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lfunc_lfunctions • Show schema
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{'Lhash': '3068736522496168010984101888176', 'a10': [-3.4270509831248424, 5.935826422901098], 'a2': [-1.3090169943749475, 2.267283942228512], 'a3': [1.3090169943749475, -2.267283942228512], 'a4': [-2.4270509831248424, -4.203775615332221], 'a5': [2.618033988749895, 0.0], 'a6': [3.4270509831248424, 5.935826422901098], 'a7': [-0.5, -0.8660254037844386], 'a8': [7.47213595499958, 0.0], 'a9': [-1.9270509831248424, -3.337750211547782], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [2.5, -2.598076211353316]]]], 'bad_primes': [7, 13], 'central_character': '91.22', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2284490074657148859384630240181', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3090169943749475, -2.267283942228512], [-1.0, -1.7320508075688772]], [[1.0, 0], 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'13.69585316563607396005583691058742'], 'prelabel': '2-91-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.17074856945180006, 'root_number': '0.8595425350987749 - 0.5110642135348272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0853742847259', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.42080627102110695534675623945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47108356443198913441640188356', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.21395122041646884883505643151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.9', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/f/a/22/1'], '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': '2-91-13.9-c1-0-4', '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': '2-91-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.08537428472590003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.42080627102110695534675623945', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3068736522496168010984101888176', 'Lhash_array': ['3068736522496168010984101888176'], 'label': '2-91-13.9-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/f/a/22/1'}