-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4048745088650762243954759608190', 'a10': [0.0, 0.0], 'a2': [0.0, -2.0], 'a3': [1.0, -1.0], 'a4': [-3.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.0, -2.0], 'a7': [-1.0, -1.0], 'a8': [0.0, 4.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-1.0, 0]]], [47, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [17, 47], 'central_character': '799.140', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '1235097806233426003149515311863', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-799-799.140-c0-0-4', 'leading_term': '0.95428861145253862609836958610987', '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/799/1/e/a/140/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9542886114525386, 1.0442622272221975, 1.1548258031201202, 1.288710705180566, 1.4478765415726487, 1.6335763371508631, 1.846480619692854, 2.0867978462349654, 2.3543582329266286, 2.648654511545887, 2.968847281975803, 3.313746759108435, 3.6817818046837365, 4.070964702541237, 4.4788578013279245, 4.902546382823795, 5.3386208985187285, 5.783170896846914, 6.231792385408055, 6.6796099224945, 7.121314335187627, 7.551216571614866, 7.963317787489524, 8.35139533034395, 8.709103816866794, 9.0300900041058, 9.308119643601119, 9.537213992173974, 9.711793150431907, 9.826822928531794, 9.8779615182304, 9.86170190123784, 9.775505666663863, 9.617923764141771, 9.388699701305056, 9.088850819091832, 8.720723556532995, 8.288019054341891, 7.7957860445644585, 7.250378726667123, 6.659378227308884, 6.03147726370048, 5.3763287544254785, 4.704360316203099, 4.02655781400029, 3.354222354085634, 2.6987062803987687, 2.0711348071532485, 1.482120847550977, 0.9414813338451478, 0.45796382502804867, 0.03899242774539378, -0.3095580164256733, -0.5835509193303525, -0.7807322800308049, -0.900823592128891, -0.945557926029935, -0.9186554468170279, -0.8257365308181875, -0.6741727337133728, -0.47287807255457615, -0.23204533584272796, 0.03716565517651138, 0.32297883406556027, 0.6133808717106022, 0.8965159566645529, 1.1610828248908176, 1.3967198017990188, 1.5943634496076904, 1.7465668003349346, 1.8477641165150966, 1.8944706523267871, 1.8854079569065252, 1.8215478139778878, 1.7060708680656211, 1.5442392456086496, 1.3431859179675831, 1.1116270360987477, 0.8595068468325053, 0.5975879273256477, 0.33700219877575266, 0.08878036356292332, -0.13662107149439667, -0.32977526934747003, -0.48270320030935704, -0.5892355646329099, -0.6453014501122664, -0.6491293352360895, -0.6013494596570556, -0.5049906252264784, -0.36536900629331187, -0.1898713506700702, 0.012360167346930935, 0.23082944772021305, 0.4541579683433046, 0.6706061828878257, 0.8686217498859505, 1.0373895560732787, 1.1673576406928259, 1.2507134786283425, 1.2817866738331478, 1.25735692593307, 1.1768500759646123, 1.0424099653301317, 0.8588395522804708, 0.633410970662442, 0.37555069566515115, 0.09641238436678479, -0.1916440424232112, -0.4756432382653602, -0.7426271042141628, -0.9802982525379994, -1.1776417495299414, -1.3254927886440526, -1.4170197960114068, -1.4480959813031253, -1.4175374007743726, -1.3271919915696089, -1.1818714815098819, -0.989126221472159, -0.7588714189491623, -0.5028815277119768, -0.2341772137672075, 0.0336640718226218, 0.28723773400365504, 0.5140423679605401, 0.7031699935949102, 0.8459163542358781, 0.936274673056696, 0.9712816815329934, 0.9511921387086552, 0.8794671187801536, 0.7625716190892696, 0.6095880023701422, 0.43166284236820435, 0.24131526229224162, 0.05164421158931349, -0.12452027635109564, -0.2754714888593723, -0.39143313322434514, -0.46526654101741804, -0.4930288849809469, -0.4743398880503367, -0.4125239282253046, -0.31450631988814276, -0.19045631979354471, -0.05318436334114764, 0.08268362311649737, 0.20171713743964967, 0.2888260769986618, 0.3304773742041858, 0.315912673198526, 0.23829186545940706, 