-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '686501956727462443056021429074', 'a10': [58.71511950137164, 0.0], 'a2': [-4.547392645829356, 0.0], 'a3': [0.0, 0.0], 'a4': [12.67877987534291, 0.0], 'a5': [-12.911820921209047, 0.0], 'a6': [0.0, 0.0], 'a7': [16.72885655075938, 0.0], 'a8': [-21.276249196588736, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.547392645829356, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [12.911820921209047, 0], [125.0, 0]], [[1.0, 0], [-16.72885655075938, 0], [343.0, 0]], [[1.0, 0], [24.92803427798384, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-134.1453585041149, 0], [4913.0, 0]], [[1.0, 0], [14.937641421890879, 0], [6859.0, 0]], [[1.0, 0], [72.0, 0], [12167.0, 0]], [[1.0, 0], [-206.1453585041149, 0], [24389.0, 0]], [[1.0, 0], [249.14163313252223, 0], [29791.0, 0]], [[1.0, 0], [-293.9545573981949, 0], [50653.0, 0]], [[1.0, 0], [250.50645144058313, 0], [68921.0, 0]], [[1.0, 0], [-432.14535850411494, 0], [79507.0, 0]], [[1.0, 0], [-159.88909962030647, 0], [103823.0, 0]], [[1.0, 0], [-194.58143401645967, 0], [148877.0, 0]], [[1.0, 0], [232.64738195357617, 0], [205379.0, 0]], [[1.0, 0], [185.00583650960147, 0], [226981.0, 0]], [[1.0, 0], [39.439278879067125, 0], [300763.0, 0]], [[1.0, 0], [920.4604253108955, 0], [357911.0, 0]], [[1.0, 0], [549.0777563082654, 0], [389017.0, 0]], [[1.0, 0], [-933.1395219945134, 0], [493039.0, 0]], [[1.0, 0], [-1095.38306207759, 0], [571787.0, 0]], [[1.0, 0], [-532.1142943856927, 0], [704969.0, 0]], [[1.0, 0], [362.66119873010086, 0], [912673.0, 0]], [[1.0, 0], [1490.5814340164598, 0], [1030301.0, 0]], [[1.0, 0], [-628.4360755123447, 0], [1092727.0, 0]], [[1.0, 0], [477.45358504114915, 0], [1225043.0, 0]], [[1.0, 0], [378.2067605429346, 0], [1295029.0, 0]], [[1.0, 0], [13.273207479425421, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-39e2-1.1-c3-0-36', 'leading_term': '0.66744312500016638246607156327830', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/w/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6674431250001663, 0.6604966212461317, 0.6397751391397116, 0.6056319228258381, 0.558652869229408, 0.49965215218171327, 0.4296658813471923, 0.3499435970241553, 0.26193736708611276, 0.16728823282591504, 0.06780974838438839, -0.03453162476038752, -0.13763947036204194, -0.23931386313549502, -0.3372813788500492, -0.42922864763906154, -0.5128393216737064, -0.585834207988145, -0.6460141874706126, -0.6913054055587596, -0.7198060830940805, -0.7298341614955607, -0.719974869510073, -0.6891271839972654, -0.6365480592211582, -0.561893222547467, -0.4652532836485461, -0.34718388329924893, -0.20872862011692275, -0.05143354204184041, 0.1226479239013321, 0.3109606037290874, 0.5104646045932221, 0.7176643678935564, 0.9286501345109115, 1.139151933658747, 1.3446059021135457, 1.5402324124792537, 1.7211251446394156, 1.8823498817342352, 2.019051459932416, 2.1265669598211576, 2.2005429068766795, 2.237053960005077, 2.2327203214113687, 2.184820908646275, 2.0913992005696205, 1.9513586121682331, 1.7645442763691064, 1.5318082202244858, 1.255055122151147, 0.9372661280311988, 0.5824985861396246, 0.19586003053911646, -0.21654470659217864, -0.6476937505247552, -1.0897556217849895, -1.5342229431606047, -1.9720707478698556, -2.393936957764986, -2.790321850462004, -3.151802619868025, -3.4692584787810246, -3.734101178095316, -3.9385053469415348, -4.07563271261162, -4.13984405690962, -4.126892722183297, -4.03409360759694, -3.86046190174713, -3.606816284178855, -3.27584199311497, -2.8721099915730544, -2.4020494551079454, -1.8738719321237474, -1.2974467670585708, -0.6841286977737182, -0.04653990681254667, 0.6016898161054359, 1.2462197964603379, 1.8723258049362543, 2.4652505598882546, 3.010568965731929, 3.4945588445255855, 3.904567341756303, 4.229362870522411, 4.459462423938189, 4.587424349063143, 4.608097243813872, 4.518816508724376, 4.319541245953453, 4.012925626629647, 3.604320512855693, 3.101702981714275, 2.515533406401584, 1.858541848057582, 1.1454476392659123, 