-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '303559857389489933748152564115,330818173041016919950287501128,818625373063300533381526442272,853009331211024049623062853646,1060323743840119435659705708843,1162020833048011420362501817278,1403809860339112763262558404904,1714074277500226551073158652391,1884266100382291111622654295738,1905419789311375386079984355975,2018124458228017895467205516393,2934959518379016369015145819133', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 56, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3685226441161823.0, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 6, -9, -198, 2565, -36018, 69255, -144342, -177147, 3188646, -43046721, 387420489]], [7, [1, -56, 1736, -48216, 1156792, -25993912, 536820382, -8915911816, 136095422008, -1945689515112, 24028474580936, -265863444556808, 1628413597910449]]], 'bad_primes': [2, 3, 7], 'central_character': '336.1', 'coefficient_field': '1.1.1.1', 'conductor': 2070481377455157458127600746496, 'conductor_radical': 42, 'degree': 24, 'euler_factors': [[1], [1, -3, 6, -9, -198, 2565, -36018, 69255, -144342, -177147, 3188646, -43046721, 387420489], [1, 0, -354, 0, 53346, 0, -3913744, 0, 238386078, 0, -66225097710, 0, 12349753291374, 0, -1034767151718750, 0, 58199726074218750, 0, -14929748535156250000, 0, 3179669380187988281250, 0, -329688191413879394531250, 0, 14551915228366851806640625], [1, -56, 1736, -48216, 1156792, -25993912, 536820382, -8915911816, 136095422008, -1945689515112, 24028474580936, -265863444556808, 1628413597910449], [1, 0, 4742, 0, 10147682, 0, 18336975648, 0, 35136366245806, 0, 55422032379705850, 0, 74318354148055569358, 0, 98183511104624075331850, 0, 110272968880699461454282126, 0, 101952068382400630504275974688, 0, 99951954979104730568807644102562, 0, 82745065559059343504605847400524342, 0, 30912680532870672635673352936887453361], [1, 0, -17694, 0, 150344127, 0, -825783978694, 0, 3311047419013899, 0, -10270057919177967660, 0, 25258100677402513310250, 0, -49571607994809486902996940, 0, 77141064612756834011656363419, 0, -92863873378440283409233917993526, 0, 81606907956862197917187854946794847, 0, -46358202918742126128973477052547969006, 0, 12646218552730347184269489080961456410641], [1, 0, -17217, 0, 160729722, 0, -865949822635, 0, 2480649769543932, 0, 2994987661331912811, 0, -48570103865944827020748, 0, 72291721329547677377496459, 0, 1445281718515176703316067360252, 0, -12177925486969072614972200519688715, 0, 54559490573666945971240925850713770362, 0, -141066899401352818587190235712715631923233, 0, 197770344305988984840145602058543169130838081], [1, 300, 83160, 15948000, 2884970160, 429462962340, 60380369111228, 7433977043645460, 869187264653707200, 91277486172699660000, 9126239049539154084600, 829900380859959867931260, 71963509971308988283216278, 5692286712318464734140512340, 429351956302172147904755532600, 29454121872122959286616055140000, 1923785140320357813034470722059200, 112856149836754835971724437167072540, 6287247845562017611937136771543838748, 306726525751833529215833527299330260460, 14132784876736183197442471222550991837360, 535862607118307229850675873375976696772000, 19165603944330754083184571633797412679227160, 474231159647058593999144938081588937831237700, 10842505080063916320800450434338728415281531281], [1, 0, 58691, 0, 1855192226, 0, 43669490183457, 0, 835010896549582396, 0, 13098051643974790616191, 0, 172460855929679516062212988, 0, 1938981719283719622456692478799, 0, 18298950194528671131207483135869116, 0, 141670416313323639519094175718159795633, 0, 890957483896871158534747945532135187999266, 0, 4172598424901464647264447330624334723097770259, 0, 10524515126174167358877236351104092889324551536161], [1, 0, -52666, 0, 2519040527, 0, -103130851328970, 0, 3368948978362405387, 0, -97485851940324492609644, 0, 2660654312384909011632366346, 0, -57986858201658108511708400707724, 0, 1191983952409580873121489206320123867, 0, -21704638904963328368749444768682499814170, 0, 315345838520787890155002806528268505411491887, 0, -3921663009329262022772164097953687164203972972266, 0, 44292268542362921407825091617016319887724139383235921], [1, -930, 569163, -261202590, 100353300315, -33216928806732, 9794533901888048, -2603356187506835040, 633073931196657625701, -141557155724308631524902, 29322254113324930701973269, -5635471353483609226766378646, 1008520666810586017753160781150, -167886327091630202474597186242986, 26023608460793267147071190201103189, -3742717711489986196236084602781529242, 498648774990320162898276800628351007461, -61088434997937823659056865523931152283040, 6846904380318211386730666390269473195179568, -691759363233429240596130022147529345086115892, 62260458085101877955208193486171150756393793115, -4827732658061817549974751803971689087637533731490, 313391688895639649932603529624144734338538360740363, -15255232995851277673289089994361181376919860503017630, 488675963633769261467693849486036510107332864779998081], [1, -764, 80360, 35913560, 14537415840, -8384323490844, -799972723059332, 358393333975450156, 165375950980271204816, -29204567104447927365944, -8979742386005317363086232, 15978484235667058571855308, 733741480468576126635183993590, 809358161989243517840186916124, -23039562185790514772896587186700888, -3795476350856126875126916362948657688, 1088661948223279676639607203073817113296, 119504919672922385399079573999827402654908, -13511582339454970537496534023424401927539428, -7173056170002622790305134421653710154707351628, 629982653158734758919734057339896765409664942240, 78832446970628450932851142379700681951246722687480, 8934940197779462728316917855152859358458352767897640, -4302791012199179541328543377917274114038938281020057708, 285273917723723876056171083405292782327767461712708093041], [1, 0, 481476, 0, 115071158562, 0, 18349339969105268, 0, 2194095027782226746511, 0, 207524579777911349744722056, 0, 15866062069248227933510977629276, 0, 985763386514799540544438505571839496, 0, 49506441877445950766866667077058243513391, 0, 1966662641848505323673012123381139380824936628, 0, 58584003484878017310364671227274789692824717509282, 0, 1164368225474441154907068041616072980272462963100588676, 0, 11487323243342943712727117998313670374759563626306467569441], [1, -1012, 1245002, -852507032, 617746830855, -325426335753288, 174692605767795850, -74974379068410274156, 32320322136164328828683, -11630781566400845334701416, 4178182940072753301958406204, -1278184307934666532591479937264, 389408847481824864652500007427738, -101624599770961532006750795372048848, 26411811249338084094692608312897955996, -5845544886324287024386420718734854669688, 1291508139809719495581150805158767127709883, -238198877932348819958700471076243189648749892, 44127235797163055236162872581078776933754606650, -6535672222643174742773578151117855968526445087384, 986400900328625612437169900706210924909029777274855, -108229654150621975849600425290371599248551167080260424, 12566771443545505431298569171504719829994794895982585498, -812156167402073386492688689004717798555887389488873169916, 63806423321775344604618774305037646254726223988233042609201], [1, 0, -437385, 0, 98505882894, 0, -16642251751296271, 0, 2374463475062057432592, 0, -286916948686756436570920197, 0, 30812765825290076853254460902508, 0, -3092739571434191400374679183138099813, 0, 275892432755488389817232330461185095430672, 0, -20843638396066899717901089467009788803468798319, 0, 1329874805364648749982004598353890877475018801190414, 0, -63650178074097895295790661784537319107280347085231557865, 0, 1568638556854706336108974223356857608957236560013645822451521], [1, 0, 362162, 0, 31342470242, 0, 2991238457561520, 0, 1746851780280097098622, 0, 230369925295695020431645054, 0, 11387103576961192305310074686062, 0, 5106002217514536541894014436402705966, 0, 858156491479311853961717992323327000004702, 0, 32569919758287047395116179347005023253190367280, 0, 7564044803722356535304412080641305372516376869079202, 0, 1937220106054664113192298708038725804374561119051494515138, 0, 118558120445975157028044470669508269904542112710719750776396721], [1, 0, -661854, 0, 202275596298, 0, -40619516236130848, 0, 7446151473115219252038, 0, -1620799166433794781581625186, 0, 356878833337049532415712506341006, 0, -68366173765065438783793988345525882226, 0, 13248173476787091402392649734074658836253478, 0, -3048393004757515553242095644727505254774771205408, 0, 640312189577008467795335724059308194776701181804667978, 0, -88373600070081805916675830465700214089730284416602321648654, 0, 5632126739027588519658984775872141857619309476789431335641625841], [1, -2358, 3274005, -3349814886, 2769988834986, -1971385890773130, 1255859174153710355, -746741883560577476418, 426090230957405107588752, -237108440693732373533355174, 128334679353086591634975445617, -66588480619025175545607616021254, 32721887318351964942932629699352712, -15114319919386953370517562292120254174, 6611850723769918501883466019230636625737, -2772780745316606076677680255471566426195534, 1130992167500009839959285296894688391230805392, -449902116304051871865928733689964338619890896618, 171742576003329332690535441280004451598253387307755, -61192497560293052575859456818113238775882874697596930, 19516146018401686517089074198283031193340578328721688426, -5357058061977764557081660502062220530821868053125130679806, 1188432140767532281885866201503398234197172267451241185113005, -194280116897592785415607797677877157786287775735721146938725598, 18701397461209715023927088008788055619800417991632621566284510161], [1, 792, -260820, -1221864760, -593843874768, 277390666295568, 608150471782500244, 218629122721527308688, -113846601773968545956328, -180988011212274352966919416, -53128697364524185126485768756, 28594737528056557096359164715864, 36246571971031922690525994899293606, 8600239043150874281972271457437404232, -4805936010341271841014955274070007711764, -4924056552363757712326164425148766716990952, -931574740564060991414884895159462841088732008, 538059188919241843091952099672015079260759073584, 450150250963290987932460074223566758846730369305396, 61753659731648169125023828782107824983331531405060656, -39761938211530200592551616208084979910269338715347083728, -24606101568800575894697372382974332525380689462377453525480, -1579737660029655045842221475124259416883592156738280674256180, 1442758596626222372968691410007114971705109208062893199377343304, 547889398733702676213614311297941818478464344374520135510515030481], [1, 0, -3844636, 0, 6901086974498, 0, -7655680355206958700, 0, 5850229234251244135613647, 0, -3245867934818370369643978238264, 0, 1341101770056839013980852537421086044, 0, -415796604020303165917927332009563786153144, 0, 96000405694084949746875879125260760756628586927, 0, -16092890978269805502794513884301796117073838077910700, 0, 1858308742753900277388170242564562264275767439188726642338, 0, -132618981972474240747646696626949292042050296728839855987094236, 0, 4418761423445010359012517479030513507821439762288727229544623559521], [1, 2904, 5932080, 9063407232, 11723795534880, 13051713462287016, 13084661733360788156, 11882917853081720537400, 9998686567349345413335744, 7801474085970581186528333184, 5709514896007979349315899880432, 3907920673578948680003412598515144, 2518322403076120372802115558298104870, 1520247576673661878648887558836565773448, 864045019272887849599011369850964331076848, 459285158104522232986650924857996083600324992, 228990400167231466716275958687780977024013906624, 105868313963513520122499962439182165391919674151800, 45349654410397013094630634927225874871555281106960764, 17597363017898203778187530124117784007154681727957761768, 6149175363847851481257673641627408790250036474698209922080, 1849305737888310317844154664432253525753299104877537853938304, 470861089203030659301564684001556870613436775368488216001903920, 89670790018845089358463937491703166020903456808133288098288350232, 12012211336350227316446820100278887925603925639507433655692782073761], [1, 1674, -336861, -2052405226, -300737318949, 1327255085709756, 406747243169844832, -281214387106447896288, 96095575106235401052789, -56509383114401672827245922, -311613333749468231753156062131, 43022558303685385389288509224302, 239148512591023504865333569120433854, 21211799123490738726949417299440633778, -75749292407574386943697844104640974975251, -6772739754254263002613939653241955275245118, 5678432736485181355092976385238937475693888949, -8193017925516573450615359277715643352098374593312, 5842682157759449541028107640754122267142872400237152, 9399901770539172573695338693102167543747941920289976324, -1050116578030404722700071021003865081428726729922329378469, -3533414416607091166457837658410816088558732314009221476796534, -285932467612431334708688415782283739364223189945453347042974461, 700566661392096746026324165117206952322153574678405656996610164886, 206336132715709669990485567530001552309415935666586885734738159549121], [1, 0, 5725470, 0, 15556843382055, 0, 26496019606387001486, 0, 31476045560037079218614955, 0, 27458324289434654054780210553060, 0, 18029617696810204667200196572666834842, 0, 8977234795274847418597191817449870385459140, 0, 3364474753494813523299751810504217832895748557755, 0, 925947363088132500469315786152835862870073881062979774, 0, 177744305762530131453171202554194192641172204257083747347655, 0, 21387199211726350621173989885069145455026852137181696185660114030, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], [1, 0, -1635561, 0, 1787180462010, 0, -817237014874197619, 0, -172174360613175733010436, 0, 757568773104150957695916528195, 0, -706211584110844416447446370021831084, 0, 376497506849041838263541094260448255145395, 0, -42525414811439248991661951990927407352100545156, 0, -100315524541875821209497125848370655490571320995065539, 0, 109025620594382108461187668219574050785020683813735247716410, 0, -49586898518502549462988443303620722778440535105607052362642314361, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], [1, 0, -6632694, 0, 20843168091903, 0, -42591475693158319462, 0, 65402812509511105939522203, 0, -80737708092210420490421078476644, 0, 81496326134313904825955347036847534922, 0, -67252250582940861563252189178132601779378276, 0, 45379241847341153089427330081763848917416570295323, 0, -24615797150432092170311166411602204883933484424564166118, 0, 10034260078643025271314555260322603477090230772289515271058943, 0, -2659757177483791505837763048491493400772176229468696661346814348406, 0, 334027661875095082935878165689897695724025886105865253311336914562753921], [1, 0, -1972821, 0, 1532459616582, 0, 656413199564007821, 0, -2176415229836155099315608, 0, 1393417118998801842405700085487, 0, -850621496750656827537818484672022020, 0, 1479140350009619670089055022886998814427687, 0, -2452439156939803274795223924784388567212339325208, 0, 785166991665894934262864987312192239935676234680215621, 