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lfunc_lfunctions • Show schema
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{'Lhash': '3036974519835226284594979142909', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 5.196152422706632], 'a4': [8.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-10.0, -15.588457268119896], 'a8': [0.0, 0.0], 'a9': [-27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2390401101205535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -5.196152422706632]]], [7, [[1.0, 0], [10.0, 15.588457268119896]]]], 'bad_primes': [3, 7], 'central_character': '21.20', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '4416715239084707281036802360949', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-8.0, 0]], [[1.0, 0], [0, -5.196152422706632]], [[1.0, 0], [0, 0], [125.0, 0]], [[1.0, 0], [10.0, 15.588457268119896]], [[1.0, 0], [0, 0], [-1331.0, 0]], [[1.0, 0], [0, 62.353829072479584], [-2197.0, 0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], [0, -155.88457268119896], 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'prelabel': '2-21-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.113121785844008, 'root_angle': -0.09077828874275753, 'root_number': '0.841697576624542 - 0.5399492471560389*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0907782887428', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39575046885036427936358363073', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.09572951414993823770614548241', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.24623828832099096945840415539', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2390401101205535, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/4/c/a/20/2'], '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': '2-21-21.20-c3-0-1', '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': '2-21-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.113121785844008, 'root_angle': -0.09077828874275753, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39575046885036427936358363073', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3036974519835226284594979142909', 'Lhash_array': ['3036974519835226284594979142909'], 'factors': ['2-21-21.20-c3-0-1'], 'label': '2-21-21.20-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/4/c/a/20/2'}