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lfunc_lfunctions • Show schema
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{'Lhash': '1759558986495114925635946147882', 'a10': [-1.851451645273498, 0], 'a2': [0, -0.3113563673187261], 'a3': [0, 0], 'a4': [3.9030572125300864, 0], 'a5': [0, -5.946406881662461], 'a6': [0, 0], 'a7': [8.671009295973706, 0], 'a8': [0, -2.4606671844054255], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '1494236634207508870439125501881', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.3113563673187261], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.946406881662461], [-25.0, 0]], [[1.0, 0], [-8.671009295973706, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-18.69822166080782, 0], [169.0, 0]], [[1.0, 0], [0, 9.599476898348282], [-289.0, 0]], [[1.0, 0], 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'3.39310500460828813051916822672', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/i/485/8'], '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': '2-33e2-3.2-c2-0-53', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.1520433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38804729487630244664989684919', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1759558986495114925635946147882', 'Lhash_array': ['1759558986495114925635946147882'], 'label': '2-33e2-3.2-c2-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/i/485/8'}