0, 1945817072650098176206605067636448647118765295797252473733382, 0, -2659064644995978258493780790633306590603828236292022103451451785821, 0, 1430768783591580504260467570192606659308868671266092320119567817646303601], [1, 888, 4337256, 3618074304, 8880338333400, 6351968828797752, 12678954108563655932, 8067686361459132456216, 16910759840056432599371400, 11595662189573876607015907776, 24332888974196189904997069184184, 16637408807285873515544650126171224, 30668599320654242747735276919643940838, 18180145813759070709020558898420703087848, 29054741960824143577863556792389201684897336, 15129709073698696451187442375204332326075577408, 24110699946801606561059702781990811746908087147400, 12569192478507706795140720375671682618230991739311912, 21585070656362278802719941006849026209338711341528799548, 11816533131880384415004961485084090641728235370075278558856, 18051899427509914532101611228803955540903149779954583509085400, 8036788672811095892871956756228277714461779698886780199995837248, 10527658716742181441739127706854666109935182246418707991736091687144, 2355273691659829607903037625617354086562631765069239507325598070250824, 2898278328002669626075520940909881169985726262104521260271822975800644321], [1, 0, 1477262, 0, -1765263900982, 0, -1009295364367190784, 0, 4606160639251358566225126, 0, -673785414631531151917506056366, 0, -9841977887675061414843454171244654066, 0, -1011170222370702098306763134992735606320734, 0, 10373956249124319019898426084478564845326648793926, 0, -3411349977771897051617895834487433359201667141354140416, 0, -8954066275346137944115467325536535186027787250681290901704182, 0, 11245295108832994589871428318833902529046635496915757928988024746238, 0, 11423942188538511596885360939762740188135840651026045719095671542305476401], [1, 3184, -935200, -8438614936, 10624512745920, 29939092492560048, -23541830866690190324, -40850945919141794406896, 83825388854535736649548544, 66121373904153786522637049464, -137813549234154042539881294074016, -15083547100911299986761055770502832, 240652330583075984843550464275815818486, -19533630918546059910555183293418512022128, -231127118695991355406503147454514750058007456, 143608567609923703622302994966116180473184617496, 235772719050409033278237237348488401923600154628864, -148798853972117463371080884463073509416393891510083504, -111049651041573824982091368816704587381939794374228266004, 182892159853666992630044352224440224481467567176097388622832, 84051404023440227402819911338416218889534953520455128528669120, -86454303104916221413497203996547977978362135834931711243994859384, -12407932904331541465444295393066322624813732166641664214002307975200, 54707578362558610618958412716832678490598642396111612751302716579439536, 22251225031182762233435645182872835048053225271229279444003393765438129041], [1, 0, -9463564, 0, 48900794801666, 0, -171080904742108941660, 0, 446845258548298346227885231, 0, -907124318333531498875908996891416, 0, 1464452490405096252524480906419087461148, 0, -1888589064388740334297005449486074674067704344, 0, 1936861095388725957555584643146114369357526125574511, 0, -1543879928116219514058112621769192246688611962818617458140, 0, 918752558553697876576220145563236399636529957933982996588436226, 0, -370175803736772733694226978021162104202966237384773691060246548842636, 0, 81437412307162418325296884344693834747274900130615053989566110375601595841]], 'euler_factors_factorization': [[1], [[[1, -3, 6, -9, -198, 2565, -36018, 69255, -144342, -177147, 3188646, -43046721, 387420489], 1]], [[[1, 0, -354, 0, 53346, 0, -3913744, 0, 238386078, 0, -66225097710, 0, 12349753291374, 0, -1034767151718750, 0, 58199726074218750, 0, -14929748535156250000, 0, 3179669380187988281250, 0, -329688191413879394531250, 0, 14551915228366851806640625], 1]], [[[1, -28, 476, -10780, 163268, -3294172, 40353607], 2]], [[[1, 0, 4742, 0, 10147682, 0, 18336975648, 0, 35136366245806, 0, 55422032379705850, 0, 74318354148055569358, 0, 98183511104624075331850, 0, 110272968880699461454282126, 0, 101952068382400630504275974688, 0, 99951954979104730568807644102562, 0, 82745065559059343504605847400524342, 0, 30912680532870672635673352936887453361], 1]], [[[1, 0, -8847, 0, 36037359, 0, -94069474274, 0, 173945448757431, 0, -206118159078589407, 0, 112455406951957393129], 2]], [[[1, 0, -17217, 0, 160729722, 0, -865949822635, 0, 2480649769543932, 0, 2994987661331912811, 0, -48570103865944827020748, 0, 72291721329547677377496459, 0, 1445281718515176703316067360252, 0, -12177925486969072614972200519688715, 0, 54559490573666945971240925850713770362, 0, -141066899401352818587190235712715631923233, 0, 197770344305988984840145602058543169130838081], 1]], [[[1, 150, 30330, 3424500, 468855630, 40538051670, 4025485422214, 278050496404530, 22057726175160030, 1105044021044185500, 67129841495276663130, 2277169054481219744850, 104127350297911241532841], 2]], [[[1, 0, 58691, 0, 1855192226, 0, 43669490183457, 0, 835010896549582396, 0, 13098051643974790616191, 0, 172460855929679516062212988, 0, 1938981719283719622456692478799, 0, 18298950194528671131207483135869116, 0, 141670416313323639519094175718159795633, 0, 890957483896871158534747945532135187999266, 0, 4172598424901464647264447330624334723097770259, 0, 10524515126174167358877236351104092889324551536161], 1]], [[[1, 0, -26333, 0, 912806819, 0, -27528483699758, 0, 542958783509025899, 0, -9317004686149616256653, 0, 210457284365172120330305161], 2]], [[[1, -465, 176469, -48543210, 12033403527, -2446560037821, 457872227799046, -72885470086725411, 10679689925170882887, -1283464130866106093910, 138998063792381587773909, -10911346826207778957427215, 699053619999045038539170241], 2]], [[[1, -382, -32782, 5434056, 8807187550, -649676877530, -374210188787594, -32908082877527090, 22596833686051007950, 706219371903876942312, -215802332655448036581742, -127376474357593447307804326, 16890053810563300749953435929], 2]], [[[1, 0, 240738, 0, 28558186959, 0, 2299629172416892, 0, 135654364989216793119, 0, 5431889527929554904767778, 0, 107178930967531784356353269521], 2]], [[[1, -253, 215237, -33567598, 17112848159, -1599304851397, 502592611936843], 4]], [[[1, 0, -437385, 0, 98505882894, 0, -16642251751296271, 0, 2374463475062057432592, 0, -286916948686756436570920197, 0, 30812765825290076853254460902508, 0, -3092739571434191400374679183138099813, 0, 275892432755488389817232330461185095430672, 0, -20843638396066899717901089467009788803468798319, 0, 1329874805364648749982004598353890877475018801190414, 0, -63650178074097895295790661784537319107280347085231557865, 0, 1568638556854706336108974223356857608957236560013645822451521], 1]], [[[1, 0, 362162, 0, 31342470242, 0, 2991238457561520, 0, 1746851780280097098622, 0, 230369925295695020431645054, 0, 11387103576961192305310074686062, 0, 5106002217514536541894014436402705966, 0, 858156491479311853961717992323327000004702, 0, 32569919758287047395116179347005023253190367280, 0, 7564044803722356535304412080641305372516376869079202, 0, 1937220106054664113192298708038725804374561119051494515138, 0, 118558120445975157028044470669508269904542112710719750776396721], 1]], [[[1, 0, -661854, 0, 202275596298, 0, -40619516236130848, 0, 7446151473115219252038, 0, -1620799166433794781581625186, 0, 356878833337049532415712506341006, 0, -68366173765065438783793988345525882226, 0, 13248173476787091402392649734074658836253478, 0, -3048393004757515553242095644727505254774771205408, 0, 640312189577008467795335724059308194776701181804667978, 0, -88373600070081805916675830465700214089730284416602321648654, 0, 5632126739027588519658984775872141857619309476789431335641625841], 1]], [[[1, -1179, 941982, -564310665, 276007099296, -128710086478551, 56963412393227764, -29214744138987984531, 14219989082023619549856, -6599131358254385842413765, 2500348955506788804587532222, -710331918966812636082391644279, 136753052840548005895349735207881], 2]], [[[1, 396, -208818, -528240452, -109541196954, 71767532435832, 113262131816538126, 21585018357998139816, -9908919457314630713226, -14371592026852389928596044, -1708698996227623963212938898, 974579398021980437294361617028, 740195513856780056217081017732809], 2]], [[[1, 0, -1922318, 0, 1602890240687, 0, -746575415906526884, 0, 205330694926204726093727, 0, -31544628506623162777951890638, 0, 2102085018129621311776010144838961], 2]], [[[1, 1452, 1911888, 1755642240, 1485047372688, 1012976615051412, 691104732915920110, 394065123857455142004, 224738495148250710194832, 103357444360857705299445120, 43786150835508167747452461648, 12936283308156979413057018572364, 3465863721549107204083472585375569], 2]], [[[1, 837, -518715, -592038158, 210634653159, 180227265033825, -13471835399034906, 88859070525012044175, 51202641880969674640839, -70956718118909549597816402, -30651653144794858471254168315, 24385509127815661264860026059563, 14364405059580771582276370834385761], 2]], [[[1, 0, 2862735, 0, 3680795850915, 0, 2710866692924348218, 0, 1203400769793216160282635, 0, 305997766303736053988322250335, 0, 34946659039493167390823397237402409], 2]], [[[1, 0, -1635561, 0, 1787180462010, 0, -817237014874197619, 0, -172174360613175733010436, 0, 757568773104150957695916528195, 0, -706211584110844416447446370021831084, 0, 376497506849041838263541094260448255145395, 0, -42525414811439248991661951990927407352100545156, 0, -100315524541875821209497125848370655490571320995065539, 0, 109025620594382108461187668219574050785020683813735247716410, 0, -49586898518502549462988443303620722778440535105607052362642314361, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], 1]], [[[1, 0, -3316347, 0, 4922505333747, 0, -4971002050523297522, 0, 4100309137124934874038963, 0, -2301022032360137825964458335227, 0, 577951262543040979328274795306257089], 2]], [[[1, 0, -1972821, 0, 1532459616582, 0, 656413199564007821, 0, -2176415229836155099315608, 0, 1393417118998801842405700085487, 0, -850621496750656827537818484672022020, 0, 1479140350009619670089055022886998814427687, 0, -2452439156939803274795223924784388567212339325208, 0, 785166991665894934262864987312192239935676234680215621, 0, 1945817072650098176206605067636448647118765295797252473733382, 0, -2659064644995978258493780790633306590603828236292022103451451785821, 0, 1430768783591580504260467570192606659308868671266092320119567817646303601], 1]], [[[1, 444, 2070060, 889930512, 1902465817572, 489080035726188, 1788118970002015102, 534430960198970234676, 2271643678539768162807588, 1161157467529029752322416496, 2951410581424801187813757740460, 691737532970739473751938030868708, 1702433061239903677780481956434843889], 2]], [[[1, 0, 1477262, 0, -1765263900982, 0, -1009295364367190784, 0, 4606160639251358566225126, 0, -673785414631531151917506056366, 0, -9841977887675061414843454171244654066, 0, -1011170222370702098306763134992735606320734, 0, 10373956249124319019898426084478564845326648793926, 0, -3411349977771897051617895834487433359201667141354140416, 0, -8954066275346137944115467325536535186027787250681290901704182, 0, 11245295108832994589871428318833902529046635496915757928988024746238, 0, 11423942188538511596885360939762740188135840651026045719095671542305476401], 1]], [[[1, 1592, -1734832, -1457454924, 6127703577856, 2685802709620504, -6478264521427780226, 3478192397237131674616, 10276772349623089873136896, -3165436554525701792929481436, -4879500868709982406463230351792, 5798832075822531940227408657949208, 4717120417286669419611030657597553321], 2]], [[[1, 0, -4731782, 0, 13255516953071, 0, -22818235851818268308, 0, 27597346752184480054812239, 0, -20510018384071219857959209991942, 0, 9024267965168278308669913635234402529], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '24-336e12-1.1-c3e12-0-2', 'leading_term': '46.335786126321987165146280949910675197583229952424607548810272370800300283570902243628037', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, '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}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.005859375', 'prec': 37}, 'plot_values': [46.33578612632201, 46.13246072787836, 45.83219767750027, 45.431209230276224, 44.926258888284856, 44.31474638333576, 43.59479226544886, 42.76532063677695, 41.82613840358339, 40.77800926814675, 39.62272055421681, 38.363158531860236, 37.004380637675986, 35.55456257136386, 34.02455857719876, 32.426046534750384, 30.77093354321106, 29.0712464444166, 27.33902532202835, 25.58622097359263, 23.82459725616363, 22.06563910452079, 20.32044016831077, 18.59936030991204, 16.912131548737563, 15.267968297677882, 13.675415264809999, 12.142508776831804, 10.676779312933913, 9.285199207185958, 7.974134503110062, 6.749301373030984, 5.615727483083094, 4.577730114077667, 3.6389128373192214, 2.8020927386455954, 2.069272985832629, 1.4416375120808929, 0.9195514143404853, 0.5025603416392821, 0.18940741445208387, -0.021940980400686195, -0.13426330034505954, -0.1510452330054906, -0.07643691628390628, 0.08479628787246626, 0.32732712899690547, 0.6453218409779141, 1.0324987309128664, 1.4821892884070098, 1.9874002938429696, 2.5408783238264143, 3.1351756478064186, 3.7627166041559783, 4.4158638549258615, 5.086982851783184, 5.768507142646517, 6.4530026214591105, 7.133228635269527, 7.802196272053483, 8.453223359332764, 9.079986830496582, 9.676573765627603, 10.237521625425767, 10.757854787494162, 11.233116769329591, 11.659397058017413, 12.033352935886331, 12.352225275666232, 12.613848483674028, 12.816654700314423, 12.959672315722102, 13.042518911772872, 13.065389514723234, 13.02904110530779, 12.934767798773525, 12.78437329821934, 12.580139816126042, 12.324791849409701, 12.021456933703302, 11.673623423801507, 11.285095714785518, 10.859947399590768, 10.402472872422626, 9.917137895838325, 9.408530530265097, 8.881313592514761, 8.340173167300886, 7.789768637170332, 7.234684760200872, 6.67938657684695, 6.128176775525734, 5.585155904832683, 5.054185798340882, 4.5388565382364225, 4.042457241337962, 3.5679509058067995, 3.1179541458969204, 2.694722101177247, 2.3001336880551735, 1.9356834628303097, 1.6024788094335691, 1.3012416242153195, 1.032314383273378, 0.7956704302848192, 0.5909282775989322, 0.4173696709374667, 0.27396113243780895, 0.15937881842497117, 0.07203589959927087, 0.010112016966591302, -0.028414858998647954, -0.04573473753635133, -0.04417075174207298, -0.02614362619898665, 0.005864079442333378, 0.04934350238320773, 0.10179434468807744, 0.160758641371906, 0.22385290417995188, 0.2887985136619491, 0.3534500707621006, 0.4158213893001747, 0.47410832038928846, 0.5267084313597773, 0.5722373916707609, 0.6095418665930199, 0.6377088069669112, 0.6560710711123863, 0.6642093299512516, 0.6619502721940939, 0.6493614565759201, 0.626742627787457, 0.5946139013782139, 0.5537012477810295, 0.504917955243114, 0.4493438863443498, 0.38820270877729085, 0.3228372667072518, 