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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '622708531372272131', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1115.110864227181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [7, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '139650.1', 'coefficient_field': '1.1.1.1', 'conductor': 139650, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1], [1, -3, 11], [1, 2, 13], [1, 6, 17], [1, 1], [1, -3, 23], [1, -3, 29], [1, -7, 31], [1, -2, 37], [1, -6, 41], [1, 10, 43], [1, 12, 47], [1, 9, 53], [1, 6, 59], [1, -1, 61], [1, -5, 67], [1, 0, 71], [1, -1, 73], [1, 13, 79], [1, 15, 83], [1, -15, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 115, 'label': '2-139650-1.1-c1-0-115', 'leading_term': '3.88592245929', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/139650/bq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8212826298114754, 0.8465241397605876, -0.137000473952496, -1.307231638215584, -1.342769394143283, -0.003476537629989558, 1.063254149296516, 0.007553308971574973, -2.492064756345942, -3.334998436612063, -0.9483894290341427, 1.76155743612322, 0.4977423348507029, -4.312565032520013, -7.136749780741681, -4.531829646963124, -0.1148547069915281, 0.6342566436807743, -1.458345237554864, -0.8540725352159881, 3.449460752406651, 5.899471943782271, 3.207629493458447, -0.4787487893561665, -0.5982752487913134, 0.902429539730372, 0.4563971149075023, -0.1611875820913426, 2.047928161085255, 4.327395309075244, 2.540904910107901, -0.7865648822599296, -0.5759281731886889, 1.640846643976962, 0.9678192314902055, -1.400425600383217, -0.9079669018316624, 1.177355530823385, 0.6855588844696678, -0.6642582853307374, 0.9836394078195237, 3.092033438774192, 1.626802101743762, -0.6379310497714964, -0.1065431566172041, 0.2097758309422759, -1.818004938977216, -1.728066364616245, 1.402336264047945, 1.052579209773914, -3.074016412623063, -2.565790268829697, 2.234723637032287, 0.816413661930275, -6.303124037914351, -6.517392412206451, 0.914707565921971, 3.397374625569282, -0.7568626799002359, -1.086285299579609, 2.978393652615539, 2.951159633996247, 0.03104070780967913, 0.9469392216930324, 2.838867924172106, 0.6976170659269161, -1.499882642268555, -0.4399736898410455, 0.07425790847388682, -0.6722891834369529, 0.4385385454793831, 1.018679129687055, -1.364255250290531, -1.750031532173304, 1.39056959141417, 1.763037948018408, -0.70940375374631, 0.005685248918565874, 1.711645165496412, 0.2241795349396952, 1.171205603603914, 6.373256312671942, 6.218739829350856, -0.01773614139323446, -1.328874116957583, 1.636699125498668, -0.285356424356372, -3.047540312809885, -0.1015758350133689, 1.080838376284108, -2.965278788740571, -2.882964964099668, 0.7012217356720699, -2.196610568980802, -6.845150309962403, -3.541228033970772, 1.177040644437601, 0.3814564504827212, 0.02218719534685314, 0.7523706335633848, -3.137480759442278, -5.884050925457839, -1.41469274517495, 1.686347755383083, -1.101308279884174, -1.644117409370205, 0.9211933151569107, 0.6185448594758792, 0.1208652073653694, 1.777398982118401, 0.5903208882086227, -2.002290068862113, -0.9200925098478435, -0.07455176436485197, -1.559665069066814, -0.3752958752049156, 1.120617710979725, -1.117678579222651, -0.9635206322806824, 2.072488473828543], 'positive_zeros': ['0.7232805192097839', '1.500545648185706', '2.000866883585809', '2.820606429800627', '3.281654737831406', '4.259380460858263', '4.582453038371817', '5.060957059031496', '5.953191053987818', '6.338536158101243', '6.845577559559684', '7.041236423973792', '7.924798503831522', '8.311352836853706', '8.842900127609664', '9.347440210842963', '9.843412284798172', '10.15389278704919', '10.90042740052875', '11.27093832498869', '11.53756567308638', '12.13862915049573', '12.56772080651601', '13.12766027207130', '13.53171239093580', '14.21849053089914', '14.70477915865960', '15.07099598875089', '15.75520747866783', '15.89040666429704', '16.55344420722843', '17.08481953003784', '17.27495776883138', '17.68640836753388', '18.12542510779684', '18.64440532231408', '19.16613331274961', '19.49940855271725'], 'prelabel': '2-139650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.39327573370395, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 622708531372272131, 'z1': {'__RealLiteral__': 0, 'data': '0.7232805192097839', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.500545648185706', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.000866883585809', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1115.110864227181, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 139650, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 0, -1, 1, 0, 3, -1, -2, 0, 0, 1, -6, -1, -1, 0, 0, -3, 3, 1, 0, 2, -1, 0, 3, 0, 7, -1, -3, 6, 0, 1, 2, 1, 2, 0, 6, 0, -10, 3, 0, -3, -12, -1, 0, 0, 6, -2, -9, 1, 0, 0, 1, -3, -6, 0, 1, -7, 0, 1, 0, 3, 5, -6, -3, 0, 0, -1, 1, -2, 0, -1, 0, -2, -13, 0, 1, -6, -15, 0, 0, 10, -3, -3, 15, 0, 0, 3, -7, 12, 0, 1, -8, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 0], 'euler31': [1, -7, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 10, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 6, 59], 'euler61': [1, -1, 61], 'euler67': [1, -5, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -1, 73], 'euler79': [1, 13, 79], 'euler83': [1, 15, 83], 'euler89': [1, -15, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -3, 11], [1, 2, 13], [1, 6, 17], [1, 1, 0], [1, -3, 23], [1, -3, 29], [1, -7, 31], [1, -2, 37], [1, -6, 41], [1, 10, 43], [1, 12, 47], [1, 9, 53], [1, 6, 59], [1, -1, 61], [1, -5, 67], [1, 0, 71], [1, -1, 73], [1, 13, 79], [1, 15, 83], [1, -15, 89], [1, 8, 97]], 'index': 115, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/139650/bq'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-139650-1.1-c1-0-115', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-139650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.39327573370395, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 622708531372272131, 'z1': {'__RealLiteral__': 0, 'data': '0.7232805192097839', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '622708531372272131', 'Lhash_array': ['622708531372272131'], 'label': '2-139650-1.1-c1-0-115', 'type': 'ECQ', 'url': 'EllipticCurve/Q/139650/bq'}