668, 12.71303502029447, 13.442626747032577, 13.618756486324957, 13.164193438550281, 12.035363100243202, 10.22740618596952, 7.776694413724736, 4.760626868133482, 1.2946364241954922, -2.4744421145533257, -6.377091241032163, -10.231484913140687, -13.85492314736879, -17.075507853929086, -19.743210285570495, -21.739515808208168, -22.9849309463257, -23.4437937756555, -23.126030022462384, -22.085728178379135, -20.41664944986779, -18.245023162508012, -15.720186446062735, -13.003828890041326, -10.258645269232249, -7.636985996501765, -5.270827911357862, -3.2637126854038137, -1.685167822055676, -0.5679649055309229, 0.09166726064371418, 0.33099983229679697, 0.21528500202425296, -0.16969053833285436, -0.7262859243557166, -1.3541424669662476, -1.9589822695554826, -2.4603280554615967, -2.7975193165259755, -2.9335843155572205, -2.8567215875082064, -2.5792166678051807, -2.13415526202508, -1.5703528526126178, -0.946059220862033, -0.32210884380342936, 0.24477950755317046, 0.707885746432625, 1.0349845070742845, 1.2110373414119397, 1.2388560655820153, 1.137725093353902, 0.9401840522570768, 0.6873654901443406, 0.4234371412089533, 0.18980491799689925, 0.01975183251478274, -0.0658679823535163, -0.061236688255040805, 0.023855899531143827, 0.1656259317056586, 0.3300237851656954, 0.47827565346052164, 0.573728087035476, 0.5893185176881085, 0.5148878266728423, 0.3635157209237186, 0.17610190290793987, 0.02353470603745136, 0.005976018868174861, 0.24903252829624817, 0.8968589234935193, 2.1025534907843046, 4.01652928585094, 6.773691843602946, 10.480406590758239, 15.202324173039012, 20.95411675094367, 27.69207480575577, 35.310328171190555, 43.64120046322271, 52.459902362631226, 61.4934402186658, 70.4332885096898, 78.9510743915123, 86.71627451658887, 93.41474915661837, 98.76750913267998, 102.54935067068708, 104.60061417274628, 104.83577825255871, 103.24812174646128, 99.90960040863871, 94.9660031999879, 88.62778666873882, 81.15728337753903, 72.85321938780828, 64.03363933667342, 55.01841491761893, 46.1125000224525, 37.59099709460327, 29.68692483241487, 22.58234346162925, 16.40340853764586, 11.219293187080822, 7.043544752920921, 3.8397277515374943, 1.5298916068155481, 0.004738960739871034, -0.8653932095862188, -1.2196072171363852, -1.1963531656111974, -0.9248100556567408, -0.5181959076567686, -0.0692613924579067, 0.35198223442121546, 0.6984379276881731, 0.9442944019734123, 1.0820035061263302, 1.1183454689093075, 1.0700770238463473, 0.9595685333272879, 0.8108853989645138, 0.6466071254600642, 0.48555510005558233, 0.34148470811507675, 0.2226865694247179, 0.13235225966763225, 0.06949893473406936, 0.030218149623411374, 0.009016435602631576, 4.5011110752773285e-05, -0.0019332619833115, -0.0009283469653360864, 0.0005189113409360115, 0.0012439439009837483, 0.001117527413964713, 0.0005728265848519377, 0.00012559386710240321, 6.324626660821556e-08, -5.76117831386727e-05, -0.0007389751164994837, -0.0029140926850779623, -0.007207061836275615, -0.013495918420598038, -0.020448307134753697, -0.02520790787735866, -0.02333125512346094, -0.009041900244802822, 0.024177084826398104, 0.08268448777386772, 0.17156237650359066, 0.2934155958820365, 0.4472516773200229, 0.6276063695744452, 0.8240748099390368, 1.0213727818519105, 1.1999989675004379, 1.3375022043458555, 1.4102845998361755, 1.3958004035682512, 1.2749503968158955, 1.034430016759866, 0.6687725020545687, 0.1818395158290131, -0.4124485687948034, -1.0902849974632762, -1.8191290803805233, -2.559871871770772, -3.2696900324587195, -3.905383591973189, -4.4269337266103355, -4.800938445857001, -5.003590856022273, -5.022897760801507, -4.859901536867486, -4.528759639507046, -4.055644995008931, -3.476546120545974, -2.834156316077643, -2.174135184767126, -1.5410930081401801, -0.9746816233992737, -0.5061825208141603, -0.15590251934524807, 0.06842589125480185, 0.1719027455258729, 0.1714465658475573, 0.09364903363753677, -0.028272295351625704, -0.15810561164198905, -0.26048799017372887, -0.30457061428538496, -0.26714009296622565, -0.13489066102446937, 0.09436641708319934, 0.41165741941781775, 0.7979443595784659, 1.2262287004980925, 1.6644343626325198, 2.078800110939013, 2.4373043415462856, 2.7127862204508872, 2.8854655460713348, 2.944615257747262, 2.8892463842752862, 2.727776887562099, 2.4767666363720156, 2.158898393152687, 1.8004587332574917, 1.4286156722297045, 1.0687975967258239, 0.7424511074469006, 0.46539781106456607, 0.24692961294303573, 0.08969298547261331, -0.009694417890193756, -0.059445175366954296, -0.07095850771435518, -0.05700309988817528, -0.029977455960261523, -0.0004612599067524456, 0.023784073086638605, 0.038280729476699846, 0.04176153287729726, 0.03563144953726148, 0.023098891748896153, 0.008151815018654834, -0.005434886608695296, -0.014892112757338514, -0.018925258837420824, -0.017798945843286174, -0.01305141700353537, -0.006921495409610576, -0.0016332112291178634, 0.001285115591527208, 0.001471440116468329, -0.00015089498975865177, -0.0016796007732099549, -0.0009483045779076533, 0.0034704114307215813, 0.011193513304676923, 0.019186283613273757, 0.021492668945795608, 0.00987188406764034, -0.024387510541422748, -0.08732589478426661, -0.1778665169680308, -0.282297928546195, -0.36810887772048956, -0.37781631916783304, -0.2235830333170389, 0.21649077395251856, 1.0995145934783, 2.615606433507863, 4.981762600296845, 8.431522356358055, 13.20053504033548, 19.508569713659913, 27.538949795873062, 37.416803098730725, 49.18784543953183, 62.799621112341974, 78.08797444786993, 94.77261341991043, 112.45676642604327, 130.63540760463695, 148.71265381833797, 166.02733968775755, 181.88560122359505, 195.59863450244774, 206.5232394730349, 214.1023663822204, 217.90269787824516, 217.6463516725183, 213.23408509867107, 204.75791094203947, 192.50175922576685, 176.92968885787585, 158.66389688390626, 138.45413446558462, 117.12641302221267, 95.53233242942765, 74.49943413459984, 54.78400423127313, 37.029670662659896, 21.734662428554316, 9.229893637487644, -0.3308380794974678, -6.968215963595274, -10.862985805107748, -12.331314132463902, -11.792238204670518, -9.730068129894335, -6.654892446418377, -3.064416904734963, 0.5901820580587082, 3.9323749757278628, 6.6792614914418245, 8.650849476951107, 9.76984767878038, 10.052888624807924, 9.59478117487388, 8.547882141747682, 7.098939681669422, 5.445786740628784, 3.77606310858335, 2.2497530033713633, 0.9867918693094363, 0.0603826923150745, -0.5039653593511095, -0.724252998589003, -0.6537543430970061, -0.36989723936233754, 0.038193608981088145, 0.48181275895354797, 0.8831063079482432, 1.182823851825405, 1.3448107105577818, 1.3571040704058874, 1.2299128719589665, 0.9911046239646062, 0.680058593770843, 0.3408546852156568, 0.015747712652791315, -0.26025962878952563, -0.46315901666630305, -0.5816887290192202, -0.61709259946103, -0.5811603682694942, -0.493006139437919, -0.3752120379624655, -0.24998888593079344, -0.1359355051104704, -0.04583055112790401, 0.014311148476503747, 0.04490919500287444, 0.05141702361480832, 0.04221800494881618, 0.026283725979416223, 0.011075652909925317, 0.0011041870080723748, -0.0025795292060256632, -0.001871548205212589, -0.00020155782742067795, -0.0005295524219248214, -0.0032110393479599874, -0.004252553006128789, 0.005542382843128448, 0.04014842132708938, 0.11641687460978023, 0.2507447557148168, 0.45462727861734964, 0.7296538235247241, 1.0626966765595471, 1.4221394135730105, 1.7559740062588503, 1.9924532026398658, 2.043724570327036, 1.8125413219072646, 1.2017059853703291, 0.12522302607199334, -1.4797540094745647, -3.6415251770987562, -6.344457211195857, -9.522970161065997, -13.060011600157615, -16.790725556542185, -20.511495295493823, -23.99394365700303, -27.0028773285241, -29.31663239820492, -30.747884583631663, -31.162783982122974, -30.496297677687334, -28.762209759670206, -26.05654799466454, -22.551161283203406, -18.48043538013021, -14.121889309142984, -9.772070048519227, -5.720044992385477, -2.221126484439531, 0.5264761200883636, 2.3996104474320146, 3.360778846395449, 3.460150517632907, 2.8286471889952485, 1.6627125171268047, 0.20228574970406984, -1.2957322421186437, -2.5857058966475956, -3.460147888082476, -3.772097842263543, -3.4504521429042505, -2.506624855199791, -1.0318215008352642, 0.8147506600000914, 2.8253946846207936, 4.768941932759405, 6.418426329587569, 7.578248083715773, 8.107698613048074, 7.938113047371673, 7.08162750745009, 5.6304691833637, 3.7467932843621683, 1.6442512528339628, -0.436756673906145, -2.257796439394719, -3.610601847007261, -4.3416906746957675, -4.370586203095354, -3.699449538376819, -2.4129197634255304, -0.6680974683547516, 1.324237395395836, 3.3250430742908637, 5.096136373863577, 6.429612864153996, 7.17408373215626, 7.254570077122019, 6.683591617812802, 5.5619470479471875, 4.068799945858512, 2.442325454647329, 0.952995773832417, -0.12749283899805838, -0.5581045494501954, -0.1575190658201225, 1.1729802405684089, 3.4354379426937682, 6.5316421856180655, 10.270509402491399, 14.385687666511398, 18.561477384727038, 22.464233282316684, 25.77579977624328, 28.22531284222774, 29.616235697315577, 29.846024472148926, 28.913488511028447, 26.915927725858086, 24.03652278730378, 20.52333747457535, 16.662494022779303, 12.748652914019589, 9.056124090291725, 5.81374321426501, 3.186096432219627, 1.2628436253689443, 0.05687912883242499, -0.48899460502727504, -0.4881917412418436, -0.09136993503677011, 0.5350681724831292, 1.230380530471637, 1.8578067489013184, 2.3176817720369285, 2.5542378455449497, 2.5558062947074567, 2.3490388248566108, 1.9885385575154264, 1.543830591963429, 1.0858445688984393, 0.6750026632918866, 0.35262495911476305, 0.1367411306300626, 0.02262723316313348, -0.01241518245842771, -0.0012320754225971032, 0.022352916726683898, 0.032127693662705376, 0.01566233249347061, -0.023367905278209606, -0.06736325284557808, -0.09122249470593723, -0.07181319500575957, 0.0015256769708364899, 0.11803078584085365, 0.2408963372271461, 0.30954587237178743, 0.2506708091647097, -0.0011680640195380059, -0.47395904533348104, -1.1217847329270894, -1.7850817502597345, -2.1524247810646195, -1.7293280080510034, 0.1802801737373195, 4.47482744485489, 12.234232340022947, 24.675322689509315, 43.08372212113697, 68.72489160312945, 102.73950642641478, 146.0305662746774, 199.1513219990536, 262.2040420612276, 334.75968350916554, 415.8076093894988, 503.74263355479786, 596.3939975419136, 691.1058396018624, 784.8830311443359, 874.527360781096, 956.8008695148344, 1028.606024387115, 1087.1635873778448, 1130.1751737437196, 1155.9584992879043, 1163.5453423913614, 1152.7351155685988, 1124.1003972498654, 1078.944509573691, 1019.2149117569677, 947.3794896174915, 866.2754777910336, 778.9425350536933, 688.4611598716428, 597.8086629240134, 509.6751782604882, 426.34078591126644, 349.6001086518855, 280.72528064456077, 220.46603461919165, 169.082862731246, 126.40700920417683, 91.91959806502653, 64.84155292812935, 44.22611193098256, 29.04658912945687, 18.273433626168497, 10.936399054223875, 6.169550774082643, 3.2387534102414746, 1.5527226361186943, 0.6600881943253658, 0.2364253758810874, 0.06429918772489036, 0.009978684442190829, 0.00010541066440604337, 0.0008097827180142419, 0.0008537876877892739, -0.0005306180811297076, -0.0012291238145974985, 2.6401574254726413e-05, 0.002720720021398143, 0.005233309853479442, 0.006061769960814116, 0.00478505339420374, 0.00231253379195714, 0.00032841438773751854, 0.00014893152343656722, 0.0014151993431480618, 0.0011154653303278304, -0.006633284999908731, -0.029787663154705244, -0.07654874538255255, -0.1527438346539658, -0.2588832262303147, -0.38749714981696426, -0.521388669551947, -0.63334810789043, -0.6876739567626117, -0.6435636771890831, -0.4601190092721926, -0.10239682758368966, 0.4523682986590376, 1.2092695265796716, 2.1518040159479805, 3.2402821955062104, 4.413040814837729, 5.590572523693428, 6.682291462686873, 7.59527891655294, 8.244048616257011, 8.560182307459089, 8.500642374074808, 8.053680111907704, 7.241515345852691, 6.119335407101697, 4.77060300991007, 3.2991673388782767, 1.818916019987189, 0.44181151241391364, -0.7334994989153588, -1.6314330438505786, -2.2065591331217536, -2.447261452203699, -2.3756067429014855, -2.0435197522123936, -1.5257946908888063, -0.9108361126133948, -0.2902676603850613, 0.2513516220863887, 0.6455159005995325, 0.8464738669902943, 0.8349608837252072, 0.6187051710883356, 0.22984640646528584, -0.2806398165471003, -0.8503314854839935, -1.4135308055264675, -1.9092067216313098, -2.2877637349050284, -2.515903465331059, -2.579135884262424, -2.481823890027711, -2.24496353171033, -1.9021719757226543, -1.4945443530253977, -1.065129571144106, -0.6537591192480836, -0.29285125503310616, -0.0046183444007482964, 0.20012786791144804, 0.3215126339018938, 0.368785324966729, 0.3575853969586574, 0.3067825888869265, 0.23539409351286378, 0.16000890227249992, 0.09302106100646824, 0.041813523622833505, 0.008869785527063767, -0.007352804224889705, -0.011055750253180393, -0.007553275554916923, -0.0018527099013151327, 0.0023939252325572737, 0.003419991510793938, 0.0013237794373285848, -0.0024243048855651515, -0.005778150246202078, -0.006996929538644046, -0.005389634794193763, -0.0017433268124756967, 0.001669446709190532, 0.0015144982359450439, -0.005833163585471346, -0.02333314872992674, -0.05234524619259213, -0.09192867441658846, -0.13854985664529063, -0.18630071513364294, -0.22763367877060026, -0.25452197800301585, -0.25986776960627594, -0.23887524172282767, -0.19015176780126497, -0.11631743492437127, -0.023973000728413837, 0.07701504291803461, 0.1748348127115596, 0.2574658066742932, 0.31455870220171284, 0.339143329493161, 0.3288608073449076, 0.2864798166545735, 0.21956606997152195, 0.13931216695391926, 0.058680443540585665, -0.009861631640229645, -0.056645230690128806, -0.07672022810930867, -0.07103925336652708, -0.046656506045364476, -0.015836918776989117, 0.005852324394679068, 0.0022217204935904805, -0.04047988875335513, -0.13060475430119786, -0.26874494439295715, -0.44640923732906906, -0.6460431933674948, -0.8425068452288169, -1.0059037621204778, -1.1054371297644823, -1.113812186638332, -1.0115849673778987, -0.7905580202859728, -0.4558532811475629, -0.026294443797710506, 0.46706083847421487, 0.9841115804928586, 1.4802438714466062, 1.9116108592724395, 2.240446128672335, 2.4396708345316456, 2.496140565525411, 2.4120628266918236, 2.204375106333219, 1.9021695057443717, 1.5425387874319463, 1.1654798577554002, 0.8085938826220237, 0.5022050040255146, 0.2659162258689273, 0.10701702034631705, 0.020891913980670414, -0.0067105075331122775, 0.004009054442122891, 0.03133081326581855, 0.05639425540206007, 0.06674058613674475, 0.05838091007660189, 0.03601176090007796, 