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lfunc_lfunctions • Show schema
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{'Lhash': '4556607511680534329826593178286', 'a10': [-2.769064584465729, 1.5271808429448168], 'a2': [-0.06609532207613347, -1.412668187650466], 'a3': [0.0, -0.4964873381971516], 'a4': [-1.9912628167993043, 0.18674151769893063], 'a5': [-0.9871887890287441, -2.0063544788536154], 'a6': [-0.7013718682423741, 0.03281549052486294], 'a7': [1.5542556032547885, -1.5542556032547885], 'a8': [0.39541695858142456, 2.8006508937863384], 'a9': [2.753500323009907, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6388032161702434, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.06609532207613347, 1.412668187650466]]], [5, [[1.0, 0], [0.9871887890287441, 2.0063544788536154]]]], 'bad_primes': [2, 5], 'central_character': '80.43', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1958931812122697647570469199299', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.06609532207613347, 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'-0.29743728472923037 + 0.9547413585117713*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.298065959276', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.59452952640116843501973373663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.26148760688914238905177044081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.53539307115159497819393723687', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6388032161702434, 'bad_primes': [2, 5], 'central_character': '80.43', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/2/j/b/43/6'], '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': '2-80-80.43-c1-0-8', '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': '2-80-80.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.799251660098522, 'root_angle': 0.29806595927637225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.59452952640116843501973373663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4556607511680534329826593178286', 'Lhash_array': ['4556607511680534329826593178286'], 'label': '2-80-80.43-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/2/j/b/43/6'}