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lfunc_lfunctions • Show schema
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{'Lhash': '1657586359625934850408461572067', 'a10': [0.0, 0.0], 'a2': [-1.8748071535809196, -0.6823739988927994], 'a3': [-0.08401859261722336, -0.4764931168199255], 'a4': [2.2832231456342624, 1.9158516993971386], 'a5': [0.0, 0.0], 'a6': [-0.167627855096735, 0.9506648070716249], 'a7': [0.848048096156426, -1.4688623898049864], 'a8': [-1.9757116509936299, -3.4220329606267565], 'a9': [0.7197060543145202, -0.26195158119166007], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [-0.7193398003386512, 0.6946583704589973]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '1098097903732381272720509776506', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-0.8767422935781548, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2717-2717.1429-c0-0-2', 'leading_term': '0.61733709838334708933133062376754', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.617337098383347, 0.6501397018109333, 0.6879023369506851, 0.730389487267575, 0.7766693611912997, 0.8252189398087569, 0.8740654506053129, 0.9209289089748431, 0.9633479144346998, 0.9987857283638953, 1.0247214096381276, 1.0387327115795018, 1.0385762924970428, 1.0222686196983095, 0.988168790076612, 0.9350627097891174, 0.8622467166397025, 0.7696077346525706, 0.65769635420091, 0.5277887851131351, 0.3819334079826872, 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'5.18868553752006660434555978030839', '5.53099012690230163518611277634292', '6.23122845552399193509569567073874', '7.36996570962543065875826224063351', '7.901179316542296920787914519406466', '8.516483066296914308343205323684143', '9.158535649190805633750899850842313'], 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.6012943833136172, 'root_number': '-0.31288182889433043216596620919911 + 0.94979206205765845740065448480847*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3006471916568086', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30760507613651658153104125518', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13408356122024047575905306743', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33718247664778354944056942002', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/1'], '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': '2-2717-2717.1429-c0-0-2', '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': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.3006471916568086, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30760507613651658153104125518', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1657586359625934850408461572067', 'Lhash_array': ['1657586359625934850408461572067'], 'label': '2-2717-2717.1429-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/1'}