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lfunc_lfunctions • Show schema
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{'Lhash': '1029661857092875416353838274181', 'a10': [0.0, -2.0627681949125805], 'a2': [-2.0627681949125805, 0.0], 'a3': [0.0, -0.6208811826369829], 'a4': [2.2550126259429053, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 1.2807339563632774], 'a7': [0.0, 0.540632339379069], 'a8': [-0.5260319340961637, 0.0], 'a9': [2.6145065570473016, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.466012588989719, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, -1.0]]], [11, [[1.0, 0], [0, -1.0]]], [17, [[1.0, 0], [-3.7524839876038163, 1.7084682972700902]]]], 'bad_primes': [5, 11, 17], 'central_character': '935.441', 'coefficient_field': 'CDF', 'conductor': 935, 'conductor_radical': 935, 'conjugate': '1388244856646878933088978133585', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0627681949125805, 0], [2.0, 0]], [[1.0, 0], [0, 0.6208811826369829], [-3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -0.540632339379069], [-7.0, 0]], 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['0.812259984657833795996830308749809', '1.92542066717225073002207237282781', '3.68416161711546605782622811060162', '4.57533664499561575959983912233684', '5.87853772675179957481296951072087', '6.86934181436637331365543539364149', '7.83788810102403334258937553479622', '8.397800771873361563634589381681915', '9.194995063519349407939141471968528', '10.03672329001735723070192418547927'], 'prelabel': '2-935-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7324005176748374, 'root_angle': -0.13599609866454923, 'root_number': '0.9101110493723228 - 0.4143644263331608*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0679980493323', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.812259984657833795996830308750', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.92542066717225073002207237283', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68416161711546605782622811060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.466012588989719, 'bad_primes': [5, 11, 17], 'central_character': '17.16', 'conductor': 935, 'conductor_radical': 935, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/935/2/f/b/441/7'], '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': '2-935-17.16-c1-0-20', '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': '2-935-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7324005176748374, 'root_angle': -0.06799804933227462, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.812259984657833795996830308750', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1029661857092875416353838274181', 'Lhash_array': ['1029661857092875416353838274181'], 'label': '2-935-17.16-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/935/2/f/b/441/7'}