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lfunc_lfunctions • Show schema
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{'Lhash': '1775775420859023477556902203048', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [0.0, 0.0], 'a4': [7.609098497755183e-80, 2.906309198757067e-79], 'a5': [-0.17364817766693036, -0.984807753012208], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.5, -0.8660254037844386], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.819091971047294, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.17364817766693036, 0.984807753012208]]]], 'bad_primes': [3, 5], 'central_character': '3645.2024', 'coefficient_field': 'CDF', 'conductor': 3645, 'conductor_radical': 15, 'conjugate': '511183519984712104571216483347', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9396926207859084, -0.3420201433256687], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], 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'root_analytic_conductor': 1.3487371764162557, 'root_angle': 0.5740740740740741, 'root_number': '-0.23061587074244017845019834929328 + 0.97304487057982383883288517278498*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28703703703703703', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40083980596807246969160995650', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30777041134171095976415363702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33987648672607902671165217875', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.819091971047294, 'bad_primes': [3, 5], 'central_character': '135.74', 'conductor': 3645, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3645/1/n/e/2024/1'], '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': '2-3645-135.74-c0-0-5', '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': '2-3645-135.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3487371764162557, 'root_angle': 0.28703703703703703, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40083980596807246969160995650', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1775775420859023477556902203048', 'Lhash_array': ['1775775420859023477556902203048'], 'label': '2-3645-135.74-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3645/1/n/e/2024/1'}