-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2683009113030638730386165685810', 'a10': [-0.4532033637001998, 0.007538856635781124], 'a2': [-0.08756427915024693, -0.023462777884122064], 'a3': [2.776163862578509, 1.1370638540175184], 'a4': [-3.456984614100692, -1.995890997535429], 'a5': [4.80743728834126, -1.3742440535312606], 'a6': [-0.21641411078277553, -0.16470269280245156], 'a7': [2.1803402683147772, -6.651775425731468], 'a8': [0.5122852236756286, 0.5122852236756286], 'a9': [6.414171583773655, 6.31335116193536], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.776163862578509, -1.1370638540175184]]], [5, [[1.0, 0], [-4.80743728834126, 1.3742440535312606]]], [7, [[1.0, 0], [-2.1803402683147772, 6.651775425731468]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.17', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '2153018744224437906022494334424', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.08756427915024693, 0.023462777884122064], [3.4641016151377544, 2.0]], [[1.0, 0], [-2.776163862578509, -1.1370638540175184]], [[1.0, 0], [-4.80743728834126, 1.3742440535312606]], [[1.0, 0], [-2.1803402683147772, 6.651775425731468]], [[1.0, 0], [-6.216111741769539, -3.5888737874234367], [60.5, 104.78907385791707]], [[1.0, 0], [-2.4276354709541805, -2.4276354709541805], [0, 169.0]], [[1.0, 0], [17.188525777295066, -4.605651601107748], [250.28134169370276, -144.5]], [[1.0, 0], [6.281384118602622, 10.879676435275991], [-180.5, 312.63517076618234]], [[1.0, 0], [0.09516224618378974, -0.3551503377202808], [-458.12743860196804, -264.5]], [[1.0, 0], [51.76285345290834, 0], [841.0, 0]], [[1.0, 0], [-2.0230396270666775, -1.1680024732682264], [480.5, 832.2504130368455]], [[1.0, 0], [4.655478335375127, -17.374481681156155], [-1185.5887777808964, -684.5]], [[1.0, 0], [44.54140149311929, 0], [1681.0, 0]], [[1.0, 0], [45.619711311378644, -45.619711311378644], [0, -1849.0]], [[1.0, 0], [14.68284666357085, -54.79712974818958], [-1913.050116959825, -1104.5]], [[1.0, 0], [-63.88168022811134, 17.117044628265653], [2432.6653592304883, -1404.5]], [[1.0, 0], [-65.69985876864968, -37.93183114580029], [1740.5, 3014.634430573631]], [[1.0, 0], [-93.3014053834794, 53.867591513922235], [1860.5, -3222.4805274818964]], [[1.0, 0], [29.91708118205712, -8.016257742628543], [3887.5880375883453, -2244.5]], [[1.0, 0], [0, 69.81567115645615], [-5041.0, 0]], [[1.0, 0], [-26.138066059729997, 7.00367369241599], [4615.049376767273, -2664.5]], [[1.0, 0], [-68.43382973246459, 39.51029001771544], [3120.5, -5404.864545018681]], [[1.0, 0], [77.2540207245036, -77.2540207245036], [0, -6889.0]], [[1.0, 0], [-18.463279013391013, 10.65977910850447], [3960.5, -6859.787223376538]], [[1.0, 0], [45.530319604355014, -45.530319604355014], [0, -9409.0]], [[1.0, 0], [12.06085488067899, -20.89001343605108], [-5100.5, -8834.325144005059]], [[1.0, 0], [0.7577721169862798, -2.8280440411518235], [-9187.66350874911, -5304.5]], [[1.0, 0], [-89.09180036525382, -23.872075960104564], [9915.124847928038, 5724.5]], [[1.0, 0], [25.014051858504345, 14.441869574030742], [5940.5, 10289.247822362915]], [[1.0, 0], [119.88733119712937, 119.88733119712937], [0, 12769.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-105-105.17-c2-0-16', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/105/3/w/a/17/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.717680709465332, 1.7424780993541995, 1.7625545630119384, 1.7768733479215395, 1.7835094874954394, 1.7797907908642343, 1.7624908369591827, 1.7280605558906605, 1.6728875022852718, 1.5935747929287185, 1.48723317887144, 1.3517791661808292, 1.1862297016161287, 0.9909804026133724, 0.768050475998581, 0.5212741222802081, 0.25641602720987977, -0.018811960933262258, -0.2948542626672439, -0.5605523952482799, -0.8035339464246907, -1.010751429587322, -1.1691615527872086, -1.2665225820371493, -1.2922737841088763, -1.238447451846962, -1.1005520075926922, -0.8783555377952473, -0.5764942440852024, -0.20483099677205302, 0.22150353019695793, 0.6824401835028575, 1.1537024696998932, 1.6079426541337956, 2.0162526710743607, 2.3499835332286474, 2.582770795766548, 2.6926309479512174, 2.6639680578017297, 2.4893151929550594, 2.1706342322867593, 1.7200129408321463, 1.1596306105751037, 0.5209125862410241, -0.15714278326486994, -0.8304080201961059, -1.452707181776501, -1.9793251131490848, -2.370674004779496, -2.5958018816098543, -2.635409581941048, -2.4840559425695004, -2.151277843785582, -1.6614317059794688, -1.0521714781274218, -0.371606903878091, 0.3256766177501414, 0.9834228765409488, 1.5489085336447033, 1.978042431690301, 2.2398271700135215, 2.3196750236966373, 2.2211542571694847, 1.9658808404177892, 1.591454127362798, 1.1475464002258466, 0.6904733919225409, 0.27677099585614606, -0.04354294431500558, -0.23325614670722572, -0.2730299947982249, -0.1645681457019864, 