0.25468346636771483, 0.18524306322372727, 0.11605576885027362, 0.048671077945643036, -0.015379792084869674, -0.07461142635722283, -0.12761074207451745, -0.17306222686070027, -0.20977198035355862, -0.23668937570621756, -0.25292626464742823, -0.25777355055977497, -0.2507149021087922, -0.2314373859365987, -0.19983887679962573, -0.15603215528142894, -0.10034563093955771, -0.033320682968153666, 0.04429424398795946, 0.1315525911025339, 0.22732239774422905, 0.33030185782312904, 0.43903752311256505, 0.5519450140360799, 0.6673318208920721, 0.7834219023909642, 0.8983817355889884, 1.0103474261855474, 1.1174524791774045, 1.2178558195343965, 1.3097697231985874, 1.3914875299784193, 1.4614101101110875, 1.5180709578636942, 1.5601594809120125, 1.5865418087777796, 1.5962793050210764, 1.5886443488087076, 1.5631331218923497, 1.5194751999772214, 1.457639794010938, 1.377838535885201, 1.2805251617029878, 1.1663926619280576, 1.036364735683283, 0.8915839796726096, 0.7333971949723805, 0.5633378642719886, 0.3831058676423016, 0.19454472887131008, -0.0003832747608289038, -0.19962377340524703, -0.4010583427819207, -0.6025335042331841, -0.8018898956285528, -0.9969910642007409, -1.1857543048993175, -1.3661796429967672, -1.5363771399664707, -1.6945925264239199, -1.8392307748066574, -1.9688772557927223, -2.0823161594197406, -2.17854590393256, -2.256791310087221, -2.3165128418711167, -2.3574120188527985, -2.379432084971358, -2.3827564578350477, -2.3678030855133003, -2.3352151254258815, -2.285848281959404, -2.2207550208361706, -2.1411659287981215, -2.0484685335390007, -1.944184008461198, -1.8299426886378047, -1.7074570710813661, -1.578493809122824, -1.444845926851198, -1.3083047389861835, -1.1706322916532539, -1.0335348059416993, -0.8986375286534225, -0.7674614105590875, -0.6414020002541977, -0.5217109780974922, -0.40948058546636823, -0.3056306515600606, -0.21089930747848154, -0.12583726362998193, -0.05080556377078933, 0.014023072710107451, 0.06865938267410511, 0.11328933159975042, 0.14826271743865782, 0.17407886070060166, 0.1913697658589817, 0.20088103724197492, 0.2034507636302567, 0.19998707250995143, 0.1914447991879406, 0.17880180768045076, 0.16303549418514293, 0.14509966257676013, 0.12590267730214824, 0.10628732450243757, 0.0870128087044762, 0.06873935121281205, 0.052015609756267456, 0.03726940385645077, 0.02480205769555672, 0.01478649608988832, 0.007269212562115992, 0.002176151721124834, -0.0006775437279334961, -0.0015740518088390577, -0.0008758312129676524, 0.0009946552914847561, 0.0035780833480538563, 0.006403821733270235, 0.009017357842954954, 0.011009009266713665, 0.012043286969003338, 0.011888235077374458, 0.010444043643616065, 0.007770217353727338, 0.00411057133387483, -8.469159796714433e-05, -0.0041404413863104705, -0.007142337998332386, -0.007927453841136743, -0.005080191603612209, 0.0030660243339215537, 0.018420931581798132, 0.04312324426374795, 0.07951996529543576, 0.1301391816579085, 0.19765643150152082, 0.28485486029058854, 0.3945795572040846, 0.5296867291667203, 0.6929883773008153, 0.8871930251767921, 1.1148434177185822, 1.378252140102131, 1.6794361894258238, 2.0200516025787887, 2.4013292982612073, 2.8240133280066697, 3.288303141876234, 3.7938022445582607, 4.339471422172681, 4.923589142743959, 5.543720451398986, 6.196695089889903, 6.87859569594885, 7.584756810966687, 8.309775280641114, 9.047532474353757, 9.791228599628923, 10.533430702182574, 11.266135541863044, 11.980846699142285, 12.668651355499387, 13.32031015903101, 13.926358313580113, 14.477214859483993, 14.963298868786051, 15.37515112546664, 15.703559726549203, 15.939688522086316, 16.07521239853369, 16.102443740415502, 16.014456104220777, 15.805213702962904, 15.46966930922536, 15.003860694264183, 14.405000188967465, 13.671551855931632, 12.803294826355218, 11.801371521667924, 10.668322505255757, 9.408110129141486, 8.026107255145178, 6.529072801581769, 4.92511313017882, 3.2236241771535044, 1.4352036928295737, -0.42844556340628037, -2.3546261398639348, -4.329770782190066, -6.339580364384577, -8.36916994424983, -10.403227491406957, -12.426186965427798, -14.422401011148347, -16.376316048307526, -18.272653990895613, -20.09660933132435, -21.83400882719398, -23.471468242022727, -24.996544505716823, -26.397876742925, -27.665317673692186, -28.7900463942164, -29.764661520811334, -30.583257770035363, -31.241483336039778, -31.736577271631337, -32.06739869112098, -32.23446119541521, -32.23987258156639, -32.0872755107337, -31.781783805899916, -31.32990662036907, -30.73943711862008, -30.019331967688718, -29.179580689375012, -28.23106387891498, -27.185402480710252, -26.054800423518046, -24.85189411967196, -23.589618970984056, -22.28100649271681, -20.93901689289257, -19.576384708915423, -18.205460811140355, -16.838073698123562, -15.485403554240241, -14.157869759487221, -12.865033177698622, -11.615514281636287, -10.416927892552328, -9.275840098990983, -8.197749158624921, -7.187053671879254, -6.247047430101201, -5.379937415788682, -4.586880680975398, -3.868035501494702, -3.2226253167765, -2.6490138438373814, -2.1447896144983307, -1.7068580806446332, -1.331539364721541, -1.014670704338746, -0.7517109591573439, -0.5378385210143249, -0.3680525668136286, -0.2372718504844333, -0.14042790600096944, -0.07255123771432462, -0.028849274871553806, -0.0047750847875598955, 0.003913931134099599, 0.0011078974411492266, -0.009692824048528281, -0.025404056338717996, -0.0433735491971116, -0.061386307188359884, -0.07766007460981172, -0.09083167066758453, -0.09993511765781886, -0.10437265394393697, -0.10387982272114968, -0.0984858954161357, -0.0884709303958774, -0.0743208028631323, -0.056681305120425185, -0.03631273277204302, -0.014046197950095735, 0.00925800032506452, 0.03274828786285707, 0.05561533612352806, 0.0771206764676213, 0.09661997728510201, 0.11358072791216353, 0.1275942784780187, 0.1383823796545297, 0.1457981817470753, 0.1498222685089433, 0.15055430646178936, 0.1482009907734774, 0.14306057603868227, 0.13550504982031913, 0.12596078965120203, 0.11488848358623448, 0.10276310950148564, 0.09005477877628563, 0.07721100869569235, 0.06464096663709143, 0.052702408038446745, 0.041691592084324734, 0.03183644201412545, 0.02329305296904826, 0.016145328107705147, 0.010407920969848607, 0.006032127813001967, 0.002914307796438181, 0.0009063524725513917, -0.00017235605589468198, -0.0005220843499107944, -0.000349633341493421, 0.00014437578836638132, 0.0007771888391374167, 0.0013939962322029108, 0.0018758881951011198, 0.002145259285268698, 0.002168331394392449, 0.0019545971111267837, 0.0015531216994431035, 0.0010457699668224032, 0.0005375878283019833, 0.00014469906258583447, -1.979418253435796e-05, 0.00013869827023981374, 0.000680076365693473, 0.0016134599841104659, 0.0028820091260811907, 0.0043495173553953215, 0.00578960697617038, 0.006878311188637439, 0.0071907625227709115, 0.006202569623481482, 0.0032963391083341157, -0.0022263695601257728, -0.011127557844627236, -0.024209878440358396, -0.04228862745107436, -0.06615919225197832, -0.09656077518073938, -0.13413746930451648, -0.1793976979392733, -0.23267333947438879, -0.29408010811894225, -0.36348070982633357, -0.440452375681238, -0.524260372708526, -0.6138390361020037, -0.7077817561398927, -0.8043411870548358, -0.9014412701226745, -0.9967029388646369, -1.0874795119867318, -1.1709049358324024, -1.243954597210678, -1.303517550215454, -1.3464789951828957, -1.3698114262887726, -1.3706724561313504, -1.3465069439228345, -1.2951507255211678, -1.214933662622476, -1.1047781869057636, -0.9642900006635085, -0.7938329300829574, -0.5945903371634015, -0.3686092367263735, -0.11882332702509725, 0.15094765627620552, 0.43602439150842287, 0.7309217963981832, 1.0294312409444095, 1.3247325866467503, 1.6095335326317524, 1.8762336482432034, 2.117112727874173, 2.324541621019724, 2.4912077066167995, 2.6103510912372885, 2.6760061934655357, 2.68324228971358, 2.6283960342326766, 2.5092894161616166, 2.325425847813374, 2.0781490792891213, 1.770765350010787, 1.408620406014475, 0.9991222681508243, 0.5517044769932796, 0.07772609134283658, -0.40969611475946865, -0.8959259320492227, -1.3651176251681119, -1.800598561721969, -2.185322058209418, -2.5023808598778006, -2.735578820151056, -2.8700529368445284, -2.8929396033189763, -2.7940791417582833, -2.5667155745005603, -2.2082014824447356, -1.7206916060179547, -1.111805804560392, -0.395244059447278, 0.4086713079471814, 1.2725356510151, 2.1614992857741524, 3.0330201623742563, 3.836746602655207, 4.514540916368713, 5.000655775984453, 5.222089727200664, 5.099102408209823, 4.545903688862107, 3.4715307408281815, 1.7808591316118114, -0.6242247511158562, -3.843499321422665, -7.9769499578560765, -13.123194960509215, -19.377815692185138, -26.83161830894519, -35.56887003059545, -45.665510768709865, -57.187376830014415, -70.1884964520079, -84.7094722569699, -100.77596126868745, -118.39729588047571, -137.5652764306051, -158.25316348124085, -180.414895646016, -203.98455601261634, -228.87617645240724, -254.9840464267679, -282.18314035417626, -310.32974569040033, -339.2623360093141, -368.80282015160276, -398.7580754741646, -428.92174871805673, -459.0763048695939, -488.9952997712885, -518.4458479268945, -547.1912530216408, -574.994150200057, -601.620660540169, -626.8423789543366, -650.4388740086102, -672.2004760500965, -691.9309659346997, -709.4501225267245, -724.5960888983248, -737.2275196141778, -747.2254746089699, -754.4950378607992, -758.9671518834768, -760.6002630493896, -759.3812286655187, -755.3243724010022, -748.4709076641176, -738.8883478906117, -726.6695652147105, -711.9315131413051, -694.8136341939127, -675.4759784916159, -654.0971330996587, -630.8725655582607, -606.0116814258116, -579.7348708267283, -552.2715153618171, -523.8559793082405, -494.7243577697257, -465.1116096230957, -435.2487816082371, -405.3603639621205, -375.6618149558338, -346.3574258858593, -317.6386159508808, -289.6816016375746, -262.645742621377, -236.67249805942313, -211.88489225108893, -188.38629585272434, -166.26000330653545, -145.56929827956338, -126.35781019751474, -108.6501449371322, -92.45285388336848, -77.75551453031774, -64.5318467081453, -52.74118263950958, -42.33008274926712, -33.234080050804565, -25.379508201773618, -18.685136962576788, -13.063951005851411, -8.424933382515572, -4.67477850152884, -1.7195077228570916, 0.5340571960899843, 2.1769376208604423, 3.29678387904581, 3.9768292450455704, 4.2950192423534235, 4.32331888887843, 4.127200059206929, 3.7653022234085025, 3.28924971344177, 2.7436278162466468, 2.166107353423602, 1.5876768195918396, 1.0329926131923899, 0.5208255106221734, 0.06458076325724038, -0.32712763929419375, -0.6498675788694915, -0.9027628670475646, -1.087868882043555, -1.2095612768120285, -1.2739511742412388, -1.2883433300855578, -1.2607467384805144, -1.1994391417098806, -1.112593731337958, -1.007971063793662, -0.8926767670502114, -0.7729836301146309, -0.654214898314483, -0.5406844228573506, -0.43568761707721204, -0.34153364077171205, -0.25961576506036865, -0.19051031831011841, -0.1340957325558398, -0.08968419298828738, -0.056158532865083446, -0.03210768205564069, -0.01595482219130339, -0.006073379002392708, -0.0008870493975396785, 0.001048830777882263, 0.0009861610065721807, -5.635744092347706e-05, -0.0013134358863040136, -0.002274583559448167, -0.0026688467108177275, -0.002435693025815388, -0.0016852722219575468, -0.0006515462304017696, 0.00035813183660571713, 0.0010134949663377865, 0.0010086359201733868, 0.00010316882799934129, -0.0018450605052997859, -0.004857466326683091, -0.008823558372050832, -0.013501570503770564, -0.018530654777090365, -0.023453768059352204, -0.027749791440690955, -0.030872918422057725, -0.032296959203197806, -0.03156200453474182, -0.02832027936637496, -0.02237853906448672, -0.013734443403436986, -0.002604550104417112, 0.010558198752859705, 0.025059091979632638, 0.03996939027408828, 0.054147625861424936, 0.0662742585977497, 0.07489892012264836, 0.0784988737024018, 0.0755458946593346, 0.06457951467457494, 0.04428377743545554, 0.013564083910694653, -0.02837938808734343, -0.08198456684121885, -0.14727002654937277, -0.2237902006081552, -0.31060586981970517, -0.40627288243767123, -0.5088505662494379, -0.6159281456358966, -0.7246710076117495, -0.831885885757678, -0.9341041434261378, -1.0276820149134824, -1.1089090520558946, -1.1741261471651976, -1.219849179446103, -1.242893977276049, -1.2405022750604744, -1.2104536486409412, -1.1511627584570836, -1.0617632684389327, -0.9421722471816237, -0.793132130935327, -0.616228485665675, -0.41388143543931954, -0.1893068553672258, 0.05354626292241065, 0.3100816427608121, 0.5751637726257403, 0.843251944820378, 1.1085466425737323, 1.3651461164009517, 1.6072095542420923, 1.8291218060623766, 2.025654489293739, 2.1921196656987947, 2.324512912672873, 2.4196298486102075, 2.4751638883089013, 2.4897792361481623, 2.4631501804163003, 2.395972519520825, 2.2899450422585557, 2.147721291619575, 1.972833056313821, 1.7695879515622257, 1.5429442942485547, 1.298367360776156, 1.041670407591773, 0.7788457209753432, 0.5158901489315078, 0.258634176378679, 0.01258084655479641, -0.21724245894564972, -0.42641485194253403, -0.6112314379649418, -0.7687882868523704, -0.8970405242008039, -0.9948321176400563, -1.0618991484535598, -1.0988493711975278, -1.1071004066677281, -1.0887969255762078, -1.0467091743420587, -0.9841147521054954, -0.9046681588016197, -0.8122629690077033, -0.7108916447047811, -0.6045079778527305, -0.49689696939915423, -0.3915572992205498, -0.291598330286979, -0.1996543808176988, -0.11782126056983654, -0.04761813734252812, 0.010026316729764671, 0.05476432104875516, 0.08679723342095563, 0.10682378539490915, 0.11597117511867376, 0.11571253531134729, 0.10777505260928284, 0.09404180776854722, 0.07645229460243808, 0.056906500024920884, 0.037175641791140746, 0.018824746765695555, 0.003149760133948034, -0.008868642322012916, -0.01659300245260921, -0.019738110916941675, -0.018361393846569717, -0.012835864698872225, -0.003806823183067374, 0.007864702606303136, 0.0211684108356006, 0.03501764246606903, 0.04832436018024326, 0.06007182633836503, 0.06938113286504183, 0.07556789613713664, 0.07818591228320593, 0.07705523282759334, 0.07227297397147528, 0.06420576560110905, 0.053463898581816174, 0.04085838073161143, 0.02734313218164842, 0.01394528118098302, 0.001686218743151587, -0.008500546051754014, -0.015850094922301838, -0.01984044024437772, -0.020255464653356786, -0.0172314741217024, -0.011282933906785118, -0.0033039125870385905, 0.005457366562519062, 0.01345229435980632, 0.018914093533357358, 0.0199672272969117, 0.014761040264436791, 0.0016233068698584894, -0.020771763550428313, -0.05322754061217458, -0.09584966224277403, -0.14787945594716123, -0.20754488740648513, -0.27193804172740743, -0.336927772115657, -0.3971154692367649, -0.445841708472226, -0.4752516789532683, -0.4764162535903255, -0.4395135339206286, -0.35407078738584763, -0.20926291084722706, 