-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '460661357261875326592360539866,1776900712187368663223759518479', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 0, 1]], [5, [1, 2, 5]], [31, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 1], [1, 2, 5], [1, 0, -13, 0, 49], [1, 10, 47, 110, 121], [1, 0, -10, 0, 169], [1, 0, -34, 0, 289], [1, -10, 63, -190, 361], [1, 0, 35, 0, 529], [1, -4, 62, -116, 841], [1, -2, 1], [1, 0, -10, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -85, 0, 1849], [1, 0, 50, 0, 2209], [1, 0, 63, 0, 2809], [1, 20, 218, 1180, 3481], [1, 28, 318, 1708, 3721], [1, 0, 62, 0, 4489], [1, 18, 223, 1278, 5041], [1, 0, -65, 0, 5329], [1, 10, 183, 790, 6241], [1, 0, -130, 0, 6889], [1, 6, 187, 534, 7921], [1, 0, 130, 0, 9409], [1, 14, 251, 1414, 10201], [1, 0, -142, 0, 10609], [1, 0, -93, 0, 11449], [1, -4, 222, -436, 11881], [1, 0, -57, 0, 12769]], 'euler_factors_factorization': [[[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, 2, 5], 1]], [[[1, 0, -13, 0, 49], 1]], [[[1, 5, 11], 2]], [[[1, -6, 13], 1], [[1, 6, 13], 1]], [[[1, 0, -17], 2]], [[[1, -5, 19], 2]], [[[1, 0, 35, 0, 529], 1]], [[[1, -2, 29], 2]], [[[1, -1], 2]], [[[1, 0, -10, 0, 1369], 1]], [[[1, -6, 41], 2]], [[[1, 0, -85, 0, 1849], 1]], [[[1, 0, 50, 0, 2209], 1]], [[[1, 0, 63, 0, 2809], 1]], [[[1, 10, 59], 2]], [[[1, 14, 61], 2]], [[[1, 0, 62, 0, 4489], 1]], [[[1, 9, 71], 2]], [[[1, 0, -65, 0, 5329], 1]], [[[1, 5, 79], 2]], [[[1, 0, -130, 0, 6889], 1]], [[[1, 3, 89], 2]], [[[1, -8, 97], 1], [[1, 8, 97], 1]], [[[1, 7, 101], 2]], [[[1, 0, -142, 0, 10609], 1]], [[[1, 0, -93, 0, 11449], 1]], [[[1, -2, 109], 2]], [[[1, 0, -57, 0, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 1, 'label': '4-930e2-1.1-c1e2-0-1', '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/930/2/d/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.546703998651683, 0.5292652364003784, 0.4828244434337068, 0.4028807460824338, 0.2893179203443511, 0.1430393737291002, -0.035589782904870096, -0.24536630049282684, -0.4831459994092494, -0.743908438728014, -1.0201822425406866, -1.302076764092797, -1.5768223894434126, -1.829276102261812, -2.042048271691129, -2.196383621077302, -2.273074371476029, -2.253597826572371, -2.1218434408614555, -1.8651778959966834, -1.4767149221491758, -0.9558355057563819, -0.3104197172343325, 0.4436742959463272, 1.2811900539400527, 2.1693465468235105, 3.0679484829897254, 3.9325118997917157, 4.716243539030998, 5.373762634208276, 5.8646320426786644, 6.156521896889438, 6.229248122700537, 6.076041069624168, 5.706569028809088, 5.1453211681706215, 4.432177458398147, 3.6178226381991774, 2.7612065107883894, 1.9231349023334041, 1.1612678090475694, 0.5240945204997923, 0.045432863585730184, -0.2586819907301247, -0.3933812774826286, -0.38341885013905364, -0.27235699173159644, -0.11642723518275937, 0.02080636756472353, 0.07697454839831311, -0.0012648641020772012, -0.25097386879763406, -0.6864554721259166, -1.296760585737533, -2.0445845513479313, -2.869935770709505, -3.696486770657911, -4.43954365485284, -5.018503249499932, -5.364396109502258, -5.433818213504079, -5.210560992986332, -4.715144914914575, -3.9972608400901755, -3.1369168121433484, -2.228892133970838, -1.3759450264238997, -0.671023293289267, -0.18773866781607454, 0.03199103135351033, -0.01724620532042868, -0.3028302502986583, -0.7594090283975518, -1.2978303880636362, -1.8202518072001341, -2.2328991141619374, -2.4644271446604327, -2.472958708921309, -2.2583100138180754, -1.856501110488382, -1.3394449695924135, -0.7975185646990058, -0.32800022759092046, -0.01413555957490351, 0.08849172266294403, -0.035173993820506205, -0.35588030499740825, -0.8025230245832453, -1.2749787124604886, -1.6592990025313852, -1.8532081638767932, -1.7821372261848885, -1.423780136776771, -0.8108629293463449, -0.03950904025689313, 0.7479053258734865, 1.3770090333697427, 1.671951231150678, 1.4839878660961654, 