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lfunc_lfunctions • Show schema
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{'Lhash': '941967481653221379185372193008', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.3580027064442275], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.6635715302985274, 2.6635715302985274], 'a8': [0, 0], 'a9': [-2.560176763598302, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.776064323404867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1600.1007', 'coefficient_field': 'CDF', 'conductor': 1600, 'conductor_radical': 10, 'conjugate': '1886160756542853476630539285214', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.3580027064442275], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6635715302985274, -2.6635715302985274], [0, 7.0]], [[1.0, 0], [-2.2066615755717844, -2.2066615755717844], [0, 11.0]], [[1.0, 0], [4.161543168691063, 0], [13.0, 0]], [[1.0, 0], [-1.690835943228669, -1.690835943228669], [0, 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'data': '0.74308132026571704710883863178', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46707487290048229756490427902', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72657404678946369697915540943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.776064323404867, 'bad_primes': [2, 5], 'central_character': '80.67', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/2/j/e/1007/3'], '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': '2-40e2-80.67-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': '2-40e2-80.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': -0.025366922883523088, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74308132026571704710883863178', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '941967481653221379185372193008', 'Lhash_array': ['941967481653221379185372193008'], 'label': '2-40e2-80.67-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/j/e/1007/3'}