0.0057382686228432895, 0.30137170300667226, 0.6872620406870265, 1.1717739896713248, 1.761560093296388, 2.461117229674544, 3.272366223005916, 4.194271459182102, 5.222537586763491, 6.3493744698187, 7.563344897006967, 8.849313422820607, 10.18850414024336, 11.558673590229919, 12.934401681118725, 14.287499841572945, 15.587531806900893, 16.802438559268715, 17.899270430198914, 18.845036465968604, 19.607524065288448, 20.156162867961278, 20.462907874809385, 20.503103704436604, 20.256303712141477, 19.707017881521956, 18.84536441289751, 17.667601773479298, 16.17652103336683, 14.381704166451751, 12.299602787967233, 9.953392242584018, 7.372617653201155, 4.592690418135605, 1.6542247214550099, -1.3977819927690829, -4.514905750014544, -7.646366558232411, -10.740185293560728, -13.74439671416426, -16.60829451907568, -19.283668883654972, -21.72599765330755, -23.895602152216703, -25.758596009535534, -27.28769268360472, -28.46285290263599, -29.27173969606551, -29.709966578733777, -29.78113053742948, -29.496640765348232, -28.875358305467717, -27.942951869279643, -26.731096054720314, -25.27654689310154, -23.620126694632543, -21.80546424382415, -19.877725189434415, -17.882345784539712, -15.863785085041883, -13.864334297335418, -11.923033095194958, -10.074694392361904, -8.349061277532467, -6.770175493853893, -5.355947714683758, -4.117942863467043, -3.0613813907720284, -2.1853180251192086, -1.483045785353334, -0.9426907323276357, -0.5479664437806393, -0.279058997237897, -0.11360661237411603, -0.027741860231002093, 0.0028449636118029024, 0.0018627013061126268, -0.008565171990015281, -0.00879054260734248, 0.017595020933248395, 0.08314990264952377, 0.19614932531821813, 0.360344772470166, 0.5749252947768034, 0.8346795703798298, 1.1303503891565427, 1.449166558995912, 1.7755300365359679, 2.0918300974939785, 2.379351317743637, 2.619235846705867, 2.793454895848514, 2.8857682675677547, 2.8826243997812453, 2.7739542336583254, 2.5538150492964493, 2.220873578949296, 1.7787002047205898, 1.2358575392489022, 0.6057751449571959, -0.09358965019230717, -0.8402965401887372, -1.6091653023072985, -2.3727057217860357, -3.102137239823042, -3.7685131369041738, -4.343893307213078, -4.802524773834338, -5.121982285703504, -5.284223276330522, -5.276513581341508, -5.092184002866715, -4.731183037189777, -4.200397692059387, -3.5137370526248715, -2.6919712337799093, -1.762201814009394, -0.7571171713406396, 0.28597075480890055, 1.3262978467774151, 2.320991805456284, 3.2265461679252, 4.000376034185655, 4.602403035326204, 4.996614504660672, 5.152535030917868, 5.046577561830238, 4.663211162712362, 3.9958495223833648, 3.0474738522135985, 1.8309584524800881, 0.3690772208695176, -1.3058171940801788, -3.1524391029655012, -5.121526986188873, -7.157088574243235, -9.197906162558567, -11.179258988875139, -13.034832594932924, -14.698803197402047, -16.107778714364144, -17.20273696766011, -17.93089410207843, -18.247417603580924, -18.116928322029235, -17.514742214880382, -16.427821467452056, -14.855422674052384, -12.809328088676965, -10.313716243498972, -7.404687443493256, -4.129414540098238, -0.5448399698987239, 3.283829415812899, 7.2848415017321475, 11.381802235664177, 15.495704053723715, 19.54699895349261, 23.457682440351554, 27.153353904831473, 30.565126337136853, 33.631351584242815, 36.299176600842, 38.525982448343825, 40.28014341631996, 41.54151218240259, 42.30161576132367, 42.563511890212176, 42.341319338719124, 41.659446505266715, 40.551549393327775, 39.05925995060291, 37.23073234839772, 35.119058863054725, 32.78066939124882, 30.2737981794453, 27.656596234909156, 24.98549276882374, 22.31376342202995, 19.690276496796624, 17.158455895417458, 14.755481864853612, 12.511741123171602, 10.450531024495518, 8.588013069393451, 6.933402410486794, 5.489383774573101, 4.252718960071813, 3.214932391186832, 2.363169593010714, 1.681150380826603, 1.150159488016752, 0.7500230953678133, 0.46003828499217264, 0.2598223459442452, 0.1300536812798708, 0.053082263816876335, 0.013394415044447893, -0.0020761687944986125, -0.00379222876972376, 0.00039530335584750056, 0.0051197150845881615, 0.007251213804155818, 0.0055537496077258984, 0.0002727869542816156, -0.007317621026311316, -0.01537962739934702, -0.021960319719737623, -0.025398631780270606, -0.024668038016578287, -0.019637050112478693, -0.011234438026901356, -0.0015108641370805424, 0.0064032255430753636, 0.008438653415960083, -0.00018270013311446216, -0.024644574016834245, -0.07017874339591489, -0.14167549635851012, -0.2432863785076404, -0.3780440726633453, -0.5475249091969632, -0.7515768268586324, -0.9881290750225917, -1.253102096413582, -1.5404249906755914, -1.8421650179161662, -2.14876772961016, -2.4494002434633693, -2.7323845587048083, -2.985702710346925, -3.19755214863039, -3.3569338970284313, -3.454222677567066, -3.4816998120849867, -3.434035505021411, -3.308665444800643, -3.106058123974673, -2.8298539953056707, -2.4868614057095866, -2.0869028861682084, -1.6425121324734737, -1.1684900254104378, -0.6813313667774185, -0.19853562642675016, 0.26215461170029664, 0.6835629871445577, 1.04990936127944, 1.3476094742422084, 1.5660108801906483, 1.6980330350686978, 1.7406784046233301, 1.6953865402328487, 1.5682113734012646, 1.3698003817103408, 1.1151646644193842, 0.823253136227657, 0.5163374224538141, 0.2192276651834803, -0.04165546376318538, -0.23933636175855416, -0.3474030991610092, -0.3411506712375293, -0.19870558543552896, 0.0979189022031448, 0.5618845225319802, 1.2007438544198534, 2.0158479253912525, 3.0019754984807614, 4.147205904969231, 5.433050179427208, 6.8348505011442535, 8.322424133686287, 9.8609380912558, 11.41200619532909, 12.935005202460385, 14.388422967682681, 15.731286176709544, 16.924616351229542, 17.932845474824862, 18.725136254817613, 19.276554772380884, 19.56906176963026, 19.592294327530293, 19.343993255457715, 18.830231474530876, 18.065321796314176, 17.071280348104025, 15.877090183544727, 14.517714452199897, 13.032885610922706, 11.46571526631568, 9.861176586280179, 8.264516606114297, 6.719663759818072, 5.2676918821701735, 3.9453921535578886, 2.783960543463915, 1.8079226058021363, 1.0343591625953128, 0.47242460309067597, 0.12317532116925972, -0.020285793854823684, 0.02764463084347102, 0.24581510953961158, 0.6073242102208078, 1.0807426921695733, 1.6315003334518392, 2.223401429082279, 2.820189331733163, 3.387092693569634, 3.8922922651902345, 4.308248953204183, 4.612839542060657, 4.790254329374523, 4.831620603658525, 4.735327031109532, 4.507036445379182, 4.1593851095969905, 3.7113703421043325, 3.1874788724148138, 2.6165846239495116, 2.030659630053966, 1.4633539282777448, 0.9485037880266057, 0.5186303826420904, 0.2034912623245018, 0.028744714388372606, 0.014782397022897664, 0.1757798344711704, 0.5190117611725669, 1.0444902282220845, 1.7448948285640218, 2.6057895077904405, 3.60613076604111, 4.719044062690845, 5.912835277922042, 7.1521946645073635, 8.399547373592705, 9.61650430075929, 10.765318142717096, 11.81030625204709, 12.719233608675665, 13.464662971663563, 14.024811455528843, 14.38423383986953, 14.53428789846699, 14.473322714197737, 14.206587251435556, 13.745884831829763, 13.108964789745313, 12.318655098350789, 11.401838149123048, 10.388295191314347, 9.309503784763617, 8.197448841685903, 7.0832273040321425, 5.995849888136678, 4.961221524630157, 4.001299829206088, 3.1334673284707497, 2.370119233136117, 1.7184974001214715, 1.1807734589422116, 0.7543611236745198, 0.4324349949856455, 0.20462559754000437, 0.05784609958996779, -0.022799497422654476, -0.05304983949838478, -0.048531156261501056, -0.023867934513041332, 0.008094822980299055, 0.03691677743475893, 0.055002686917381916, 0.057835974869619736, 0.043994056657777184, 0.014945381965683943, -0.025360512216273737, -0.07108893012819534, -0.11527004774830471, -0.15065898231275188, -0.1706564016131613, -0.1702356061584059, -0.14682171407097008, -0.10106908949584921, -0.037486924966502, 0.03513086677251972, 0.10350682200357719, 0.14993715539889227, 0.15261958139324563, 0.08626297957063823, -0.07704058612751524, -0.3667195807794735, -0.8124378407468427, -1.4426704646249195, -2.2832006608709725, -3.355603614957422, -4.675787022255723, -6.252658521557708, -8.086987761422213, -10.17052527411757, -12.485418665530625, -15.003953446322681, -17.688761311878405, -20.493411090572806, -23.363384029388417, -26.237425617411155, -29.049237823287708, -31.729460325811825, -34.207875710058275, -36.41576227951027, -38.28831038366263, -39.767057832897336, -40.802174452242674, -41.354407237969546, -41.396882694488255, -40.91650663635834, -39.91491180180994, -38.40892232024878, -36.43050462432824, -34.02619311597458, -31.25599839612578, -28.19182828359194, -24.91548570445289, -21.516228811921774, -18.088031957591422, -14.726657851998768, -11.526663939767728, -8.578395702526604, -5.965078547782553, -3.760117112822123, -2.0246978993412155, -0.8057808735001373, -0.13455142209026813, -0.02539590138227156, -0.47544700269836787, -1.4646906019441683, -2.956641739881126, -4.899592998052136, -7.228331751202763, -9.866277737300239, -12.727978300599535, -15.721870895271369, -18.753217004741764, -21.72714134356271, -24.55162424823868, -27.140271136393398, -29.414887170284175, -31.307741688479112, -32.763478855868335, -33.740646879751715, -34.21254369446434, -34.16761849736403, -33.60940282473232, -32.55595618151037, -31.03884455704475, -29.10166617403516, -26.79826962306243, -24.190725487830235, -21.347111053251606, -18.339190095885005, -15.240081080916138, -12.12198518881417, -9.053978313814758, -6.100064527223759, -3.317472635363936, -0.7551779055962753, 1.5470117922353954, 3.559054591419476, 5.260945416034007, 6.642637697367571, 7.70363919912727, 8.452315744976243, 8.904946519571695, 9.08457634448522, 9.019710434994446, 8.742986080616003, 8.289760402626815, 7.696607448886068, 6.999995195062182, 6.235093957854162, 5.434741210054049, 4.628588603556107, 3.8424479900646773, 3.0978441431532526, 2.4117658275809624, 1.796601166033671, 1.2603068421619046, 0.806693745691739, 0.43584862678456693, 0.14466794997741622, -0.07254447011220384, -0.22344850885208326, -0.3170379622407159, -0.3630375600274965, -0.3713504563821997, -0.3515752660363005, -0.31260927464891664, -0.2623449309635707, -0.2074441543733863, -0.1532204485603827, -0.10361351739900793, -0.061241969455081376, -0.027520725563421392, -0.0028279166036649568, 0.013294816997915326, 0.02192467218892129, 0.02453784406582078, 0.02280098130424386, 0.01838563153849029, 0.012814215536940206, 0.007342813263979728, 0.0028850167619836374, -2.3380706473281947e-05, -0.0012217543705906942, -0.0008890598938193599, 0.0005180665585631366, 0.0023457744367829272, 0.0038337713700895932, 0.004208216859742792, 0.002768959534689687, -0.0010355656425351679, -0.007551123561024546, -0.016881645862238993, -0.028875846078182388, -0.04313632219679305, -0.059049290853063326, -0.07583166720534425, -0.09259108889765892, -0.10839395910210978, -0.12233645922177039, -0.13361113257546717, -0.1415652337097667, -0.14574739041796744, -0.1459400497569556, -0.14217032441940325, -0.1347034505985453, -0.12401961147244844, -0.11077572171543429, -0.09575539407918787, -0.07981147704606077, -0.06380470996594519, -0.048542921656304756, -0.03472693533483445, -0.022906377929534576, -0.013448591328090611, -0.006522516400224013, -0.002097539965592212, 4.086828704304721e-05, 0.0002610509610304034, -0.0009564641694753217, -0.003068546425176844, -0.00552287353970964, -0.00781059520353891, -0.009513693774999983, -0.010342956237350317, -0.01016317688142801, -0.009003178312755704, -0.007049451681349317, -0.0046235269122112625, -0.0021443627237385026, -7.859341883024862e-05, 0.001117468257341403, 0.001059341376436492, -0.0005061395065428644, -0.0036488137164171182, -0.00821587326042799, -0.013809799077814494, -0.019787070069431995, -0.02527981893162807, -0.02924108099568917, -0.030512012058343186, -0.02790807244251856, -0.020319066081050212, -0.006816236166385545, 0.013240980496032478, 0.04010702281679228, 0.07356974953160918, 0.11289574204420255, 0.15680869977043646, 0.20350673517068935, 0.25072228061357194, 0.29582602354545445, 0.3359756068281792, 0.3683003994633357, 0.3901145119201839, 0.39915011055171074, 0.39379763651655086, 0.3733385111098257, 0.33815484334747453, 0.2899003851724791, 0.23161760226319883, 0.1677872796307628, 0.10429978795633203, 0.04833893886015175, 0.008173272715028702, -0.007138165611062818, 0.011878832269416108, 0.07466765580369715, 0.1901400813700902, 0.36614082192038416, 0.6089012070910303, 0.9225084820813266, 1.3084187129130542, 1.7650374040443164, 2.2874059300646583, 2.8670409305147784, 3.491888389938697, 4.146434780193834, 4.811986448930735, 5.467114504268126, 6.088258439197768, 6.650474008023037, 7.128303323635028, 7.496738596479052, 7.732249672771042, 7.813825191435841, 7.723992087231078, 7.449775923114943, 6.983464484554716, 6.32324260215207, 5.473648120266703, 4.4458080877248625, 3.25743451449616, 1.9325681514207618, 0.5010690344791792, -1.0021443185710475, -2.5380895913360053, -4.064899366246868, -5.5391744001887835, -6.917508771899651, -8.157936403350924, -9.221375668179054, -10.073024185240618, -10.683631874627498, -11.030601404149808, -11.098889638873795, -10.88164347631779, -10.380504678938506, -9.605635512173308, -8.575442130877676, -7.316017823402913, -5.860309119760471, -4.2469053264507215, -2.5187051437250663, -0.7214641093509879, 1.0977451157122529, 2.892111131066125, 4.6166425050258955, 6.229614682265883, 7.693862897685747, 8.97787962694244, 10.056678369126795, 10.91242943929623, 11.534895433761841, 11.921372231451272, 12.076387268608734, 12.011184171761052, 11.743007919020311, 11.294118778342423, 10.6906880773883, 9.96161868149445, 9.137330051567298, 8.248559801488332, 7.325230742012448, 6.395446285565696, 5.484649755468118, 4.614833380054871, 3.8040277663491198, 3.0660093411906573, 2.41019553730875, 1.8417607632623563, 1.3619301404343869, 0.9684208945388493, 0.6559980182766002, 0.41710744254832466, 0.24254861615148643, 0.12214921345368414, 0.045405752808513604, 0.002061323670271737, -0.017401657956190583, -0.021375068589342086, -0.016857884585511893, -0.009311403081115185, -0.0026316624458535003, 0.0007728451499667739, -0.00018438989293922888, -0.005499762234318435, -0.014353683981071622, -0.025402149796937515, -0.03706213804684052, -0.04776948561648647, -0.05619040590512678, -0.06137384289323752, -0.06283775499847216, -0.06058843735432481, -0.05507786322438812, -0.04710929852909926, -0.037705745676296, -0.02795879710655559, -0.018877001017268365, -0.011252850042526326, -0.005565472147060439, -0.0019324827653742613, -0.00012191614028847004, 0.00037271291339227857, 