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lfunc_lfunctions • Show schema
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{'Lhash': '2644400000051268381387430700748', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.4142135623730951, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [1.4142135623730951, 0.0], 'a7': [-1.4142135623730951, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7046797978377994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [353, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 353], 'central_character': '1412.1411', 'coefficient_field': 'CDF', 'conductor': 1412, 'conductor_radical': 706, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], 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['2.08606377780688723998127967378162', '2.83702548198863313840827315370591', '3.60940052259749619040295720700922', '4.35337409978058536130211544522108', '5.58090832885078982276496348297130', '6.72708374155202454511857865652619', '6.98730282094887284546760242655089', '8.161235601154553648736112282171759', '8.992777642670557168512939515592026', '9.569568749220059068855373010091202'], 'prelabel': '2-1412-1412.1411-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8394520819187951, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08606377780688723998127967378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83702548198863313840827315371', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60940052259749619040295720701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7046797978377994, 'bad_primes': [2, 353], 'central_character': '1412.1411', 'conductor': 1412, 'conductor_radical': 706, 'degree': 2, 'index': 6, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1412/1/d/b/1411/2', 'ArtinRepresentation/2.1412.8t6.a.a'], 'is_instance_Artin': True, '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': '2-1412-1412.1411-c0-0-6', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1412-1412.1411-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8394520819187951, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08606377780688723998127967378', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24598288
{'Lhash': '2644400000051268381387430700748', 'Lhash_array': ['2644400000051268381387430700748'], 'label': '2-1412-1412.1411-c0-0-6', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1412.8t6.a.a'}
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id: 19815745
{'Lhash': '2644400000051268381387430700748', 'Lhash_array': ['2644400000051268381387430700748'], 'label': '2-1412-1412.1411-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1412/1/d/b/1411/2'}