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lfunc_lfunctions • Show schema
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{'Lhash': '3125378626230069005945360487568', 'a10': [1.9809683233130595, 3.4311377841627495], 'a2': [-0.35731707620545344, 1.3335254828107126], 'a3': [0.9284373359725716, -0.5360335458494633], 'a4': [0.08143608721134693, 0.047017146873220984], 'a5': [2.029247351189925, -2.029247351189925], 'a6': [0.38306787870194414, 1.4296287860632875], 'a7': [-2.32988832073271, -1.2536428570024687], 'a8': [-2.0442138812749833, 2.0442138812749833], 'a9': [-0.9253360754481028, 1.602729096752502], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.32988832073271, 1.2536428570024687]]], [13, [[1.0, 0], [3.549261355551521, -0.6346210128797963]]]], 'bad_primes': [7, 13], 'central_character': '91.76', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '3185975244950610206714855324799', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'5.92808023983707360040315939324438', '6.91367343571081113995775427650478', '9.122288847692069748165466664089132', '9.651399022717627665430651524661523', '10.51323947008924305427600854890880', '11.75254016350530410260211924600755', '12.69554848717986018201854692044676', '14.04808417716519391588111246553174'], 'prelabel': '2-91-91.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.24481451872032917, 'root_number': '0.7185316888188336 - 0.6954942215167247*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12240725936', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.46548901224625454702084300880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34364895138901415043640605549', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.92808023983707360040315939324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '91.76', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/bc/a/76/4'], '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': '2-91-91.76-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': '2-91-91.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.12240725936016458, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46548901224625454702084300880', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3125378626230069005945360487568', 'Lhash_array': ['3125378626230069005945360487568'], 'label': '2-91-91.76-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/bc/a/76/4'}