0.00019723934784047578, -4.910134516209185e-05, -3.495541750254781e-05, 6.725120768780578e-05, -0.0006445135021373675, -0.003990720507642161, -0.012834997717198685, -0.031119360416673035, -0.06378816475109667, -0.11658625922063207, -0.1957248562481393, -0.3074179997015836, -0.4573031430530366, -0.6497701165876336, -0.8872331404933186, -1.169391187575138, -1.492532270839809, -1.8489273436613212, -2.226376659459526, -2.60796622340545, -2.9720865873331763, -3.2927509982844603, -3.5402417897197695, -3.682098325218978, -3.684440394717997, -3.513601289469813, -3.1380337160912455, -2.5304063285984504, -1.6697854812014383, -0.5438350490906915, 0.8490901761257234, 2.498082879850882, 4.37819364308521, 6.44941706876545, 8.656247306302209, 10.927900508388165, 13.179271466191695, 15.312671775329765, 17.220320658226505, 18.787558352320872, 19.89672965389389, 20.43162509605656, 20.282337994963594, 19.350387599710054, 17.553916165623956, 14.832530259424168, 11.151772655535655, 6.5069531626784025, 0.926012867822399, -5.528541064612645, -12.75888072171008, -20.632430033610525, -28.983821342479064, -37.618255510010414, -46.31622845594245, -54.83959685126219, -62.93897934034114, -70.36170047390839, -76.86063179728886, -82.20329979552842, -86.18034893863623, -88.61393664396991, -89.3654514413304, -88.34219303225116, -85.50271399871066, -80.86056200238978, -74.48621244950986, -66.50706684585559, -57.10534472254074, -46.513793540655804, -35.00914122080893, -22.903920022791695, -10.537047955150735, 1.7367566257408433, 13.558371980811323, 24.576083305800818, 34.45738322778248, 42.90033018887706, 49.64403988131219, 54.47822662952907, 57.25181618318252, 57.87760213713848, 56.335082579805835, 52.671262601791405, 46.99909798868588, 39.49362822107526, 30.385934343524166, 19.955140043507402, 8.518749120844943, -3.5783237348235164, -15.97566703349601, -28.309869114277223, -40.22701855168347, -51.394979366107655, -61.514257355823275, -70.32738081882809, -77.62656172420955, -83.25937858936878, -87.1323024567006, -89.21197380011964, -89.52425839260954, -88.15143083243743, -85.22686348663206, -80.92799249710203, -75.46836989162091, -69.08754958790212, -62.04072321825376, -54.58836404265195, -46.986123579376596, -39.475381336790804, -32.274810001541816, -25.57329138217498, -19.524406998772296, -14.242506579443326, -9.800764568746683, -6.231165614453807, -3.5262649085983573, -1.6423792484897857, -0.5044094878869043, -0.011855849560645074, -0.045651993375631084, -0.47547251772061555, -1.1671662089741528, -1.9899726586436064, -2.8231655387995582, -3.5618366319343946, -4.121583104063899, -4.441907974303776, -4.488205468908207, -4.2523589475392125, -3.75190826268386, -3.0278839864052682, -2.1414719472330077, -1.1697145718849902, -0.20045804488422114, 0.673135123450977, 1.3582135067290975, 1.7677324349142698, 1.8255473780390383, 1.4708676583200684, 0.661838241699309, -0.6219790658661165, -2.378207244707279, -4.581411226614518, -7.184032873645108, -10.118417313592294, -13.299789178077367, -16.630024678737524, -20.002022794939656, -23.30445478601795, -26.426658931508722, -29.26352699152814, -31.720287502655893, -33.71629866252611, -35.18828187709673, -36.092754285651225, -36.40734711699544, -36.13124516238035, -35.28467624617527, -33.90749354649647, -32.056944700185696, -29.804756466079212, -27.23369129642831, -24.43382264391408, -21.49873708128925, -18.521326744673246, -15.589891238710994, -12.78472289789188, -10.175277629488981, -7.8179789176756, -5.75472417904307, -4.012127042430695, -2.6014926290575207, -1.5194881721333824, -0.7494399418631237, -0.2631623801086309, -0.02319218304106201, 0.014694953029563095, -0.10121255304637373, -0.3212597962092437, -0.5969852305514505, -0.8834258435542229, -1.1410704229606434, -1.3373871230981793, -1.4478774042039815, -1.45663535429252, -1.3564213055539265, -1.1482714787787525, -0.8406904700633232, -0.4485047316232087, 0.008534006705220705, 0.5073020371669508, 1.022919291607815, 1.530335271626006, 2.0058011806642018, 2.428156064596107, 2.7798704872253985, 3.0478139370640633, 3.2237076619920977, 3.3042701885399186, 3.2910858572076687, 3.1901711781482796, 3.0113311440396537, 2.7673562682232236, 2.473113669823249, 2.144593009363728, 1.7979662220374792, 1.4487140361563742, 1.1108634841584495, 0.7963799734615447, 0.5147334519184745, 0.27264896408075795, 0.07403841380324443, -0.07990009254960251, -0.19042448519882885, -0.2608691620379931, -0.29618041081535695, -0.30240452805483653, -0.28616635963333215, -0.25417116417739055, -0.21276370324776095, -0.16757022257977194, -0.12323689295308723, -0.08327278107352157, -0.04999684547700744, -0.024579953151963804, -0.007171596634689812, 0.002909143493390549, 0.006941417358218074, 0.006553192507155243, 0.0034764187095311866, -0.0006699254580306539, -0.004551942078479535, -0.007237173884955532, -0.00824937303494846, -0.007561814920334367, -0.005535060983773771, -0.002809827092514091, -0.0001698019707270035, 0.0016080023345444302, 0.0018969388071535282, 0.00034025799169470146, -0.0030691661378753608, -0.007960345023256031, -0.013613676689860625, -0.019049676338685383, -0.023172346784444135, -0.0249568792772295, -0.023666250232158115, -0.019078057156674277, -0.011699680085482571, -0.0029485822917805237, 0.004723662468608324, 0.007781352359065479, 0.0016428499459056225, -0.019184802776054652, -0.060873479587453455, -0.12994980494298516, -0.2328927334430255, -0.375674875099545, -0.5632801302581478, -0.7992272536832362, -1.0851304332975589, -1.4203250598828616, -1.8015956689178383, -2.2230311346866682, -2.6760273742135112, -3.1494498105053395, -3.62995851268611, -4.102488851208799, -4.550870276946997, -4.958588313702707, -5.309706346617551, -5.5896329386396735, -5.785894077771887, -5.888859890887169, -5.892353366018441, -5.794100019751416, -5.5959849976664255, -5.304094015588332, -4.928526347027454, -4.482982026980338, -3.9841870636528816, -3.4511011189162843, -2.9038772229584384, -2.3627573381124263, -1.8469845244695764, -1.3737684908856733, -0.9573580962746719, -0.6082806108572919, -0.3327998292400536, -0.13263400439453082, -0.004961176752242149, 0.057277708484288044, 0.06480208378380306, 0.03112963705122617, -0.02852197884227162, -0.09849818140577468, -0.16405636509003432, -0.21271717723312078, -0.2355317669548943, -0.2281793713364869, -0.19181549122717295, -0.13360158856593224, -0.06686405891387388, -0.0108447037007642, 0.00997725135944769, -0.033023385428272094, -0.17115282988047487, -0.436627292420969, -0.8605796083494213, -1.4709437179059035, -2.2903305348997725, -3.3340154261498145, -4.6081534404010425, -6.108336422361979, -7.8186087380787725, -9.711017423373216, -11.74575775567736, -13.871976317242815, -16.02930350520161, -18.149838206740746, -20.160657383856243, -21.9867652724638, -23.55434141933552, -24.794173323746143, -25.64503147216003, -26.056854990536277, -25.993626321189932, -25.435761030688194, -24.38187835276919, -22.849896468029645, -20.877412197899194, -18.520878105894507, -15.854034329997438, -12.96559940254112, -9.956234731581647, -6.934814224834011, -4.014297754522398, -1.3073404088092202, 1.0781929768412384, 3.0436135945977, 4.503501800041391, 5.389325329980487, 5.652426657921159, 5.2662187411281405, 4.227476125785624, 2.556647268901254, 0.2971618059224343, -2.4861733161326236, -5.709634482464422, -9.273792704374172, -13.067334989941987, -16.97132936970205, -20.863749067269246, -24.624104045543238, -28.13807135148969, -31.30169624267588, -34.02498555942471, -36.234790317108, -37.87698977527531, -38.917847150968015, -39.3445043704951, -39.164623664588675, -38.40522153522409, -37.11077517208109, -35.340711221951025, -33.16649874978023, -30.668523659467496, -27.93220312240938, -25.04435671164463, -22.089845836922816, -19.14851844673718, -16.292575823039254, -13.584452255827333, -11.075269242986272, -8.803895181408286, -6.796611320162268, -5.067373140129348, -3.6185506805058916, -2.442085919530746, -1.5210964163584884, -0.8317193611041297, -0.3450766807066981, -0.02925607013309947, 0.14879326702639306, 0.2215385904542859, 0.21938711312877865, 0.1695075981604718, 0.09498193397706972, 0.014293689942257944, -0.05885146364402276, -0.11540151966914976, -0.15056560343195988, -0.16321413947619398, -0.15513893890788197, -0.1302383157747819, -0.09369058831207963, -0.051173588689960275, -0.008178908275940497, 0.030542577911499735, 0.06137905502742209, 0.08208643212861488, 0.09185100157739619, 0.09120133758021985, 0.08179385275535025, 0.06610563660257043, 0.04707265281756131, 0.027711954398235646, 0.01076481793669146, -0.0016067839868519568, -0.00804534035165508, -0.008125814334749841, -0.002377777536912846, 0.00779585394412511, 0.020292467454431244, 0.03255682841873483, 0.041875336622311236, 0.045688480536485, 0.041891863237281474, 0.029097124889617285, 0.006827754247342297, -0.024369366593719792, -0.06290990399265048, -0.10625918275388135, -0.15111522112387482, -0.19367427744839044, -0.22995974490302518, -0.25618967753303634, -0.2691369572636764, -0.266462380081604, -0.2469909877999845, -0.21090408159047286, -0.15982547417300458, -0.09678954015929268, -0.026087365920125085, 0.04700341920379282, 0.11659013120133628, 0.1766142550643725, 0.22134876807532386, 0.24590959901299086, 0.24673057323237654, 0.2219706109534725, 0.17181965171136976, 0.0986720477731215, 0.007150891216558497, -0.0960279842127455, -0.202351849108395, -0.3019548967795529, -0.3841872909076608, -0.4382769830905131, -0.4540460732922541, -0.42263725077215947, -0.33718234504835737, -0.1933748657210372, 0.01009330868527404, 0.2712622654719686, 0.5848268594544114, 0.942263882596878, 1.332162445031504, 1.7407431210963529, 2.152538724228206, 2.5511983347177023, 2.92038176737824, 3.2447212183259233, 3.5106670326037617, 3.707238699972488, 3.8266395327728495, 3.864684822066393, 3.82101530829296, 3.699081618762973, 3.5059002802176242, 3.251597028175834, 2.948767473656303, 2.611701517033531, 2.2555266167826784, 1.8953261433663946, 1.5452127421909332, 1.2175380351610332, 0.9222664549416502, 0.6665388804693716, 0.4544527492146755, 0.2870691303259616, 0.1626400494770566, 0.07703240465125628, 0.02430924541059104, -0.002583921157608636, -0.011087776628788642, -0.008319865482645442, -0.0004509454551843812, 0.007772526708633874, 0.01330924930405582, 0.014875749630278141, 0.012759394963080203, 0.00840215857334146, 0.0037880191532587305, 0.0006881476186632124, -0.00016351352727409809, 0.00012213101335630888, -0.0021077117197047246, -0.013539072261120829, -0.04408895699392554, -0.1067393597466379, -0.21696136394628726, -0.39171381078006334, -0.6480371076736433, -1.00130418223499, -1.463230853260656, -2.03977816500699, -2.7291194864340236, -3.5198675140716857, -4.389772297571991, -5.305110791591051, -6.220965653895133, -7.082561517510268, -7.8277928874516185, -8.391021754772183, -8.708171394440905, -8.72299026549311, -8.39434812411717, -7.7043554378935255, -6.666975591001649, -5.336738409616452, -3.81710662194949, -2.267990782469852, -0.911862488942235, -0.038017501900151615, -0.004490896859241534, -1.2372204023275808, -4.226148324426545, -9.518005983332738, -17.70567243515746, -29.41414209878837, -45.2832875025573, -65.94776079693673, -92.01473714770525, -124.04080890258554, -162.50730870573167, -207.79631803925395, -260.1682783387574, -319.74020366897776, -386.46712223301336, -460.1272941755382, -540.3119367149213, -626.420131021933, -717.6594306893443, -813.0525086704084, -911.452134935014, -1011.5685172862829, -1111.9954312737323, -1211.2381483894376, -1307.7442841719937, -1399.940260787831, -1486.2697341776814, -1565.2327590495927, -1635.4244620719476, -1695.5719839067312, -1744.568486138577, -1781.503099063864, -1805.6929219568844, -1816.7234506998866, -1814.4386164569314, -1798.9365852604342, -1770.5654951133051, -1729.9123729954204, -1677.7856519810896, -1615.1919168665497, -1543.3076898767513, -1463.4472196654117, -1377.0274238869372, -1285.5350097563867, -1190.4929896572307, -1093.4237599776754, -995.8003580255629, -899.0107590378924, -804.3299008692996, -712.8965085720431, -625.6951782427242, -543.543976487427, -467.08760935430473, -396.79619112664085, -332.97041822170826, -275.7481988254341, -225.11631532339422, -180.92729279851784, -142.91503341029988, -110.71511319571628, -83.88667194176499, -61.934207330370604, -44.328531624613255, -30.52625019785152, -19.987282233382214, -12.189983235818687, -6.643342922803317, -2.896660642249431, -0.5464640240984958, 0.7593181440575453, 1.319674780406011, 1.3809987475585255, 1.1394980953945022, 0.7451446620966153, 0.3067438556891454, -0.1022831406398288, -0.43777968380353244, -0.6787384678296794, -0.8214831941960202, -0.8743684206009863, -0.8531635870780764, -0.7772232533266877, -0.6664718540637419, -0.5392126476331597, -0.41070633731685025, -0.29242720594167465, -0.19188162348165075, -0.11286270805782973, -0.05600939956005181, -0.019543354200444465, -7.245425591646599e-05, 0.006631620518643235, 0.004952327004727409, -0.0011096972297905904, -0.008307191513111756, -0.014343589350574991, -0.01791230272145918, -0.018605815068921637, -0.016729739282457082, -0.013063150099464824, -0.008604174641313213, -0.0043351730735675855, -0.0010345994808223084, 0.0008465285365994492, 0.0012355176990209251, 0.0004178221693871141, -0.0010443974649330986, -0.0024382782571830968, -0.0030495998923619843, -0.0023127983675987405, 5.96626559141791e-05, 0.003986370078919125, 0.008977055463676043, 0.014149848310298519, 0.018304938491280124, 0.02004724586835912, 0.017944896300580764, 0.010705967720358629, -0.002646216285799642, -0.022620455360832126, -0.04914538049857038, -0.08151151462165994, -0.11837668780232767, -0.15783735537814142, -0.19756163691184966, -0.23497343101625492, -0.267471390210679, -0.2926624133666372, -0.30858851030922674, -0.31392574354742975, -0.308121846230307, -0.2914678079869265, -0.2650932211821043, -0.23088150277966932, -0.19131022053289617, -0.14922938976683767, -0.10759738860946046, -0.06919939877122282, -0.036376454337902125, -0.01079388373478738, 0.006724688519266202, 0.016275124881082976, 0.018845841542217016, 0.016182742090640752, 0.010551965645254763, 0.004416298299260515, 5.113591625484747e-05, -0.0008656228048222067, 0.0023507755958536635, 0.009054371040746965, 0.017032143642809732, 0.022407366368081015, 0.01971255621755314, 0.00214989308683426, -0.037959577484182, -0.10855090531208969, -0.21704393951042705, -0.36947147563731303, -0.5695663822445876, -0.8178779017344567, -1.1109968773928398, -1.4409770388499104, -1.7949990699992728, -2.155349211195488, -2.4997705831174994, -2.802235404176267, -3.0340331418376287, -3.1652002960404504, -3.166237575424418, -3.010020936933665, -2.6737994154124616, -2.1411663183859404, -1.403831797161769, -0.46304931031207663, 0.6693718331388495, 