0.7184970853874201, -0.6416317235005606, -2.5290230562580427, -4.792604528837375, -7.215004759349485, -9.543090451712727, -11.517169173487728, -12.918394992093823, -13.587147602603142, -13.46315134232127, -12.575207247806075, -11.054048783176786, -9.093473299457594, -6.9335474204963266, -4.812655375086321, -2.9378594506135283, -1.45472727072859, -0.4287932003262669, 0.15080472174046303, 0.3651617663855878, 0.33430566401824413, 0.1930795502223862, 0.056212440567623284, -0.0021626752449697625, 0.03734720953811912, 0.14153248729232518, 0.23800617379995131, 0.24026670406680545, 0.07325180694788362, -0.29856140967190253, -0.8581643810014412, -1.5296179848169975, -2.190746594805424, -2.6972839208135184, -2.9109394390858756, -2.737879740251273, -2.1460472907066066, -1.1879441459731215, 0.012624911119169512, 1.2733227152108149, 2.3918809470317446, 3.186545441535348, 3.530901629112515, 3.3908391023434152, 2.8247510150634043, 1.9872818011992561, 1.0884828727189606, 0.3616176306172163, 0.007278441573786555, 0.15408438355741721, 0.8273266329026431, 1.9407045319280742, 3.310618061993875, 4.6943100393074655, 5.833648275099552, 6.517344363571223, 6.612350941163997, 6.106686499764461, 5.09504233014525, 3.7735568849502332, 2.383473321359996, 1.169320940505239, 0.31978659407576004, -0.06738678207094605, -0.005447569105491469, 0.3914749852515395, 0.9358182002128773, 1.4212577819586947, 1.6648698752060334, 1.5652242203933422, 1.1143081245940738, 0.41201297882202087, -0.36795641085620834, -1.018835825985736, -1.3509941748995444, -1.2531665941546666, -0.7081404637112548, 0.17607106197873415, 1.2104422070495757, 2.144176144131413, 2.743470998291869, 2.8318689141000135, 2.3473410503131777, 1.3511162518461621, 0.025432063713248024, -1.375522443170585, -2.571568861438305, -3.336467269704299, -3.5318832112453196, -3.160045612922766, -2.3408842864580595, -1.3011893793778608, -0.30341819906128575, 0.4081229306024653, 0.6715106204764526, 0.4442304081938891, -0.1903696461257486, -1.046429712374951, -1.8845411107388645, -2.4811851273272225, -2.678343485379193, -2.439706467017362, -1.8450629924187196, -1.0858824877562512, -0.4013110676320076, -0.024710468925043323, -0.11459922029172301, -0.7132513644762006, -1.7308401903762998, -2.9679635788551035, -4.158341796502198, -5.04632362692493, -5.4339508569706325, -5.250972191138838, -4.545696873741726, -3.492440662995047, -2.3208806249881406, -1.268226554324454, -0.5050726001275367, -0.09485601314860224, 0.018728723594512612, -0.008505208494428164, 0.023513121893087022, 0.29122925104434544, 0.8852879132549613, 1.765042542409533, 2.7571789335862062, 3.5885748515266385, 3.950345589441435, 3.5888492934073124, 2.3694435672491894, 0.34157117134576653, -2.267461102463368, -5.08213224721458, -7.6538853879630535, -9.570224343591978, -10.521771601133654, -10.40342113309707, -9.293855450674753, -7.472974027110086, -5.312849314882108, -3.2198122061328314, -1.5191770917979275, -0.4023619830808063, 0.10761083781498201, 0.13614860828233882, -0.09688547763952549, -0.3557749965536039, -0.456163955817441, -0.32419633483345983, 0.0008481234677681272, 0.38271805438331774, 0.6503931509588136, 0.6616355022958984, 0.3573319466434039, -0.20854562083758343, -0.8842639019251184, -1.467061006736166, -1.7675089705094658, -1.686862802322516, -1.2481440755273772, -0.6172133826551321, -0.049388005679454124, 0.17424263407103582, -0.1581324355281292, -1.1112741751108457, -2.562097988855876, -4.208635816137267, -5.626968816005561, -6.38730879050867, -6.1443265489564265, -4.767868847446445, -2.3561815464793443, 0.7365222660878425, 4.001450918903634, 6.8734441123520424, 8.862576358620265, 9.679939930085729, 9.273089262198223, 7.86009246755238, 5.829983222435411, 3.6663081052237163, 1.8034951525576979, 0.536148978319085, -0.040326157966576424, -0.030667934121153696, 0.3208260258929516, 0.7191737393381753, 0.9128260831044798, 0.773730303943147, 