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lfunc_lfunctions • Show schema
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{'Lhash': '1382478075716524624587305861914', 'a10': [1.3839016636201054, -4.834281710348611], 'a2': [-0.9828437041394504, -1.0168668807830474], 'a3': [-0.9875273925208216, -1.4229510353561106], 'a4': [-0.06803650646688886, 1.9988424234510787], 'a5': [1.7778309631957978, 3.0792935555242367], 'a6': [-0.4763667004252388, 2.40272236571893], 'a7': [0.7934555116166296, 2.523970750837892], 'a8': [2.09942591234415, -1.8953656213453731], 'a9': [-1.0495792980420544, 2.8104062512600465], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9828437041394504, 1.0168668807830474]]], [3, [[1.0, 0], [0.9875273925208216, 1.4229510353561106]]], [7, [[1.0, 0], [-0.7934555116166296, -2.523970750837892]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'6.23339438475832082105932705333124', '7.76758963970938187009544135030015', '8.856909037709107639249469611993078', '9.809134476371044028786496383515854', '10.31211288107932690321670809839354', '11.59194104243450857512564265189152', '12.84470007806998910987663742892372'], 'prelabel': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.0036486570899486458, 'root_number': '0.9999343051851648 - 0.011462343297148061*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00182432854497', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09058290625794011426296884400', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.40296521138567192703956817661', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26397591698371328829243171134', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/11/7'], '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': '2-168-168.11-c1-0-3', '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': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.0018243285449743229, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09058290625794011426296884400', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1382478075716524624587305861914', 'Lhash_array': ['1382478075716524624587305861914'], 'label': '2-168-168.11-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/11/7'}