1.9705967877796107, 3.4069172388948736, 4.934602267505025, 6.501502517533081, 8.049244546520283, 9.515964425366201, 10.839474695718522, 11.960782490754157, 12.82759105150907, 13.397579480014757, 13.641342331191755, 13.544737389050258, 13.110447329982865, 12.358638639098414, 11.326629491753094, 10.0671456835285, 8.645564472985809, 7.136217866021369, 5.617867123190443, 4.168413223062679, 2.85932963872629, 1.7501024571648667, 0.8830009778928337, 0.27853341170830614, -0.06807015533663573, -0.18904010648346284, -0.14466027515858854, -0.022045677219024944, 0.06797081870910668, -0.004213994652204564, -0.38032787538485435, -1.2061126061987302, -2.622087825490992, -4.753612053006586, -7.700733297417934, -11.52836970585643, -16.25738331329813, -21.857111616422106, -28.23999756929006, -35.25898972771135, -42.70757825155595, -50.32267887017311, -57.79067289934937, -64.75645112033823, -70.83523460361025, -75.62679958126935, -78.73159685014518, -79.7681377854681, -78.39092528393809, -74.30861992451072, -67.30216452244694, -57.23799790559153, -44.07919113977824, -27.893666804079782, -8.858561133460391, 12.739619582535346, 36.509222482065184, 61.96203889223074, 88.5260590792052, 115.56201046980135, 142.3837451111796, 168.2812463341566, 192.5436657809652, 214.48484798830557, 233.4676721331837, 248.92667571989827, 260.38833478410726, 267.48818068886067, 269.98406234777985, 267.7650212047497, 260.85558279898845, 249.41655988122787, 233.73837801463435, 214.22937576148252, 191.40137456506417, 165.85102895447312, 138.23862783734458, 109.26520557405293, 79.64878936362277, 50.10072244005777, 21.302973905274786, -6.112768995605649, -31.583899119593323, -54.632376541078585, -74.8759490673927, -92.03539192104711, -105.93790185850384, -116.51607741287569, -123.80306243379329, -127.92436001024103, -129.08680255301846, -127.56530556235442, -123.68870185967623, -117.82426077118083, -110.36067021138152, -101.69249166423707, -92.20586302382735, -82.265896358508, -72.20615464841782, -62.32012764097322, -52.855322108518635, -44.0098844992952, -35.93162808374704, -28.719423304218413, -22.425956195282836, -17.062186296168708, -12.603258083219824, -8.99517795390418, -6.161848849886956, -4.012082929653338, -2.446259814026019, -1.3623643437771764, -0.6611625889310068, -0.25038032836361424, -0.0478084428929957, 0.01666242475933568, 1.361079113810046e-05, -0.05400429415392586, -0.11418995441393508, -0.16059597953662186, -0.182802551822043, -0.17794114722878612, -0.14863617772668075, -0.10103008262138483, -0.04300869879340194, 0.017285566701313617, 0.07259671701292733, 0.11733118637197411, 0.14797454395302337, 0.16318311708424274, 0.16360493946442112, 0.151497898153009, 0.13021951370746834, 0.10366315503599612, 0.07570791544100532, 0.04973776768466852, 0.02828055457095606, 0.012788955333994942, 0.003570816272566618, -0.0001382034061375798, 1.976891323269893e-05, 0.0018100618272034804, 0.0027440102899399543, 0.0004306482574690174, -0.007097333169006552, -0.021117521912172664, -0.04203929495420454, -0.06932900587715175, -0.10154174249594328, -0.13645386056165643, -0.17128068962178947, -0.2029559339990598, -0.22844390617828841, -0.24505313764993467, -0.2507202495280873, -0.24423614411300007, -0.22539318924671942, -0.19503673783633954, -0.15501274083522107, -0.10801701957587899, -0.05736518619444629, -0.00670207660283356, 0.040323861441037924, 0.0803918066015004, 0.11081528316483277, 0.12979607820844385, 0.1366014582193494, 0.1316477710404105, 0.11647824304756837, 0.09363511535722426, 0.06643419373412171, 0.03866299913122431, 0.014229632291175506, -0.003210076243050726, -0.010615420868715838, -0.005881946627043159, 0.011908247768177555, 0.04233119515631544, 0.08357855103156213, 0.13253591250856941, 0.18497962524451975, 0.2358826759751612, 0.27981429837092003, 0.31138978398512196, 0.32574018772032254, 0.31896878328852035, 0.28855754572604625, 0.23369032170215578, 0.1554652033037657, 0.05697185244641721, -0.056777463912211557, -0.17905894517880502, -0.30178262836135605, -0.4159587740606003, -0.5122759234893383, -0.5817039500219123, -0.6160985289109285, -0.6087732518643026, -0.5549971218255769, -0.4523844026998918, -0.30113733098107376, -0.10412896327939743, 0.1331766439121264, 0.40296623622850397, 0.6954670695626518, 0.9994481671486583, 1.302795913771001, 1.5932272750859444, 1.8589811305284887, 2.0894644286536432, 2.2758347572538526, 2.411447499851622, 2.492164474707395, 2.5165091772587687, 2.48565955173145, 2.4032832484321545, 2.2752306917349867, 2.1091115140488594, 1.9137891363834787, 1.6988173322939482, 1.4738686621364774, 1.2481857755940182, 1.0300841764845607, 0.826560382207395, 0.6430168590243047, 0.48311440323023824, 0.34875377751178127, 0.24017876332543603, 0.1561840878204913, 0.09440473820883206, 0.05165757553461593, 0.02430343661287592, 0.00860019070496295, 0.0010171312955971517, -0.0015138973932503443, -0.0014282334260584846, -0.00044804414984992385, 0.0004077393269247838, 0.0007313341845290818, 0.0005676272334136826, 0.00021117870104883424, -1.5345966624813195e-05, 2.6328538948406014e-05, 0.00011340376074494951, -0.0004558043335583939, -0.002903462302999419, -0.008927656897380913, -0.020570288149795335, -0.0400050155972005, -0.06926150244036336, -0.10990976134191432, -0.1627342117622335, -0.2274322083239184, -0.3023717858159782, -0.38443748026078545, -0.4689851297196146, -0.5499261730896582, -0.6199498821523712, -0.6708799248071933, -0.6941508732280199, -0.6813793027299658, -0.6249944212538906, -0.5188860349066166, -0.35902408257863355, -0.14398286395200002, 0.12466332465737288, 0.4421164812199344, 0.8003306484339854, 1.1881937055243144, 1.5919240562231494, 1.9956712688148317, 2.3822943249489885, 2.734277416896112, 3.0347412595138312, 3.268504922481337, 3.423047450886461, 3.4893653520019674, 3.462680078861223, 3.3429444666282584, 3.134998689826678, 2.8484649161781594, 2.497366072500977, 2.099469484936732, 1.6753873293672028, 1.2474909029630994, 0.83867081366931, 0.47102178680174456, 0.16457712258422727, -0.06385351746127095, -0.20167365990694255, -0.24125493575252596, -0.1803889817528378, -0.0224146247746638, 0.22398104258886226, 0.5452767898351261, 0.9239232675549934, 1.3393935201198237, 1.7693946288973468, 2.191167135128233, 2.5827923833362467, 2.924426794051245, 3.199402249266175, 3.395148990623134, 3.503759735670298, 3.5222626307323344, 3.452608294382327, 3.3013819338806396, 3.0791529537682494, 2.79962324766122, 2.478629554719496, 2.1330586883998213, 1.779751551219094, 1.434470396413578, 1.1110030409240583, 0.8204552291413896, 0.5707339716114664, 0.36632820958940804, 0.20834436546496837, 0.09477526905895453, 0.021003126699129734, -0.019534913606566073, -0.03458114796573573, -0.032257899010754265, -0.02030083835621172, -0.0053867497312600305, 0.007392331477869897, 0.01487088795824625, 0.015942106629629037, 0.01147574870720878, 0.004037373005250664, -0.0025590828232003094, -0.003818221895986101, 0.004807521881716155, 0.027288337955953975, 0.06644899327512696, 0.12351835521194694, 0.19784197108138277, 0.28678786783978955, 0.38585906046947743, 0.48901432640985587, 0.5891647398484829, 0.6788021683428143, 0.7507030199009483, 0.7986408834115909, 0.8180384228062445, 0.8064917694487048, 0.7641096810679143, 0.6936243799527401, 0.600250676398863, 0.4912919759874665, 0.37551491112234053, 0.2623316689813555, 0.16086821154148173, 0.07900087267131235, 0.022453201476210542, -0.005951955442794536, -0.006796409199719839, 0.015747594676136803, 0.0541019167204536, 0.0978616206263891, 0.13475756405144412, 0.15195729202078806, 0.13762581683754263, 0.082631316698092, -0.017739882895780323, -0.16221065108792113, -0.34224018645841603, -0.5412017450331716, -0.7341428723944018, -0.8882298054528505, -0.9639311870689248, -0.9169384542793007, -0.7007892171889445, -0.270090766452602, 0.4158281506540861, 1.389067655953397, 2.6693286158543397, 4.260378038113646, 6.147086588302343, 8.293305326892154, 10.640911006336077, 13.110140031823315, 15.601095876291962, 17.996727318551372, 20.16718146760118, 21.975467943876822, 23.284365675547452, 23.963638593385213, 23.897610606977647, 22.99270007018055, 21.184435542099532, 18.4436367887539, 14.780749691642164, 10.248399752315018, 4.94211331109298, -1.0011408476695138, -7.406650883554569, -14.067770957884333, -20.75365054145788, -27.21911758435813, -33.215585237722884, -38.50270762881011, -42.860508417817904, -46.100295539172215, -48.074456362248284, -48.68465262415736, -47.88784919598095, -45.699798151836596, -42.1957240900181, -37.508074109778114, -31.821300663494085, -25.364067424513856, -18.399269608550508, -11.211880464558037, -4.095329712398148, 2.6622152521607543, 8.791310848628477, 14.053778643291619, 18.25367776296704, 21.246139760127193, 22.94360896524541, 23.319248811225552, 22.407380381588464, 20.300497882941087, 17.143151122202955, 13.123240762912282, 8.461480642631996, 3.3994534541023875, -1.81307782245178, -6.930907113590306, -11.725484457435451, -15.995737896725265, -19.577061394640253, -22.348069211447733, -24.23494276574664, -25.212754658198385, -25.303921192903054, -24.574120137857978, -23.125995269805433, -21.091100161803276, -18.620622534054316, -15.875485320467257, -13.016438746862406, -10.194741581434434, -7.544090418384481, -5.173847929837983, -3.1640474423307827, -1.5630669483921467, -0.38751954034348185, 0.3757847512576018, 0.7660383990341764, 0.8431490794376093, 0.681398692965263, 0.3625323676445304, -0.031220914329546687, -0.42368169307481945, -0.7503440968199926, -0.9628940015020367, -1.0323316344230395, -0.9503299968287285, -0.7289443447973063, -0.3987218112226163, -0.0053594775718028, 0.3948226501913247, 0.7402451679070672, 0.9698743216447709, 1.0293693573682103, 0.87689307416868, 0.4873322577403322, -0.14509553953146473, -1.0060093027307615, -2.0618344638956163, -3.2623235725736026, -4.54437868030875, -5.836822162628177], 'positive_zeros': ['0.23946650388903427875713569665326', '0.26096952344869793127910113341943', '0.64578155283160375270690354002767', '0.67290571318109831008641384081701', '0.836447948393048858269632719188853', '0.916672806243928519755480437736564', '1.10741071718529465301268641954237', '1.35216618616488050546472995675864', '1.48642386162484006500971061297459', '1.50311117982220118156072339866499', '1.56433660804343454577520562738725', '1.59201948696641822343299596588060', '1.92054676043969794898203573390176', '2.30489252008179561673121799831690', '2.31527482245549568783838564309406', '2.40589288554845625328020620534390', '2.57680342924427340015158676598794', '2.59422633061877871388284351458817', '2.65836803083807922302193598515774', '2.66247382358156692672086102588476', '2.72260839566187879189768621719875', '2.92059807705488800198905509585118', '3.04781559496624860243982888138922', '3.13771542317066004459633119502296', '3.20958424895438755211897050277818', '3.70157267120420125299584839621342', '3.78605761221020899900156707352882', '3.93932131854150714319198897900612', '3.95481450751363973231452357900791', '3.99387681509463886786834327904368', '4.01408844657321335281585860176925', '4.09692830462124958078513581955144', '4.16223473831538819484836491619118', '4.31123995309346437394772506048076', '4.46515249260122874435137511738017', '4.59848869606365800111307149003754', '4.67128403551375835877428216586399', '4.70711561491265161870557585330738', '4.79971049705225644759869590934164', '4.84206289273925582708816153874509', '4.87552830426865712699904432388702', '4.96275878641873398025903734298792', '5.16530662550722136492299669603272', '5.40117359294278861788251456664018', '5.40929946866665191575599510418020', '5.42280743057346020431908107678590', '5.54807037378705516037836882200208', '5.65269980970256431058294367629937', '5.73182032623686577954377575680015', '5.85437051816526314479805248481161', '6.12165818169907828042811691137655', '6.13431504455973465346614535320729', '6.15843957277302318441424478449839', '6.20603339503387610874149613612686', '6.22258868273828360190917939001143', '6.39505603327670653328869670524359', '6.47944826828593609431858643501592', '6.50815196179685020666279626293951', '6.73077227159969238674231165222978', '6.73689286823398089586494070160324', '6.88233435036840257936812942643945', '6.88234127918333654759027115822305', '7.11699891957337068525490081514472', '7.14110794363006248791000434551892', '7.17420137554534778179175768470958', '7.22766667499837987216089684769468', '7.25748291227948730036468767682111', '7.50956390265439695602286114795381', '7.51027992279522079213856133620421', '7.70106436085459786416878545792944', '7.84352123323279613344374986946369', '7.922718558539933115898095616571165', '7.974542046356813571624458160295403', '7.990358517907219073881712987840073', '8.020228221553633976063825628984800', '8.179480859948325930206712942131830', '8.187436982924762638873549230994703', '8.256133118036771891612369556131522', '8.272073275588989481782033158774498', '8.334255556945228407971353404110785', '8.456985758749109916179006039466584', '8.464571637361225100856178275397284', '8.632836000377782658479251826272256', '8.750370127460112968721364728385373', '8.947680299119972898518792628529695', '8.980274948836794367330897774889126', '8.987931296795307447913706432510124', '9.094488456862205311867572771344846', '9.109704077443453514629307394759903', '9.118526826256321124786868328875234', '9.124849418860039668647028430491287', '9.277813286133475782966541458787621', '9.387608267902169869115791912616306', '9.532363196576232772283183264323475', '9.625243167621124223082782519923369', '9.803098276314712954507286047095630', '9.807319686572748599357962344139711', '9.891891692609708537911578478133002', '9.929070549166978075731359571905713', '10.13795196281853396695106670030664', '10.14391614637673299304494465659286', '10.21864590925269550838100352562185', '10.35026453599062375624644230822233', '10.43340281787721103595026281927834', '10.45805620955342251187035548336059', '10.50043403029812847928395913300216', '10.51833535998373708054093387009954', '10.57820866832094693679580921606561', '10.59446691118417452315217830459858', '10.81672337969843148777431261605051', '10.83725947355933259561475442368956', '10.89427445827534719178146289544409', '10.90112835966695136273192027291256', '11.09489407473924266202679887408471', '11.14520985412450438076639580991323', '11.35620243161220968322656890590458', '11.39169849941171699881778673518754', '11.44452592088238500954911908229778', '11.50687321005123966814204461487403', '11.57369170985079003161599040166272'], 'prelabel': '24-336e12-1.1-c3e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e12-0', 'trace_hash': 