0.011333984724406651, -0.0002142677003978735, 0.01631512243496516, 0.07103623572182201, 0.16569326297857281, 0.29176687261764356, 0.43078775715260537, 0.5570425146727065, 0.6424133528625167, 0.6626550025993455, 0.6040574278109525, 0.4692397982424335, 0.2808186546839806, 0.08191138925112852, -0.06713906243146439, -0.09585020262898507, 0.06613163735882525, 0.4768466015665426, 1.1696946337245226, 2.14308996961484, 3.3544096407669146, 4.719375925147622, 6.117826646041555, 7.4059149622022895, 8.433661547543053, 9.065834513846388, 9.203346437212664, 8.801899276860981, 7.8845805904951, 6.5455704751571835, 4.943046784526391, 3.2806973306909915, 1.7788198627528105, 0.6376221501922382, -0.0031938390799801505, -0.10339547801290441, 0.24591703956720776, 0.8033738624889178, 1.1757730241636488, 0.8361281116281409, -0.838386146912602, -4.510706136696645, -10.814872048758502, -20.28028244456706, -33.25716749766293, -49.85181378970167, -69.8796840775598, -92.84320419042045, -117.93873773561239, -144.0943508138441, -170.03668820905642, -194.3845190091775, -215.7660317301957, -232.92798462856314, -244.83922853294968, -250.7788088581359, -250.397801630097, -243.7485312629723, -231.27818880108433, -213.78758586151628, -192.35941983103538, -168.26357479070572, -142.84928093257298, -117.4351427295209, -93.20799325197115, -71.14025585319767, -51.933157082189005, -35.9906406283855, -23.423854267656797, -14.07997130570175, -7.597760825773898, -3.477998357412385, -1.1582101315054085, -0.0826128383971085, 0.24050602699172038, 0.199449848749652, 0.06047062569986983, -0.030514644531357386, -0.028938561073323713, 0.039426728874240334, 0.11497106779667596, 0.13942819947099475, 0.08366357190428247, -0.03638772628376736, -0.1578730436591285, -0.18296905208605693, -0.0017229777076523745, 0.47891590020385644, 1.305672165710906, 2.4550863665743132, 3.8203737373998155, 5.21250147036343, 6.376741487774264, 7.023444602762859, 6.86937575655911, 5.68400879242343, 3.3340020771824537, -0.18114080590123513, -4.708413787606663, -9.940077293515717, -15.434305887513686, -20.656784039471994, -25.037729556821134, -28.0382192361725, -29.217870024456776, -28.29526912210993, -25.193120553884608, -20.061714261286493, -13.276832258954233, -5.411274979131244, 2.8175658901725855, 10.618655618893897, 17.208969040571407, 21.89657733393405, 24.155568548539865, 23.6843135394044, 20.440212510148193, 14.644036045491081, 6.756086049283301, -2.57263538324914, -12.568569024738832, -22.415018274616443, -31.333719581758498, -38.659463297653254, -43.899771256583875, -46.773656416496095, -47.22614576163398, -45.41819485432925, -41.69449087525185, -36.53408317659788, -30.490514144238798, -24.129265830455562, -17.969582100265544, -12.435042265770972, -7.821604516152757, -4.284184655093266, -1.8410429562728177, -0.3935515291367966, 0.2427691790477497, 0.3010760515041024, 0.025297365485490008, -0.3635472864330958, -0.6929016024782669, -0.8536820911943788, -0.8039950171946108, -0.5624377060087684, -0.1932209526580697, 0.21375493936941656, 0.5643488130018053, 0.7793695342130291, 0.808909441943493, 0.6401124683982874, 0.2978039088591498, -0.16142338599990386, -0.6601232946845469, -1.1137367175277304, -1.4447346807853265, -1.5948796383903854, -1.5337938846246575, -1.2627348972525236, -0.813300463088633, -0.2415889839469419, 0.38099748957747404, 0.978693961202139, 1.4823704778000515, 1.838817200403056, 2.0168775468710876, 2.0098888051698256, 1.8344174667183855, 1.5258234805368032, 1.1316178471460139, 0.7038188115189644, 0.2915429836190993, -0.06509667575181308, -0.3390299592584058, -0.5178526725120977, -0.6030986683855095, -0.6075883689861528, -0.5515359563108242, -0.45822476147832497, -0.3500037712371423, -0.2451187412381748, -0.1559171554798476, -0.08845769622045672, -0.04330601355885102, -0.017129054656169283, -0.004611476518698468, -0.00023418578995286756, 0.0004376995779053347, 0.00014290187153971035, -1.3762128106996426e-05, 7.21920757158843e-06, -2.341622031436114e-05, 0.00010826702723218805, 0.0014207464156168073, 0.005595262610762023, 0.014331092315797959, 0.0283548571077194, 0.046363104470339096, 0.06423228322236574, 0.07480403020386768, 0.06844824003896958, 0.034440919310033416, -0.03699876355465727, -0.15234718802457517, -0.3125518658400104, -0.5114463123479643, -0.7352463984028894, -0.9634111053755978, -1.17091458002257, -1.3317027843480354, -1.4228803258239242, -1.4289702572131846, -1.3451581090176359, -1.1790798622887257, -0.9506563763390592, -0.6897540601827828, -0.4318485965453587, -0.21223647721472108, -0.05964395439029623, 0.009732770042136083, -0.0033007509844765297, -0.0788566387929127, -0.1788607151167011, -0.25107077793133714, -0.2358652026027725, -0.0749726968633348, 0.2790394927175889, 0.8539296956564719, 1.6512990198951898, 2.6434275386027544, 3.774073734028178, 4.963345110404022, 6.11611897817542, 7.132944456230039, 7.921957530055182, 8.41015604261765, 8.552443835217975, 8.337157604791862, 7.7872928622142, 6.957271087593483, 5.925742641023139, 4.785497507065952, 3.6320086783176717, 2.5522140066206997, 1.6148523325658537, 0.8642105573800619, 0.31781247524652745, -0.03197480181289774, -0.2129913533843891, -0.2660605153405668, -0.2368516943053684, -0.16823884802865743, -0.09436617153964277, -0.03723275922353563, -0.0060839355235618574, 0.0006518022047380273, -0.00838864329639183, -0.02203458261395219, -0.030781507419736284, -0.029704771462485298, -0.019463885876911086, -0.005316564451466314, 0.005425378499209269, 0.0066609851439307114, -0.0035687702501336345, -0.021502080912815604, -0.03815186100926906, -0.04209094699850214, -0.0241219900226886, 0.017174469264313545, 0.07046155019302296, 0.10884220986339446, 0.09062927522843074, -0.03549262276886312, -0.32098436259871094, -0.8048130752419493, -1.499907142314741, -2.381563832781608, -3.3809450249803032, -4.386441229650096, -5.254664348238597, -5.831236812204709, -5.979570816848603, -5.613774709566636, -4.730048839433767, -3.4298183268957603, -1.9277243863588973, -0.538676384099465, 0.35949422414454485, 0.3877874372416507, -0.7520822663602785, -3.1850728628807716, -6.772393073511934, -11.037925610862866, -15.126860801234015, -17.810293347879394, -17.545621133745282, -12.596588846506096, -1.2092963008184316, 18.16773644272924, 46.639264786683846, 84.62107869838448, 131.63013777755566, 186.1380832352207, 245.51598547549656, 306.0911445455615, 363.3285112264242, 412.14354355607816, 447.30879499243076, 463.92104513799546, 457.8909453807249, 426.4053615833348, 368.3120226338505, 284.38054173347257, 177.40377997078363, 52.11805650358563, -85.06152245189135, -226.47518961872504, -363.788227870218, -488.6467731804556, -593.3592862987465, -671.5384440286548, -718.6416274909061, -732.358419831295, -712.7871796137532, -662.3891813452241, -585.7332559729239, -489.0584019320878, -379.70024581132395, -265.44018270266713, -153.84246638074436, -51.64384689342206, 35.74721697247412, 104.59821456648851, 153.0212773995018, 180.95695299883707, 189.98682904995388, 183.0061359772292, 163.80415047196428, 136.60186766675807, 105.57319676383223, 74.44250080903282, 46.185989137378314, 22.85374614662136, 5.518118979554846, -5.661102849841997, -11.27708019816015, -12.45318531483344, -10.592691025335096, -7.13588072380765, -3.354631073799326, -0.20618915347703887, 1.7425003390364684, 2.3194380540785984, 1.6907053595068509, 0.2590429846646903, -1.461540528412256, -2.9706557728795717, -3.885522394310129, -4.009467977933279, -3.3574028813873227, -2.138364292449137, -0.7021454658090069, 0.5377246500103596, 1.1894659650138897, 0.9614887093387597, -0.2795694601689225, -2.480445053207932, -5.406367430326393, -8.677880605854744, -11.83264530990463, -14.401784754874246, -15.985854614458836, -16.319320627107356, -15.313567746881352, -13.071954246929197, -9.875157266174138, -6.139693675688556, -2.356506481994402, 0.9806921446134417, 3.4463999563455925, 4.743158430906662, 4.7417695578269266, 3.496597328817756, 1.2344855554209715, -1.6802844047670749, -4.7994966336517475, -7.655676122284959, -9.82554197384705, -10.983971881316027, -10.942164909864529, -9.665632421724876, -7.2708595497303214, -4.002520238776838, -0.19568299698348346, 3.770818998884257, 7.522948725556327, 10.735354097357245, 13.16519101422062, 14.672355434399673, 15.224801379830245, 14.889809039299417, 13.814125946368636, 12.19699700550919, 10.258912977398634, 8.212758143020046, 6.240811548337683, 4.479615003344118, 3.01347264643451, 1.8759749646024726, 1.0578624709450923, 0.5188885764512357, 0.20115218281213793, 0.041611866217766434, -0.01793687887429851, -0.024385492991245303, -0.010518310049106954, 0.004589905016730319, 0.012933772296981685, 0.013837175112489709, 0.010185582427452773, 0.005453467093202625, 0.0019549830951052388, 0.00033550751050926894, -7.231549163026661e-07, -1.2059320249279306e-05, -0.00019316704184846296, -0.00017858856257183155, 0.0010655546116326326, 0.004548398153180375, 0.010348000525782369, 0.016883744275160237, 0.020736990293013673, 0.01724561805215059, 0.0018685962434164545, -0.027946461387863754, -0.07087816181438973, -0.12039141891736534, -0.16446822319988486, -0.18674613857242964, -0.1690987538227345, -0.09533797510096244, 0.04461086106955533, 0.2509348622614767, 0.5114920274395784, 0.8014920321413631, 1.0857546074443376, 1.3235217902829457, 1.47526009101899, 1.5103916473275296, 1.4145954169747423, 1.1951876427738772, 0.8827708208339072, 0.5287556124729523, 0.1986839731776399, -0.03797106885400949, -0.1200619967100732, -0.007058625471422777, 0.3108878342295881, 0.8072281089798109, 1.419226404641367, 2.0548054290278297, 2.6056404333407714, 2.964983658418852, 3.047713375505541, 2.8094434509138084, 2.2613584806634015, 1.4777063978354188, 0.5936939795492144, -0.20649711556682687, -0.7106911130187228, -0.7063368334797837, -0.011180528712322058, 1.4973025703426226, 3.858107145613545, 7.012349434728273, 10.801024625991335, 14.97590441711965, 19.222768813494927, 23.194373201098966, 26.549076354575437, 28.990127536556553, 30.301154845891276, 30.374013448427235, 29.21860321028356, 26.958890247771055, 23.815794695633155, 20.078863131054614, 16.070804387586332, 12.109835092362522, 8.47491162465287, 5.378315551063363, 2.9488193404499916, 1.2269915061869732, 0.17236965270785903, -0.31947998187617366, -0.3933281829978193, -0.20814231407188094, 0.08739696972435518, 0.37415714075280654, 0.5742392876673594, 0.6538887268078932, 0.6182120594977959, 0.49975660366020297, 0.34391765749188896, 0.19446608695388024, 0.0821994081904166, 0.018890230895837197, -0.002496199006259154, -0.0016908007157459507, -0.0007347947515069277, -0.011851102665842656, -0.026520622410142376, -0.008551432608283848, 0.1067845256391736, 0.40666485771545513, 0.9882128436349681, 1.941360098079329, 3.329880664121982, 5.173936178678118, 7.437423537139127, 10.02278691141477, 12.774841342519895, 15.493735760116522, 17.955692436205478, 19.93884500601011, 21.250578977139998, 21.752414542750927, 21.378729569544166, 20.146467922969283, 18.15466763855115, 15.57373521051276, 12.622924702992284, 9.543334742522317, 6.569670466166003, 3.9042678680421963, 1.6968585484506677, 0.032557969255679255, -1.0707746422947848, -1.6561093376652105, -1.813392592791396, -1.6609225929666063, -1.3251477610744717, -0.922086515904269, -0.5430549023612736, -0.2464709862523988, -0.05635880958704818, 0.03304678940277825, 0.04814321329044681, 0.02439448396672981, -0.004996466750102706, -0.01793526787652342, -0.008272495051036851, 0.013978351500100537, 0.026671140433567775, 0.002588499923675605, -0.08224667211922847, -0.240975990801553, -0.4707779723021352, -0.7513965765127164, -1.047720707117212, -1.315942858567152, -1.5120908280210452, -1.6012292101788324, -1.5650513414142029, -1.4063542268614275, -1.1493388036085088, -0.8354537538723305, -0.5154166071241397, -0.238832898224507, -0.043365882484930694, 0.054418924339834376, 0.06463723429046524, 0.024792318795141183, -0.004845439820072818, 0.04933303917834116, 0.26146564361017055, 0.6921352849272704, 1.3754543090836495, 2.309715008984752, 3.453401111342203, 4.72745061029257, 6.023643549273209, 7.2179576929963565, 8.186900224951788, 8.824316128997468, 9.056079685754986, 8.850408195004183, 8.222237881453223, 7.231050612127007, 5.9725757804563155, 4.565741124553926, 3.1369530527778324, 1.804138488008115, 0.6628811660635892, -0.22346260819374905, -0.8280108060278961, -1.159063036478299, -1.254038371239756, -1.1700138234613557, -0.9726865807992187, -0.725668968489549, -0.4817815491938103, -0.2775015704094551, -0.13105891146511814, -0.043979259460836334, -0.005281405404813938, 0.0028562540677736677, -0.0007227145496227118, -0.0009392523725671668, 0.010597258837161987, 0.034880331083780095, 0.0668338783254076, 0.09802230341441696, 0.11986176839341338, 0.1264412612267646, 0.11625083246946438, 0.09245245778894631, 0.061731254767140475, 0.03213547133138964, 0.010566996531276063, 0.0006625846784761181, 0.001692473388222457, 0.008824832822254193, 0.014727505945961974, 0.01209373771731021, -0.003616870614410255, -0.03206519265959583, -0.06731503371857092, -0.09892510180673109, -0.11480513733623976, -0.10529378529792403, -0.06749387593921255, -0.00866881374758473, 0.052462795595539055, 0.08737469798886881, 0.06259004948396533, -0.052710818865299554, -0.2775281981790491, -0.6101109883355496, -1.021330815033152, -1.4523286630204655, -1.8178522018724417, -2.015789563796408, -1.942160687617301, -1.5094663823316756, -0.665494778293938, 0.5908451390983462, 2.2000253210048952, 4.0413766997768565, 5.942884316892704, 7.700939996049705, 9.107861743181354, 9.983346323852814, 10.204883686093202, 9.731785476851758, 8.618010281544601, 7.0104041558483265, 5.131357813562287, 3.247068027635382, 1.623958537925089, 0.4824725648036218, -0.04469436987700645, 0.057294077781583755, 0.6731449718038552, 1.5667330879975274, 2.4124140165116126, 2.8451892241857655, 2.5231767673228602, 1.193257819965684, -1.250539898548361, -4.726093679066467, -8.94793259405373, -13.442573202941078, -17.59510890431578, -20.723331382455026, -22.168879170449443, -21.39311844011804, -18.06443357949595, -12.123804009451707, -3.818116493791876, 6.305173760586018, 17.443187224667916, 28.61816492762584, 38.783932010101395, 46.9449518133085, 52.27260966704295, 54.20346970609113, 52.506502522033955, 47.31038365153491, 39.08760522391675, 28.596222804796128, 16.785102925298492, 4.682241088849558, -6.720388398704175, -16.571291515275338, -24.240590816091323, -29.36901029897772, -31.880719874712177, -31.96117964523778, -30.005785558212782, -26.548658166747146, -22.18288013757866, -17.483680101073062, -12.944563093861023, -8.933537668395017, -5.673093095923815, -3.2431490263662988, -1.6023785371727575, -0.624108431334183, -0.13749035865461245, 