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lfunc_lfunctions • Show schema
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{'Lhash': '250357664254007652299829308075', 'a10': [0, 0], 'a2': [0, 0], 'a3': [5.291502622129181, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -8.0], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.20152800459251, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '800.49', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '2033629896943243553527220806200', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-5.291502622129181, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 8.0], [-343.0, 0]], [[1.0, 0], [0, -15.874507866387544], [-1331.0, 0]], [[1.0, 0], [52.91502622129181, 0], [2197.0, 0]], [[1.0, 0], [0, -14.0], [-4913.0, 0]], [[1.0, 0], [0, 37.04051835490427], [-6859.0, 0]], [[1.0, 0], [0, -152.0], [-12167.0, 0]], [[1.0, 0], [0, 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'6.02206083705438186429303512542332', '7.12447500476795847599562724242091', '8.054766369998452507362854110881649', '8.622005786734525383311999479649162', '9.472019794690649143179166188417604'], 'prelabel': '2-800-40.29-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.870336818860667, 'root_angle': -0.3813051728658706, 'root_number': '-0.734557779283875707188975367335865598068363198581857783 - 0.678546143525656581378227348563551562706837612332411359*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3813051728658707', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19749737365243462584561029094', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.06453418984421874801960520088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80091466844116728181909144656', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.20152800459251, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/4/f/a/49/3'], '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': '2-800-40.29-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-800-40.29-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.870336818860667, 'root_angle': -0.3813051728658706, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19749737365243462584561029094', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '250357664254007652299829308075', 'Lhash_array': ['250357664254007652299829308075'], 'factors': ['2-800-40.29-c3-0-4'], 'label': '2-800-40.29-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/4/f/a/49/3'}