474316101557812143, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23946650388903427875713569665', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.26096952344869793127910113342', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.64578155283160375270690354003', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3685226441161823.0, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2070481377455157458127600746496, 'conductor_radical': 42, 'degree': 24, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, 56, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -300, 0, 168, 0, 0, 0, 354, 0, 0, 0, 0, 0, 930, 0, 0, 0, 0, 0, 764, 0, 0, 0, 0, 0, 1012, 0, 0, 0, 0, 0, 1400, 0, 0, 0, 0, 0, 0, 0, -900, 0, 0, 0, 2358, 0, 168, 0, 0, 0, -792, 0, 0, 0, 0, 0, -2904, 0, 1062, 0, 0, 0, -1674, 0, 207, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2790, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 4742, 0, 10147682, 0, 18336975648, 0, 35136366245806, 0, 55422032379705850, 0, 74318354148055569358, 0, 98183511104624075331850, 0, 110272968880699461454282126, 0, 101952068382400630504275974688, 0, 99951954979104730568807644102562, 0, 82745065559059343504605847400524342, 0, 30912680532870672635673352936887453361], 'euler13': [1, 0, -17694, 0, 150344127, 0, -825783978694, 0, 3311047419013899, 0, -10270057919177967660, 0, 25258100677402513310250, 0, -49571607994809486902996940, 0, 77141064612756834011656363419, 0, -92863873378440283409233917993526, 0, 81606907956862197917187854946794847, 0, -46358202918742126128973477052547969006, 0, 12646218552730347184269489080961456410641], 'euler17': [1, 0, -17217, 0, 160729722, 0, -865949822635, 0, 2480649769543932, 0, 2994987661331912811, 0, -48570103865944827020748, 0, 72291721329547677377496459, 0, 1445281718515176703316067360252, 0, -12177925486969072614972200519688715, 0, 54559490573666945971240925850713770362, 0, -141066899401352818587190235712715631923233, 0, 197770344305988984840145602058543169130838081], 'euler19': [1, 300, 83160, 15948000, 2884970160, 429462962340, 60380369111228, 7433977043645460, 869187264653707200, 91277486172699660000, 9126239049539154084600, 829900380859959867931260, 71963509971308988283216278, 5692286712318464734140512340, 429351956302172147904755532600, 29454121872122959286616055140000, 1923785140320357813034470722059200, 112856149836754835971724437167072540, 6287247845562017611937136771543838748, 306726525751833529215833527299330260460, 14132784876736183197442471222550991837360, 535862607118307229850675873375976696772000, 19165603944330754083184571633797412679227160, 474231159647058593999144938081588937831237700, 10842505080063916320800450434338728415281531281], 'euler2': [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], 'euler23': [1, 0, 58691, 0, 1855192226, 0, 43669490183457, 0, 835010896549582396, 0, 13098051643974790616191, 0, 172460855929679516062212988, 0, 1938981719283719622456692478799, 0, 18298950194528671131207483135869116, 0, 141670416313323639519094175718159795633, 0, 890957483896871158534747945532135187999266, 0, 4172598424901464647264447330624334723097770259, 0, 10524515126174167358877236351104092889324551536161], 'euler29': [1, 0, -52666, 0, 2519040527, 0, -103130851328970, 0, 3368948978362405387, 0, -97485851940324492609644, 0, 2660654312384909011632366346, 0, -57986858201658108511708400707724, 0, 1191983952409580873121489206320123867, 0, -21704638904963328368749444768682499814170, 0, 315345838520787890155002806528268505411491887, 0, -3921663009329262022772164097953687164203972972266, 0, 44292268542362921407825091617016319887724139383235921], 'euler3': [1, -3, 6, -9, -198, 2565, -36018, 69255, -144342, -177147, 3188646, -43046721, 387420489, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -930, 569163, -261202590, 100353300315, -33216928806732, 9794533901888048, -2603356187506835040, 633073931196657625701, -141557155724308631524902, 29322254113324930701973269, -5635471353483609226766378646, 1008520666810586017753160781150, -167886327091630202474597186242986, 26023608460793267147071190201103189, -3742717711489986196236084602781529242, 498648774990320162898276800628351007461, -61088434997937823659056865523931152283040, 6846904380318211386730666390269473195179568, -691759363233429240596130022147529345086115892, 62260458085101877955208193486171150756393793115, -4827732658061817549974751803971689087637533731490, 313391688895639649932603529624144734338538360740363, -15255232995851277673289089994361181376919860503017630, 488675963633769261467693849486036510107332864779998081], 'euler37': [1, -764, 80360, 35913560, 14537415840, -8384323490844, -799972723059332, 358393333975450156, 165375950980271204816, -29204567104447927365944, -8979742386005317363086232, 15978484235667058571855308, 733741480468576126635183993590, 809358161989243517840186916124, -23039562185790514772896587186700888, -3795476350856126875126916362948657688, 1088661948223279676639607203073817113296, 119504919672922385399079573999827402654908, -13511582339454970537496534023424401927539428, -7173056170002622790305134421653710154707351628, 629982653158734758919734057339896765409664942240, 78832446970628450932851142379700681951246722687480, 8934940197779462728316917855152859358458352767897640, -4302791012199179541328543377917274114038938281020057708, 285273917723723876056171083405292782327767461712708093041], 'euler41': [1, 0, 481476, 0, 115071158562, 0, 18349339969105268, 0, 2194095027782226746511, 0, 207524579777911349744722056, 0, 15866062069248227933510977629276, 0, 985763386514799540544438505571839496, 0, 49506441877445950766866667077058243513391, 0, 1966662641848505323673012123381139380824936628, 0, 58584003484878017310364671227274789692824717509282, 0, 1164368225474441154907068041616072980272462963100588676, 0, 11487323243342943712727117998313670374759563626306467569441], 'euler43': [1, -1012, 1245002, -852507032, 617746830855, -325426335753288, 174692605767795850, -74974379068410274156, 32320322136164328828683, -11630781566400845334701416, 4178182940072753301958406204, -1278184307934666532591479937264, 389408847481824864652500007427738, -101624599770961532006750795372048848, 26411811249338084094692608312897955996, -5845544886324287024386420718734854669688, 1291508139809719495581150805158767127709883, -238198877932348819958700471076243189648749892, 44127235797163055236162872581078776933754606650, -6535672222643174742773578151117855968526445087384, 986400900328625612437169900706210924909029777274855, -108229654150621975849600425290371599248551167080260424, 12566771443545505431298569171504719829994794895982585498, -812156167402073386492688689004717798555887389488873169916, 63806423321775344604618774305037646254726223988233042609201], 'euler47': [1, 0, -437385, 0, 98505882894, 0, -16642251751296271, 0, 2374463475062057432592, 0, -286916948686756436570920197, 0, 30812765825290076853254460902508, 0, -3092739571434191400374679183138099813, 0, 275892432755488389817232330461185095430672, 0, -20843638396066899717901089467009788803468798319, 0, 1329874805364648749982004598353890877475018801190414, 0, -63650178074097895295790661784537319107280347085231557865, 0, 1568638556854706336108974223356857608957236560013645822451521], 'euler5': [1, 0, -354, 0, 53346, 0, -3913744, 0, 238386078, 0, -66225097710, 0, 12349753291374, 0, -1034767151718750, 0, 58199726074218750, 0, -14929748535156250000, 0, 3179669380187988281250, 0, -329688191413879394531250, 0, 14551915228366851806640625], 'euler53': [1, 0, 362162, 0, 31342470242, 0, 2991238457561520, 0, 1746851780280097098622, 0, 230369925295695020431645054, 0, 11387103576961192305310074686062, 0, 5106002217514536541894014436402705966, 0, 858156491479311853961717992323327000004702, 0, 32569919758287047395116179347005023253190367280, 0, 7564044803722356535304412080641305372516376869079202, 0, 1937220106054664113192298708038725804374561119051494515138, 0, 118558120445975157028044470669508269904542112710719750776396721], 'euler59': [1, 0, -661854, 0, 202275596298, 0, -40619516236130848, 0, 7446151473115219252038, 0, -1620799166433794781581625186, 0, 356878833337049532415712506341006, 0, -68366173765065438783793988345525882226, 0, 13248173476787091402392649734074658836253478, 0, -3048393004757515553242095644727505254774771205408, 0, 640312189577008467795335724059308194776701181804667978, 0, -88373600070081805916675830465700214089730284416602321648654, 0, 5632126739027588519658984775872141857619309476789431335641625841], 'euler61': [1, -2358, 3274005, -3349814886, 2769988834986, -1971385890773130, 1255859174153710355, -746741883560577476418, 426090230957405107588752, -237108440693732373533355174, 128334679353086591634975445617, -66588480619025175545607616021254, 32721887318351964942932629699352712, -15114319919386953370517562292120254174, 6611850723769918501883466019230636625737, -2772780745316606076677680255471566426195534, 1130992167500009839959285296894688391230805392, -449902116304051871865928733689964338619890896618, 171742576003329332690535441280004451598253387307755, -61192497560293052575859456818113238775882874697596930, 19516146018401686517089074198283031193340578328721688426, -5357058061977764557081660502062220530821868053125130679806, 1188432140767532281885866201503398234197172267451241185113005, -194280116897592785415607797677877157786287775735721146938725598, 18701397461209715023927088008788055619800417991632621566284510161], 'euler67': [1, 792, -260820, -1221864760, -593843874768, 277390666295568, 608150471782500244, 218629122721527308688, -113846601773968545956328, -180988011212274352966919416, -53128697364524185126485768756, 28594737528056557096359164715864, 36246571971031922690525994899293606, 8600239043150874281972271457437404232, -4805936010341271841014955274070007711764, -4924056552363757712326164425148766716990952, -931574740564060991414884895159462841088732008, 538059188919241843091952099672015079260759073584, 450150250963290987932460074223566758846730369305396, 61753659731648169125023828782107824983331531405060656, -39761938211530200592551616208084979910269338715347083728, -24606101568800575894697372382974332525380689462377453525480, -1579737660029655045842221475124259416883592156738280674256180, 1442758596626222372968691410007114971705109208062893199377343304, 547889398733702676213614311297941818478464344374520135510515030481], 'euler7': [1, -56, 1736, -48216, 1156792, -25993912, 536820382, -8915911816, 136095422008, -1945689515112, 24028474580936, -265863444556808, 1628413597910449, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -3844636, 0, 6901086974498, 0, -7655680355206958700, 0, 5850229234251244135613647, 0, -3245867934818370369643978238264, 0, 1341101770056839013980852537421086044, 0, -415796604020303165917927332009563786153144, 0, 96000405694084949746875879125260760756628586927, 0, -16092890978269805502794513884301796117073838077910700, 0, 1858308742753900277388170242564562264275767439188726642338, 0, -132618981972474240747646696626949292042050296728839855987094236, 0, 4418761423445010359012517479030513507821439762288727229544623559521], 'euler73': [1, 2904, 5932080, 9063407232, 11723795534880, 13051713462287016, 13084661733360788156, 11882917853081720537400, 9998686567349345413335744, 7801474085970581186528333184, 5709514896007979349315899880432, 3907920673578948680003412598515144, 2518322403076120372802115558298104870, 1520247576673661878648887558836565773448, 864045019272887849599011369850964331076848, 459285158104522232986650924857996083600324992, 228990400167231466716275958687780977024013906624, 105868313963513520122499962439182165391919674151800, 45349654410397013094630634927225874871555281106960764, 17597363017898203778187530124117784007154681727957761768, 6149175363847851481257673641627408790250036474698209922080, 1849305737888310317844154664432253525753299104877537853938304, 470861089203030659301564684001556870613436775368488216001903920, 89670790018845089358463937491703166020903456808133288098288350232, 12012211336350227316446820100278887925603925639507433655692782073761], 'euler79': [1, 1674, -336861, -2052405226, -300737318949, 1327255085709756, 406747243169844832, -281214387106447896288, 96095575106235401052789, -56509383114401672827245922, -311613333749468231753156062131, 43022558303685385389288509224302, 239148512591023504865333569120433854, 21211799123490738726949417299440633778, -75749292407574386943697844104640974975251, -6772739754254263002613939653241955275245118, 5678432736485181355092976385238937475693888949, -8193017925516573450615359277715643352098374593312, 5842682157759449541028107640754122267142872400237152, 9399901770539172573695338693102167543747941920289976324, -1050116578030404722700071021003865081428726729922329378469, -3533414416607091166457837658410816088558732314009221476796534, -285932467612431334708688415782283739364223189945453347042974461, 700566661392096746026324165117206952322153574678405656996610164886, 206336132715709669990485567530001552309415935666586885734738159549121], 'euler83': [1, 0, 5725470, 0, 15556843382055, 0, 26496019606387001486, 0, 31476045560037079218614955, 0, 27458324289434654054780210553060, 0, 18029617696810204667200196572666834842, 0, 8977234795274847418597191817449870385459140, 0, 3364474753494813523299751810504217832895748557755, 0, 925947363088132500469315786152835862870073881062979774, 0, 177744305762530131453171202554194192641172204257083747347655, 0, 21387199211726350621173989885069145455026852137181696185660114030, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], 'euler89': [1, 0, -1635561, 0, 1787180462010, 0, -817237014874197619, 0, -172174360613175733010436, 0, 757568773104150957695916528195, 0, -706211584110844416447446370021831084, 0, 376497506849041838263541094260448255145395, 0, -42525414811439248991661951990927407352100545156, 0, -100315524541875821209497125848370655490571320995065539, 0, 109025620594382108461187668219574050785020683813735247716410, 0, -49586898518502549462988443303620722778440535105607052362642314361, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], 'euler97': [1, 0, -6632694, 0, 20843168091903, 0, -42591475693158319462, 0, 65402812509511105939522203, 0, -80737708092210420490421078476644, 0, 81496326134313904825955347036847534922, 0, -67252250582940861563252189178132601779378276, 0, 45379241847341153089427330081763848917416570295323, 0, -24615797150432092170311166411602204883933484424564166118, 0, 10034260078643025271314555260322603477090230772289515271058943, 0, -2659757177483791505837763048491493400772176229468696661346814348406, 0, 334027661875095082935878165689897695724025886105865253311336914562753921], 'euler_factors': [[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], [1, -3, 6, -9, -198, 2565, -36018, 69255, -144342, -177147, 3188646, -43046721, 387420489, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -354, 