-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '499717227592210136853080113682,2535997237782707094964947048282', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.0327185866685, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3, 3]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '912.1', 'coefficient_field': '1.1.1.1', 'conductor': 831744, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1, 3, 3], [1, 0, 2, 0, 25], [1, 2, 15, 14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, -8, 19], [1, 0, -19, 0, 529], [1, 18, 139, 522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -82, 0, 2209], [1, -18, 187, -954, 2809], [1, 6, 127, 354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, -58, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -2, 0, 9409], [1, 0, -94, 0, 10201], [1, 0, -194, 0, 10609], [1, -6, 223, -642, 11449], [1, 0, 25, 0, 11881], [1, -24, 370, -2712, 12769]], 'euler_factors_factorization': [[1], [[[1, 3, 3], 1]], [[[1, 0, 2, 0, 25], 1]], [[[1, 1, 7], 2]], [[[1, 0, -10, 0, 121], 1]], [[[1, -7, 13], 1], [[1, 7, 13], 1]], [[[1, 0, -31, 0, 289], 1]], [[[1, -8, 19], 1]], [[[1, 0, -19, 0, 529], 1]], [[[1, 9, 29], 2]], [[[1, -4, 31], 1], [[1, 4, 31], 1]], [[[1, -10, 37], 1], [[1, 10, 37], 1]], [[[1, 0, 41], 2]], [[[1, 2, 43], 2]], [[[1, 0, -82, 0, 2209], 1]], [[[1, -9, 53], 2]], [[[1, 3, 59], 2]], [[[1, 8, 61], 2]], [[[1, 0, -59, 0, 4489], 1]], [[[1, 12, 71], 2]], [[[1, -11, 73], 2]], [[[1, 0, -110, 0, 6241], 1]], [[[1, 0, -58, 0, 6889], 1]], [[[1, 6, 89], 2]], [[[1, -14, 97], 1], [[1, 14, 97], 1]], [[[1, 0, -94, 0, 10201], 1]], [[[1, -20, 103], 1], [[1, 20, 103], 1]], [[[1, -3, 107], 2]], [[[1, 0, 25, 0, 11881], 1]], [[[1, -12, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 6, 'label': '4-912e2-1.1-c1e2-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/912/2/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.505371038019835, 0.4936612751954073, 0.4548740284742542, 0.3912178581283712, 0.3023462480387126, 0.1876303547078458, 0.04778164923231881, -0.11554020855577182, -0.29946309793423304, -0.4997295315856871, -0.710007310626096, -0.9221736262026068, -1.1260187740565628, -1.3098094975420822, -1.4604912781700694, -1.564583878562373, -1.6090939929444417, -1.5825628437561854, -1.4766394041279003, -1.286954974881516, -1.015046099379425, -0.6685924729305348, -0.2631044197453453, 0.17894013135923192, 0.6273622080071898, 1.0465095463510592, 1.3960685573765999, 1.6345035383023276, 1.7215514982100615, 1.6221792711852996, 1.310185261234632, 0.7715192853161589, 0.007667319836168752, -0.962944237489849, -2.103548053675619, -3.3604030989910303, -4.664957801117292, -5.937856333162001, -7.095287783693769, -8.054203600881028, -8.741945402646454, -9.100160802560062, -9.095253765232352, -8.71821587142926, -7.992620798607928, -6.96853400610788, -5.725282920849671, -4.3596809970847925, -2.9827448062723305, -1.704969335843974, -0.6289129704591228, 0.16393958835310393, 0.6204513024882699, 0.7228260950025693, 0.49081037016143897, -0.01983030769968212, -0.7233874032616022, -1.5128797227004531, -2.273953434320545, -2.8956577885489665, -3.2877308031532966, -3.38678007027714, -3.170311596723978, -2.653198478161704, -1.8928793392012406, -0.9754797396329203, -0.01083634015801569, 0.8870202998232215, 1.6109266245937368, 2.0776936561187473, 2.2374915938478135, 2.0813107718388997, 1.6413458645931949, 0.986549641981585, 0.21143185819317487, -0.5758869067267148, -1.272419845378153, -1.79081145114779, -2.076947827503222, -2.110609837021019, -1.913688717406794, -1.5383564225354907, -1.063242088321476, -0.5742423684003679, -0.15358424087356992, 0.13667587365368017, 0.2631324876080565, 0.22616076292969586, 0.05802792896454865, -0.1848059021346925, -0.4345537337249885, -0.6254950841332344, -0.7102075877008349, -0.6674421911803612, -0.5108811751798512, -0.28397140076049093, -0.05505885089704687, 0.09893595825320964, 