0.31680434708683736, -0.312395215230377, -0.9049291747603028, -1.2687901776896486, -1.2934044083507785, -0.9980824316060686, -0.5119996498340743, -0.034715655839845955, 0.24575465308837235, 0.22584271125707767, -0.06880838037187294, -0.4770075714100341, -0.7502466169695985, -0.6357187484991724, 0.040035914396466706, 1.2882470378641913, 2.9445311361718973, 4.688610314457395, 6.127138282834561, 6.909105537095354, 6.812019822439015, 5.835981184681133, 4.183862584566217, 2.235821347220774, 0.42754034180539213, -0.8607862076325069, -1.4063395459561319, -1.2096134974434427, -0.47055973478495566, 0.4688129490545731, 1.2424334673299529, 1.5753084817099081, 1.3599807322626916, 0.6949280617066306, -0.1657181158543761, -0.8961469169027108, -1.212383848096663, -0.9793119074029849, -0.24981055577599393, 0.7343611194497441, 1.6266537736519144, 2.085780763786114, 1.8836943563371769, 0.9967167897428784, -0.3925103417420162, -1.9367312282709126, -3.230423617812312, -3.946259995367566, -3.915400011749174, -3.2109145121883027, -2.087823386815822, -0.9312247011325069, -0.10145023769647622, 0.1688657459191815, -0.13335526772847317, -0.8003176885169864, -1.4609202984325012, -1.71667835438216, -1.259400500333453, -0.01159164578279208, 1.857797369988057, 3.939097408631032, 5.71038580960615, 6.678495968027903, 6.521150724785926, 5.195934234827307, 2.9458329815567774, 0.24016224876996609, -2.346738169814871, -4.315065481289246, -5.326333572019671, -5.33260928415307, -4.504192984610403, -3.2120946783557867, -1.8537080578898892, -0.7656242780984488, -0.11617241260222264, 0.11150220280253957, 0.07688495481497958, 0.0017297079246765346, 0.06703661148883434, 0.34364929870189265, 0.7689800534679644, 1.1803724735872108, 1.3901279401977955, 1.2709412924197954, 0.8182331099058184, 0.15883926655356737, -0.48151375525969237, -0.8807556347311745, -0.8870291669975465, -0.5189045954322243, 0.05624254503382483, 0.5426228971761005, 0.6377712531523309, 0.13586322534501308, -0.9800425084525685, -2.509223739606954, -4.07857034153788, -5.265070925952128, -5.712422015511186, -5.288884987928678, -4.101012561700379, -2.511240227509848, -0.9858953740429787, 0.03798842873458394, 0.32429826039008175, -0.06391294902831163, -0.7636076616019607, -1.2100411809915215, -0.8036827283610586, 0.8681471268632773, 3.905511402759877, 7.992078515339859, 12.478950181386892, 16.529104764527933, 19.326088164838197, 20.3277322475644, 19.349191899097978, 16.6755134802965, 12.89562728862445, 8.798732613436908, 5.110790387545112, 2.3465319651219407, 0.6987886144025025, 0.04278126624924911, 0.04196085218583597, 0.29187027713218705, 0.46773302988414267, 0.42454257014886637, 0.2032871765659205, -0.020612437974618966, -0.04928819043691031, 0.23314201857339956, 0.7980284137116368, 1.4754460004829795, 2.0161027744953572, 2.2057273657859273, 1.9400082109657828, 1.296530710012325, 0.49052781702426407, -0.1909822862788668, -0.513526488219436, -0.3993183135633011, 0.0317517128858002, 0.4821257727995825, 0.5809459559281024, 0.025857203914342836, -1.3026108957219165, -3.257763403815887, -5.460551586531493, -7.401585989174638, -8.585228553647218, -8.715664314246176, -7.752578272140843, -5.97271950695859, -3.834568130423759, -1.8660211512632832, -0.4750028700308613, 0.16415458557614118, 0.14494241129168942, -0.22269214440656637, -0.5481367681675771, -0.5164712599545724, 0.0009664924050125786, 0.8898893855455687, 1.8543206673697674, 2.532438375330296, 2.6366338188608918, 2.0828908500953434, 1.0095738094255826, -0.2559019867972972, -1.3282240162216588, -1.9127032912322826, -1.8987469278688989, -1.4169748710867212, -0.747965900218314, -0.2127415870403653, -0.002504688712776443, -0.07671778938318022, -0.14062810230092945, 0.25855200908362963, 1.5701236719065284, 4.021366581924817, 7.4943217462700416, 11.464190344470962, 15.107157722659908, 17.522068358556798, 17.96029052891678, 16.11143090112684, 12.162923208173853, 6.826201465171006, 