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lfunc_lfunctions • Show schema
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{'Lhash': '1823464452195699880988872053306', 'a10': [0.0, 0.0], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [1.0, 0.0], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [0.0, 0.0], 'a8': [-0.5, -0.8660254037844386], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [3, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.1051', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '2153944697085084163130015427309', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 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'8.929169300938310182303125130055333', '9.521618508322374557271220242216726'], 'prelabel': '2-1368-1368.1051-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.82626928859903, 'root_angle': -0.2198105599716541, 'root_number': '0.18855038512135346065610314015828 - 0.98206351743183561330850769264016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2198105599716541', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43845981839743621590915414958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40723046801462471112230810726', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49145132306645658100101960287', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6827209372819473, 'bad_primes': [2, 3, 19], 'central_character': '1368.1051', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/1/en/b/1051/1'], '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': '2-1368-1368.1051-c0-0-0', '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': '2-1368-1368.1051-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.82626928859903, 'root_angle': -0.2198105599716541, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43845981839743621590915414958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1823464452195699880988872053306', 'Lhash_array': ['1823464452195699880988872053306'], 'factors': ['2-1368-1368.1051-c0-0-0'], 'label': '2-1368-1368.1051-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/1/en/b/1051/1'}