0.10717571865519136, -0.07813431643519017, -0.46944222427733606, -1.0380072559901088, -1.7161318790865103, -2.4062283295295144, -3.000388445342361, -3.396113114773765, -3.5232435220112905, -3.3510040319788654, -2.9056920564593764, -2.2579292894941516, -1.5201277288826616, -0.8167873172991796, -0.265891382789122, 0.05093129437227325, 0.1050521558436207, -0.068787421091112, -0.3769728081054795, -0.6832584020948529, -0.8390066923670086, -0.7130194104825317, -0.23107921394179562, 0.6066017697113939, 1.7043437818011635, 2.886169486922225, 3.911689856720751, 4.521493488374644, 4.4819951883328395, 3.634759253480046, 1.9369598066989897, -0.5177841564512473, -3.5010054862935256, -6.670324862284846, -9.627479700632037, -11.961567861226218, -13.340997309344809, -13.537392605842626, -12.504620013665837, -10.349069669793517, -7.356313582823228, -3.9083581680181045, -0.4541901398418673, 2.586829816006494, 4.875600840904339, 6.211356026436678, 6.5558480464270925, 6.024446247210794, 4.859574004670612, 3.3713915247065405, 1.8777172738544996, 0.6437788669501023, -0.1670656894295707, -0.5090607284443477, -0.4572717962295774, -0.17081808175561725, 0.14733588944634016, 0.30665050654071224, 0.17436479752751816, -0.2936272372126658, -1.044388719058111, -1.9415857140545065, -2.8050053994922477, -3.447188807770094, -3.732040878418053, -3.5924567599722814, -3.0647438954042254, -2.262425143119318, -1.3661412055209052, -0.5681071561148646, -0.03702810277951006, 0.12601775040660704, -0.0932776084656025, -0.6201831130154613, -1.3127435393356226, -1.9940644672037995, -2.5017842506602355, -2.716854998180438, -2.602044327418617, -2.1936268114596746, -1.6013864633447419, -0.965249548038348, -0.42612616116864216, -0.08294730715207656, 0.028970607149138943, -0.05448440868190744, -0.23997805270261074, -0.40526028967047445, -0.43938406118118023, -0.2730284874801398, 0.09232429818684641, 0.5879707789796877, 1.0881834337019198, 1.4488490323701488, 1.5456952785364424, 1.3124817372303454, 0.7646716150954916, 0.0005468995393839855, -0.8218942640118515, -1.5197248190657504, -1.942316639440791, -2.000872371868968, -1.7112398613143631, -1.1769380213832001, -0.5803430330946022, -0.12189417353177122, 0.026155627278537343, -0.2245537244148947, -0.8508624003958503, -1.716219552410381, -2.6051302143134176, -3.2719383512198483, -3.5207738433797524, -3.246524887763216, -2.4937287310017107, -1.4304820069705764, -0.3335492458395436, 0.5022822874450915, 0.8342678273583997, 0.5562014689567542, -0.25681749322591296, -1.3455373693541903, -2.3143419207527223, -2.713708286483978, -2.162945083961815, -0.4365605253210934, 2.435151673733063, 6.171495094286779, 10.253518436708555, 14.03854077577607, 16.87948464854493, 18.263502973033845, 17.9316226260345, 15.928050917392564, 12.60324058776477, 8.539063964543821, 4.41474208203531, 0.889279012176647, -1.5732927295521588, -2.7386437389512586, -2.6912739928547493, -1.7332258907868552, -0.3453153364023757, 0.9807086410181991, 1.8342049079861653, 1.9930413938300937, 1.4551518849519791, 0.41906730800506525, -0.787529691675979, -1.8028171845207905, -2.3416265394686686, -2.253740636568859, -1.575247149587491, -0.4880432558308522, 0.721077268994043, 1.7574828335377328, 2.390702425952567, 2.5143292474012973, 2.1633218518847532, 1.4912762144073024, 0.7125331141917751, 0.04139893656345953, -0.38068739279245906, -0.5048548099962099, -0.39273198006175775, -0.16928848722126064, 0.016839639217036007, 0.05596998982131004, -0.0879057513421297, -0.36452286229275915, -0.6600084260170083, -0.8377332575037499, -0.7991100850771486, -0.5168431108187006, -0.06605034439268993, 0.4025155284781928, 0.6959728977513027, 0.646472814164617, 0.16633471010786485, -0.7148631975829774, -1.8484700822565345, -2.9975892544192786, -3.9086368457913854, -4.366610398632418, -4.278053226614456, -3.6721460452928683, -2.7188164885659925, -1.6536103232613155, -0.7279543330922192, -0.12313736851483355, 