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lfunc_lfunctions • Show schema
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{'Lhash': '327248050971983127727175842563', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 4.47213595499958], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 31.304951684997057], 'a8': [0, 0], 'a9': [7.0, 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': '800.449', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '2282877436531857319155078116644', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.47213595499958], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -31.304951684997057], [-343.0, 0]], [[1.0, 0], [8.94427190999916, 0], [1331.0, 0]], [[1.0, 0], [0, 62.0], [-2197.0, 0]], [[1.0, 0], [0, -46.0], [-4913.0, 0]], [[1.0, 0], [107.33126291998991, 0], [6859.0, 0]], [[1.0, 0], [0, -192.3018460649819], [-12167.0, 0]], 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'6.24934413170939122678204713824861', '6.92841329893006576580853625040499', '7.40568510119078044886644859482649', '8.380547769992236014226950755942152', '9.394392308519436368264363520578276'], 'prelabel': '2-800-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.870336818860667, 'root_angle': 0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25815319372157042234637789427', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.33194586535707554332950589761', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46713464785166697088206785957', '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': '5.4', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/4/c/l/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-c3-0-5', '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': '2-800-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.870336818860667, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25815319372157042234637789427', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '327248050971983127727175842563', 'Lhash_array': ['327248050971983127727175842563'], 'label': '2-800-5.4-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/4/c/l/449/3'}