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lfunc_lfunctions • Show schema
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{'Lhash': '814471902300553876245551677917', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.419577777801791, 2.419577777801791], 'a4': [0, 0], 'a5': [-2.541357576424429, 2.541357576424429], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0, 8.708713245664503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.309192042213452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 7], 'central_character': '1792.1345', 'coefficient_field': 'CDF', 'conductor': 1792, 'conductor_radical': 14, 'conjugate': '2921531407397743343523506895094', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.419577777801791, -2.419577777801791], [0, 3.0]], [[1.0, 0], [2.541357576424429, -2.541357576424429], [0, -5.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0.7647394947802231, -0.7647394947802231], [0, -11.0]], [[1.0, 0], [1.265822237782554, 1.265822237782554], [0, 13.0]], [[1.0, 0], 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'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64250504212589441840089431135', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48457104555494894113945998187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82166200675829642751070992941', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.309192042213452, 'bad_primes': [2, 7], 'central_character': '16.13', 'conductor': 1792, 'conductor_radical': 14, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1792/2/m/g/1345/8'], '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': '2-1792-16.13-c1-0-14', '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': '2-1792-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7827492703341377, 'root_angle': 0.4791666666666667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64250504212589441840089431135', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '814471902300553876245551677917', 'Lhash_array': ['814471902300553876245551677917'], 'label': '2-1792-16.13-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1792/2/m/g/1345/8'}