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lfunc_lfunctions • Show schema
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{'Lhash': '1133620172604144563206751370259', 'a10': [2.2071067811865475, -3.822821082744905], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [2.2071067811865475, 3.822821082744905], 'a6': [-1.0, 0.0], 'a7': [1.6213203435596426, 2.0907702751760278], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.372062081298178, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-1.6213203435596426, -2.0907702751760278]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '798.571', 'coefficient_field': 'CDF', 'conductor': 798, 'conductor_radical': 798, 'conjugate': '2350438766228503649914701290201', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 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[0]], 'group': 'GL2', 'index': 6, 'label': '2-798-7.4-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/798/2/j/h/571/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.602841022618228, 1.4694581044235193, 1.3164756027711626, 1.1370916852317865, 0.9242056167128503, 0.6725952036839213, 0.3808938963282857, 0.05314981229740466, -0.300144678854022, -0.6616314364433784, -1.007355839574944, -1.3078074615721482, -1.5297800906010206, -1.6390305292839973, -1.6036174057906072, -1.3976863233257664, -1.0053531724872482, -0.4242428958047011, 0.3318134896380287, 1.2314172059043207, 2.2259943783317997, 3.252211891161723, 4.2364658065275895, 5.1012216067895935, 5.772695473280247, 6.189096156792322, 6.308443022034485, 6.114881295134363, 5.622464917506199, 4.875588319354756, 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'9.409915357832134564743516490227765', '9.774938809319603898872846878857374'], 'prelabel': '2-798-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.18978452306496227, 'root_number': '0.8274608818879864 - 0.5615233645585515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0948922615325', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.894268635537305127880504935690', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.19838035359858025859853378702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31731730877847880282540004773', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.372062081298178, 'bad_primes': [2, 3, 7, 19], 'central_character': '7.4', 'conductor': 798, 'conductor_radical': 798, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/798/2/j/h/571/2'], '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': '2-798-7.4-c1-0-6', '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': '2-798-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.524294372948246, 'root_angle': -0.09489226153248113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.894268635537305127880504935690', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1133620172604144563206751370259', 'Lhash_array': ['1133620172604144563206751370259'], 'label': '2-798-7.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/798/2/j/h/571/2'}