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lfunc_lfunctions • Show schema
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{'Lhash': '1108980087863152864509420189192', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [5.3808315196468595, 0.0], 'a6': [0.0, 0.0], 'a7': [3.380831519646859, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.45157553074648, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1872.1', 'coefficient_field': 'CDF', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.3808315196468595, 0], [125.0, 0]], [[1.0, 0], [-3.380831519646859, 0], [343.0, 0]], [[1.0, 0], [-68.90415759823429, 0], [1331.0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [-9.523326078587436, 0], [4913.0, 0]], [[1.0, 0], [133.18914671611546, 0], [6859.0, 0]], [[1.0, 0], [-196.5699782357623, 0], 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[[1.0, 0], [-664.4766739214126, 0], [1295029.0, 0]], [[1.0, 0], [-1817.9847714755042, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-1872-1.1-c3-0-36', 'leading_term': '3.07447644877362606650724308958', '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/1872/4/a/w/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.074476448773626, 3.0600626179651496, 3.0169965853541303, 2.945803827578407, 2.847357078304297, 2.7228715602342506, 2.5738979665421104, 2.4023128722250706, 2.2103061975413785, 2.0003653102083665, 1.7752553434504612, 1.537995325361699, 1.2918297623364159, 1.0401953953640495, 0.786682951522384, 0.5349938417375592, 0.28889190654412394, 0.05215048004534419, -0.17150477633537187, -0.378456629907854, 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'4.03833329328810967555860041409844', '4.62262067871413703320465491537817', '5.89232823700541636274441888206114', '6.42627984549524220529400092020874', '7.12739095616712879146210117513187', '8.281073546339059322219168207294220', '8.912648666238608395715275536247515'], 'prelabel': '2-1872-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.874831035983803976234536379550', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.74138147313860836409829207790', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88293077683429334838876597402', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.45157553074648, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1872, 'conductor_radical': 78, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1872/4/a/w/1/2'], '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': '2-1872-1.1-c3-0-36', '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': '2-1872-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.509594451297657, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.874831035983803976234536379550', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1108980087863152864509420189192', 'Lhash_array': ['1108980087863152864509420189192'], 'factors': ['2-1872-1.1-c3-0-36'], 'label': '2-1872-1.1-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1872/4/a/w/1/2'}