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lfunc_lfunctions • Show schema
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{'Lhash': '1783551905375494604487350567971', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.618033988749895, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.613633852426616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 59], 'central_character': '2832.1', 'coefficient_field': 'CDF', 'conductor': 2832, 'conductor_radical': 354, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [5.0, 0]], [[1.0, 0], [1.618033988749895, 0], [7.0, 0]], [[1.0, 0], [4.23606797749979, 0], [11.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [-3.8541019662496847, 0], [17.0, 0]], [[1.0, 0], [-5.854101966249685, 0], [19.0, 0]], [[1.0, 0], [-1.8541019662496845, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 36, 'label': '2-2832-1.1-c1-0-36', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2832/2/a/m/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.973238324759588e-61, 0.14384932010145324, 0.28712067154863175, 0.4291932186933383, 0.5693631349840739, 0.7068087495482409, 0.8405630942813195, 0.9694954613664746, 1.0923030078462546, 1.2075128820521104, 1.313494844804301, 1.4084839432570064, 1.4906124733885382, 1.5579502292087188, 1.6085518648368857, 1.6405100693976367, 1.6520131562094227, 1.6414055839827442, 1.6072498514965634, 1.548388136716132, 1.4640019891559126, 1.3536683361382789, 1.2174100368887057, 1.05573922124386, 0.8696916900067899, 0.6608507386283576, 0.431358900469895, 0.18391629415897692, -0.07823549681951673, 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'7.56355736386737833666702231335664', '8.297383721934684444907930520465215'], 'prelabel': '2-2832-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.755379464609172, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40697437058317306517107496252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71779722904219588949226758799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43411685479387234769702805391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.613633852426616, 'bad_primes': [2, 3, 59], 'central_character': '1.1', 'conductor': 2832, 'conductor_radical': 354, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2832/2/a/m/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': '2-2832-1.1-c1-0-36', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2832-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.755379464609172, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40697437058317306517107496252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1783551905375494604487350567971', 'Lhash_array': ['1783551905375494604487350567971'], 'label': '2-2832-1.1-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2832/2/a/m/1/1'}