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lfunc_lfunctions • Show schema
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{'Lhash': '2586467241365166792590801381657', 'a10': [-1.1248444488869593, -1.4659258262890682], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [1.1248444488869593, -1.4659258262890682], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-0.9659258262890683, -0.25881904510252074], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1243', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '742073136618813510356576172953', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0], 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'8.550003453549906757520847215806987', '8.968604085769015501170310569408026'], 'prelabel': '2-3332-476.291-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.9249734719753893, 'root_number': '-0.97235046162651564808834420690209 - 0.23352640059466921035269707481208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46248673598769463', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04036288934781870613153549600', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96917741610359589758718964647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62955722604908126287703879846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.291', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bp/b/1243/1'], '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': '2-3332-476.291-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.291-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.46248673598769463, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04036288934781870613153549600', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2586467241365166792590801381657', 'Lhash_array': ['2586467241365166792590801381657'], 'label': '2-3332-476.291-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bp/b/1243/1'}