0.09204064313035304, -0.02368237201972825, -0.31477243652069, -0.5882545056751112, -0.6931865091030577, -0.5717733418319434, -0.29770002905224385, -0.04482940109980166, -0.03691860253235708, -0.4585271181634631, -1.3775590902752157, -2.6983465278039422, -4.166367278282874, -5.420140774378778, -6.106967113813639, -5.968661507368425, -4.969221564075855, -3.2900927520015744, -1.3435491388381477, 0.3624807091947978, 1.3323674829606373, 1.2425505681895628, 0.035047808078084976, -2.045776759059694, -4.512505850104018, -6.744538174064324, -8.183200616527591, -8.447499143679103, -7.497329084773146, -5.593707641407724, -3.2869886677857503, -1.2188053721049992, 0.023433885497636628, 0.0931480863510191, -1.025093952639432, -3.0048920723173076, -5.277299344574128, -7.17495068437167, -8.152189183693014, -7.895659339194107, -6.464963031090815, -4.217046638556883, -1.752608553461147, 0.2962774384244774, 1.4194383160609971, 1.3808206865852788, 0.2739805262948212, -1.5145825204445311, -3.4309518016917595, -4.902643123601114, -5.528224270903233, -5.147506004180531, -3.91497208123226, -2.1988359815185254, -0.49450914523592315, 0.7476817039305993, 1.2381528836722595, 0.9229656519977049, -0.019523948213907086, -1.2479772471586592, -2.381697403364447, -3.0992176820637964, -3.251007960595228, -2.855868841373162, -2.101301561408619, -1.2398937458533072, -0.5164818359990638, -0.08188889881608533, 0.03848911977288194, -0.06803813061449286, -0.25428549992482574, -0.3782746454296253, -0.3677617621086552, -0.23558140497007862, -0.07416613686235975, 0.001334137400091921, -0.09182873909038053, -0.3542267138723292, -0.6925480971444975, -0.9438248055753347, -0.94368979609841, -0.5831730606809461, 0.1185875788746283, 1.0221180898420783, 1.8811690624255164, 2.4334081898354007, 2.480515989881461, 1.9652952963496226, 1.0033008856235368, -0.14538137968580803, -1.1563488764576173, -1.7358646057819098, -1.7336448446817385, -1.173684397881156, -0.2701229635130349, 0.6644161825852222, 1.3113815700170615, 1.463860423948744, 1.095231586780726, 0.36817254681858347, -0.43300706240434833, -0.9971811665887641, -1.1308940351062675, -0.8073846958561439, -0.22035959618040654, 0.317838294964409, 0.4727281208479184, 0.050907211577009365, -0.8972519783412043, -2.0417905374801313, -2.8459511772918904, -2.7039942086097777, -1.169969323394293, 1.9122187183539505, 6.251735535032602, 11.194484815117727, 15.813131508228025, 19.173209000999773, 20.569562087828572, 19.713712026757996, 16.837459316912504, 12.60380321290922, 7.942070196695838, 3.7871796340801427, 0.8192158523786222, -0.6719887588108067, -0.8611304708191518, -0.24868781475852308, 0.5087019338285623, 0.8452754295166711, 0.46746253793797465, -0.5639632386015289, -1.8819244902547905, -2.9471283532378667, -3.2888632171328642, -2.6335776807372873, -1.0786125944267522, 0.9967226577430564, 2.9861813538621678, 4.302231436746724, 4.533949389573531, 3.595654356260561, 1.7432228929035867, -0.5056299173505647, -2.553534157411086, -3.885484145017723, -4.258648599309516, -3.7142289930265777, -2.5845851482498174, -1.322851093544849, -0.3706078320627054, 0.0028097885910297648, -0.23316066236351052, -0.8817526494100535, -1.6177336426461195, -2.1068942941489786, -2.1502826803844477, -1.7235520177380457, -1.0004352051843657, -0.2497447438096871, 0.2561391254859707, 0.356092357354082, 0.05210633427234194, -0.4981185009259823, -1.0551520762142164, -1.3864432579588026, -1.3733446699094052, -1.033542088996182, -0.5282652329483447, -0.07354946897645363, 0.13848429229631154, 0.025721354926382032, -0.35486521490568657, -0.8283818850046085, -1.1839868312045017, -1.2485165055262397, -0.9798945219479778, -0.4602226588661615, 0.11445901890808878, 0.5366322845773108, 0.6627190595588437, 0.4806939510134356, 0.11339365090211372, -0.23668680722475247, -0.38561630720463486, -0.25533610005995805, 0.06251450335739576, 0.33462773460244505, 0.26459884631722724, -0.37893214006391196, -1.640481667696396, -3.3241012571715927, -5.025506245790836, -6.239328969124619, -6.563362014264732, -5.812002204347927, -4.171923040099149, -2.1103955299715116, -0.29992258394720606, 0.6452969751333034, 