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lfunc_lfunctions • Show schema
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{'Lhash': '2922691049607843093380344462934', 'a10': [0.0, 0.0], 'a2': [0.6427876096865394, -0.766044443118978], 'a3': [0.17364817766693036, -0.984807753012208], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [0.0, 0.0], 'a6': [-0.6427876096865394, -0.766044443118978], 'a7': [0.0, 0.0], 'a8': [-0.8660254037844386, -0.5], 'a9': [-0.9396926207859084, -0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.652903321840504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6427876096865394, 0.766044443118978]]], [3, [[1.0, 0], [-0.17364817766693036, 0.984807753012208]]], [23, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 23], 'central_character': '3312.2437', 'coefficient_field': 'CDF', 'conductor': 3312, 'conductor_radical': 138, 'conjugate': '656386042576119085686942808285', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6427876096865394, 0.766044443118978]], [[1.0, 0], 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30559670707499222327654737909', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11484178502334324256748151399', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12614550354495853281006534681', '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': '3312.2437', 'conductor': 3312, 'conductor_radical': 138, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3312/1/bp/a/2437/3'], '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': '2-3312-3312.2437-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': '2-3312-3312.2437-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2856528776619698, 'root_angle': -0.40972222222222227, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30559670707499222327654737909', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2922691049607843093380344462934', 'Lhash_array': ['2922691049607843093380344462934'], 'factors': ['2-3312-3312.2437-c0-0-5'], 'label': '2-3312-3312.2437-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3312/1/bp/a/2437/3'}