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lfunc_lfunctions • Show schema
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{'Lhash': '832598752923665354814632976370', 'a10': [-0.01987872340788267, 0.11273784266033397], 'a2': [0.28247876970969155, 1.6020167110825514], 'a3': [-0.8241804762145416, 0.6915695336151368], 'a4': [-0.6072780456792374, 0.22103113255059356], 'a5': [0.06612847300428668, 0.024068795811036457], 'a6': [-1.340719436666847, -1.1249971848193618], 'a7': [0.0, 0.0], 'a8': [1.1010916778881694, 1.9071467298935738], 'a9': [-0.3199394954522204, 1.8144670439358404], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.434072428181207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.316086232436689, -2.829058518137058]]]], 'bad_primes': [7, 19], 'central_character': '931.883', 'coefficient_field': 'CDF', 'conductor': 931, 'conductor_radical': 133, 'conjugate': '2322238011672528505646763944917', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.28247876970969155, -1.6020167110825514], [-1.8793852415718169, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65680460591724820128343047426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89360500429755114807754804084', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11342313752810653922121536306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.434072428181207, 'bad_primes': [7, 19], 'central_character': '19.9', 'conductor': 931, 'conductor_radical': 133, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/931/2/w/b/883/4'], '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': '2-931-19.9-c1-0-14', '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': '2-931-19.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': 0.49878597976141115, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65680460591724820128343047426', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '832598752923665354814632976370', 'Lhash_array': ['832598752923665354814632976370'], 'label': '2-931-19.9-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/931/2/w/b/883/4'}