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lfunc_lfunctions • Show schema
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{'Lhash': '1389564289595473260685822983448', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.1213203435596424, 2.1213203435596424], 'a4': [0, 0], 'a5': [3.5355339059327378, 3.5355339059327378], 'a6': [0, 0], 'a7': [0, 26.06628392024063], 'a8': [0, 0], 'a9': [0, -9.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [2.1213203435596424, -2.1213203435596424]]], [5, [[1.0, 0], [-3.5355339059327378, -3.5355339059327378]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.241', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '1241721679295941715234462533776', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.1213203435596424, -2.1213203435596424]], [[1.0, 0], [-3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [0, -26.06628392024063], [-343.0, 0]], [[1.0, 0], [-36.788447019628954, 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0.8424755747132566739305898518428177375575002139643975057*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15945129145745884', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09617294335307723270708081589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.19911754891803478819669257559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36184330799072651542273603965', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '16.5', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/s/a/241/2'], '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': '2-960-16.5-c3-0-34', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-960-16.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.15945129145745884, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09617294335307723270708081589', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1389564289595473260685822983448', 'Lhash_array': ['1389564289595473260685822983448'], 'label': '2-960-16.5-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/s/a/241/2'}