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lfunc_lfunctions • Show schema
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{'Lhash': '729482740676985576428757264173', 'a10': [2.6203867971054593, 0.0], 'a2': [1.3659699202041191, 0.0], 'a3': [-0.1469190863308078, 0.0], 'a4': [-0.13412617709755273, 0.0], 'a5': [1.918334187559482, 0.0], 'a6': [-0.2006870526317556, 0.0], 'a7': [-1.8778320027138615, 0.0], 'a8': [-2.9151521638354656, 0.0], 'a9': [-2.9784147820717206, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3659699202041191, 0], [2.0, 0]], [[1.0, 0], [0.1469190863308078, 0], [3.0, 0]], [[1.0, 0], [-1.918334187559482, 0], [5.0, 0]], [[1.0, 0], [1.8778320027138615, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 138, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/45'], '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': '2-8041-1.1-c1-0-138', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57546041515355145202725250986', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '729482740676985576428757264173', 'Lhash_array': ['729482740676985576428757264173'], 'label': '2-8041-1.1-c1-0-138', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/e/1/45'}