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lfunc_lfunctions • Show schema
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{'Lhash': '2294757531927720578519281429219', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.9510565162951535, 0.30901699437494745], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [-0.8090169943749475, 0.41221474770752686], 'a8': [0.0, 0.0], 'a9': [-0.5877852522924731, -0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [-0.9510565162951535, 0.30901699437494745]]], [19, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.778', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '1685288585085569943813034996492', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], 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'label': '2-1045-1045.778-c0-0-1', 'leading_term': '1.2401365740551290924715584301135', '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/1045/1/br/b/778/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.2401365740551291, 1.2669354534128876, 1.3090108590470568, 1.365304938224418, 1.433745939744819, 1.5115702451181794, 1.5956281485529875, 1.6826149046255385, 1.7692183606044878, 1.8522023169924695, 1.9284513227765112, 1.9949981132390595, 2.0490475686605767, 2.088004737428937, 2.109510053686717, 2.1114821237092953, 2.0921668358112613, 2.05019062880552, 1.9846152446005054, 1.8949910227425524, 1.7814056795459894, 1.6445255100617475, 1.4856260415635045, 1.3066093494677664, 1.110005522966197, 0.8989561413100517, 0.677178094022901, 0.44890664729032886, 0.2188173179565868, 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'8.486796404254573692869262747553097', '9.616202831958590247556163256259426', '10.40299027851685110339392460519368'], 'prelabel': '2-1045-1045.778-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.15407497710965348, 'root_number': '0.88512172158526668576821149320447 + 0.46535957922657361620988162258572*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07703748855482674', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81024450389923655527135178909', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81605443740388489398273946657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70503937752948131578165567643', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'bad_primes': [5, 11, 19], 'central_character': '1045.778', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/1/br/b/778/1'], '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': '2-1045-1045.778-c0-0-1', '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': '2-1045-1045.778-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': 0.07703748855482674, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81024450389923655527135178909', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2294757531927720578519281429219', 'Lhash_array': ['2294757531927720578519281429219'], 'label': '2-1045-1045.778-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/1/br/b/778/1'}