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lfunc_lfunctions • Show schema
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{'Lhash': '3131688957541991255308572339626', 'a10': [0.0, 0.0], 'a2': [1.6510934089371754, 0.0], 'a3': [-2.3772028539729577, 0.0], 'a4': [0.7261094450357825, 0.0], 'a5': [0.0, 0.0], 'a6': [-3.924983963901393, 0.0], 'a7': [0.3772028539729577, 0.0], 'a8': [-2.1033122990087403, 0.0], 'a9': [2.651093408937175, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '3131688957541991255308572339626', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6510934089371754, 0], [2.0, 0]], [[1.0, 0], [2.3772028539729577, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3772028539729577, 0], [7.0, 0]], [[1.0, 0], [1.3772028539729577, 0], [11.0, 0]], [[1.0, 0], [2.8216716648926528, 0], [13.0, 0]], 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'6.37029850032284263600142052055973', '7.43647634996632542907942242135810', '8.840502704715681938073667789668897', '9.929999269860691039043409127078006', '10.99557923397817890835730887740757'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47046698591722202765913608213', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.12650126542128489161939162915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83824677001158109884965668823', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/e/1/3'], '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': '2-475-1.1-c1-0-23', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47046698591722202765913608213', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3131688957541991255308572339626', 'Lhash_array': ['3131688957541991255308572339626'], 'label': '2-475-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/e/1/3'}