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lfunc_lfunctions • Show schema
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{'Lhash': '1587035243216583062291959188828', 'a10': [-6.878002150695126, 0.0], 'a2': [-2.0489173395223053, 0.0], 'a3': [-1.0, 0.0], 'a4': [2.198062264195162, 0.0], 'a5': [3.3568958678922094, 0.0], 'a6': [2.0489173395223053, 0.0], 'a7': [2.246979603717467, 0.0], 'a8': [-0.40581320741451476, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1587035243216583062291959188828', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0489173395223053, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.3568958678922094, 0], [5.0, 0]], [[1.0, 0], [-2.246979603717467, 0], [7.0, 0]], [[1.0, 0], [-4.939001075347563, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'6.45385532909737390433362921761033', '7.34056233531221372370716228875009', '8.506509273980416654680785872432070', '9.365669293112238223844295430787701', '9.718590993472648888920182265333399', '10.94693369393660235677203284829186'], 'prelabel': '2-507-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25195005858148234988264507219', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05843232776131367445206750053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31631134428115154031449675131', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/a/l/1/1'], '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': '2-507-1.1-c1-0-5', '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': '2-507-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25195005858148234988264507219', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1587035243216583062291959188828', 'Lhash_array': ['1587035243216583062291959188828'], 'label': '2-507-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/a/l/1/1'}