0.03396281476354411, 0.042391316752587484, -0.0023511888956959538, -0.03782270742271844, -0.04305316032812254, -0.025164251862763935, -0.00312057334088857, 0.006889973427107193, 0.0009394189436220168, -0.010161261121142679, -0.005345683690192075, 0.0370741848810599, 0.12771310095711969, 0.255966059088741, 0.38464529525029534, 0.4514874245245117, 0.37799464634920227, 0.08432033128533216, -0.4925999126579575, -1.3814135467141597, -2.5631265929211726, -3.965554580666087, -5.467359424707058, -6.911777142446762, -8.12823261394, -8.958399207248615, -9.282220982705088, -9.039231017788282, -8.241044550715962, -6.97204929221267, -5.378376911828547, -3.6467744294018574, -1.976790643900017, -0.5509469355935227, 0.49207050451724527, 1.076695271073799, 1.1990804589162103, 0.9237511932489247, 0.36915938086581634, -0.31507083997586477, -0.9750041950159013, -1.4785243753092878, -1.7361506357850767, -1.7131132463832957, -1.4308938891241545, -0.9578604221610373, -0.392011247299664, 0.16044759528056765, 0.6064374939566761, 0.8831555200139574, 0.9679351881548762, 0.8792823297095957, 0.669361472689463, 0.4099124340980977, 0.17484074967884497, 0.02330654791278637, -0.013072353625159686, 0.06376340736497085, 0.22025273435681658, 0.4005618818280137, 0.5412280269370168, 0.5875940568219455, 0.5082042727767548, 0.3038789393834731, 0.009310515251509584, -0.31334801227872106, -0.5876706476666904, -0.7401591619705097, -0.717719973786714, -0.5014796056659243, -0.11364055394825329, 0.384545565579223, 0.9037583689339971, 1.3446501299541969, 1.6193877060056128, 1.672151457540846, 1.4939006998416606, 1.1273739865752228, 0.6607478267989397, 0.21044110738100044, -0.10416777649065527, -0.1894215628081345, -0.0037020968860342674, 0.42436088109243314, 0.9903777002650753, 1.5238242570486729, 1.8124658580314763, 1.6383216994825942, 0.8194039947103228, -0.75012913200749, -3.069088056691016, -6.014382104967134, -9.347255394028926, -12.739991588677501, -15.819239541504153, -18.219809600065783, -19.6402810156189, -19.89109870478574, -18.92678150113763, -16.856314122559546, -13.929363025622715, -10.50004385408069, -6.973867474291067, -3.7465076155956054, -1.1446073706143085, 0.6213444937665416, 1.4839980876713534, 1.5213883295951096, 0.9340327260580419, 0.0005431641336911401, -0.9792214754557869, -1.7426291273622985, -2.11367619837136, -2.0343388458871203, -1.5722605560922343, -0.9035524007157129, -0.2741055361364678, 0.053168029510286596, -0.14492003289255748, -1.0020110037187935, -2.5289983817049677, -4.604114180628087, -6.9886308255181735, -9.36581214645772, -11.396626744030181, -12.78038609036283, -13.308871522758274, -12.903871853148528, -11.63090144079905, -9.686454165551984, -7.361209433287508, -4.986249966437521, -2.872688733075502, -1.2564743471744102, -0.25924690671515394, 0.1269332180272053, 0.02783386997722671, -0.34943274470086577, -0.7701640358108618, -1.0318120320616893, -1.0167268616051857, -0.7248988880941158, -0.27841964601071306, 0.104849697082476, 0.16470293381411544, -0.3306260868904749, -1.5104995172703233, -3.3408615788127793, -5.591228031211224, -7.840640920144154, -9.526998926208897, -10.036194918028476, -8.819438365516223, -5.520462527725443, -0.09031896721207049, 7.133067508647503, 15.402351918305564, 23.606820821112336, 30.38277019310274, 34.27818453284624, 33.95130757076629, 28.375534203960655, 17.020201887397036, -0.021342691006486413, -21.9786983516389, -47.438667198161156, -74.4668381562612, -100.80384311393779, -124.1124678007613, -142.24387492224727, -153.4877694471629, -156.77452490984038, -151.80614648693413, -139.08291228971768, -119.82870483995167, -95.83157813743799, -69.22293455570085, -42.22683375965547, -16.913618993137263, 5.010367311876524, 22.352104561049227, 34.505501305913214, 41.44618720423981, 43.655705938295235, 41.99260286421425, 37.53384110045461, 31.411887429553737, 24.67099448880454, 18.160162743800925, 12.470301035383882, 7.921122769873032, 4.590400460537328, 2.3724115419915455, 1.0500104391894316, 0.3651238020863152, 0.07556845678169609, -0.008967043540950279, -0.013333425274705208, -0.002227052984268964, 0.002600705436270662, 0.0015437478608411454, 9.28673778916197e-05, 1.0633873593261073e-05, -0.0007583005868979563, -0.0029274050391486076, -0.0019077954352732743, 0.007417435891896309, 0.010836104753319082, -0.06311865091135055, -0.39720550654493963, -1.3481345118721042, -3.5054419110298745, -7.731056844026346, -15.163658583089816, -27.174769706952368, -45.26951326731481, -70.93338932039315, -105.43608419244472, -149.6126547226859, -203.65520734469618, -266.9639210551623, -338.04562912481504, -414.4990055788793, -493.1027662183505, -570.003937574285, -640.9932435520753, -701.842611922493, -748.6704853234216, -778.2954300547343, -788.5383066596022, -778.4381463603812, -748.3562983778793, -699.9561690864575, -636.0602929952927, -560.4006586791161, -477.30072863385533, -391.31988222146794, -306.8228999732175, -227.63843426843295, -156.80902913680976, -96.43742282057639, -47.635723377467876, -10.571893230113323, 15.402381568581202, 31.565773933568455, 39.61049109911379, 41.421761483982415, 38.87759474909868, 33.68698452900223, 27.2774533705265, 20.735232505482944, 14.794868955639007, 9.86865380445091, 6.1016647630307554, 3.4444732938734477, 1.7280758572307315, 0.7301611361563292, 0.22628814786880663, 0.02336102747788175, -0.023909587125832136, -0.010475496905078676, 0.012035607792972521, 0.023394832462158177, 0.02196220268069575, 0.013869283032763052, 0.005714387185271277, 0.001030074715831968, -0.000161460817141759, 9.381171301975771e-05, -0.00027681304696446535, -0.001769099554356267, -0.002713289066075439, 0.00022373303844480568, 0.01076644834883779, 0.03152345104838526, 0.06279115606399377, 0.10205937985203281, 0.14435862813509936, 0.18332619188205074, 0.21266800935983812, 0.22760306766034477, 0.22590917791020107, 0.2083218483808827, 0.1782320334202931, 0.14080740854358842, 0.10175555223301273, 0.06612613538804739, 0.03742579610274941, 0.01720978345390593, 0.005179396843356794, -0.0003185861355179778, -0.0015829367707017685, -0.0008573788371967109, 0.00018111398688390494, 0.0006471614307766016, 0.00038590001746830735, -0.00028864784246970457, -0.0009242600038176428, -0.0012011296018815145, -0.001058484258045739, -0.000661799626860409, -0.00026126636313669293, -3.2847565212703496e-05, 1.089032040312839e-05, -4.800630939011705e-06, 6.177553936578862e-05, 0.00022944539371426548, 0.00034096823744529057, 0.00017511734437822843, -0.0002739907380981776, -0.00045857257883012535, 0.0009055719997101494, 0.005594853079434249, 0.014968828085807632, 0.02830350284987921, 0.04052270769148331, 0.039790690569728386, 0.005673572301060371, -0.09127917269349657, -0.28773928957824046, -0.6231028635532285, -1.132339461121726, -1.8369259826447402, -2.735316301861884, -3.794958802831207, -4.948107267632149, -6.0934377541170095, -7.104725459337648, -7.846600812322187, -8.195863791289767, -8.065267575858622, -7.425657464520101, -6.321586027476604, -4.873729585869886, -3.2673341925837236, -1.726236136238296, -0.4748484139691442, 0.30627063124430126, 0.5232572419917366, 0.20099498365115664, -0.5043313798773075, -1.3185295518571256, -1.8907789381673126, -1.8599766259341175, -0.9371638257001476, 1.0099677151191253, 3.887824868650144, 7.340910229613014, 10.764529070513865, 13.37382330372938, 14.327711715959701, 12.896225611883464, 8.649300821683262, 1.6369507080059758, -7.473546634856563, -17.33692173262671, -25.972414957900902, -30.924003375390246, -29.536224592461775, -19.32456208498821, 1.5991161282153419, 34.10061947025166, 77.66034625856078, 130.14156735124385, 187.76234443731, 245.26462016614894, 296.2903623278222, 333.94689861064154, 351.5076513237216, 343.1739760303929, 304.8096413610555, 234.5561177724394, 133.24538688163253, 4.5469607925317925, -145.18487023476234, -307.3623294964489, -471.87607811045376, -627.9965348786177, -765.3679015447871, -875.0107268383398, -950.2692386328031, -987.360178908398, -985.6119201251383, -947.3947771469925, -877.7438682627195, -783.7300719453849, -673.6619776556477, -556.2176284091265, -439.60771700065914, -330.8619338130575, -235.3092762019479, -156.29459519309356, -95.1416238400039, -51.341619160162864, -22.9206198047198, -6.920833982622212, 0.07969480201675117, 1.4755705324188175, 0.22308155051857273, -1.4344923650579386, -2.088493883820784, -1.142909411875731, 1.322466916012411, 4.762571721923645, 8.405589990563573, 11.47673225348125, 13.373723496683075, 13.773595706222624, 12.664911461710272, 10.312974125025088, 7.175857648985179, 3.7951408710789294, 0.6861755260024396, -1.7532325071139565, -3.2992420139874756, -3.9171735979648568, -3.7384407236145902, -3.0090206727928854, -2.02348148655719, -1.059547568734667, -0.326122559052183, 0.06665072909849735, 0.11222553832406372, -0.1102073059509254, -0.46948894207659264, -0.8228780079942587, -1.0534192182657576, -1.0963572561063135, -0.9497566667535248, -0.6685879966262989, -0.3455568777696785, -0.08417314655178898, 0.02916338961372473, -0.052435203959548975, -0.3242847496182756, -0.7306592520989356, -1.1772690537674997, -1.55246507776083, -1.752199407577821, -1.7031715878099492, -1.3791984473094252, -0.8074734393683684, -0.06364037372939531, 0.7430510940992572, 1.4914495280646094, 2.0718350399886853, 2.4057931245777873, 2.459129345300977, 2.2456876490838313, 1.8218565996623384, 1.2734107994936699, 0.6977506024615526, 0.1853160361871048, -0.1961384980736148, -0.41154585765523166, -0.4612877381209407, -0.37676451597531313, -0.2102731703626252, -0.021741593691168973, 0.13468707324349857, 0.22143477631093747, 0.2234563500041887, 0.14858846536854764, 0.022836422748035913, -0.1178543313265101, -0.23718193278482697, -0.3071698536752543, -0.3140878422305571, -0.2605231793099728, -0.1634610254022968, -0.04913955653864059, 0.05388337774681761, 0.12171206379379244, 0.1405116483139293, 0.10916374211967024, 0.03873811518365967, -0.05090845612325231, -0.13652048551795856, -0.19726682475965618, -0.2195746619183645, -0.1998923834232153, -0.14484928602685024, -0.06893474436014278, 0.009591377705210295, 0.07345619043466224, 0.11059136288160672, 0.11679163315570296, 0.09622293256875993, 0.05974575426767126, 0.021567860478826403, -0.004851979934834064, -0.010558197750346339, 0.0064751350651312085, 0.040898230084108964, 0.08161503810677478, 0.11502240366631655, 0.12898511515302866, 0.11647563337372357, 0.07787879312415838, 0.021286784240415742, -0.03938861025436613, -0.08810073331504416, -0.11128266882704466, -0.1022397004083748, -0.06415398767144621, -0.010806992455531786, 0.035371949907147406, 0.04769579932947863, 0.001188713354367848, -0.12119250937519244, -0.3235141783319484, -0.5942134733069806, -0.9065872362134443, -1.222513415652482, -1.4987948182604671, -1.6949223733538408, -1.780704153064818, -1.742179103121268, -1.58454481032057, -1.3314182909213539, -1.0204981990424042, -0.696449700346798, -0.4024290315214949, -0.17197566157315597, -0.022917236647790377, 0.04539414352549129, 0.050875556346906006, 0.02395891701044638, 0.0003529831297434348, 0.01286630888239359, 0.08400715591257532, 0.22088983418206926, 0.4134762704769549, 0.6364751113464026, 0.854457909632018, 1.0290921602146625, 1.1269698830967296, 1.126412338588569, 1.0218719628968682, 0.8251243921513188, 0.5630473373572229, 0.2721258832198918, -0.008511739115430463, -0.2441162737355787, -0.4100515454014712, -0.4951881764855772, -0.5024574946782362, -0.4466885678065512, -0.3504053948658342, -0.23863175694616365, -0.13386915656266984, -0.052269118968875664, -0.0016641541005689802, 0.018353728443416272, 0.014595707555321349, -0.0026598010197876757, -0.02286434751170366, -0.03787263415662574, -0.04347514195159704, -0.039574351772559836, -0.02918939111622946, -0.016766243856924195, -0.006401135532850356, -0.0005295538252495935, 0.0005778256904472691, -0.0015335720527094915, -0.004463250929585091, -0.006099416179860706, -0.005482023626001067, -0.0030534389139537195, -0.0002210322249494245, 0.0015471046144036923, 0.0016374643754385586, 0.0006805493476653104, 5.464199985923349e-07, 2.991965277179762e-05, -0.0019817541309981586, -0.014228408555788457, -0.051593990253199655, -0.13493069835846985, -0.2877740935470632, -0.5305528481032636, -0.8731659844408967, -1.3075728382549765, -1.802534977088827, -2.3026577243538835, -2.7332849010653684, -3.0117614714810146, -3.064084509497698, -2.842779192165189, -2.342692855003766, -1.6103798535031864, -0.7432420257817485, 0.12357635331800595, 0.8419467498303843, 1.2835858760504448, 1.374634809127511, 1.1238855580121248, 0.6363529480840949, 0.10564271566175987, -0.21773478836554588, -0.07976927829592975, 0.7100471747896787, 2.2115180193640764, 4.303551677923247, 6.667150706754956, 8.813455950131868, 10.161358838288074, 10.159057141232473, 8.433013238647728, 4.938064689278881, 0.07617477956413637, -5.249596507275797, -9.673692830807767, -11.514750828124017, -9.028122779669276, -0.74108992540994, 14.173004960362842, 35.54196044408488, 61.9308955611167, 90.53504196278384, 117.2911512098641, 137.21334559926663, 144.9399461814592, 135.44167892297173, 104.80695192299218, 50.99596382709708, -25.55423497302549, -121.58382989381255, -231.00776255219887, -345.2993079261553, -454.24974952261783, -547.0377856474613, -613.4904032413617, -645.3779377656684, -637.5877980782351, -589.0183976481562, -502.86120177873954, -386.3752168168492, -250.1533630663842, -106.93975370102008, 29.85801271084139, 147.7708223735921, 236.77288817838289, 290.4869850876798, 306.9254296621414, 288.663959100007, 242.4228900882987, 178.1116283172065, 107.46699682395074, 42.472131134764005, -6.224656915449474, -30.692212659239722, -26.722064983746307, 5.746373397069211, 62.791800413279745, 137.21274672553332, 219.64342369254513, 299.90862925352315, 368.41689777637583, 417.39569135365605, 441.80537895722205, 439.8238451403259, 412.8615550588464, 365.13699027626143, 302.9039548131679, 233.46652935830045, 164.1393604857668, 101.3058148989087, 49.69582294191342, 11.976753930703532, -11.315658874931668, -21.534094733820723, -21.43601798026914, -14.56100796953218, -4.5810303390355624, 5.272579869580308, 12.625643504914802, 16.175789216912438, 15.698037076921107, 11.869421460259524, 5.967565684059188, -0.4872661516989431, -6.076439769610521, -9.753669167089866, -10.998761968737151, -9.84758588588947, -6.810343640632962, -2.7084244967386377, 1.5284289853877413, 5.060804084175714, 7.29648582257423, 7.980243876219921, 7.206952544299879, 5.364175227518375, 3.0231782020263807, 0.8051897842406354, -0.7483754061227043, -1.2768096494609698, -0.6553687946585919, 1.0022391033186642, 