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lfunc_lfunctions • Show schema
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{'Lhash': '1383491721617560565399677997352', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [2.0, 0], 'a5': [-0.5, 2.179449471770337], 'a6': [0, 0], 'a7': [0, 4.358898943540674], 'a8': [0, 0], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.5, -2.179449471770337]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1084', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'conjugate': '2121710025708124561295769971152', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-2.0, 0]], [[1.0, 0], [0, 0], [-3.0, 0]], [[1.0, 0], [0.5, -2.179449471770337]], [[1.0, 0], [0, -4.358898943540674], [-7.0, 0]], [[1.0, 0], [-5.0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, -4.358898943540674], [-17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 8.717797887081348], [-23.0, 0]], [[1.0, 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'root_analytic_conductor': 3.7964453854679796, 'root_angle': -0.42821685343564686, 'root_number': '0.22360679774997896964091736687312762354406183596115257243 - 0.97467943448089639068384131998996002992525839003374910320*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21410842671782343', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09138253188100489468037931358', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52684418489301665659941999425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37818609089530100132707616139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '5.4', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/b/d/1084/2'], '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': '2-1805-5.4-c1-0-80', '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': '2-1805-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': -0.21410842671782343, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09138253188100489468037931358', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1383491721617560565399677997352', 'Lhash_array': ['1383491721617560565399677997352'], 'label': '2-1805-5.4-c1-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/b/d/1084/2'}