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lfunc_lfunctions • Show schema
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{'Lhash': '1611166756905748546973080008489', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [0.4400711179528193, 0.0663300485369759], 'a6': [0.0, 0.0], 'a7': [-0.9555728057861407, 1.655100649952743], 'a8': [0.0, 0.0], 'a9': [0.07473009358642425, -0.9972037971811801], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.407736115321163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [-0.07473009358642425, -0.9972037971811801]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [19, 43], 'central_character': '817.56', 'coefficient_field': 'CDF', 'conductor': 817, 'conductor_radical': 817, 'conjugate': '1713951982878924450153491610179', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [-0.4400711179528193, -0.0663300485369759], 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'7.66356479712478644635645816018987', '8.973350889920821618843560702577847', '9.695559338484607027435684945815865', '10.11592710066312861490265933013362'], 'prelabel': '2-817-817.56-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6385421797510036, 'root_angle': -0.013999186079923764, 'root_number': '0.99903304710157173439324256783218 - 0.043965563785180241786776768646429*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.006999593039961882', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27098646631467067223071798463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22859805939290852114761419683', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12731297901676339112287174979', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.407736115321163, 'bad_primes': [19, 43], 'central_character': '817.56', 'conductor': 817, 'conductor_radical': 817, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/817/1/bz/a/56/1'], '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': '2-817-817.56-c0-0-0', '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': '2-817-817.56-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6385421797510036, 'root_angle': -0.006999593039961882, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27098646631467067223071798463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1611166756905748546973080008489', 'Lhash_array': ['1611166756905748546973080008489'], 'label': '2-817-817.56-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/817/1/bz/a/56/1'}