3.389251155893185, 6.082732764573418, 8.633406406541349, 10.649836135835898, 11.861751763761191, 12.153246605147118, 11.56356155489653, 10.259690369964424, 8.489888472849383, 6.529597457451828, 4.63113429116816, 2.986101098205329, 1.7056174446706962, 0.8191367774340081, 0.28875411580741134, 0.03316635424250406, -0.04538816505218794, -0.03731717800872249, -0.00977117320881686, -0.00031740969918014455, -0.019266623073161182, -0.057905519406383756, -0.09906788720226356, -0.1266855056820377, -0.131973625211844, -0.11533682111586929, -0.08449178197919913, -0.05032084237854746, -0.02237224342202307, -0.005681853561534343, 0.00013953135210561897, -0.0004498552615287907, -0.0017175647447635316, 0.00041556265150542943, 0.00656920998412123, 0.013936594423934183, 0.018085449912133948, 0.015690679731351083, 0.006899373963999413, -0.00394328761436445, -0.009922951951297894, -0.005306387956046678, 0.009884288622487657, 0.02659754646109074, 0.027162241004019858, -0.008750567539815911, -0.09205645114604448, -0.20744837296572546, -0.29513034585664727, -0.2358511136449412, 0.15541661490207379, 1.1224824974351755, 2.9449339238208077, 5.8994583768831586, 10.209398141932732, 15.989821097752465, 23.19780521449222, 31.598420572477437, 40.75565675608243, 50.05427250905282, 58.753648930872046, 66.06899694724669, 71.27172659893795, 73.79731363162402, 73.32620974307416, 69.83611091312889, 63.61577014496013, 55.23483944333692, 45.47305076875515, 35.21893386542239, 25.35356745620836, 16.637567689608062, 9.619087050738168, 4.577050221337226, 1.5077901711807327, 0.1557443950112946, 0.08128699845650983, 0.7524977914391149, 1.6439273417293667, 2.3248811781982353, 2.5211823391827397, 2.14098243802984, 1.263180130121001, 0.09400775279874182, -1.0969566336997147, -2.0468954906644, -2.561315849388711, -2.555108181139279, -2.066077265479652, -1.2400251042152213, -0.2924547414048636, 0.5433762989440983, 1.069904167759876, 1.1683077841129945, 0.8220352295550555, 0.11622751571413234, -0.7861221216656175, -1.6845697429040685, -2.3879345741733786, -2.7563979908822027, -2.729648979803637, -2.3353456672667696, -1.6769356451500839, -0.9047067943825683, -0.17772793876517065, 0.37376197139752754, 0.6763604391820203, 0.7253453607461026, 0.5779819068164087, 0.3307116275256167, 0.08691465908301337, -0.07541531675544823, -0.12618501947150892, -0.08800668239241355, -0.02012315805952173, 0.016342321525679254, 0.004383831040762856, 0.017083454302550784, 0.25079763800736565, 1.0341709641335022, 2.8057005251587506, 6.058722586885023, 11.259703900663098, 18.752173607837378, 28.66314625714685, 40.830400571953966, 54.768132817404826, 69.68568083005782, 84.55266952883117, 98.20676390096553, 109.49032834013987, 117.39514352635982, 121.19289806662987, 120.53099210568926, 115.47857037306045, 106.51569111989473, 94.4677116434541, 80.3957027286302, 65.46046383843895, 50.78134781154818, 37.31105309522017, 25.743917545957736, 16.4690510525786, 9.570615329335459, 4.869891566728127, 2.001251314868565, 0.5027228560810674, -0.09626184884993373, -0.2040705437652244, -0.12226515882414572, -0.030392402586440326, 0.0025588603654047104, -0.012529972658054195, -0.024703327254433863, 0.018616469410820183, 0.14311445259228744, 0.3341440438318388, 0.5393268810363977, 0.6842427740507162, 0.6954104641907806, 0.5231295771634271, 0.15781413994529145, -0.36433803193189557, -0.9675577868863051, -1.5527484078212082, -2.0195092988002976, -2.2884537669769527, -2.318478428109906, -2.1150474304829103, -1.7278259846079074, -1.2385612259181393, -0.7423523010976383, -0.3268655867838198, -0.054338491461257764, 0.049651069707602455, -0.0016513580315033064, -0.16317307054557365, -0.3716360922944543, -0.5620317623695036, -0.6828327873950583, -0.7064308799185567, -0.6327091069804215, -0.4854985040815675, -0.3034568289168122, -0.12820538802006373, 0.0069333829713993985, 0.0846350112119085, 0.10588505832678274, 0.08666198167687152, 0.05034882458289455, 0.018425009211926115, 0.002456522321025304, 8.257411417745652e-06, -0.004075574993037637, -0.031239021430221857, -0.09947889850231714, -0.2132911467578859, -0.35661704362552576, -0.49151557850184263, -0.563884210059793, -0.5156609311536214, -0.3010339224758468, 0.09724052497124322, 0.6558482801013302, 1.3071293358884806, 1.9457490458747169, 2.4458105597232063, 2.6859190267129245, 2.576365334284536, 2.082570567532789, 1.2392249034524017, 0.15103149632709764, -1.0212924076401306, -2.087916316638043, -2.864881033299566, -3.21026417633534, -3.053946416278572, -2.4143515462829583, -1.3979897147188038, -0.18112465755503435, 1.0233063197457095, 2.007089774812312, 2.6080769420252787, 2.742811105479861, 2.4221132617942818, 1.7467049531587888, 0.8840015655242439, 0.03104189879151654, -0.6283656056965755, -0.9628856166193459, -0.9206396560096781, -0.5379598690523504, 0.07200821341801028, 0.74822626930454, 1.3215396818823772, 1.6560354254795357, 1.682166402018079, 1.4135467207088726, 0.9430269376493404, 0.41846463482700746, 0.003345852652069501, -0.1677622302394293, -0.027694670860298476, 0.40105581010680236, 1.0070820544121992, 1.6153701455603788, 2.0328515754443597, 2.1046111588975642, 1.7677346176848598, 1.089078709152146, 0.2756123481900362, -0.3488942231641143, -0.40008044370951157, 0.48609533715447495, 2.562446761388791, 5.889099512000381, 10.279768475941957, 15.289237434052465, 20.248896547675166, 24.34826100838384, 26.75147678185646, 26.730541503122776, 23.792804991830153, 17.780158602382645, 8.921325229187083, -2.173813260952026, -14.57917858395086, -27.16787772377232, -38.76033276632916, -48.281709241002424, -54.905200519565696, -58.16176156414259, -57.98377542596596, -54.68693440771501, -48.89879435427528, -41.447867867383906, -33.23381325251954, -25.10094703718652, -17.73495143201842, -11.596942295121623, -6.901272953977863, -3.6351577481599087, -1.6109900928261662, -0.5373837209426645, -0.09322768764186617, 0.009492546542920165, -0.015756411596245332, -0.0457440282384057, -0.03901725295625587, -0.009848256738139934, 0.005537981403957185, -0.019879840116422513, -0.083582754655776, -0.1483453687622308, -0.15206310144599602, -0.028311521263492182, 0.26932474150075825, 0.7468703669135114, 1.3599676133680907, 2.017810565328545, 2.6007677569034837, 2.9877616571066934, 3.0868813491878435, 2.8615974546471383, 2.3445760763676167, 1.6359261542718317, 0.8856105318408073, 0.26341045996255286, -0.07706356294922481, -0.032312260463098784, 0.4268334777935445, 1.2462999190568949, 2.2973831462871743, 3.4012302159766565, 4.364023156305988, 5.015347156172785, 5.241550724005163, 5.00705401286199, 4.359354364067924, 3.4169358666493506, 2.342379377217441, 1.3080957867704661, 0.46222095767978516, -0.09816748231209252, -0.34120199750297087, -0.29950818365391063, -0.055824352972933367, 0.28082170846283866, 0.6022491923007953, 0.8250482317425373, 0.9059285502939789, 0.8455317024179206, 0.6807785099089843, 0.46873553493016784, 0.26706283869161374, 0.11680664951336076, 0.03253647788148281, 0.0027075013697797235, -1.0213545409514144e-05, -0.0015074806469557226, -0.007264807257775792, 0.012434616264648765, 0.12792959218399413, 0.44321457463532443, 1.0766195691176808, 2.1324412343059285, 3.669511502586014, 5.674104819268136, 8.044322225025958, 10.591112645851409, 13.05830092523559, 15.16062863079935, 16.62871391215981, 17.2546620523409, 16.92965155692981, 15.66548207199521, 13.595484479270272, 10.954269937510515, 8.040023207654958, 5.166528366326011, 2.6141103404512753, 0.5887592478038156, -0.8031373930223143, -1.5603947681626753, -1.7730588624101535, -1.5929977266833417, -1.1962850695589005, -0.7458369854716069, -0.36197927600086105, -0.10748448804422009, 0.011320206535831821, 0.029742894528529448, 0.0017008914730902809, -0.024314676799952938, -0.023209779835815247, -4.587944608708157e-05, 0.016323265737078443, -0.00911420153654625, -0.0938287993114899, -0.21529394211257874, -0.2973611051310567, -0.2113486415768672, 0.20566455740419853, 1.1174228710138547, 2.646485794037632, 4.832741363113032, 7.602517471824451, 10.75698529344452, 13.985051728120569, 16.901030198529437, 19.10206767173464, 20.235724984719912, 20.06527382649947, 18.519866241575937, 15.718941372208722, 11.964708323835133, 7.702451086094376, 3.4545883745431873, -0.26015585531541235, -3.0091188328158354, -4.515403924779308, -4.697730742588861, -3.6755399994262348, -1.7397984777618416, 0.7041797131049112, 3.2105504115187777, 5.369339080030848, 6.871443213202375, 7.551025263895786, 7.398913085547703, 6.5464931694871025, 5.225288778976273, 3.7118288568840527, 2.269699188948214, 1.1003758360684357, 0.31200024176250235, -0.08850452745612114, -0.18132907508263718, -0.10268693119463347, -0.0049220590097079995, -0.01727658802243202, -0.21587258217187172, -0.6087924092811475, -1.1383964661681427, -1.6990667300102107, -2.1652744445556373, -2.42291348126915, -2.396565045550455, -2.0667273936144066, -1.4736608911480455, -0.7077115901758453, 0.11125039591792953, 0.8598850382819377, 1.4359843702836095, 1.7766052860882398, 1.866386626552517, 1.7351198738166929, 1.446132238808151, 1.0789690955432494, 0.7108315550810514, 0.401084065963623, 0.18201237574486523, 0.05722392244538465, 0.007112817458634082, -0.0008535206740741563, -0.0002443811365280859, -0.015481770203630188, -0.055928035959584545, -0.11541730905391365, -0.17671908057656294, -0.2190731221025067, -0.2262248657537201, -0.19244133592556795, -0.12474049254277383, -0.040782097901315525, 0.03680470027665417, 0.08781157811743284, 0.10119138124803499, 0.07894734050837766, 0.035779730005019786, -0.005666334270611335, -0.022782868043319603, -0.001992722933397894, 0.05396412789161643, 0.12294688669948908, 0.16586971885023916, 0.13456796532980353, -0.016514022884095512, -0.31753620265684807, -0.7725828698171863, -1.3539828077350085, -2.003467990649592, -2.64044946044174, -3.175992426056639, -3.5296497467464336, -3.6455173300706125, -3.5039163477855597, -3.125997672834298, -2.5701941748532495, -1.9211184204197669, -1.272694324108057, -0.710345638585793, -0.2958971252656184, -0.058168895509857134, 0.009044219014967969, -0.058345055270225675, -0.20567480080064862, -0.3732600717082248, -0.5095765028530476, -0.5809655124130176, -0.5759845810251885, -0.5039772790932815, -0.388898501814012, -0.2605277245151337, -0.14567953385746968, -0.06171386453124854, -0.013790675955782889, 0.003712734486015256, 0.0027930740747401698, -0.0036949920191224413, -0.0066768941697269565, -0.0031529335486563136, 0.004342979217754607, 0.010524679797501211, 0.010950526547842475, 0.004741410032732229, -0.004862557072104757, -0.012406057412893553, -0.01365762829574979, -0.008660119487602673, -0.002171816885251765, 1.5172790279569587e-06, -0.001500020652841164, 0.008929073556461243, 0.0661460469598118, 0.21749042338080735, 0.49830911427550223, 0.8855840837886794, 1.2302509579383774, 1.1753112478814487, 0.07388841728950662, -3.072683050727854, -9.633591774322321, -21.30230764137284, -39.97015936479524, -67.51623269273131, -105.52888588599943, -155.00251481965648, -216.03372340617457, -287.57169792631464, -367.2763647440055, -451.52442211672536, -535.5872306936764, -613.9806396535937, -680.9599364087278, -731.1075968008166, -759.941901773438, -764.4646454480351, -743.5685526928781, -698.2401642938452, -631.5201716323704, -548.2168110147184, -454.4223698775751, -356.8890676631755, -262.2082917445839, -176.1096908430076, -102.92856230866543, -45.28143453094135, -3.9803476965451217, 21.820595619644134, 34.28690364100839, 36.439753490587385, 31.645989255163535, 23.14115714615618, 13.651292503469518, 5.156040495623889, -1.1924393206962227, -5.008080598822007, -6.50269136112839, -6.260448671906144, -5.005690806743217, -3.4077144967191555, -1.9540555942754219, -0.9020022737041781, -0.29904358343387655, -0.049365699354371524, 0.0025642947483620563, -0.0015908719224240592, 0.0210693935621068, 0.08517814786207019, 0.1575434276883603, 0.19314917694924055, 0.16881411448521405, 0.09923698146630562, 0.027911232103375535, -0.0041553647564185545, 0.0008830566252469441, -0.033790490670371, -0.26345881184163866, -0.8858992936442379, -2.0651716024759286, -3.828632053915378, -5.96316710254832, -7.943983602648085, -8.928609572134476, -7.83891662273322, -3.536019038830281, 4.929963996362202, 18.036241407895147, 35.52823489585724, 56.250995015936105, 78.13328039676958, 98.35459531132422, 113.6915864980276, 121.0116592898533, 117.84586231327026, 102.94825651888739, 76.73923210553988, 41.53856910576603, 1.5204928192465357, -37.63581158086545, -69.37712985564109, -87.11575492470185, -85.163775136879, -59.62377242694018, -9.094894856815246, 64.92696401638091, 158.06514191698076, 263.5102463114392, 372.77978453833833, 476.70025443474805, 566.4774940113177, 634.7056788723115, 676.1778870230618, 688.3942856788268, 671.7117628111432, 629.1330912321122, 565.7856152220936, 488.18091373144875, 403.3719424802272, 318.1298106458207, 238.2489747900623, 168.0661350789949, 110.22396512253131, 65.65220377067641, 33.80718925239383, 13.063275175354637, 1.1635738034111875, -4.346792828558774, -5.764868385165623, -4.987526173377492, -3.3930539169512204, -1.8344771187141005, -0.7163433809347494, -0.11887790982165165, 0.0661707973986705, 0.016662419849979418, -0.10414622466729015, -0.191487826509367, -0.20725561926776329, -0.16349394861636057, -0.09552182320958648, -0.0371143770743913, -0.005497475376635931, 0.001552306905032919, -0.0010630089198276418, 0.003055207214051068, 0.021963410464385037, 0.051084881501980844, 0.07589237258953048, 0.0800389300453534, 0.055265435282354246, 0.008709214116164973, -0.03587690601520309, -0.04436285947190261, 0.015361190271686101, 0.15865803914969845, 0.3720652919437476, 0.6083557692533127, 0.7913999168908346, 0.8307328137463814, 0.6428460955363022, 0.17404928384236254, -0.5810913418629013, -1.5709575908835105, -2.690740139778415, -3.798877962909188, -4.742827796457662, -5.388489982535633, -5.646578228159843, -5.489815851193403, -4.95712634154301, -4.1441414840422715, -3.1819579465280987, -2.209734928479908, -1.3477595493711407, -0.6770795893461516, -0.22985157262113998, 0.008350412935427756, 0.086085755167856, 0.06769827314452681, 0.014462601649110448, -0.02974962985635996, -0.0449974492422022, -0.03327429817960668, -0.00990535053189788, 0.007824162687593585, 0.01032199445701356, -2.8145943602120444e-05, -0.011430645550972854, -0.011026960638823934, 0.004325090890417071, 0.019464490422824506, -0.0010858904425881171, -0.10597019195170924, -0.3410261750035994, -0.7280842160464468, -1.2447466347453018, -1.8124197815873067, -2.298835610590328, -2.5381502952278816, -2.3670388714819866, -1.6701424113184693, -0.42336957618358545, 1.278130572086396, 3.215988472276721, 