0.35631510505635766, -1.1311353829939028, -3.374078142640254, -5.6395908766104945, -7.172164815765274, -7.407218423848973, -6.241216439723067, -4.011244879368904, -1.470799545518903, 0.5181098882791191, 1.2372073462759303, 0.39027973460088905, -1.787694784561244, -4.578926939790845, -7.0312011455750865, -8.220819793460048, -7.6245435743071015, -5.213930048669035, -1.5801084730595116, 2.3705152430058822, 5.644404413480111, 7.441991644282451, 7.41858886550185, 5.917784359742272], 'positive_zeros': ['0.39420738451292526617359265396551', '1.41257393692893365059355368388899', '2.00054907663525184032548186890271', '3.17224876554612289124470968073932', '3.43549569003335863127305592153182', '4.12571298516247816773420089957663', '4.64152189035303064600392259548858', '5.27897725139969926680995703297234', '5.51609030431458289553462675498655', '6.01787168329570719286958867728737', '6.16856297446901935037821256247841', '7.04780362551873855628173892356968', '7.16953367436832341250413445636991', '7.51993362264571322451593200574990', '8.050569957155588787338996736995507', '8.758646213835674476160718874746168', '9.358588007630277367990214762527138', '9.594327308765145281382590752132280', '9.778709980490372354394574336032907', '10.50687907800007814205506569116435'], 'prelabel': '4-912e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 192709712840679172, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39420738451292526617359265397', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41257393692893365059355368389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.00054907663525184032548186890', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 53.0327185866685, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 831744, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 6, 0, 0, 0, -2, 0, -9, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -11, 0, 0, 0, 18, 0, 0, 0, -24, 0, -6, 0, -16, 0, -12, 0, 0, 0, 0, 0, 0, 0, -24, 0, 22, 0, 6, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 54, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -23, 0, 169], 'euler17': [1, 0, -31, 0, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -19, 0, 529], 'euler29': [1, 18, 139, 522, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 4, 90, 172, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -18, 187, -954, 2809], 'euler59': [1, 6, 127, 354, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, -110, 0, 6241], 'euler83': [1, 0, -58, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 3, 0, 0], [1, 0, 2, 0, 25], [1, 2, 15, 14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, -8, 19, 0, 0], [1, 0, -19, 0, 529], [1, 18, 139, 522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -82, 0, 2209], [1, -18, 187, -954, 2809], [1, 6, 127, 354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, -58, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -2, 0, 9409]], 'index': 6, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-256.1-r', 'EllipticCurve/2.2.57.1/256.1/r', 'ModularForm/GL2/Q/holomorphic/912/2/f/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-912e2-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-912e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 192709712840679172, 'z1': {'__RealLiteral__': 0, 'data': '0.39420738451292526617359265397', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 17413591
{'Lhash': '499717227592210136853080113682,2535997237782707094964947048282', 'Lhash_array': ['499717227592210136853080113682', '2535997237782707094964947048282'], 'label': '4-912e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/a'}
-
id: 9488062
{'Lhash': '_499717227592210136853080113682', 'Lhash_array': ['_499717227592210136853080113682'], 'label': '4-912e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/256.1/r'}
-
id: 9487807
{'Lhash': '_499717227592210136853080113682', 'Lhash_array': ['_499717227592210136853080113682'], 'label': '4-912e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-256.1-r'}