1.1271182367447603, -3.8682910583078485, -7.289651207632727, -8.749565710580685, -8.306941917803552, -6.503610979902966, -4.064895113538462, -1.7456207747855144, -0.06803759660238956, 0.7575001999839605, 0.835266264220514, 0.4732157786793455, 0.025809671989350053, -0.25291816395992484, -0.27804587915797974, -0.13654011235354363, 0.0015666276149835271, -0.017357396830962154, -0.24147291214604583, -0.591456607853192, -0.8944738483531147, -0.985828698973249, -0.7783093664570474, -0.3377922247374066, 0.1556817967569657, 0.46508096392790177, 0.4243393557316601, 0.015577002501888128, -0.6082622262032724, -1.1088600012255785, -1.1440831309491626], 'positive_zeros': ['0.36339773528994289038468446488678', '1.40172750430398820767725177858809', '2.63243592550045901050677890798219', '2.98857294562736104201925937534846', '3.12450224960058915117254787890737', '4.29577267265008237659604437345662', '4.36839168767893088398497180252564', '5.19178200871947861699615301854963', '5.30221655571935217398086244201502', '5.87805932560752718461395752671106', '6.22374225769867074162870602737368', '7.29121855227043982553249199145844', '7.61616000176016779642244096715314', '7.64378437401921216055901242366262', '7.953132079078275551480790536103343', '8.561884869855235754382523425159994', '9.192122096228278683362482097396530', '9.211098191991994807640338601732712', '10.10600486064744863422335040362771', '10.18874160642155211997753089142375'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, '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': 681575109279052251, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36339773528994289038468446489', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40172750430398820767725177859', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63243592550045901050677890798', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, -2, 0, 0, 0, -1, 0, -10, 0, 0, 0, 0, 1, 0, 0, 10, 2, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 12, 0, 0, 10, 2, 0, 0, 0, 13, 0, 0, 0, 0, 0, 20, 0, 0, 0, -20, 0, -28, 0, 0, -1, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, -10, 0, 0, -10, -2, 1, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -20, 0, 0, 0, 10, 1], 'euler11': [1, 10, 47, 110, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 35, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, -2, 1, 0, 0], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, -85, 0, 1849], 'euler47': [1, 0, 50, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 0, 63, 0, 2809], 'euler59': [1, 20, 218, 1180, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 0, 62, 0, 4489], 'euler7': [1, 0, -13, 0, 49], 'euler71': [1, 18, 223, 1278, 5041], 'euler73': [1, 0, -65, 0, 5329], 'euler79': [1, 10, 183, 790, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, 6, 187, 534, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 1, 0, 0], [1, 2, 5, 0, 0], [1, 0, -13, 0, 49], [1, 10, 47, 110, 121], [1, 0, -10, 0, 169], [1, 0, -34, 0, 289], [1, -10, 63, -190, 361], [1, 0, 35, 0, 529], [1, -4, 62, -116, 841], [1, -2, 1, 0, 0], [1, 0, -10, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -85, 0, 1849], [1, 0, 50, 0, 2209], [1, 0, 63, 0, 2809], [1, 20, 218, 1180, 3481], [1, 28, 318, 1708, 3721], [1, 0, 62, 0, 4489], [1, 18, 223, 1278, 5041], [1, 0, -65, 0, 5329], [1, 10, 183, 790, 6241], [1, 0, -130, 0, 6889], [1, 6, 187, 534, 7921], [1, 0, 130, 0, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/d/b'], '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': '4-930e2-1.1-c1e2-0-1', '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': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 681575109279052251, 'z1': {'__RealLiteral__': 0, 'data': '0.36339773528994289038468446489', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '460661357261875326592360539866,1776900712187368663223759518479', 'Lhash_array': ['460661357261875326592360539866', '1776900712187368663223759518479'], 'label': '4-930e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/d/b'}