5.074050399567163, 6.491831949920243, 7.137183409589603, 6.783342744311335, 5.372473046457174, 3.048753042112769, 0.1493461469042018, -2.8496707767108345, -5.424805778700991, -7.116499705038645, -7.635822710542774, -6.940166757694706, -5.256240088287309, -3.0385390521114126, -0.8617785206693979, 0.7300578187306215, 1.3856432325012404, 1.0816750544443825, 0.1958875447163799, -0.5076994466144703, 0.010431041921822924, 2.8708723526622837, 9.029625316180713, 19.028421045125814, 32.79433641752824, 49.53719443814474, 67.77764559203061, 85.51482998577892, 100.51824001748788, 110.7045818161457, 114.49871097147106, 111.1279963740619, 100.79146196398213, 84.66244986730618, 64.71726011083621, 43.41610825083963, 23.29275366522698, 6.529065536235303, -5.40381399786457, -11.966846631696557, -13.591605416152072, -11.526064749086187, -7.516715227971603, -3.390526444408354, -0.6232616372182135, 0.014139641331951627, -1.349545739126061, -3.701420319505382, -5.372752611121855, -4.4396562868818235, 0.7806976511640022, 11.23800473591607, 26.764401688312404, 45.88489565313181, 65.87602679140379, 83.08082365769, 93.43959744658468, 93.15346300616409, 79.3687856522596, 50.76168854696889, 7.914167901131052, -46.60827330252269, -108.50516007051587, -172.25227197667772, -231.80513943189686, -281.38754953083486, -316.243129688736, -333.2363646360651, -331.21624838046057, -311.09594902715537, -275.6480593882674, -229.0591976432328, -176.32261049362793, -122.56767803731148, -72.4282793429428, -29.5383935686527, 3.7834829574673923, 26.63931495237525, 39.446738268473, 43.65547581447043, 41.36564035318078, 34.9221482811179, 26.550330344036265, 18.081188115326288, 10.792482419088037, 5.368554073025439, 1.961650038957574, 0.3236205915247287, -0.029307577654087945, 0.3455181026829415, 0.9483723823311813, 1.4207972984744353, 1.5774982291594868, 1.3930201577885166, 0.9565756910112919, 0.41368987984377564, -0.08889306794384796, -0.44348473100117664, -0.6013573290243043, -0.5726510194879352, -0.41118320481899284, -0.19147960579443873, 0.014450968452171871, 0.15468743333049245, 0.20608743845845084, 0.1737840893539391, 0.08356587539452469, -0.02939442870913977, -0.13177410779687881, -0.2003995107217442, -0.2259336385268639, -0.2119704434520105, -0.17088646058615892, -0.11834983884837158, -0.06832874040755478, -0.029881043230277887, -0.006201017287712024, 0.004374811745831267, 0.006221398803192855, 0.004117911869926171, 0.0015765361872304203, 0.00019840312514349362, -1.0936049069884215e-05, 0.00021845222299441997, 0.00027980080030168416, 0.0001081591484577174, -3.2668887711853275e-06, -2.3267579778619705e-05, -0.0008384120699064394, -0.0044953524875873336, -0.01373639433821894, -0.030838519885043804, -0.05610552127353165, -0.08660935985282771, -0.11582682332968854, -0.13462838430693513, -0.1336831650517052, -0.10685374556166635, -0.054716553983160686, 0.012893336420900016, 0.07635470685675019, 0.10842216710967117, 0.0789391418627277, -0.038725590548982225, -0.2608414215987383, -0.5876956304689162, -1.0006799720581414, -1.4630621780635211, -1.9246280342845703, -2.329490851766748, -2.6255949591443217, -2.773981677560975, -2.755862490971152, -2.5759738286853495, -2.2614795691105845, -1.856659401042999, -1.4146326512683085, -0.9878328122810929, -0.6186918168236191, -0.3335654767193418, -0.1406224731123176, -0.03162277562284942, 0.013237029716993429, 0.018856613042865806, 0.008817204934289896, 0.00049940343281895, 0.002673185064353312, 0.015772990906103637, 0.03435576743462151, 0.050721180152484155, 0.058474447713098295, 0.05496601036350448, 0.04198701535933997, 0.0246858732486478, 0.009219715292649115, 8.625872704822222e-05, -0.0018930617897719194, -0.0002276971762822354, -0.0018070838222003943, -0.014634149295868197, -0.0449650136161723, -0.094778045098612, -0.1604083510645439, -0.2328369856395468, -0.2996234358951537, -0.34796661415502794, -0.36802595336464494, -0.3555387018519196, -0.31298716018391926, -0.24897162124866498, -0.17578704911490226, -0.10617083740577321, -0.05017384578753379, -0.013031681597555871, 0.005402942055045031, 0.009615812851224191, 0.006238253399594458, 0.0015209447887489218, -0.0006380999976884379, 0.0005396562220437331, 0.003331933300604379, 0.005152151836774684, 0.0044061905628317525, 0.001629732407774857, -0.0008019881795318008, -0.0005355199556034904, 0.001932571464990738, 0.0007243596110349331, -0.016137678550548634, -0.06440899206294445, -0.15788803979027857, -0.30013447528416953, -0.47578753657017714, -0.6445249058147147, -0.7408150485797745, -0.6817199231659103, -0.3831368820586336, 0.2176290353353328, 1.1375923825227794, 2.328544557627949, 3.669033906325875, 4.973395022495828, 6.020028030237282, 6.5953782642945535, 6.545945188005863, 5.826830440307454, 4.53375832698589, 2.9070573739814236, 1.300892638765323, 0.11846025869252062, -0.27749077097324776, 0.33851000357973565, 1.972960577475465, 4.369952787227879, 7.024264991714782, 9.259114152221596, 10.362408192359611, 9.759100153951957, 7.18865081179952, 2.84778278879073, -2.538636324103481, -7.745385905738391, -11.183329875150722, -11.133236601008486, -6.044323005366464, 5.152218878444821, 22.77323069371717, 46.213486923516705, 73.9181478481309, 103.5169633747346, 132.1101161214992, 156.66591265365918, 174.47561666319316, 183.60125996926615, 183.15508821928202, 173.41491426842708, 155.7574401537869, 132.41607727417517, 106.1097033513146, 79.61239873676855, 55.34379400567748, 35.05322815626394, 19.649789026308035, 9.198940601133225, 3.0715415650657873, 0.20018900704380732, -0.6222296708310453, -0.47163902030265875, -0.1077316156933489, 0.09236094943639847, 0.08158081623284485, 0.004380288843507635, 0.028685930775128793, 0.21160045958614324, 0.4491720674528869, 0.5311977190183835, 0.28304192826504476, -0.26230651910745323, -0.7464699303149251, -0.5142365285094049, 1.1376929474209199, 4.461582516292713, 8.541957385574708, 10.464693277961645, 4.5386513460279545, -18.225235945265727, -70.1841856686034, -166.52923636622887, -324.07462418387144, -559.4109150174746, -886.5830553922578, -1314.5651917614898, -1844.882884572005, -2469.7628061029704, -3171.1600485330787, -3920.923257751442, -4682.217709256299, -5412.155103573347, -6065.4016559845295, -6598.38079078215, -6973.757143585373, -7164.870420755144, -7158.063485839043, -6953.8808842721055, -6566.936889670019, -6024.327962292969, -5362.808370974866, -4625.097385333755, -3855.780899181337, -3097.2983141511995, -2386.466107467669, -1751.8919093894374, -1212.4944598772668, -777.1878821468607, -445.63698470436964, -209.86502329569421, -56.40746957252949, 31.32867334630581, 70.7607672428971, 78.19631242367366, 67.46340691116797, 49.15817092548689, 30.468599007385432, 15.463715879043002, 5.6958957794095495, 0.9537173492500611, 0.018741197064127024, 1.3145474401634178, 3.3809671333841096, 5.151509984114726, 6.0500022147022765, 5.9485249004593905, 5.041191342724616, 3.6872689640922105, 2.2664940052228286, 1.0771597156257129, 0.28613645766888507, -0.07416863615187638, -0.07565992512671554, 0.15166610207719464, 0.4662934776790621, 0.7509533256943574, 0.9322367279154826, 0.9841063657880479, 0.919210437980453, 0.7737212563134578, 0.591328030651582, 0.4105554389331392, 0.25751332558012097, 0.1441029268441966, 0.07026561513733826, 0.02853069091651597, 0.008709514660675878, 0.0013932174995534294, -0.0002349800910372536, -9.225722906763532e-05, 0.00016488781397535948, 0.00018036197095602912, 8.130726909624008e-05, 1.2285456408698121e-05, 5.363599051428373e-07, 6.354605411773732e-06, 3.056038298884036e-06, 1.4170623069779286e-07, 1.0650135390777673e-05, 1.669977948204575e-05, -1.7003561101829797e-05, -8.023205009830043e-05, -5.7235229989965024e-05, 0.0002585433160562413, 0.0010374290918965118, 0.0022122081353464986, 0.0033185794700985112, 0.003525287803825958, 0.001953735065049106, -0.0017407322109179492, -0.006718795076462366, -0.010561188791849314, -0.009466811347601682, 0.0007585365153296488, 0.023022165345568654, 0.057059280989916354, 0.09810226894148696, 0.13688116818511073, 0.16149263836245079, 0.16110538316353568, 0.13071556900146825, 0.07544791680863529, 0.012486757071354944, -0.031144067063763575, -0.02593161751345403, 0.04807074774461016, 0.1866399679756952, 0.3479961302559403, 0.4453469420302617, 0.3499015225620758, -0.09268583803932584, -1.032577978845474, -2.5767753655063586, -4.7481447134908406, -7.452029668646011, -10.460377973221823, -13.421263078864126, -15.897304292182408, -17.430463545988875, -17.624198695858148, -16.228456881285908, -13.20994859894449, -8.790630889400548, -3.441741886801606, 2.171401069785179, 7.288638609574668, 11.18327236580046, 13.297345617464613, 13.352009255051666, 11.408253624053904, 7.864556065460251, 3.3886709141139373, -1.2054839397312058, -5.112698096191744, -7.692102046296412, -8.591047192799566, -7.8102238425273605, -5.694717757752981, -2.8513575700148963, -0.009021711661665342, 2.148070782580302, 3.1368461811151755, 2.7854857636185266, 1.2699483260316538, -0.9363062820380247, -3.1873823562000654, -4.835713398878834, -5.4084353596476245, -4.746283494648688, -3.0689280388876505, -0.9463309894947789, 0.8231592033365824, 1.4052078755376984, 0.15160362262161328, -3.1984281692700063, -8.387016169487831, -14.613415793563313, -20.632132873464858, -24.962375106845858, -26.17035327612234, -23.165694200153144, -15.451340394446081, -3.273714649504103, 12.361567786118961, 29.81666232335345, 47.07074103375748, 62.0462899616444, 72.9513265593118, 78.57277078070814, 78.46562350696647, 73.00317105671941, 63.2809268996461, 50.89579189307847, 37.646056732822466, 25.21512969141603, 14.896331402659097, 7.396461044388125, 2.7893277553475455, 0.6019974724598014, -0.00036995631520124944, 0.02176126499054486, -0.18393569226663586, -1.1793495550419615, -3.1390261316207653, -5.851493114959454, -8.80939709546666, -11.360515751748359, -12.880680261732605, -12.927990830692874, -11.34513484722983, -8.291978348666863, -4.207635414787949, 0.29359068631288987, 4.555257992544346, 8.008844848945355, 10.273528606746218, 11.207053943284924, 10.902027263339273, 9.634891500784974, 7.784706306933229, 5.74366488734757, 3.8403797906839787, 2.2911483642180364, 1.1855785895617266, 0.5036183461975179, 0.15361511805896635, 0.017295789909622102, -0.011922871262603055, -0.006392382230730211, -0.0001243221086692541, 0.0005156933594133381, 9.114484194055482e-06, 0.0004282419533429896, -0.0018373674367101872, -0.008903674879328456, -0.009597017297788033, 0.027184416099659606, 0.144564627355342, 0.37102148314521444, 0.6793029725711722, 0.9442926427807785, 0.9190377492712215, 0.24737357169807864, -1.4851430942751491, -4.6784552084637525, -9.633721502375273, -16.47599640768231, -25.101014666478164, -35.15753493895372, -46.06925620659494, -57.09265655822894, -67.40084295065003, -76.1797027771621, -82.72169015043617, -86.50421310327576, -87.24311578266332, -84.91625645884557], 'positive_zeros': ['0.10825706632679258635360455874999', '0.26512459208611921806128814012797', '0.76297326103762787394005385552548', '1.02146925367122762901840987462235', '1.14522633961299544255791614652214', '1.16910553672279480192056533942217', '1.52385376132949931977552105724408', '1.56201327682714092690743358828641', '1.69491017288764090557004220601242', '1.99755064699342348727652420379086', '2.08722869571862524433982341014285', '2.23407725220550549929032229678169', '2.34602497499229229261589002136357', '2.39451353829254491026770772904211', '2.49071078637066401221928321429268', '2.68773553083683797449845834260366', '2.68908430737767456604877369373940', '2.73000152537449838374614107166538', '2.91589639941264496792319099523688', '3.23829373841088735411106114939798', '3.26014392114705490427152221697144', '3.34214014808263500421882144759608', '3.34961795409989662784877299079947', '3.41864965395403729910714755149139', '3.42071960558415044116746557829286', '3.63409029676305589064330915256296', '3.68938642318005316063893050996228', '3.87236494851724605967228919680170', '3.90960802614772315777528798469137', '4.10837837550872020640314920000936', '4.21623491613533889645173339489382', '4.38231872036453389023391747881427', '4.56435458000215151691236704002756', '4.59550937691774711533506257285887', '4.61180020966965048895209721159086', '4.65891237354220929603585914838661', '4.73376173253909935509704277017918', '4.77169294591676266083162836540552', '4.82558696578187842902816131348542', '5.01057083568692735415638567865086', '5.05135856991110003713158344368315', '5.33468593298165074391683364620773', '5.34322619330605735318086113948099', '5.38916051242331350707671932014172', '5.41237667505948924686997216195265', '5.41438502334537938249381724003541', '5.46684133858223835827953500284370', '5.65365524298172145440208653983922', '5.72436985348625344223956305427151', '5.75582316581898929064531559277129', '5.89336514902468575432167746146546', '6.06100646258279122653551904142689', '6.08301328856159202755332833712601', '6.18397529816965881690424606921395', '6.26688018533525329656286858163663', '6.28739131984038355139740053337360', '6.36156764574078866352997470779035', '6.36660832090504608841269492823585', '6.67192114236798560048218625224115', '6.71997090172633183415682935251262', '6.85163669563923634860585531508874', '6.87193336410669702094728097777388', '6.91412534827963263430886338534821', '6.91572204326723053211699795222022', '6.91679002278921590197432124932579', '6.98708694077748555200481699385921', '7.11190797096484576127138253823434', '7.27054852377895917001840475035115', '7.30299687571664515306954695306894', '7.34871972003398701485825518481151', '7.51463156979200030998506258935067', '7.55481144706274935005954415815952', '7.60603635403062537086237685305579', '7.65970668680825106195182778336434', '7.67907791018642994690443039890874', '7.69774462672846434441974684145877', '7.73732915790387707471290443383342', '7.79379367935626944955094123773848', '8.077811994296712131146298977132319', '8.139335946670904217562553244441952', '8.242833841376511148983524224961664', '8.280581862329791243089597909348239', '8.359781164880443851421843009510532', '8.443031607755895994028158875497253', '8.493592353112041771357344203436894', '8.518153467704726592213929375454574', '8.519259695691493863263546248379209', '8.544075682570909977111968107075961', '8.649156996395107440752134323699915', '8.818619601129643290319262408583287', '8.868225093574596633019494116394505', '8.926366538447554541486032721824013', '9.013933504717810751072804773982543', '9.073006888365541010670787930833606', '9.162853366591946773079593969237792', '9.181010522231483353929967235851055', '9.352091793159606088000350683016887', '9.376280071058669097279653715283