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lfunc_lfunctions • Show schema
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{'Lhash': '2479734037786592439074562985577', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.0], 'a4': [0, 0], 'a5': [8.104686356149273, -7.701562118716424], 'a6': [0, 0], 'a7': [0, -22.209372712298546], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [-8.104686356149273, 7.701562118716424]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.769', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '132683951884584787249959461447', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [-8.104686356149273, 7.701562118716424]], [[1.0, 0], [0, 22.209372712298546], [-343.0, 0]], [[1.0, 0], [1.790627287701454, 0], [1331.0, 0]], [[1.0, 0], [0, -58.209372712298546], [-2197.0, 0]], [[1.0, 0], [0, -18.984378812835757], 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'positive_zeros': ['1.95616523775568600498664745670176', '2.80073767316836507443678076120812', '3.77553096644257448858535320743264', '5.30778269588247831751305868735708', '5.63703641658160895088353320896254', '6.60169732000237952391599215220318', '7.73023831391309734830218666382148', '8.696048629718463407870908186203257', '9.389641359705812230403928354378957', '10.13163772418681391627659010430456'], 'prelabel': '2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.7418835504063522, 'root_number': '-0.6888486572154892084424432849923045630552481947892162736 - 0.7249051851465938074818256537381479479013735686007333861*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3709417752031761', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95616523775568600498664745670', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80073767316836507443678076121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77553096644257448858535320743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 69, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/f/p/769/2'], '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': '2-960-5.4-c3-0-69', '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': '2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.3709417752031761, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95616523775568600498664745670', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2479734037786592439074562985577', 'Lhash_array': ['2479734037786592439074562985577'], 'label': '2-960-5.4-c3-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/f/p/769/2'}