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lfunc_lfunctions • Show schema
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{'Lhash': '5926459684215736846024112186348', 'a10': [39.740852297878796, -5.291695641784708e-60], 'a2': [1.0, -1.7320508075688772], 'a3': [-1.8117376914898995, -4.870072539216931], 'a4': [-2.0, -3.4641016151377544], 'a5': [9.935213074469699, 17.20829382900411], 'a6': [-10.246950765959598, -1.7320508075688772], 'a7': [2.935213074469699, -5.083938176021969], 'a8': [-8.0, 0.0], 'a9': [-20.435213074469697, 17.646587959178472], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [1.8117376914898995, 4.870072539216931]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '3158048706273011418423348683686', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.8117376914898995, 4.870072539216931]], 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[1295029.0, 0]], [[1.0, 0], [-825.3635374788638, -1429.5715816281713], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-18-9.7-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/7/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.169178110274332, 1.2217443297538606, 1.2828815025947926, 1.3532477154597833, 1.4329242384194283, 1.5213905048887728, 1.6175022739945664, 1.719471641018215, 1.824851061194277, 1.9305273724632415, 2.0327348924744513, 2.1270984705371947, 2.2087177486431893, 2.272302861780138, 2.312369441602715, 2.323497103846836, 2.300650620927336, 2.239556787249402, 2.1371227761274487, 1.9918739318447432, 1.8043810009004313, 1.5776395418310516, 1.317358591665244, 1.0321126488499481, 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'13.25250709963598213379394897253479', '14.63683679109220782921056131412070', '16.22742338922348381242242736621815', '16.71630551852798337783752917682192', '17.87140107662534098706355907881701'], 'prelabel': '2-18-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.3288229802984496, 'root_number': '0.5122207083627314 + 0.858853855975731*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.164411490149', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.67515235124625793810476954388', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.81611137140904375916041931556', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.632252995053353520206374177106', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/b/7/1'], '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': '2-18-9.7-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.1644114901492248, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.67515235124625793810476954388', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5926459684215736846024112186348', 'Lhash_array': ['5926459684215736846024112186348'], 'label': '2-18-9.7-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/7/1'}