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lfunc_lfunctions • Show schema
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{'Lhash': '510997454560471588793440665817', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [-2.2354306390906804, -0.05338405955556282], 'a6': [0, 0], 'a7': [0, 4.508742812862443], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.09986161255473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [2.2354306390906804, 0.05338405955556282]]], [67, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '4020.1609', 'coefficient_field': 'CDF', 'conductor': 4020, 'conductor_radical': 2010, 'conjugate': '1780653859978938187162485674498', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [2.2354306390906804, 0.05338405955556282]], [[1.0, 0], [0, -4.508742812862443], [-7.0, 0]], [[1.0, 0], [-0.971194671080722, 0], [11.0, 0]], [[1.0, 0], [0, 1.873371764791036], [-13.0, 0]], 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'2.54840865881914459902347325652121', '3.50003389635570127384856585932833', '4.31272636961553581900640899675627', '4.76082270275259615024077108380306', '6.09158293623378268889074323434015', '6.99145553273647535855593196475554', '7.23467889221038453880464376566853', '7.85005705103318610642126506186507'], 'prelabel': '2-4020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.9923999231106493, 'root_number': '-0.999714973598512039576472627086333076470206137295992570447 - 0.0238740772162271367452789100756489614954876555081094155*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.49619996155532464', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40310591457020646475558901802', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.07329176963190896397977778097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54840865881914459902347325652', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.09986161255473, 'bad_primes': [2, 3, 5, 67], 'central_character': '5.4', 'conductor': 4020, 'conductor_radical': 2010, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4020/2/g/c/1609/20'], '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': '2-4020-5.4-c1-0-16', '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': '2-4020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.665673976902901, 'root_angle': -0.49619996155532464, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40310591457020646475558901802', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '510997454560471588793440665817', 'Lhash_array': ['510997454560471588793440665817'], 'label': '2-4020-5.4-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4020/2/g/c/1609/20'}