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lfunc_lfunctions • Show schema
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{'Lhash': '7327413605299354603837910954701', 'a10': [2.613340798452839, -2.1928533001223154], 'a2': [-1.9396926207859084, -1.6275953626987474], 'a3': [0.6133407984528387, -0.22323779409789932], 'a4': [0.766044443118978, 4.344453923279833], 'a5': [-0.23395555688102196, 1.3268278963378768], 'a6': [-1.5530334192387472, -0.565257937423568], 'a7': [-0.766044443118978, -1.3268278963378768], 'a8': [3.053033419238747, -5.288008999327243], 'a9': [-1.9717815070238645, 1.654521135305906], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [-0.8190778623577252, 4.281251155374501]]]], 'bad_primes': [19], 'central_character': '19.16', 'coefficient_field': 'CDF', 'conductor': 19, 'conductor_radical': 19, 'conjugate': '3747178488850007951849164207674', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9396926207859084, 1.6275953626987474], [0.3472963553338607, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.78031012960520657860516432631', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.60518620624050872929393087320', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.964246542321939847993066642946', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'bad_primes': [19], 'central_character': '19.16', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/2/e/a/16/1'], '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': '2-19-19.16-c1-0-0', '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': '2-19-19.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3895070780363725, 'root_angle': 0.1665627857076632, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '5.78031012960520657860516432631', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7327413605299354603837910954701', 'Lhash_array': ['7327413605299354603837910954701'], 'label': '2-19-19.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/2/e/a/16/1'}