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  • lfunc_lfunctions • Show schema
    {'Lhash': '1535853764824106615023726180399', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7320508075688772, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, 1.5], 'a8': [0.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7320508075688772, 0]]]], 'bad_primes': [2, 3], 'central_character': '576.193', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '2343793188599922424907151084654', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7320508075688772, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-2.5, -4.330127018922194]], [[1.0, 0], [-0.8660254037844386, -1.5], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.8660254037844386, -1.5], [-5.5, 9.526279441628825]], [[1.0, 0], [1.5, -2.598076211353316], 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-0.1400860292850246, -0.16824021959243496], 'positive_zeros': ['1.21157499120624372355627940871578', '2.78894453054846726077968288433647', '3.87577459947347825383008362617308', '4.77990081670115806645181361534208', '6.10719887708062703033876344820152', '7.42316762803947496260423256938842', '7.939256226723225574227808044498471', '8.791993175268844883188276758469623', '9.670137959497789114141263133758257', '10.50153886123028986620237201452242'], 'prelabel': '2-24e2-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.11111111111111113, 'root_number': '0.766044443118978 - 0.6427876096865394*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.111111111111', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21157499120624372355627940872', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.78894453054846726077968288434', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.87577459947347825383008362617', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.599383156425752, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/2/i/k/193/2'], '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': '2-24e2-9.4-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-24e2-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21157499120624372355627940872', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1535853764824106615023726180399', 'Lhash_array': ['1535853764824106615023726180399'], 'factors': ['2-24e2-9.4-c1-0-9'], 'label': '2-24e2-9.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/2/i/k/193/2'}