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lfunc_lfunctions • Show schema
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{'Lhash': '1856107652248434649191267227047', 'a10': [6.1569226826798555, 3.477398895654953], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [-2.9937794442741206, -0.19309230704959882], 'a4': [1.7320508075688772, 1.0], 'a5': [4.841664564289492, 1.2483125597795774], 'a6': [-4.01890208455061, -1.3595683266370844], 'a7': [-0.4004815899415367, -6.988534502749335], 'a8': [2.0, 2.0], 'a9': [8.925430721916527, 1.1561515593851117], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [3, [[1.0, 0], [2.9937794442741206, 0.19309230704959882]]], [5, [[1.0, 0], [-4.841664564289492, -1.2483125597795774]]], [7, [[1.0, 0], [0.4004815899415367, 6.988534502749335]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.17', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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'positive_zeros': ['1.46421076274034714545633197373809', '3.23254233562530004909944707165528', '5.12488579322873372793010294960329', '5.59761864406744940622264482461827', '6.44100705988944279908996176869194', '8.019122059658594818645922895872824', '9.547848428274389188409411162874337', '10.27081491186128046290514193435166', '11.32205641692176086760004933828490', '12.19728618982389908129578992942966'], 'prelabel': '2-210-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.05062016708659677, 'root_number': '0.9873816829927877 - 0.15835849232147323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0253100835433', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46421076274034714545633197374', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23254233562530004909944707166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12488579322873372793010294960', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.17', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/w/b/17/1'], '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': '2-210-105.17-c2-0-13', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-210-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': -0.025310083543298386, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46421076274034714545633197374', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1856107652248434649191267227047', 'Lhash_array': ['1856107652248434649191267227047'], 'label': '2-210-105.17-c2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/w/b/17/1'}