773', '9.487666916040145870658749463190378', '9.500419456951288968648937582619472', '9.526985909318899981550404798098274', '9.562379484710145900426748758712192', '9.601541250351429518195336110582141', '9.647936922588478836167344664267260', '10.05575848726249632086470890770859', '10.05650416436588479443667124822888', '10.07532737191160124113194384133259', '10.09367486673953932345483122815408', '10.14396049609647729558315105514510', '10.14638288945512874098201425869181', '10.16625253058848583348422339636706', '10.25949400174949967727557722488427', '10.40119024899604175851984078611180', '10.47272254368801208944807204468737', '10.51932975942703913554360819833065', '10.63295757288180843525660479385978', '10.71432109839992438962756309883422', '10.74503668186257016354308860314842', '10.76856387561409349147339841093461', '10.80817434832164461041429531734000', '10.82297637738347456407043949203934', '10.92376667719909118684520195215355', '11.00654174896036306220879644417096', '11.05179960561132629774143024926235', '11.06326115498927314309107388635163', '11.16450484398519243153680764185439', '11.30108994339983195953342925105297', '11.31098793082894464473584517305304', '11.36614311110453062510149452872343', '11.36806969529709063782543683367291', '11.46468951604371630613360675613979', '11.48226106428778770762916164190657', '11.62493248415321370944165296594792', '11.63611851681291137053270565684995', '11.66889169090886047493642138432142', '11.93083077749211224253090143740589', '11.95737655115400107858833640131549', '11.97262343709418238167002438604470', '12.00567690870570099632569795960238', '12.03128934413930111734748420053763', '12.11683852784730572812734729944944', '12.21606903046156223819738001859128', '12.28698506021886136647534260941505', '12.43342773459326130687720028014234', '12.45368503921009534818124452911387', '12.50368486429840415485058297546670', '12.55208255955021097435234882244142', '12.62024312973568063759638026348422', '12.70937385601935643661129583148855', '12.82139054159663593407593257749746', '12.84174693868091380389140516442542', '12.85583584980199403592705276027121', '12.86454994420864002996349298723934', '12.94179651115547139082786588139813', '13.07609057923098832561431543481548', '13.08538917883582524853210954767951', '13.29594136384567130765119880377873', '13.36059462285024927532098590907837', '13.46594257750043330574705781574850', '13.62874437820227864478017853605206'], 'prelabel': '32-12e32-1.1-c2e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.980837147972613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e16-0', 'trace_hash': 855774822548338242, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10825706632679258635360455875', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.26512459208611921806128814013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.76297326103762787394005385553', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 3156172308.1058936, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 34182189187166852111368841966125056, 'conductor_radical': 6, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, 6, 0, 0, 0, 4, 0, 0, -32, 0, 0, 0, 0, 26, 0, 0, -32, 0, 0, 0, 128, 0, 0, 0, 0, 0, -32, 0, 0, -8, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 160, -192, 0, 0, 0, 0, -336, 0, 0, 0, 160, 0, 0, 0, 0, 0, 128, 0, -32, 0, 0, 24, 0, 0, 320, 0, 0, 0, -512, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, -128, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 32, 512, 8480, 137032, 1636576, 18165248, 219655136, 2263228700, 21867108000, 253620152832, 2916953293728, 33797606438392, 431768458252384, 5293166227138048, 61910274521995104, 703855220885889990, 7491143217161407584, 77497246731528160768, 764904161670051651424, 7244817096612104559352, 75658256120708606202528, 795968684556265691023872, 8304030623946757937028000, 103994747384483599296220700, 1221264393643890740902536416, 12220670499948695842018446848, 133221785980516668883794428896, 1349728568031268563530552995912, 10106613703992673592061925813280, 73835487286527607827290144809472, 558380872604365034193881720121632, 2111377674535255285545615254209921], 'euler13': [1, 0, 0, 3200, 7608, 95360, 5120000, 68335872, 2004669468, 7270355200, 184268595200, 4889456013184, 5354592144136, 669839496880000, 7008632866619392, 70586941744778752, 2398056097119178950, 11929193154867609088, 200173563303516454912, 3233187312095855920000, 4367905310396995202056, 674053031939570500537216, 4293105416369593808691200, 28626124880126031417452800, 1333940359929609046405794588, 7684738295176870566317023488, 97305414527389693126661120000, 306280955401774982827806707840, 4129628261008210861166297506488, 293546656618459573306878771228800, 0, 0, 442779263776840698304313192148785281], 'euler17': [1, 0, 1936, 5888, 1970104, 12118784, 1412088752, 12342981120, 803992020380, 8384758342144, 385156459019152, 4284704575184128, 159049561847732232, 1754956969783214336, 56986337962883453232, 598166401551176027136, 17699896684274407333702, 172870090048289871842304, 4759555932997988897389872, 42360394950173251076989184, 1109491164547107826349538312, 8637938288797125779076873472, 224400717837231097263723382672, 1411807385876012504979853451776, 39123209970216247349866931642780, 173580385880837474525376256750080, 5739055454852175186987568798891952, 14234273794978469606239527330450176, 668749185151602171785786035156550584, 577616721466425684522335197824841472, 54887715035215868918645487860698047376, 0, 2367911594760467245844106297320951247361], 'euler19': [1, 32, 512, -2656, -523448, -8424608, 1945088, 4454446304, 107916937244, -703649376, -30601835632128, -698985761087712, 998616856187896, 253693358084547040, 3161998119961945600, -30474951661580761248, -1910909655870418467642, -11001457549830654810528, 412074756991560712537600, 11935227534935987982742240, 16960072330872362657151736, -4285528014488222255165241312, -67731499355399346164889220608, -562220555870954483221958496, 31127713926547623702996478011164, 463829690679844028766014887069664, 73115806292591152730397659237888, -114321765590792791654590700633616288, -2564247658685593345039959330637191608, -4697012278412155302375467373195101536, 326866782169983241283381922259938632192, 7374931772710246881456304620989865388832, 83198449060887472631428936505541918917761], 'euler2': [1, 0, -6, -4, 10, 56, 88, -128, -496, -512, 1408, 3584, 2560, -4096, -24576, 0, 65536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -128, 11088, -703360, 37418488, -1719054464, 71192321008, -2695787852672, 94963463800604, -3133315670487680, 97608794561723984, -2881444739461007744, 80972669723070041032, -2170372074719910288000, 55638543600337855059568, -1364769401046612538272128, 32076997834145946433448774, -721963013153658032745955712, 15569945679662145697724568688, -321292959541936345484326032000, 6341049546846612329389018049992, -119368202810791358519006027497856, 2139060074082408660121065881078864, -36324015721076064717500264536853120, 582373927212729564239528154295772444, -8745542615130426331486171769039235968, 122177116844122975978330716463342682608, -1560637466328161065379884377642483222656, 17970257449593941260499095894184096342008, -178690474825862624479024292019028921095040, 1490159053679180176208754967727478284501328, -9100076645267374467121862948661887590201472, 37608910510519071039902074217516707306379521], 'euler29': [1, 32, 512, -18368, -1552984, -20596992, 304715776, 25469097376, 491466517980, -9791032230816, -347423504794624, -2649303176415616, 694517140133881240, 20658732330776531008, 190851587110380169728, -11485440538974369182240, -825511918710437437518010, -9659255493277444482263840, 134985701383016796825389568, 12288295772642566683038037568, 347429708091906261612770751640, -1114581009523248128213672338816, -122923572029394124477602295235584, -2913402246673399205822631354830496, 122987763056454027065527520746127580, 5360157068985091075692931429304357536, 53933039619676501706832037612223666176, -3065912485852378435676636899888916259072, -194410148006867402337936613313365933238104, -1933792253116779126640356744769334708731328, 45332941738570348306746760204906215750328832, 2382812750133603932873376583270382965376659232, 62623297589448778360828428329074752308805325441], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -7312, 0, 29025544, 0, -80335806576, 0, 171125889681052, 0, -295006946315669072, 0, 423507628633392203064, 0, -514807310246870517530800, 0, 534544428224191949216973638, 0, -475435361966500107220561946800, 0, 361205860749311633126295498919224, 0, -232365992571959154769108053280691792, 0, 124480928883555283432512372945523642012, 0, -53968833982798547907484231483371363928176, 0, 18007814989012006396727795042356541234498824, 0, -4189513653245889742853916344818291077714715792, 0, 529144398052420314716929933900838757437386767361], 'euler37': [1, 96, 4608, 145952, 4040888, 217733344, 12932982272, 602883756192, 21839639792924, 655265530977504, 21703692469355008, 815191556064282016, 35433653736114978312, 1467845464506621375840, 50867428451208042071552, 1465079699916707177725984, 43181875126876200893659590, 2005694109185972126306872096, 95333750573544515336861967872, 3766089872615510619356602558560, 124459980725454940457402518361352, 3919917377017695306048158128103584, 142874365875275818372623258034037248, 5905293130321981955930416013149196256, 269446816147411178023745063078939270684, 10182739083597405563517698021971929022368, 299042671345538323243211413530790200591872, 6892279360058368588727890523815164520992736, 175112920437535849046858269928673978179517368, 8658743533427367681727180434867343437927188768, 374249082483169821377980583689543656211184890368, 10673895706655405947217821230645526361523169060704, 152214200233450528559804138174517974884637692126081], 'euler41': [1, 0, -13840, 0, 102706104, 0, -524939980080, 0, 2044068651261084, 0, -6376104819902485008, 0, 16402857938643748508168, 0, -35383360569917421812676272, 0, 64577774780000237359256539206, 0, -99984920347410423778809915042992, 0, 130975594183964147316577669339960328, 0, -143867179257987808259948724187240773648, 0, 130327836327428627758263533192221310642844, 0, -94577272396201366241415571692902103329164080, 0, 52288817022836677339754428612357436314532476344, 0, -19910587654352744331498189290377125594313655706640, 0, 4065214023175683899921868126254722311886802750234881], 'euler43': [1, -160, 12800, -978464, 71106632, -3813053664, 178619596288, -8719368905312, 336417491247900, -9339737479444512, 288453906337733120, -7137460469658328480, -129151507673078938376, 13166699894046358977184, -444909531434654535928320, 28972919499885413370278176, -1725860576868082036875113530, 53570928155288129321644347424, -1521057150978328362086276344320, 83231490187496868731360371674016, -1509548687837068929080749572115976, -154251100701786455099704084452111520, 11526511599283975053699449693148101120, -690069841169201212548904345148858265888, 45959347805131236616846050940888629327900, -2202506774663292515595320792900595941019488, 83425384132219209728594707834387496433868288, -3292903018667363424129999428899641159211808736, 113541085637070176903456488799040510541683196232, -2888848033840853858437622085436880595374137960736, 69875789182349331644715482041701831060558996492800, -1615004177477048927638486578688833570387169806439840, 18663392025969146670022260524972832947786731075670401], 'euler47': [1, 0, -24144, 0, 280869112, 0, -2097883923184, 0, 11327375509374492, 0, -47271044690493269328, 0, 159378111080716584342216, 0, -447837309295947983522369904, 0, 1069451862014464590113083289158, 0, -2185303209262560752182421495520624, 0, 3794997890552929841601714620665202376, 0, -5492492790697802075734747006265493492048, 0, 6422365603496382914720509973369815941845532, 0, -5804149811601969119174985502258382340206124784, 0, 3791862421616779449515053523942013352026525646072, 0, -1590557026786853140797198116121630204596987902319184, 0, 321463340914028260476243062478235279920395730789296641], 'euler5': [1, 0, 0, -32, -344, -5664, 512, -145600, 223452, 2255168, 20875776, 67282720, 753060504, -1881828576, 2740220928, -75471830656, -399298967994, -1886795766400, 1712638080000, -29403571500000, 294164259375000, 657057812500000, 5096625000000000, 13764453125000000, 34096069335937500, -555419921875000000, 48828125000000000, -13504028320312500000, -20503997802734375000, -47683715820312500000, 0, 0, 23283064365386962890625], 'euler53': [1, -160, 12800, -602944, 3948712, 1481707264, -105845942272, 3791430241760, 34861972067036, -14471440004155872, 1098860393015073792, -54880211634179791488, 1349758970889735695512, 17264917459299251320000, -1853658370277165714728448, -16562877726012460012653408, 5168183120809487531686006854, -46525123532369000175543423072, -14626256151162940805916239103488, 382665865430285765535809940280000, 84035575657552168608684076721511832, -9597861385825702742638183560963126912, 539824952603700609723101838569018268672, -19969809540319112647568076276372227283168, 135134383349547902989533848962368780910556, 41282759798405789748356760661092786290812640, -3237364540580026851537576611559091487297923072, 127300919681547610483917934009535941216524510976, 952963638614918140606811320515739527079739471272, -408742302834945234868084424680060517972525248250176, 24374421582918186280531772612807345185963770774540800, -855846877830214815775171865867197907842152901321063840, 15025461748906708859452861070130993269553796873817927041], 'euler59': [1, -128, 8192, -1121408, 136226184, -9279937408, 700645040128, -71627082366848, 5234572115355804, -316007889653226112, 25502997282495045632, -1933332663772110218880, 109616149725595055398840, -6942765907527045516409216, 514753163863417494131859456, -29693308567434592900791332224, 1551148300110104846432558538438, -103362407123239817887654627471744, 6237449912425184470111122629615616, -292849570924032438522237153010435456, 16094987232709893287572215966762387640, -988158714157281547667574057570499850880, 45374866922385004013931376318655031713792, -1957158906943328129915769705443377912815232, 112853068885090981244908191013139679262871964, -5375433217101460040442041576389108558855361408, 183036745352664748592495038226134208339748118528, -8438967281469639479612015154077154543503289931648, 431229904897938978480921955113961460928772736127624, -12357082684872196580104906312376497460537241998284928, 314229004550458559856419523786837759416542508999647232, -17091111950627285107190568160968472508265382403558937728, 464798130469793589516643498190087912509935907396786423681], 'euler61': [1, 32, 512, -38048, -60439624, -1520787552, -16996289024, 2981900088544, 