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lfunc_lfunctions • Show schema
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{'Lhash': '1975291704843076746346554193273', 'a10': [-1.025806296635574, -1.7767486244968853], 'a2': [-0.8660254037844386, -0.5], 'a3': [-0.6628271480711836, 0.3826834323650898], 'a4': [0.5, 0.8660254037844386], 'a5': [1.7767486244968853, 1.025806296635574], 'a6': [0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-1.2071067811865475, 2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.6490421915474017, 3.252498152742188]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '141879543372259549049774976169', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0.6628271480711836, -0.3826834323650898], [1.5, 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[29.5, -51.09549882328188]], [[1.0, 0], [5.667106170925683, -9.815715819930398], [-30.5, -52.827549630850754]], [[1.0, 0], [1.481229321192522, 2.565564441966208], [-33.5, 58.023702053557386]], [[1.0, 0], [2.134031517638854, 0], [71.0, 0]], [[1.0, 0], [5.41261751976796, 9.374928546175548], [-36.5, 63.21985447626402]], [[1.0, 0], [-7.3484692283495345, -4.242640687119285], [39.5, 68.41600689897065]], [[1.0, 0], [12.315334296325464, 0], [83.0, 0]], [[1.0, 0], [5.826837742047155, 3.364126338895196], [44.5, 77.07626093681505]], [[1.0, 0], [0, -9.238795325112868], [-97.0, 0]], [[1.0, 0], [-0.929830313258958, -1.6105133449822004], [-50.5, 87.4685657822283]], [[1.0, 0], [5.811124242582109, 3.3550541457491403], [51.5, 89.20061658979718]], [[1.0, 0], [12.776771049422225, 7.3766722047581395], [53.5, 92.66471820493493]], [[1.0, 0], [-5.196152422706632, 3.0], [54.5, -94.39676901250381]], [[1.0, 0], [0.5973216737364816, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-1078-77.54-c1-0-34', 'leading_term': '0.210735047740759520116695602330640333406418222741084144', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.21073504774075952, 0.3171033322645948, 0.4208461191739993, 0.5219230659983942, 0.620153994809165, 0.7151873311873143, 0.8064790689308324, 0.8932830565662573, 0.9746526732547024, 1.0494533948268723, 1.116385376044473, 1.1740149755453522, 1.220814078570243, 1.255206073386738, 1.2756173601623653, 1.2805332798877496, 1.26855732590913, 1.2384724358682249, 1.1893030618864593, 1.120376592696463, 1.0313825674927852, 0.9224279930206468, 0.7940869679748125, 0.6474427460671852, 0.48412034338079324, 0.30630782712466753, 0.11676451973071054, 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'7.67895446795075772444785757059054', '8.717640700403015362656416342203974', '9.512202781703047959549355912304519', '9.886864072584029895311543138210681'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.8424104593819831, 'root_number': '-0.8799296863006539387875286317085458458804173140530750732 + 0.475103933015537929682239867505068597783686560597887628*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4212052296909916', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55823040235806519100957783765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59767376682175970932933774079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40094223838665528236022682339', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/7'], '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': '2-1078-77.54-c1-0-34', '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': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.42120522969099156, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55823040235806519100957783765', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1975291704843076746346554193273', 'Lhash_array': ['1975291704843076746346554193273'], 'label': '2-1078-77.54-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/901/7'}