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lfunc_lfunctions • Show schema
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{'Lhash': '2676131240878641962583284044513', 'a10': [1.3349141674889562e-60, -5.464101615137754], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [0.0, 0.0], 'a4': [1.7320508075688772, 1.0], 'a5': [-1.0, -3.732050807568877], 'a6': [0.0, 0.0], 'a7': [0.6339745962155614, -0.36602540378443865], 'a8': [2.0, 2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '432.253', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '1713848610320611496638315997273', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, -0.36602540378443865]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 3.732050807568877], [-4.330127018922194, 2.5]], [[1.0, 0], [-0.6339745962155614, 0.36602540378443865], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.1527777777777778, 'root_number': '0.8870108331782217 + 0.4617486132350339*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0763888888889', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11109531316975509083974371164', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29064747477102895528235410514', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05398443062836417607547467566', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '144.13', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/y/b/253/1'], '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': '2-432-144.13-c1-0-16', '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': '2-432-144.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.0763888888888889, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11109531316975509083974371164', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2676131240878641962583284044513', 'Lhash_array': ['2676131240878641962583284044513'], 'label': '2-432-144.13-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/y/b/253/1'}