0.3926181310440478, -0.3823254379121292, -1.1609451749418813, -1.9244555146230393, -2.654211306196024, -3.332201427432035, -3.9415337971418167, -4.466897533044039, -4.894988318144593, -5.214883802543764, -5.418357069378855, -5.500117809069826, -5.4579728359634405, -5.292899892556624, -5.0090312525733, -4.613546378069578, -4.11647572145573, -3.5304205987370105, -2.870196800166404, -2.1524121537877896, -1.3949905244645209, -0.6166566312849922, 0.1636024747473285, 0.9270824743296636, 1.6558961777166006, 2.3334802161883084, 2.9450577355751926, 3.4780421189141615, 3.922368619582887, 4.270743121993847, 4.518799991043574, 4.6651640341239045, 4.711414876762185, 4.661955430505412, 4.5237894886054, 4.30621669833767, 4.020456107767373, 3.6792120559260444, 3.2961982667822194, 2.8856375330503883, 2.461755269392222, 2.0382854322706123, 1.6280068270288561, 1.2423266595499507, 0.8909263748214595, 0.5814824187942744, 0.3194716484396087, 0.1080678049284158, -0.051868118603069696, -0.1617045017622833, -0.22486730816116335, -0.2465880238242868, -0.23358270395200845, -0.19367630816367792, -0.13538874121069547, -0.06750059137844278, 0.0013826017830718064, 0.063248660203577, 0.11106150596864556, 0.13909168154747195, 0.1431802391463164, 0.1209244561926528, 0.07177722776578971, -0.0029442327790331216, -0.1001407438185224, -0.2151008457101465, -0.341750168649414, -0.4729691550670941, -0.6009646106213368, -0.7176779617347586, -0.8152112340072203, -0.8862507307927575, -0.9244682462375416, -0.9248804153811084, -0.8841484685255897, -0.8008031604445764, -0.6753828905824735, -0.5104768859199257, -0.3106696206745224, -0.08238720931781766, 0.1663488719841849, 0.4262509165222584, 0.6871630518934845, 0.9385107814949394, 1.169781746163337, 1.3710155361934617, 1.5332794672091101, 1.6491073801818998, 1.7128797557659303, 1.7211257156362807, 1.6727307383724659, 1.5690380166659126, 1.4138361552316272, 1.2132311473834818, 0.9754060376602299, 0.7102771254804451, 0.4290607316558902, 0.1437691825756996, -0.13334146925780566, -0.39034658061178557, -0.6162237523832594, -0.8013917153614178, -0.9381904426508502, -1.0212778042426107, -1.0479214704063915, -1.0181692874639152, -0.9348868085197973, -0.8036568283837452, -0.632542370368337, -0.43172129753140054, -0.21300725104473073, 0.010722368460974956, 0.22616547220661723, 0.42027141696577175, 0.5809214614966502, 0.697579570205551, 0.7618799760457335, 0.7681199604615953, 0.7136299682060951, 0.5989983253888053, 0.42813427009822225, 0.2081604670270837, -0.05086566731122695, -0.3363940268091844, -0.6339710690805445, -0.9279521612573566, -1.2023059110908043, -1.441473633499997, -1.631242949793321, -1.7595922118290193, -1.8174621641858157, -1.799413090024177, -1.7041296177172258, -1.5347412806809715, -1.2989346075545272, -1.0088416666165605, -0.6807002086403311, -0.3342913927861432, 0.007827958264229442, 0.32127106660896776, 0.5809077230418092, 0.7620462523238539, 0.8416591752956296, 0.7995966770606534, 0.619730341661454, 0.2909706251746221, -0.1918947480538871, -0.8275879539489944, -1.607991562217228, -2.518089322266629, -3.5362117951871492, -4.63458788524962, -5.780189340047766, -6.935841462912466, -8.061560268586838, -9.11606474736095, -10.058403366939263, -10.849626937928287, -11.454435894057523, -11.842729159739642], 'positive_zeros': ['0.54155455502002189805770486355545', '1.48814742020961620584734487151777', '2.71586862987272771262392252406604', '3.91381682397942018357553417481375', '4.95161516443529261689380002836837', '6.03227056226892833532949985796051', '7.34494006453727997070147313591240', '7.76847883819536442882545404717846', '8.123266130715833526068522251774907', '8.954697438118362192628865652430269'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54155455502002189805770486356', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48814742020961620584734487152', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71586862987272771262392252407', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/w/1/1'], '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': '2-39e2-1.1-c3-0-36', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54155455502002189805770486356', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '686501956727462443056021429074', 'Lhash_array': ['686501956727462443056021429074'], 'label': '2-39e2-1.1-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/w/1/1'}