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lfunc_lfunctions • Show schema
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{'Lhash': '5980817723622454958701276511852', 'a10': [6.0, 0.0], 'a2': [0.0, -1.4142135623730951], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [0.0, 4.242640687119285], 'a6': [0.0, 0.0], 'a7': [-4.0, 0.0], 'a8': [0.0, 2.8284271247461903], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '18.17', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '4261528175825625988770814566311', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.242640687119285], [-25.0, 0]], [[1.0, 0], [4.0, 0], [49.0, 0]], [[1.0, 0], [0, 16.97056274847714], [-121.0, 0]], [[1.0, 0], [-8.0, 0], [169.0, 0]], [[1.0, 0], [0, -12.727922061357855], [-289.0, 0]], [[1.0, 0], [16.0, 0], [361.0, 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'17.17386069467369261541271057370849', '18.41989986415510726525675866417522'], 'prelabel': '2-18-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.19591327601530362, 'root_number': '0.816496580927726 + 0.5773502691896257*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0979566380077', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.71803328341868101997909002331', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.74703699913736062741911446047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.564573240899659569950682875282', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/3/b/a/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': '2-18-3.2-c2-0-1', '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': '2-18-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.09795663800765181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.71803328341868101997909002331', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5980817723622454958701276511852', 'Lhash_array': ['5980817723622454958701276511852'], 'label': '2-18-3.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/3/b/a/17/1'}