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lfunc_lfunctions • Show schema
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{'Lhash': '619318729830057843815651222569', 'a10': [1.868073346760148, 0.0], 'a2': [-1.7412819046988133, 0.0], 'a3': [-2.8586184657299767, 0.0], 'a4': [1.032062671631527, 0.0], 'a5': [-1.0728150000980259, 0.0], 'a6': [4.977660606813493, 0.0], 'a7': [2.8516487197965343, 0.0], 'a8': [1.6854517547705352, 0.0], 'a9': [5.171699532612407, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7412819046988133, 0], [2.0, 0]], [[1.0, 0], [2.8586184657299767, 0], [3.0, 0]], [[1.0, 0], [1.0728150000980259, 0], [5.0, 0]], [[1.0, 0], [-2.8516487197965343, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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['0.48855633383406667747980291600193', '1.27336050345294759233051049099234', '2.14069101230844569959054593162440', '3.72811966566619225653856761566213', '4.54490197044011010223298145560063', '5.12763928417868535451210240088221', '5.68663923646543910788261840586804', '6.60635002500559846547404070479535', '7.49640508014089234071640915383537', '7.58118465934304583352431586887597'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48855633383406667747980291600', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27336050345294759233051049099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.14069101230844569959054593162', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 101, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/14'], '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': '2-8041-1.1-c1-0-101', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48855633383406667747980291600', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '619318729830057843815651222569', 'Lhash_array': ['619318729830057843815651222569'], 'label': '2-8041-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/14'}