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lfunc_lfunctions • Show schema
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{'Lhash': '1049551501591907266529687979015', 'a10': [-7.44136498906337, 0.0], 'a2': [-2.5233651443679053, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.6326283481891408, 0.0], 'a5': [2.9489846151169723, 0.0], 'a6': [0.0, 0.0], 'a7': [-33.160509239844615, 0.0], 'a8': [24.30663862247067, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 127.97514280245146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [241, [[1.0, 0], [241.0, 0]]]], 'bad_primes': [3, 241], 'central_character': '2169.1', 'coefficient_field': 'CDF', 'conductor': 2169, 'conductor_radical': 723, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5233651443679053, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.9489846151169723, 0], [125.0, 0]], [[1.0, 0], [33.160509239844615, 0], [343.0, 0]], [[1.0, 0], [63.42923279132171, 0], [1331.0, 0]], [[1.0, 0], [-1.9883334129257562, 0], [2197.0, 0]], [[1.0, 0], [-58.94756200260618, 0], [4913.0, 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'3.20383986061971750724387197750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 127.97514280245146, 'bad_primes': [3, 241], 'central_character': '1.1', 'conductor': 2169, 'conductor_radical': 723, 'degree': 2, 'index': 136, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2169/4/a/e/1/11'], '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': '2-2169-1.1-c3-0-136', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2169-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.312609902336925, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.827950147621864179190104000803', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1049551501591907266529687979015', 'Lhash_array': ['1049551501591907266529687979015'], 'label': '2-2169-1.1-c3-0-136', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2169/4/a/e/1/11'}