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lfunc_lfunctions • Show schema
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{'Lhash': '2056179833901464627264343837060', 'a10': [-0.8660254037844386, -0.5], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.8660254037844386, 0.5], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, -3.9689140359382235e-80], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.12975690328458064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-0.8660254037844386, 0.5]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.67', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '3878654179046808743488151449767', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.5, 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-2.0288607608829268, -1.8478798562644587, -1.5556660754460605, -1.1910063473108963, -0.7965912698587507], 'positive_zeros': ['1.62203988506869908403098881592532', '3.77569788738540120686663690816336', '4.17384474787399573304638830109533', '5.68704839423958358998488005223607', '6.89070881870377856157680103898412', '8.391931884171576661919441095690302', '9.149893248015773131784832409971012', '10.35372006464948839885250191312672', '11.14612006845730062092668287833767', '12.06923163799886955169739283318487'], 'prelabel': '2-260-260.67-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.36021785531061706, 'root_angle': -0.5013322883285173, 'root_number': '-0.0041854950047298255442335094664655 - 0.99999124077742070074196957942480*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25066614416425864', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62203988506869908403098881593', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.12975690328458064, 'bad_primes': [2, 5, 13], 'central_character': '260.67', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/1/be/a/67/1'], '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': '2-260-260.67-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': '2-260-260.67-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.36021785531061706, 'root_angle': -0.25066614416425864, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62203988506869908403098881593', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2056179833901464627264343837060', 'Lhash_array': ['2056179833901464627264343837060'], 'label': '2-260-260.67-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/1/be/a/67/1'}