0.09568686092314005, -0.10814609462655247, -0.3632789210602388, -0.653459912615515, -0.9563324010975843, -1.244039540252507, -1.4842097890006496, -1.641295668315574, -1.6782166528100146, -1.558236881402595, -1.246990954848193, -0.7145575581452949, 0.06252803615509701, 1.0994346298686095, 2.401478044480868, 3.9629463803379803, 5.766392586249365, 7.782458915260979, 9.970272923833695, 12.278426437358089, 14.646518774604802, 17.007215083526912, 19.28874155937149, 21.417713251994016, 23.322168675903995, 24.93466986870531, 26.195317972337627, 27.054533552388968, 27.475458029823926, 27.435847641557174, 26.929353687714833, 25.96611145082788, 24.572593687256006, 22.790721279261756, 20.676261556071314, 18.296581881735012, 15.727860299529494, 13.051884364857532, 10.352592070334802, 7.712523584615706, 5.209358433272598, 2.9127092803464634, 0.8813306875448584, -0.8391202639343138, -2.217663692512961, -3.238844295119241, -3.902812905920133, -4.224649839553874, -4.232978254380722, -3.967953614803192, -3.478748198048503, -2.8206755678178004, -2.052117509624361, -1.2314240686620923, -0.4139555898255498, 0.3505758352225918, 1.0203286320035618, 1.5630091108234738, 1.9569296041857906, 2.19141119043792, 2.2665344862631507, 2.192280721087347, 1.9871407137160069, 1.6762992846702507, 1.289525242303674, 0.8589110367556948, 0.41661070531108724, -0.0072803280027006366, -0.3865742248505721, -0.7004613629520136, -0.9345242562628122, -1.0812496241436893, -1.1400288856028065, -1.116672537767241, -1.02249643624087, -0.8730657344643724, -0.6867033123716405, -0.48288255951830095, -0.28062857342928565, -0.09704701669884376, 0.05391348670877846, 0.16238036943487125, 0.22309920373120787, 0.23557103515243255, 0.20378922629891583, 0.1356112765823427, 0.041829085814725095, -0.06497617102739907, -0.17169269439812285, -0.2659408561111442, -0.3372319832081778, -0.3779248304895191, -0.38389917086566777, -0.354890156118958, -0.2944559313754163, -0.209582162267709, -0.10995818575848881, -0.006987935561700584, 0.08737769549915712, 0.16188377390952896, 0.2071779647486377, 0.21687021315131594, 0.18834493530106977, 0.12324396940836758], 'positive_zeros': ['3.19389671564216599440055642828241', '3.86665528610201218482511266895605', '5.08622314534893812886407372603766', '5.74635104893792175643103972436780', '6.70849618064936116204528590557804', '7.67952333185749838503850381613656', '8.517647138644809170150742433872234', '9.149004211195580521395692797171576', '9.594040985757889731963605525406790', '10.30813916166489070980551840416184'], 'prelabel': '2-799-799.140-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': -0.7110104348113153, 'root_number': '-0.61541220940263568453061943924181 - 0.78820543801610915221774562678970*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35550521740565766', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.19389671564216599440055642828', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86665528610201218482511266896', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.08622314534893812886407372604', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.39875294509376896, 'bad_primes': [17, 47], 'central_character': '799.140', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/1/e/a/140/1'], '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': '2-799-799.140-c0-0-4', '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': '2-799-799.140-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6314688789590259, 'root_angle': -0.35550521740565766, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.19389671564216599440055642828', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4048745088650762243954759608190', 'Lhash_array': ['4048745088650762243954759608190'], 'label': '2-799-799.140-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/1/e/a/140/1'}