2018049968078364, 40394929489472928, 275088896591278592, -106313082771719258656, -45042859320290008592120, -716503209267746480098016, -1881770414874206829193728, 2374239565266043975563213664, 727531884046275952665257798342, 8834545422354949633070718043744, -26054693962852302758130516085248, -36914513572332223337489820293367776, -8635045530007332393450369640198025720, -75837684012235257272478539035681044256, 730181930507715075956726036306729964032, 398973953764462715268504351165757985497248, 74166754614213041825415492722132736373995804, 407783940373892409492826009414227308146615264, -8648699503302341210543242609413807832983693824, -2879551958378001106630412404894196487561803479392, -425831509637567421889503450998126820687979283360584, -997487686455595834984361408280915341677644012352928, 49946532296737050993800623047445395947956445684982272, 11615690417259910421745757397471519895146620899613689632, 1350687001332003958728623852374735172807518011483204347521], 'euler67': [1, -320, 51200, -6047552, 641735304, -64228593856, 5982745065472, -525110406070976, 43992629224199580, -3502096836597496384, 267198268901850048512, -19906861744922068822080, 1452416951976727517992120, -103061266987555377988785088, 7141615968030041699303675904, -487804437589338070744177941952, 32904927223065445517751311967174, -2189754120338538599570614781422528, 143911567507305501917713988886288384, -9322755475981627749160772086312295872, 589779578533085125858313455047891668920, -36286980158629190964198042997668583993920, 2186408326228342046021326537719503646943232, -128639809544168174813112855549363875062966336, 7253986810986234678621398403276418014374989980, -388684366853248517964353058626632075825057851584, 19879092349412107477898739757007825851172836636672, -958018892490632578339453043786362824676175956705984, 42968599306971490817615113791774729073769303333282184, -1817709519089971127692730265942293218931177568385825088, 69081925909389100925678441059675990896951571900428339200, -1938179783795297962846065761980534519602597539131392591680, 27189028279553414235049966267283185807800188603627566700161], 'euler7': [1, 0, 336, -896, 58376, -263552, 7407024, -39795456, 757778332, -4246975232, 64072810512, -358262212224, 4568044589112, -24788168573056, 279500753010928, -1432888676504064, 14752709956620358, -70211545148699136, 671081307979238128, -2916303244451465344, 26333868015357446712, -101200207605265243776, 886850172071843856912, -2880396592160634675968, 25183194694504055685532, -64803461685446965119744, 591023231480803234095024, -1030441156996143666290048, 11183745963071945007072776, -8411182382532387857861504, 154555476279032626888205136, 0, 1104427674243920646305299201], 'euler71': [1, 512, 201744, 56254976, 13334748280, 2640692651520, 463721900725296, 71822582790153728, 10087539873984698908, 1281533895294227735040, 149578753624082666366224, 16008541217716991792554496, 1586531743774045246375645512, 145287048222533985248020993536, 12376373818709017395122609264304, 978084861433718526221159012464128, 72053716823970739027227311635230534, 4930525786487375090680862581831669248, 314504463417785381868306702512137935024, 18611312127350621900343114875330105734656, 1024508475975584611882491175572827888674632, 52111700560049108089321999277072877278429696, 2454539891711673509371207994541047583332275984, 106010035366148777339882216535449070953122890240, 4206480150543226281850122017273336437534576419868, 150977175246556526942047920988592870127626993796608, 4913880397730004169580778918976381755746333068635696, 141059236459363619022541067101954605123253307829880320, 3590750182213011563828951429702436558585007321663490680, 76362125884101120380762701527162791348105186250614391296, 1380493580719140793947133005500035837291045700832090848784, 17661208699576971984550711347705748353167829652837357363712, 173887017684702179246328390437079448141248104062408434512641], 'euler73': [1, 0, -42768, 0, 946714744, 0, -14391245893936, 0, 167549428359087132, 0, -1579092364147683166224, 0, 12431125925178146870479176, 0, -83211218053743713189923429296, 0, 477990969232323851403899754270022, 0, -2363052224193764919402324316694268336, 0, 10025206955966061014687204222669908157256, 0, -36164449193556131500267145282734319906866704, 0, 108970441980869065421050966224100320962219969052, 0, -265800379188431140047017281295855916748245432633136, 0, 496555485216069339122503522948341872374586239474154104, 0, -637028737809508333054430813890192766263583467389141953808, 0, 422991386556309150149363832086603107763045099853453376062721], 'euler79': [1, 0, -62928, 0, 1905826568, 0, -37296559235888, 0, 534425714020543644, 0, -6018997282533146289808, 0, 55719824438563216525904696, 0, -436059000346206004998920193136, 0, 2929869749724252435562307026190662, 0, -16984533384263751937394346435182844016, 0, 84533036542191154857672699133007751110456, 0, -355671644320424164978230065489486786554653328, 0, 1230044452883634612617334624119049598764934791324, 0, -3343571340248160653599764615720802038541919305783088, 0, 6654777933452895172349946037478306278263205573396627208, 0, -8558595187601530498590654945696182392611530339877340985808, 0, 5297450670659957549009604563595170759963655420038456036451841], 'euler83': [1, -160, 12800, -895904, 107479624, -16432771168, 1654826188288, -174484645067104, 18280323695716892, -1483531366054758688, 116856254345162512896, -11468497917913001109536, 1366230707693329274647800, -120877910851657649855602144, 8917938316345038560246232576, -740834868592221092687137649376, 61671226222619243489644185991366, -5103611409731811107521691266551264, 423230379275302386749543544632464896, -39519869305905648816355633895676903136, 3077150810247510247335822671565904759800, -177945686049722700149588984619570812389664, 12490765931265373648548534148890056555936256, -1092420964995984155570123865099443669485982752, 92732797115079963555989346760985188617375111452, -6097655398787066900299546229255953304728456253536, 398395324232612542964619385367707223114795175321088, -27253911408269568727273654526441134649933673775027552, 1228005623141667205092173933789916062915231195411813704, -70516683301185795495827033999423698173733099523983446176, 6940592652953801409733220519656103964265418760877550604800, -597671784827484223895651951998886252622805873046068076455840, 25733505785478367615107164358252046214490685371339768616901761], 'euler89': [1, 0, -81008, 0, 3201135736, 0, -82544801381712, 0, 1567286911309649436, 0, -23398814610877335886704, 0, 285472189102998157435756872, 0, -2909237845695713148204132464336, 0, 25036289222433160823905054207568710, 0, -182532102040961247011492396273293216976, 0, 1123786623962130138494850058387671580450632, 0, -5779282663689345401733205072037200452228284784, 0, 24287824330763877053282311203215947422818373613596, 0, -80258282135852284438470158204153476259290072689548112, 0, 195282914984273870762746216186288257723995687838973651576, 0, -310061680192030639259528238560452122383480734622957208603248, 0, 240148684864128390378794468324923219083866317778128398613374721], 'euler97': [1, 0, 76432, 232448, 3001425784, 15854050304, 80617465349552, 544041740544000, 1656877944527714588, 12587985920266725376, 27565039357597995290512, 219887145530657392067584, 383075562467330745780676680, 3057500955957496305351185408, 4527285108585971726697834270768, 34760406346449901605547724599296, 45918202346304448047444859096398406, 327060663313747124206598540754776064, 400797295545123003650887772248250357808, 2546812701356249824375486900748568876032, 3002329282466308061593796633144617581969480, 16215008630836305420474016198078687363695616, 19125791988807964639819181701421754384507950992, 82178938689134700072609891665117992389902854144, 101774333076789378439170915781420889182014115160348, 314429610823518326108472943591141428233498716416000, 438393215981794447500496057730173963289731501423570352, 811182150430481310014960264370535857788000427494644736, 1444938062707497296192209251533763360274177986531711702904, 1052909161983592131070078841986050854282537568980502612992, 3257495192144822749974924435877391012865527232082177311543952, 0, 3773075507922571775273744352333525624409237957166570157859261441], 'euler_factors': [[1, 0, -6, -4, 10, 56, 88, -128, -496, -512, 1408, 3584, 2560, -4096, -24576, 0, 65536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -32, -344, -5664, 512, -145600, 223452, 2255168, 20875776, 67282720, 753060504, -1881828576, 2740220928, -75471830656, -399298967994, -1886795766400, 1712638080000, -29403571500000, 294164259375000, 657057812500000, 5096625000000000, 13764453125000000, 34096069335937500, -555419921875000000, 48828125000000000, -13504028320312500000, -20503997802734375000, -47683715820312500000, 0, 0, 23283064365386962890625], [1, 0, 336, -896, 58376, -263552, 7407024, -39795456, 757778332, -4246975232, 64072810512, -358262212224, 4568044589112, -24788168573056, 279500753010928, -1432888676504064, 14752709956620358, -70211545148699136, 671081307979238128, -2916303244451465344, 26333868015357446712, -101200207605265243776, 886850172071843856912, -2880396592160634675968, 25183194694504055685532, -64803461685446965119744, 591023231480803234095024, -1030441156996143666290048, 11183745963071945007072776, -8411182382532387857861504, 154555476279032626888205136, 0, 1104427674243920646305299201], [1, 32, 512, 8480, 137032, 1636576, 18165248, 219655136, 2263228700, 21867108000, 253620152832, 2916953293728, 33797606438392, 431768458252384, 5293166227138048, 61910274521995104, 703855220885889990, 7491143217161407584, 77497246731528160768, 764904161670051651424, 7244817096612104559352, 75658256120708606202528, 795968684556265691023872, 8304030623946757937028000, 103994747384483599296220700, 1221264393643890740902536416, 12220670499948695842018446848, 133221785980516668883794428896, 1349728568031268563530552995912, 10106613703992673592061925813280, 73835487286527607827290144809472, 558380872604365034193881720121632, 2111377674535255285545615254209921], [1, 0, 0, 3200, 7608, 95360, 5120000, 68335872, 2004669468, 7270355200, 184268595200, 4889456013184, 5354592144136, 669839496880000, 7008632866619392, 70586941744778752, 2398056097119178950, 11929193154867609088, 200173563303516454912, 3233187312095855920000, 4367905310396995202056, 674053031939570500537216, 4293105416369593808691200, 28626124880126031417452800, 1333940359929609046405794588, 7684738295176870566317023488, 97305414527389693126661120000, 306280955401774982827806707840, 4129628261008210861166297506488, 293546656618459573306878771228800, 0, 0, 442779263776840698304313192148785281], [1, 0, 1936, 5888, 1970104, 12118784, 1412088752, 12342981120, 803992020380, 8384758342144, 385156459019152, 4284704575184128, 159049561847732232, 1754956969783214336, 56986337962883453232, 598166401551176027136, 17699896684274407333702, 172870090048289871842304, 4759555932997988897389872, 42360394950173251076989184, 1109491164547107826349538312, 8637938288797125779076873472, 224400717837231097263723382672, 1411807385876012504979853451776, 39123209970216247349866931642780, 173580385880837474525376256750080, 5739055454852175186987568798891952, 14234273794978469606239527330450176, 668749185151602171785786035156550584, 577616721466425684522335197824841472, 54887715035215868918645487860698047376, 0, 2367911594760467245844106297320951247361], [1, 32, 512, -2656, -523448, -8424608, 1945088, 4454446304, 107916937244, -703649376, -30601835632128, -698985761087712, 998616856187896, 253693358084547040, 3161998119961945600, -30474951661580761248, -1910909655870418467642, -11001457549830654810528, 412074756991560712537600, 11935227534935987982742240, 16960072330872362657151736, -4285528014488222255165241312, -67731499355399346164889220608, -562220555870954483221958496, 31127713926547623702996478011164, 463829690679844028766014887069664, 73115806292591152730397659237888, -114321765590792791654590700633616288, -2564247658685593345039959330637191608, -4697012278412155302375467373195101536, 326866782169983241283381922259938632192, 7374931772710246881456304620989865388832, 83198449060887472631428936505541918917761], [1, -128, 11088, -703360, 37418488, -1719054464, 71192321008, -2695787852672, 94963463800604, -3133315670487680, 97608794561723984, -2881444739461007744, 80972669723070041032, -2170372074719910288000, 55638543600337855059568, -1364769401046612538272128, 32076997834145946433448774, -721963013153658032745955712, 15569945679662145697724568688, -321292959541936345484326032000, 6341049546846612329389018049992, -119368202810791358519006027497856, 2139060074082408660121065881078864, -36324015721076064717500264536853120, 582373927212729564239528154295772444, -8745542615130426331486171769039235968, 122177116844122975978330716463342682608, -1560637466328161065379884377642483222656, 17970257449593941260499095894184096342008, -178690474825862624479024292019028921095040, 1490159053679180176208754967727478284501328, -9100076645267374467121862948661887590201472, 37608910510519071039902074217516707306379521], [1, 32, 512, -18368, -1552984, -20596992, 304715776, 25469097376, 491466517980, -9791032230816, -347423504794624, -2649303176415616, 694517140133881240, 20658732330776531008, 190851587110380169728, -11485440538974369182240, -825511918710437437518010, -9659255493277444482263840, 134985701383016796825389568, 12288295772642566683038037568, 347429708091906261612770751640, -1114581009523248128213672338816, -122923572029394124477602295235584, -2913402246673399205822631354830496, 122987763056454027065527520746127580, 5360157068985091075692931429304357536, 53933039619676501706832037612223666176, -3065912485852378435676636899888916259072, -194410148006867402337936613313365933238104, -1933792253116779126640356744769334708731328, 45332941738570348306746760204906215750328832, 2382812750133603932873376583270382965376659232, 62623297589448778360828428329074752308805325441], [1, 0, -7312, 0, 29025544, 0, -80335806576, 0, 171125889681052, 0, -295006946315669072, 0, 423507628633392203064, 0, -514807310246870517530800, 0, 534544428224191949216973638, 0, -475435361966500107220561946800, 0, 361205860749311633126295498919224, 0, -232365992571959154769108053280691792, 0, 124480928883555283432512372945523642012, 0, -53968833982798547907484231483371363928176, 0, 18007814989012006396727795042356541234498824, 0, -4189513653245889742853916344818291077714715792, 0, 529144398052420314716929933900838757437386767361], [1, 96, 4608, 145952, 4040888, 217733344, 12932982272, 602883756192, 21839639792924, 655265530977504, 21703692469355008, 815191556064282016, 35433653736114978312, 1467845464506621375840, 50867428451208042071552, 