0, 53346, 0, -3913744, 0, 238386078, 0, -66225097710, 0, 12349753291374, 0, -1034767151718750, 0, 58199726074218750, 0, -14929748535156250000, 0, 3179669380187988281250, 0, -329688191413879394531250, 0, 14551915228366851806640625], [1, -56, 1736, -48216, 1156792, -25993912, 536820382, -8915911816, 136095422008, -1945689515112, 24028474580936, -265863444556808, 1628413597910449, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 4742, 0, 10147682, 0, 18336975648, 0, 35136366245806, 0, 55422032379705850, 0, 74318354148055569358, 0, 98183511104624075331850, 0, 110272968880699461454282126, 0, 101952068382400630504275974688, 0, 99951954979104730568807644102562, 0, 82745065559059343504605847400524342, 0, 30912680532870672635673352936887453361], [1, 0, -17694, 0, 150344127, 0, -825783978694, 0, 3311047419013899, 0, -10270057919177967660, 0, 25258100677402513310250, 0, -49571607994809486902996940, 0, 77141064612756834011656363419, 0, -92863873378440283409233917993526, 0, 81606907956862197917187854946794847, 0, -46358202918742126128973477052547969006, 0, 12646218552730347184269489080961456410641], [1, 0, -17217, 0, 160729722, 0, -865949822635, 0, 2480649769543932, 0, 2994987661331912811, 0, -48570103865944827020748, 0, 72291721329547677377496459, 0, 1445281718515176703316067360252, 0, -12177925486969072614972200519688715, 0, 54559490573666945971240925850713770362, 0, -141066899401352818587190235712715631923233, 0, 197770344305988984840145602058543169130838081], [1, 300, 83160, 15948000, 2884970160, 429462962340, 60380369111228, 7433977043645460, 869187264653707200, 91277486172699660000, 9126239049539154084600, 829900380859959867931260, 71963509971308988283216278, 5692286712318464734140512340, 429351956302172147904755532600, 29454121872122959286616055140000, 1923785140320357813034470722059200, 112856149836754835971724437167072540, 6287247845562017611937136771543838748, 306726525751833529215833527299330260460, 14132784876736183197442471222550991837360, 535862607118307229850675873375976696772000, 19165603944330754083184571633797412679227160, 474231159647058593999144938081588937831237700, 10842505080063916320800450434338728415281531281], [1, 0, 58691, 0, 1855192226, 0, 43669490183457, 0, 835010896549582396, 0, 13098051643974790616191, 0, 172460855929679516062212988, 0, 1938981719283719622456692478799, 0, 18298950194528671131207483135869116, 0, 141670416313323639519094175718159795633, 0, 890957483896871158534747945532135187999266, 0, 4172598424901464647264447330624334723097770259, 0, 10524515126174167358877236351104092889324551536161], [1, 0, -52666, 0, 2519040527, 0, -103130851328970, 0, 3368948978362405387, 0, -97485851940324492609644, 0, 2660654312384909011632366346, 0, -57986858201658108511708400707724, 0, 1191983952409580873121489206320123867, 0, -21704638904963328368749444768682499814170, 0, 315345838520787890155002806528268505411491887, 0, -3921663009329262022772164097953687164203972972266, 0, 44292268542362921407825091617016319887724139383235921], [1, -930, 569163, -261202590, 100353300315, -33216928806732, 9794533901888048, -2603356187506835040, 633073931196657625701, -141557155724308631524902, 29322254113324930701973269, -5635471353483609226766378646, 1008520666810586017753160781150, -167886327091630202474597186242986, 26023608460793267147071190201103189, -3742717711489986196236084602781529242, 498648774990320162898276800628351007461, -61088434997937823659056865523931152283040, 6846904380318211386730666390269473195179568, -691759363233429240596130022147529345086115892, 62260458085101877955208193486171150756393793115, -4827732658061817549974751803971689087637533731490, 313391688895639649932603529624144734338538360740363, -15255232995851277673289089994361181376919860503017630, 488675963633769261467693849486036510107332864779998081], [1, -764, 80360, 35913560, 14537415840, -8384323490844, -799972723059332, 358393333975450156, 165375950980271204816, -29204567104447927365944, -8979742386005317363086232, 15978484235667058571855308, 733741480468576126635183993590, 809358161989243517840186916124, -23039562185790514772896587186700888, -3795476350856126875126916362948657688, 1088661948223279676639607203073817113296, 119504919672922385399079573999827402654908, -13511582339454970537496534023424401927539428, -7173056170002622790305134421653710154707351628, 629982653158734758919734057339896765409664942240, 78832446970628450932851142379700681951246722687480, 8934940197779462728316917855152859358458352767897640, -4302791012199179541328543377917274114038938281020057708, 285273917723723876056171083405292782327767461712708093041], [1, 0, 481476, 0, 115071158562, 0, 18349339969105268, 0, 2194095027782226746511, 0, 207524579777911349744722056, 0, 15866062069248227933510977629276, 0, 985763386514799540544438505571839496, 0, 49506441877445950766866667077058243513391, 0, 1966662641848505323673012123381139380824936628, 0, 58584003484878017310364671227274789692824717509282, 0, 1164368225474441154907068041616072980272462963100588676, 0, 11487323243342943712727117998313670374759563626306467569441], [1, -1012, 1245002, -852507032, 617746830855, -325426335753288, 174692605767795850, -74974379068410274156, 32320322136164328828683, -11630781566400845334701416, 4178182940072753301958406204, -1278184307934666532591479937264, 389408847481824864652500007427738, -101624599770961532006750795372048848, 26411811249338084094692608312897955996, -5845544886324287024386420718734854669688, 1291508139809719495581150805158767127709883, -238198877932348819958700471076243189648749892, 44127235797163055236162872581078776933754606650, -6535672222643174742773578151117855968526445087384, 986400900328625612437169900706210924909029777274855, -108229654150621975849600425290371599248551167080260424, 12566771443545505431298569171504719829994794895982585498, -812156167402073386492688689004717798555887389488873169916, 63806423321775344604618774305037646254726223988233042609201], [1, 0, -437385, 0, 98505882894, 0, -16642251751296271, 0, 2374463475062057432592, 0, -286916948686756436570920197, 0, 30812765825290076853254460902508, 0, -3092739571434191400374679183138099813, 0, 275892432755488389817232330461185095430672, 0, -20843638396066899717901089467009788803468798319, 0, 1329874805364648749982004598353890877475018801190414, 0, -63650178074097895295790661784537319107280347085231557865, 0, 1568638556854706336108974223356857608957236560013645822451521], [1, 0, 362162, 0, 31342470242, 0, 2991238457561520, 0, 1746851780280097098622, 0, 230369925295695020431645054, 0, 11387103576961192305310074686062, 0, 5106002217514536541894014436402705966, 0, 858156491479311853961717992323327000004702, 0, 32569919758287047395116179347005023253190367280, 0, 7564044803722356535304412080641305372516376869079202, 0, 1937220106054664113192298708038725804374561119051494515138, 0, 118558120445975157028044470669508269904542112710719750776396721], [1, 0, -661854, 0, 202275596298, 0, -40619516236130848, 0, 7446151473115219252038, 0, -1620799166433794781581625186, 0, 356878833337049532415712506341006, 0, -68366173765065438783793988345525882226, 0, 13248173476787091402392649734074658836253478, 0, -3048393004757515553242095644727505254774771205408, 0, 640312189577008467795335724059308194776701181804667978, 0, -88373600070081805916675830465700214089730284416602321648654, 0, 5632126739027588519658984775872141857619309476789431335641625841], [1, -2358, 3274005, -3349814886, 2769988834986, -1971385890773130, 1255859174153710355, -746741883560577476418, 426090230957405107588752, -237108440693732373533355174, 128334679353086591634975445617, -66588480619025175545607616021254, 32721887318351964942932629699352712, -15114319919386953370517562292120254174, 6611850723769918501883466019230636625737, -2772780745316606076677680255471566426195534, 1130992167500009839959285296894688391230805392, -449902116304051871865928733689964338619890896618, 171742576003329332690535441280004451598253387307755, -61192497560293052575859456818113238775882874697596930, 19516146018401686517089074198283031193340578328721688426, -5357058061977764557081660502062220530821868053125130679806, 1188432140767532281885866201503398234197172267451241185113005, -194280116897592785415607797677877157786287775735721146938725598, 18701397461209715023927088008788055619800417991632621566284510161], [1, 792, -260820, -1221864760, -593843874768, 277390666295568, 608150471782500244, 218629122721527308688, -113846601773968545956328, -180988011212274352966919416, -53128697364524185126485768756, 28594737528056557096359164715864, 36246571971031922690525994899293606, 8600239043150874281972271457437404232, -4805936010341271841014955274070007711764, -4924056552363757712326164425148766716990952, -931574740564060991414884895159462841088732008, 538059188919241843091952099672015079260759073584, 450150250963290987932460074223566758846730369305396, 61753659731648169125023828782107824983331531405060656, -39761938211530200592551616208084979910269338715347083728, -24606101568800575894697372382974332525380689462377453525480, -1579737660029655045842221475124259416883592156738280674256180, 1442758596626222372968691410007114971705109208062893199377343304, 547889398733702676213614311297941818478464344374520135510515030481], [1, 0, -3844636, 0, 6901086974498, 0, -7655680355206958700, 0, 5850229234251244135613647, 0, -3245867934818370369643978238264, 0, 1341101770056839013980852537421086044, 0, -415796604020303165917927332009563786153144, 0, 96000405694084949746875879125260760756628586927, 0, -16092890978269805502794513884301796117073838077910700, 0, 1858308742753900277388170242564562264275767439188726642338, 0, -132618981972474240747646696626949292042050296728839855987094236, 0, 4418761423445010359012517479030513507821439762288727229544623559521], [1, 2904, 5932080, 9063407232, 11723795534880, 13051713462287016, 13084661733360788156, 11882917853081720537400, 9998686567349345413335744, 7801474085970581186528333184, 5709514896007979349315899880432, 3907920673578948680003412598515144, 2518322403076120372802115558298104870, 1520247576673661878648887558836565773448, 864045019272887849599011369850964331076848, 459285158104522232986650924857996083600324992, 228990400167231466716275958687780977024013906624, 105868313963513520122499962439182165391919674151800, 45349654410397013094630634927225874871555281106960764, 17597363017898203778187530124117784007154681727957761768, 6149175363847851481257673641627408790250036474698209922080, 1849305737888310317844154664432253525753299104877537853938304, 470861089203030659301564684001556870613436775368488216001903920, 89670790018845089358463937491703166020903456808133288098288350232, 12012211336350227316446820100278887925603925639507433655692782073761], [1, 1674, -336861, -2052405226, -300737318949, 1327255085709756, 406747243169844832, -281214387106447896288, 96095575106235401052789, -56509383114401672827245922, -311613333749468231753156062131, 43022558303685385389288509224302, 239148512591023504865333569120433854, 21211799123490738726949417299440633778, -75749292407574386943697844104640974975251, -6772739754254263002613939653241955275245118, 5678432736485181355092976385238937475693888949, -8193017925516573450615359277715643352098374593312, 5842682157759449541028107640754122267142872400237152, 9399901770539172573695338693102167543747941920289976324, -1050116578030404722700071021003865081428726729922329378469, -3533414416607091166457837658410816088558732314009221476796534, -285932467612431334708688415782283739364223189945453347042974461, 700566661392096746026324165117206952322153574678405656996610164886, 206336132715709669990485567530001552309415935666586885734738159549121], [1, 0, 5725470, 0, 15556843382055, 0, 26496019606387001486, 0, 31476045560037079218614955, 0, 27458324289434654054780210553060, 0, 18029617696810204667200196572666834842, 0, 8977234795274847418597191817449870385459140, 0, 3364474753494813523299751810504217832895748557755, 0, 925947363088132500469315786152835862870073881062979774, 0, 177744305762530131453171202554194192641172204257083747347655, 0, 21387199211726350621173989885069145455026852137181696185660114030, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], [1, 0, -1635561, 0, 1787180462010, 0, -817237014874197619, 0, -172174360613175733010436, 0, 757568773104150957695916528195, 0, -706211584110844416447446370021831084, 0, 376497506849041838263541094260448255145395, 0, -42525414811439248991661951990927407352100545156, 0, -100315524541875821209497125848370655490571320995065539, 0, 109025620594382108461187668219574050785020683813735247716410, 0, -49586898518502549462988443303620722778440535105607052362642314361, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], [1, 0, -6632694, 0, 20843168091903, 0, -42591475693158319462, 0, 65402812509511105939522203, 0, -80737708092210420490421078476644, 0, 81496326134313904825955347036847534922, 0, -67252250582940861563252189178132601779378276, 0, 45379241847341153089427330081763848917416570295323, 0, -24615797150432092170311166411602204883933484424564166118, 0, 10034260078643025271314555260322603477090230772289515271058943, 0, -2659757177483791505837763048491493400772176229468696661346814348406, 0, 334027661875095082935878165689897695724025886105865253311336914562753921]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/bc/d'], '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': '24-336e12-1.1-c3e12-0-2', 'motivic_weight': 3, '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}], 'nu_real_doubled': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '24-336e12-1.1-c3e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e12-0', 'trace_hash': 474316101557812143, 'z1': {'__RealLiteral__': 0, 'data': '0.23946650388903427875713569665', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '303559857389489933748152564115,330818173041016919950287501128,818625373063300533381526442272,853009331211024049623062853646,1060323743840119435659705708843,1162020833048011420362501817278,1403809860339112763262558404904,1714074277500226551073158652391,1884266100382291111622654295738,1905419789311375386079984355975,2018124458228017895467205516393,2934959518379016369015145819133', 'Lhash_array': ['303559857389489933748152564115', '330818173041016919950287501128', '818625373063300533381526442272', '853009331211024049623062853646', '1060323743840119435659705708843', '1162020833048011420362501817278', '1403809860339112763262558404904', '1714074277500226551073158652391', '1884266100382291111622654295738', '1905419789311375386079984355975', '2018124458228017895467205516393', '2934959518379016369015145819133'], 'label': '24-336e12-1.1-c3e12-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d'}