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lfunc_lfunctions • Show schema
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{'Lhash': '1619909384152711371097514809103', 'a10': [2.135779205069857, -1.854305041569798], 'a2': [0.927152520784899, 1.0678896025349285], 'a3': [0.0, 0.0], 'a4': [-0.28077640640441515, 1.9801930738204856], 'a5': [0.0, -2.0], 'a6': [0.0, 0.0], 'a7': [0.9364263849242712, 0.0], 'a8': [-2.3749501475193555, 1.536102794997064], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.32415184008541, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.927152520784899, -1.0678896025349285]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-3.092176064328943, 1.1993528201455856]]]], 'bad_primes': [2, 3, 11], 'central_character': '792.307', 'coefficient_field': 'CDF', 'conductor': 792, 'conductor_radical': 66, 'conjugate': '1740611886556414691031754953799', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.927152520784899, -1.0678896025349285]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.0], [-5.0, 0]], [[1.0, 0], 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-2.496525011031828], 'positive_zeros': ['1.27788318315871964800276847795550', '2.62687916222941356985628125369140', '3.59735045193346706993218474089232', '4.51532812623545281199652719349930', '5.65551213860679786242790385505133', '6.56004756049905768836581429189789', '7.29263093655188580613641386330948', '8.750860101579290565329673736462141', '9.451222439991436409949420899446840', '10.42137492151073899423323569560205'], 'prelabel': '2-792-88.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.514786639078037, 'root_angle': -0.15026155572276018, 'root_number': '0.586454918137971 - 0.8099818695451063*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.150261555723', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27788318315871964800276847796', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62687916222941356985628125369', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59735045193346706993218474089', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.32415184008541, 'bad_primes': [2, 3, 11], 'central_character': '88.43', 'conductor': 792, 'conductor_radical': 66, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/792/2/h/i/307/11'], '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': '2-792-88.43-c1-0-31', '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': '2-792-88.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.514786639078037, 'root_angle': -0.15026155572276018, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27788318315871964800276847796', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1619909384152711371097514809103', 'Lhash_array': ['1619909384152711371097514809103'], 'factors': ['2-792-88.43-c1-0-31'], 'label': '2-792-88.43-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/792/2/h/i/307/11'}