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lfunc_lfunctions • Show schema
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{'Lhash': '350900687389645452118382905969', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.7557353782323307], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 172.4242843714177], 'a8': [0, 0], 'a9': [242.42886403808802, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 128.30705585038453, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '800.449', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '1676934001325166107759714034548', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.7557353782323307], [-243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -172.4242843714177], [-16807.0, 0]], [[1.0, 0], [391.5400592489501, 0], [161051.0, 0]], [[1.0, 0], [0, 149.24533193465345], [-371293.0, 0]], [[1.0, 0], [0, -1187.7359958039603], [-1419857.0, 0]], [[1.0, 0], [-685.0332113387334, 0], [2476099.0, 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-4.818679570208066], 'positive_zeros': ['0.27681183389687099342744382259764', '1.21357507274859323491321590127711', '2.55442155886327519466000580246295', '3.78141817063589530651375721245251', '4.56692722171304283951590048244853', '5.46150561942609743568482034057022', '6.95802845569915738881736842882124', '7.20900424848506809401022529105346', '8.154080101409346909197454274523265', '9.311519342706840130389196881268703'], 'prelabel': '2-800-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.327270450129834, 'root_angle': -0.8524163823495667, 'root_number': '-0.8944271909999158785636694674925104941762473438446102897 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27681183389687099342744382260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.21357507274859323491321590128', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55442155886327519466000580246', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 128.30705585038453, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/6/c/k/449/3'], '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': '2-800-5.4-c5-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-800-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.327270450129834, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27681183389687099342744382260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '350900687389645452118382905969', 'Lhash_array': ['350900687389645452118382905969'], 'label': '2-800-5.4-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/6/c/k/449/3'}