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lfunc_lfunctions • Show schema
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{'Lhash': '2408625615324918586587416966192', 'a10': [7.0, -1.0], 'a2': [1.0, 1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 2.0], 'a5': [3.0, -4.0], 'a6': [0.0, 0.0], 'a7': [8.0, 8.0], 'a8': [-2.0, 2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4523223792426725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.0, 4.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '90.37', 'coefficient_field': 'CDF', 'conductor': 90, 'conductor_radical': 30, 'conjugate': '2908888533524499833078169245438', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 4.0]], [[1.0, 0], [-8.0, -8.0], [0, 49.0]], [[1.0, 0], [4.0, 0], [121.0, 0]], [[1.0, 0], [3.0, -3.0], [0, -169.0]], [[1.0, 0], [19.0, 19.0], [0, 289.0]], [[1.0, 0], [0, 8.0], [-361.0, 0]], [[1.0, 0], [-20.0, 20.0], [0, -529.0]], [[1.0, 0], [0, -38.0], [-841.0, 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1.5659892653663603, 'root_angle': -0.2213754264756499, 'root_number': '0.767751730118527 - 0.6407474392457674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.110687713238', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90007058324373184107056649676', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79411676590324652133929518839', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23742088478129338331876892094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4523223792426725, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 90, 'conductor_radical': 30, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/90/3/g/c/37/1'], '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': '2-90-5.2-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-90-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5659892653663603, 'root_angle': -0.11068771323782495, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90007058324373184107056649676', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2408625615324918586587416966192', 'Lhash_array': ['2408625615324918586587416966192'], 'label': '2-90-5.2-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/90/3/g/c/37/1'}