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lfunc_lfunctions • Show schema
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{'Lhash': '2398430931629616369789545275875', 'a10': [0.9095819933142937, -1.5754422260701315], 'a2': [1.0042622326286854, 1.7394332110354382], 'a3': [-0.8795280556681622, 1.5233872790995246], 'a4': [-1.0170852637687038, 1.7616433524769881], 'a5': [-0.4528607985851646, -0.784377911905721], 'a6': [-3.533107235379501, -8.068144439084182e-61], 'a7': [0.23770861493893497, -2.6350511597279875], 'a8': [-0.068632340549634, 0.0], 'a9': [-0.047139201414835394, -0.0816474918787176], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.23770861493893497, 2.6350511597279875]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.53', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '5380283428363465137192248658953', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0042622326286854, -1.7394332110354382], 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'6.59877797205958214651940996321703', '8.103002994600222945331782699947615', '9.764835585924940091771901797572979', '11.08989564986948798115249852632368', '11.80458218704909615986894830037314', '12.50615895860765964737112535821339', '13.31393303437901177366850286674279'], 'prelabel': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.6178564148013521, 'root_number': '-0.3618548854400035 - 0.9322344350447488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.308928207401', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89202839583541384462979097762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51892770271674247484985365349', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.31618080681637123914031186301', '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': '7.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/c/53/5'], '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': '2-91-7.4-c1-0-2', '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': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.30892820740067606, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89202839583541384462979097762', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2398430931629616369789545275875', 'Lhash_array': ['2398430931629616369789545275875'], 'label': '2-91-7.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/c/53/5'}