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lfunc_lfunctions • Show schema
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{'Lhash': '2399888017789730892400667464151', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.6180339887498949, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-0.6180339887498949, 0.0], 'a7': [1.618033988749895, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.1', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '2399888017789730892400667464151', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [7.0, 0]], [[1.0, 0], [-3.8541019662496847, 0], [11.0, 0]], [[1.0, 0], [-4.0901699437494745, 0], [13.0, 0]], [[1.0, 0], 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[[1.0, 0], [-8.562305898749054, 0], [109.0, 0]], [[1.0, 0], [-18.94427190999916, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-230-1.1-c1-0-4', '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/230/2/a/c/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8010757939453297, 1.8070666885414421, 1.823544738880306, 1.8462383035793, 1.8686563463024126, 1.8828139230201113, 1.879965985221669, 1.851275190501262, 1.788414945677282, 1.684139751486212, 1.5328485520034425, 1.3311435822557542, 1.078362130627431, 0.7770386431562526, 0.4332418988082627, 0.05672702768209575, -0.3391549761449062, -0.7378368259240126, -1.1202316702625772, -1.4657494467834322, -1.7536039958200493, -1.9643472343846733, -2.081531458192175, -2.093369040690969, 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'8.377340443911295124746456879665543', '9.140306759551471116968745802586523', '10.82084895697821165088256119832565', '11.19558779221915460508966203867874', '12.15772750434465927058119918654810'], 'prelabel': '2-230-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89317783414266679508333114377', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67058546540356043216825506916', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89069048655957089784278056400', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/a/c/1/1'], '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': '2-230-1.1-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': '2-230-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89317783414266679508333114377', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2399888017789730892400667464151', 'Lhash_array': ['2399888017789730892400667464151'], 'label': '2-230-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/a/c/1/1'}