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lfunc_lfunctions • Show schema
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{'Lhash': '1568006481951172772803763372775', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2225209339563144, -0.9749279121818236], 'a4': [0.0, 0.0], 'a5': [-0.5261348597302384, 2.305147435807454], 'a6': [0.0, 0.0], 'a7': [2.1030252447367603, -1.6053924193168125], 'a8': [0.0, 0.0], 'a9': [-0.9009688679024191, -0.4338837391175581], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]]], [7, [[1.0, 0], [-2.1030252447367603, 1.6053924193168125]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.169', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '1641568618011013579365916980616', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0.5261348597302384, -2.305147435807454], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16984283626842643066360723680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '49.22', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/q/b/169/1'], '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': '2-588-49.22-c1-0-5', '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': '2-588-49.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': 0.01695017319806307, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23693901274441626283865783721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1568006481951172772803763372775', 'Lhash_array': ['1568006481951172772803763372775'], 'label': '2-588-49.22-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/q/b/169/1'}