1465079699916707177725984, 43181875126876200893659590, 2005694109185972126306872096, 95333750573544515336861967872, 3766089872615510619356602558560, 124459980725454940457402518361352, 3919917377017695306048158128103584, 142874365875275818372623258034037248, 5905293130321981955930416013149196256, 269446816147411178023745063078939270684, 10182739083597405563517698021971929022368, 299042671345538323243211413530790200591872, 6892279360058368588727890523815164520992736, 175112920437535849046858269928673978179517368, 8658743533427367681727180434867343437927188768, 374249082483169821377980583689543656211184890368, 10673895706655405947217821230645526361523169060704, 152214200233450528559804138174517974884637692126081], [1, 0, -13840, 0, 102706104, 0, -524939980080, 0, 2044068651261084, 0, -6376104819902485008, 0, 16402857938643748508168, 0, -35383360569917421812676272, 0, 64577774780000237359256539206, 0, -99984920347410423778809915042992, 0, 130975594183964147316577669339960328, 0, -143867179257987808259948724187240773648, 0, 130327836327428627758263533192221310642844, 0, -94577272396201366241415571692902103329164080, 0, 52288817022836677339754428612357436314532476344, 0, -19910587654352744331498189290377125594313655706640, 0, 4065214023175683899921868126254722311886802750234881], [1, -160, 12800, -978464, 71106632, -3813053664, 178619596288, -8719368905312, 336417491247900, -9339737479444512, 288453906337733120, -7137460469658328480, -129151507673078938376, 13166699894046358977184, -444909531434654535928320, 28972919499885413370278176, -1725860576868082036875113530, 53570928155288129321644347424, -1521057150978328362086276344320, 83231490187496868731360371674016, -1509548687837068929080749572115976, -154251100701786455099704084452111520, 11526511599283975053699449693148101120, -690069841169201212548904345148858265888, 45959347805131236616846050940888629327900, -2202506774663292515595320792900595941019488, 83425384132219209728594707834387496433868288, -3292903018667363424129999428899641159211808736, 113541085637070176903456488799040510541683196232, -2888848033840853858437622085436880595374137960736, 69875789182349331644715482041701831060558996492800, -1615004177477048927638486578688833570387169806439840, 18663392025969146670022260524972832947786731075670401], [1, 0, -24144, 0, 280869112, 0, -2097883923184, 0, 11327375509374492, 0, -47271044690493269328, 0, 159378111080716584342216, 0, -447837309295947983522369904, 0, 1069451862014464590113083289158, 0, -2185303209262560752182421495520624, 0, 3794997890552929841601714620665202376, 0, -5492492790697802075734747006265493492048, 0, 6422365603496382914720509973369815941845532, 0, -5804149811601969119174985502258382340206124784, 0, 3791862421616779449515053523942013352026525646072, 0, -1590557026786853140797198116121630204596987902319184, 0, 321463340914028260476243062478235279920395730789296641], [1, -160, 12800, -602944, 3948712, 1481707264, -105845942272, 3791430241760, 34861972067036, -14471440004155872, 1098860393015073792, -54880211634179791488, 1349758970889735695512, 17264917459299251320000, -1853658370277165714728448, -16562877726012460012653408, 5168183120809487531686006854, -46525123532369000175543423072, -14626256151162940805916239103488, 382665865430285765535809940280000, 84035575657552168608684076721511832, -9597861385825702742638183560963126912, 539824952603700609723101838569018268672, -19969809540319112647568076276372227283168, 135134383349547902989533848962368780910556, 41282759798405789748356760661092786290812640, -3237364540580026851537576611559091487297923072, 127300919681547610483917934009535941216524510976, 952963638614918140606811320515739527079739471272, -408742302834945234868084424680060517972525248250176, 24374421582918186280531772612807345185963770774540800, -855846877830214815775171865867197907842152901321063840, 15025461748906708859452861070130993269553796873817927041], [1, -128, 8192, -1121408, 136226184, -9279937408, 700645040128, -71627082366848, 5234572115355804, -316007889653226112, 25502997282495045632, -1933332663772110218880, 109616149725595055398840, -6942765907527045516409216, 514753163863417494131859456, -29693308567434592900791332224, 1551148300110104846432558538438, -103362407123239817887654627471744, 6237449912425184470111122629615616, -292849570924032438522237153010435456, 16094987232709893287572215966762387640, -988158714157281547667574057570499850880, 45374866922385004013931376318655031713792, -1957158906943328129915769705443377912815232, 112853068885090981244908191013139679262871964, -5375433217101460040442041576389108558855361408, 183036745352664748592495038226134208339748118528, -8438967281469639479612015154077154543503289931648, 431229904897938978480921955113961460928772736127624, -12357082684872196580104906312376497460537241998284928, 314229004550458559856419523786837759416542508999647232, -17091111950627285107190568160968472508265382403558937728, 464798130469793589516643498190087912509935907396786423681], [1, 32, 512, -38048, -60439624, -1520787552, -16996289024, 2981900088544, 2018049968078364, 40394929489472928, 275088896591278592, -106313082771719258656, -45042859320290008592120, -716503209267746480098016, -1881770414874206829193728, 2374239565266043975563213664, 727531884046275952665257798342, 8834545422354949633070718043744, -26054693962852302758130516085248, -36914513572332223337489820293367776, -8635045530007332393450369640198025720, -75837684012235257272478539035681044256, 730181930507715075956726036306729964032, 398973953764462715268504351165757985497248, 74166754614213041825415492722132736373995804, 407783940373892409492826009414227308146615264, -8648699503302341210543242609413807832983693824, -2879551958378001106630412404894196487561803479392, -425831509637567421889503450998126820687979283360584, -997487686455595834984361408280915341677644012352928, 49946532296737050993800623047445395947956445684982272, 11615690417259910421745757397471519895146620899613689632, 1350687001332003958728623852374735172807518011483204347521], [1, -320, 51200, -6047552, 641735304, -64228593856, 5982745065472, -525110406070976, 43992629224199580, -3502096836597496384, 267198268901850048512, -19906861744922068822080, 1452416951976727517992120, -103061266987555377988785088, 7141615968030041699303675904, -487804437589338070744177941952, 32904927223065445517751311967174, -2189754120338538599570614781422528, 143911567507305501917713988886288384, -9322755475981627749160772086312295872, 589779578533085125858313455047891668920, -36286980158629190964198042997668583993920, 2186408326228342046021326537719503646943232, -128639809544168174813112855549363875062966336, 7253986810986234678621398403276418014374989980, -388684366853248517964353058626632075825057851584, 19879092349412107477898739757007825851172836636672, -958018892490632578339453043786362824676175956705984, 42968599306971490817615113791774729073769303333282184, -1817709519089971127692730265942293218931177568385825088, 69081925909389100925678441059675990896951571900428339200, -1938179783795297962846065761980534519602597539131392591680, 27189028279553414235049966267283185807800188603627566700161], [1, 512, 201744, 56254976, 13334748280, 2640692651520, 463721900725296, 71822582790153728, 10087539873984698908, 1281533895294227735040, 149578753624082666366224, 16008541217716991792554496, 1586531743774045246375645512, 145287048222533985248020993536, 12376373818709017395122609264304, 978084861433718526221159012464128, 72053716823970739027227311635230534, 4930525786487375090680862581831669248, 314504463417785381868306702512137935024, 18611312127350621900343114875330105734656, 1024508475975584611882491175572827888674632, 52111700560049108089321999277072877278429696, 2454539891711673509371207994541047583332275984, 106010035366148777339882216535449070953122890240, 4206480150543226281850122017273336437534576419868, 150977175246556526942047920988592870127626993796608, 4913880397730004169580778918976381755746333068635696, 141059236459363619022541067101954605123253307829880320, 3590750182213011563828951429702436558585007321663490680, 76362125884101120380762701527162791348105186250614391296, 1380493580719140793947133005500035837291045700832090848784, 17661208699576971984550711347705748353167829652837357363712, 173887017684702179246328390437079448141248104062408434512641], [1, 0, -42768, 0, 946714744, 0, -14391245893936, 0, 167549428359087132, 0, -1579092364147683166224, 0, 12431125925178146870479176, 0, -83211218053743713189923429296, 0, 477990969232323851403899754270022, 0, -2363052224193764919402324316694268336, 0, 10025206955966061014687204222669908157256, 0, -36164449193556131500267145282734319906866704, 0, 108970441980869065421050966224100320962219969052, 0, -265800379188431140047017281295855916748245432633136, 0, 496555485216069339122503522948341872374586239474154104, 0, -637028737809508333054430813890192766263583467389141953808, 0, 422991386556309150149363832086603107763045099853453376062721], [1, 0, -62928, 0, 1905826568, 0, -37296559235888, 0, 534425714020543644, 0, -6018997282533146289808, 0, 55719824438563216525904696, 0, -436059000346206004998920193136, 0, 2929869749724252435562307026190662, 0, -16984533384263751937394346435182844016, 0, 84533036542191154857672699133007751110456, 0, -355671644320424164978230065489486786554653328, 0, 1230044452883634612617334624119049598764934791324, 0, -3343571340248160653599764615720802038541919305783088, 0, 6654777933452895172349946037478306278263205573396627208, 0, -8558595187601530498590654945696182392611530339877340985808, 0, 5297450670659957549009604563595170759963655420038456036451841], [1, -160, 12800, -895904, 107479624, -16432771168, 1654826188288, -174484645067104, 18280323695716892, -1483531366054758688, 116856254345162512896, -11468497917913001109536, 1366230707693329274647800, -120877910851657649855602144, 8917938316345038560246232576, -740834868592221092687137649376, 61671226222619243489644185991366, -5103611409731811107521691266551264, 423230379275302386749543544632464896, -39519869305905648816355633895676903136, 3077150810247510247335822671565904759800, -177945686049722700149588984619570812389664, 12490765931265373648548534148890056555936256, -1092420964995984155570123865099443669485982752, 92732797115079963555989346760985188617375111452, -6097655398787066900299546229255953304728456253536, 398395324232612542964619385367707223114795175321088, -27253911408269568727273654526441134649933673775027552, 1228005623141667205092173933789916062915231195411813704, -70516683301185795495827033999423698173733099523983446176, 6940592652953801409733220519656103964265418760877550604800, -597671784827484223895651951998886252622805873046068076455840, 25733505785478367615107164358252046214490685371339768616901761], [1, 0, -81008, 0, 3201135736, 0, -82544801381712, 0, 1567286911309649436, 0, -23398814610877335886704, 0, 285472189102998157435756872, 0, -2909237845695713148204132464336, 0, 25036289222433160823905054207568710, 0, -182532102040961247011492396273293216976, 0, 1123786623962130138494850058387671580450632, 0, -5779282663689345401733205072037200452228284784, 0, 24287824330763877053282311203215947422818373613596, 0, -80258282135852284438470158204153476259290072689548112, 0, 195282914984273870762746216186288257723995687838973651576, 0, -310061680192030639259528238560452122383480734622957208603248, 0, 240148684864128390378794468324923219083866317778128398613374721], [1, 0, 76432, 232448, 3001425784, 15854050304, 80617465349552, 544041740544000, 1656877944527714588, 12587985920266725376, 27565039357597995290512, 219887145530657392067584, 383075562467330745780676680, 3057500955957496305351185408, 4527285108585971726697834270768, 34760406346449901605547724599296, 45918202346304448047444859096398406, 327060663313747124206598540754776064, 400797295545123003650887772248250357808, 2546812701356249824375486900748568876032, 3002329282466308061593796633144617581969480, 16215008630836305420474016198078687363695616, 19125791988807964639819181701421754384507950992, 82178938689134700072609891665117992389902854144, 101774333076789378439170915781420889182014115160348, 314429610823518326108472943591141428233498716416000, 438393215981794447500496057730173963289731501423570352, 811182150430481310014960264370535857788000427494644736, 1444938062707497296192209251533763360274177986531711702904, 1052909161983592131070078841986050854282537568980502612992, 3257495192144822749974924435877391012865527232082177311543952, 0, 3773075507922571775273744352333525624409237957166570157859261441]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/3/m/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '32-12e32-1.1-c2e16-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '32-12e32-1.1-c2e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.980837147972613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e16-0', 'trace_hash': 855774822548338242, 'z1': {'__RealLiteral__': 0, 'data': '0.10825706632679258635360455875', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '137232135108105863622251405146,336085348293233505420795311872,967183512312438527701439346493,1294866112531013223074433073808,1451746856807591762623942053326,1482017335356797121264211233059,1931714135209384842329762774687,1980087067934388647578926888382,2148553897993950060879227384356,2532196276647501268322839575553,2645876708941299678173130037337,2832029369714542483646938414942,2973939967699396196048717529647,3407109558920056432060070830100,3696337820918772331239153620014,4132723398472477533549245210594', 'Lhash_array': ['137232135108105863622251405146', '336085348293233505420795311872', '967183512312438527701439346493', '1294866112531013223074433073808', '1451746856807591762623942053326', '1482017335356797121264211233059', '1931714135209384842329762774687', '1980087067934388647578926888382', '2148553897993950060879227384356', '2532196276647501268322839575553', '2645876708941299678173130037337', '2832029369714542483646938414942', '2973939967699396196048717529647', '3407109558920056432060070830100', '3696337820918772331239153620014', '4132723398472477533549245210594'], 'factors': ['2-12e2-16.3-c2-0-0', '2-12e2-16.3-c2-0-1', '2-12e2-16.11-c2-0-3', '2-12e2-16.3-c2-0-4', '2-12e2-16.3-c2-0-5', '2-12e2-16.11-c2-0-4', '2-12e2-16.11-c2-0-9', '2-12e2-16.11-c2-0-10', '2-12e2-16.11-c2-0-11', '2-12e2-16.3-c2-0-11', '2-12e2-16.3-c2-0-13', '2-12e2-16.3-c2-0-14', '2-12e2-16.11-c2-0-15', '2-12e2-16.3-c2-0-17', '2-12e2-16.11-c2-0-16', '2-12e2-16.11-c2-0-18'], 'label': '32-12e32-1.1-c2e16-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/3/m/c'}