-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2145669904962438446531965500195', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.9555728057861407, 0.2947551744109042], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6234898018587335, -0.7818314824680298], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6602630117134622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]]]], 'bad_primes': [3, 7], 'central_character': '1323.431', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '1854924940605558316527586002041', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [-0.09318690248616854, 0.11685267970729736], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0.6234898018587335, 1.0799160148203788], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0.9555728057861407, -1.655100649952743], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.826238774315995, 0.5633200580636221], [0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0.6583217782434021, -0.3170310594102608], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [0, 0], [-0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [0, 0], [0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [1.400968867902419, -0.43214166466688053], [0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [0.8262387743159949, -1.4310875362987383], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [-0.4400711179528193, 0.0663300485369759], [0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [-0.7330518718298263, -1.2696830865927278], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [-0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [0.14779084036989015, 1.9721317093630037], [-0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [-0.05460393788372161, -0.1391285647066539], [-0.7330518718298263, 0.6801727377709194]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1323-147.137-c0-0-0', 'leading_term': '1.401849417655789300761613304480', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1323/1/br/a/431/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4018494176557894, 1.4159104177631527, 1.4441902305271321, 1.4852852083108434, 1.5369238003643197, 1.5962554793395498, 1.6601275516482048, 1.7253017934386992, 1.7886003382160665, 1.8469935152788217, 1.8976497549118065, 1.9379655711411452, 1.965588224686866, 1.9784384010217801, 1.9747362861248874, 1.953031824166295, 1.9122383689696296, 1.8516680491976913, 1.7710666983743695, 1.670645990381848, 1.5511103731655405, 1.4136764565054951, 1.2600826582908482, 1.0925871361854524, 0.9139523229896773, 0.7274147417787443, 0.5366391981615931, 0.3456569271351994, 0.1587878038042512, -0.019452699500869603, -0.18446052574803123, -0.3316621181185966, -0.45664307389825615, -0.5552832860917781, -0.6238949647890404, -0.6593594783036808, -0.6592586003433063, -0.6219955164321708, -0.5469008508894638, -0.4343190421193108, -0.2856706318546752, -0.10348645121151938, 0.10858971518922578, 0.3458326310723967, 0.6025029815048212, 0.8719512388143332, 1.1467574423955205, 1.4189050293711198, 1.6799855265865027, 1.9214295915466781, 2.1347586208732094, 2.3118499823222907, 2.4452079235642636, 2.528231419403404, 2.555469686714514, 2.5228558647638293, 2.4279094610576184, 2.2698986222211226, 2.0499541160996264, 1.7711281018854041, 1.438392301302165, 1.0585720320135659, 0.6402146754663575, 0.19339346182356398, -0.2705501120597135, -0.7393194469470948, -1.200023394513372, -1.6395737579489928, -2.0451073111018037, -2.404418279103253, -2.7063860437021208, -2.9413821828169895, -3.1016408870707397, -3.181577356888463, -3.1780399891360194, -3.090484003226734, -2.921056596597253, -2.6745866940528447, -2.358475773304014, -1.9824899937836935, -1.5584577898044665, -1.0998810576969333, -0.6214719040336102, -0.13863045813599387, 0.3331176807027917, 0.7787033495339403, 1.1840923933969347, 1.5368374158561007, 1.8265793831423536, 2.045476920329099, 2.188543305216594, 2.2538742924841184, 2.242753897759589, 2.1596300049608406, 2.0119569563802795, 1.8099079343803353, 1.565965709850442, 1.2944059615388266, 1.0106926008468204, 0.7308091123786862, 0.4705536024010589, 0.24482782574006848, 0.0669517678494756, -0.051964724674043686, -0.10356330293620583, -0.08266447297178066, 0.012441704328495087, 0.1798586713934948, 0.41411072611989175, 0.7063378966029641, 1.0446538333422424, 1.414654404672202, 1.800057167380823, 2.18344503935051, 2.5470816821609836, 2.873761632351037, 3.1476553720368616, 3.355108506615696, 3.4853551419500617, 3.53110845720254, 