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lfunc_lfunctions • Show schema
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{'Lhash': '2362650624567502848032446245982', 'a10': [0.0, 0.0], 'a2': [0.984807753012208, -0.17364817766693036], 'a3': [0.9396926207859084, 0.3420201433256687], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [0.984807753012208, 0.17364817766693036], 'a7': [0.0, 0.0], 'a8': [0.8660254037844386, -0.5], 'a9': [0.766044443118978, 0.6427876096865394], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.652903321840504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.984807753012208, 0.17364817766693036]]], [3, [[1.0, 0], [-0.9396926207859084, -0.3420201433256687]]], [23, [[1.0, 0], [0.8660254037844386, 0.5]]]], 'bad_primes': [2, 3, 23], 'central_character': '3312.1931', 'coefficient_field': 'CDF', 'conductor': 3312, 'conductor_radical': 138, 'conjugate': '1952049540274788840387772771139', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.984807753012208, 0.17364817766693036]], [[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86380271041730921038176491567', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24552741887518829739683369115', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47099454825626821147586218183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.652903321840504, 'bad_primes': [2, 3, 23], 'central_character': '3312.1931', 'conductor': 3312, 'conductor_radical': 138, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3312/1/bw/b/1931/3'], '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': '2-3312-3312.1931-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3312-3312.1931-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2856528776619698, 'root_angle': 0.034722222222222224, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86380271041730921038176491567', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2362650624567502848032446245982', 'Lhash_array': ['2362650624567502848032446245982'], 'label': '2-3312-3312.1931-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3312/1/bw/b/1931/3'}