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lfunc_lfunctions • Show schema
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{'Lhash': '2103951102636049182513531936047', 'a10': [0.6678611509564877, -1.2897671826556527], 'a2': [-0.4281846582021865, -1.3478345219203567], 'a3': [1.5158742730710808, -1.5158742730710808], 'a4': [-1.6333157969605534, 1.1542441281631508], 'a5': [0.7262124176872122, 0.7262124176872122], 'a6': [-2.692221783628557, -1.3940735686437], 'a7': [0.0, 0.0], 'a8': [2.255090848919946, 1.7072097888418745], 'a9': [0.0, -1.5957496235175557], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.260271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.4281846582021865, 1.3478345219203567]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.197', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'conjugate': '1179900982664292440725356264596', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4281846582021865, 1.3478345219203567]], [[1.0, 0], [-1.5158742730710808, 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{'__RealLiteral__': 0, 'data': '0.366675680593', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65972477136621967543372523463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.46136248623753125993507164185', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34713438407665924111478008608', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.260271518468385, 'bad_primes': [2, 7], 'central_character': '16.5', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/2/m/i/197/4'], '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': '2-28e2-16.5-c1-0-60', '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': '2-28e2-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.502053460353792, 'root_angle': 0.36667568059279826, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65972477136621967543372523463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2103951102636049182513531936047', 'Lhash_array': ['2103951102636049182513531936047'], 'label': '2-28e2-16.5-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/2/m/i/197/4'}