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lfunc_lfunctions • Show schema
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{'Lhash': '2124592374990862453398254959526', 'a10': [-2.2837160219020936, -0.8312046554891848], 'a2': [0.2802116886011023, -0.6496037108449901], 'a3': [0.0, 0.0], 'a4': [1.0290168850225667, 1.0906941776712638], 'a5': [-0.19973942202076328, -3.429393434775247], 'a6': [0.0, 0.0], 'a7': [2.6323618898293963, 0.6238812285917302], 'a8': [2.326456633908038, -0.8467609660536692], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.55', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1585980344369335215574034979550', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2802116886011023, 0.6496037108449901], [-1.3724832757374672, -1.4547472831460975]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.19973942202076328, 3.429393434775247], [-4.966191788709715, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67600786416095111827899047249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83355231997359164681245153646', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17420911500723743365889250285', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.34', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/d/55/5'], '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': '2-3e6-81.34-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': 0, 'prelabel': '2-3e6-81.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.16761538633590942, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67600786416095111827899047249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2124592374990862453398254959526', 'Lhash_array': ['2124592374990862453398254959526'], 'label': '2-3e6-81.34-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/d/55/5'}