3.4889962868814273, 3.359816093012241, 3.148591767608303, 2.8644239130658953, 2.520135187973321, 2.1317225081786484, 1.7176378553348126, 1.2979286567968893, 0.8932766685473883, 0.5239805673873602, 0.2089316594082474, -0.03536605031484279, -0.19568088550185714, -0.26279638222066753, -0.23207060420718975, -0.10377859013571282, 0.11678527592942803, 0.41945657678441556, 0.7896008992351766, 1.2087507355803828, 1.6554528092658092, 2.1062877972318708, 2.5370144670309274, 2.923782501933394, 3.2443532314709125, 3.4792654710207307, 3.6128849045457976, 3.634279954969297, 3.5378747373920536, 3.323840168179509, 2.9981971315691305, 2.5726201657579733, 2.0639456892837216, 1.493404534973768, 0.8856136459726245, 0.2673753791032993, -0.33365582600578025, -0.8903712976898334, -1.3775975270926952, -1.7734031241752926, -2.060252356127226, -2.2259412431874805, -2.2642628065897923, -2.175361852201503, -1.965755942836286, -1.648017114828029, -1.2401274673227274, -0.7645399686651557, -0.24699264843511662, 0.28486120722739244, 0.802933039295469, 1.2802081206833251, 1.6921999463133517, 2.0182680146485175, 2.2427237614312854, 2.35566049225254, 2.353458132284475, 2.2389316834371567, 2.021112465031251, 1.7146723792761391, 1.3390223674837942, 0.9171356715900155, 0.47416331012346463, 0.03592226923054883, -0.37265455615725634, -0.7290142608250041, -1.0143353495157097, -1.2146519077729563, -1.321680412126898, -1.3332961831813952, -1.25362711152138, -1.0927552454119867, -0.8660407722637855, -0.5931064120296206, -0.29654182303997306, -0.0004059345479956063, 0.27138103092782584, 0.4966556484146742, 0.6565369166673518, 0.7367607936555256, 0.7287351928901221, 0.6302428998538362, 0.4457406415098648, 0.18622699336497678, -0.13132150847655416, -0.484919389005242, -0.8488935214907718, -1.1954803618895444, -1.4966036559571443, -1.725723585249827, -1.8596413372469407, -1.8801432716442457, -1.775376359731742, -1.5408610872855688, -1.1800687727192605, -0.7045160862670395, -0.1333589380543494, 0.5075009524515869, 1.186752524524261, 1.8693817795029628, 2.518650221817346, 3.0982283338900976, 3.574354999335444, 3.9178896461008814, 4.106128102155408, 4.1242656373888575, 3.966410769311486, 3.636079995371549, 3.146135098216355, 2.518159120665118, 1.7813023629787423, 0.9706635603547729, 0.12530154856849132, -0.7140027883415841, -1.5070973493091278, -2.216776911245327, -2.8109236553160253, -3.264335328588058, -3.5601251183093123, -3.690603918227215, -3.657588361697364, -3.4721147195388418, -3.1535771460748956, -2.7283462908895806, -2.2279584800034624, -1.6869941965044837, -1.140785488311071, -0.6231037124349046, -0.16398079394507606, 0.2121913017903757, 0.4881564599231425, 0.6547861934184677, 0.711501721253251, 0.6660993710052003, 0.5339930764399526, 0.3369278624563097, 0.10125494579440117], 'positive_zeros': ['1.69263510353415156345136098572267', '2.43189292073389740998427817481734', '3.71600699375093988717230750028512', '4.88027351676927085870128965539238', '6.00562923699590937731487376015398', '6.20525788248326433027249029301774', '7.66596976799529336451474911651109', '7.940643047489370963387158194880148', '9.107732001437310395481740746970534', '9.870968251957206685687320060443715'], 'prelabel': '2-1323-147.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8125656968599292, 'root_angle': 0.04081632653061225, 'root_number': '0.99179001382324610895744277721886 + 0.12787716168450601059056272223114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.02040816326530612', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69263510353415156345136098572', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43189292073389740998427817482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71600699375093988717230750029', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6602630117134622, 'bad_primes': [3, 7], 'central_character': '147.137', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/1/br/a/431/1'], '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': '2-1323-147.137-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1323-147.137-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8125656968599292, 'root_angle': 0.020408163265306124, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69263510353415156345136098572', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2145669904962438446531965500195', 'Lhash_array': ['2145669904962438446531965500195'], 'label': '2-1323-147.137-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/1/br/a/431/1'}