0.06861656207919511, 0.38308577476633265, 0.7199545503536325, 1.0115885490387133, 1.1898420285246825, 1.1949195704626498, 0.9838011554651113, 0.5371494589736461, -0.13626722522630103, -0.998357005327284, -1.9840557618468837, -3.00718363076942, -3.9692916575962314, -4.770568424274806, -5.321554074360745, -5.554229183969806, -5.431042496406695, -4.950627443390475, -4.149320504682606, -3.0980974641001913, -1.895127127744726, -0.6547312927777865, 0.505946124373781, 1.4808946893734205, 2.187998991361756, 2.5788788127635525, 2.644417166611694, 2.4151327949999737, 1.9562449610590564, 1.3580214945114104, 0.7226908838999107, 0.14973212676907385, -0.2783544037445125, -0.5077008004544642, -0.5203768925014569, -0.3361737485991977, -0.008494132892787797, 0.38513011705571626, 0.7565257853670186, 1.0223314546435, 1.118994572746229, 1.0148724413152006, 0.7173632769191179, 0.27370529445187064, -0.23495665849201147, -0.7055670601947113, -1.0295354941083292, -1.1110199027850756, -0.8842175206364485, -0.32678582667245115, 0.5329935225706743, 1.6167924018356008, 2.804853173087797, 3.951651521409579, 4.906423960664827, 5.535494598119067, 5.742915288814117, 5.486067297912714, 4.783563428563834, 3.7139463923912825, 2.405128480218627, 1.0160285067417685, -0.28681703224777033, -1.3539909159550478, -2.0752904567840886, -2.395542206117373, -2.3214746765207566, -1.9184451034290535, -1.2975181680938266, -0.5950536000524478, 0.05171506768269261, 0.5288794423185856, 0.7655791249282233, 0.7457243228277318, 0.5095685197260499, 0.1447736561655561, -0.2314904265974754, -0.4962050502340599, -0.5455918033269903, -0.31694798559364584, 0.19695574068810473, 0.9438111179986383, 1.8190740856276602, 2.68355661578221, 3.388264969205935, 3.8019878851680837, 3.8364904388033847, 3.4644752208068095, 2.7267053410336537, 1.7266395636933891, 0.613259483545137, -0.4449611477499977, -1.2902213661320356, -1.8040492856762855, -1.928946915589381, -1.6787278464128288, -1.1353271559241405, -0.432430574915127, 0.27115424033832825, 0.8233807928672608, 1.1099358828350447, 1.0781506061180954, 0.7489270153726617, 0.21399294839957436, -0.3813679202519077, -0.8670730196318651, -1.083072337320077, -0.9134718497799776, -0.31310521266987157, 0.678989856064772, 1.942291235965739, 3.293678284967671, 4.5192432485201595, 5.413138384734199, 5.816029332618583, 5.645634130008973, 4.9132396234402815, 3.722753692780869, 2.252261537334268, 0.7215312298030927, -0.6482485418014635, -1.6746089712073113, -2.245906341991309, -2.3390692516991645, -2.0195683751010756, -1.423822761636505, -0.7278737341280408, -0.10900019728673027, 0.29159164373928853, 0.3971231309100797, 0.20869415720228526, -0.19889553352513156, -0.6978437129191827, -1.1398210819725474, -1.3928552948719242, -1.374218220223604, -1.071724611212206, -0.5483696738001788, 0.0710648583648449, 0.6287188676703646, 0.9713887393519227, 0.9887605912302425, 0.6432396493366842, -0.015896799255256545, -0.8579699277085292, -1.6956151222381346, -2.323980643788174, -2.5661869073420775, -2.31509424462709, -1.561870326267459, -0.40443436078120876, 0.9669280022578101, 2.3045301870715775, 3.351973213965221, 3.8964759364189994, 3.8136834775260184, 3.095147203106325, 1.8522236678025188, 0.29515039002770355, -1.308562559618463, -2.687727768339317, -3.62166302650177, -3.983351631757636, -3.7623371147017823, -3.062553869558893, -2.075840438808531, -1.0372839345668057, -0.1725730501987051, 0.3507378373513605, 0.45714258572019356, 0.17486237348707456, -0.3769131716924497, -1.0217078567528703, -1.5719591059983662, -1.8764279955822842, -1.857295442690472, -1.527967095844406, -0.9873325357669765, -0.39200982429097875, 0.08643275519059902, 0.3084810996517624, 0.20591400143005412, -0.19696350870209203, -0.7860058618260937, -1.3838551677131865], 'positive_zeros': ['2.11652099762157364958750364124232', '3.68672503049185785509317888533773', '5.47125816509984864068410708863885', '6.94134543153785729880670181212312', '8.479869251156742358684679327203516', '8.968415575798710157549654451086571', '9.977560228605197857998599347141239', '11.69367406616808279713381282270119', '12.91330869036835424092657125837104', '13.50282604319791319131872913472166'], 'prelabel': '2-105-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.08604780455309298, 'root_number': '0.9636835834318042 + 0.2670467206764333*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0430239022765', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11652099762157364958750364124', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.68672503049185785509317888534', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47125816509984864068410708864', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'bad_primes': [3, 5, 7], 'central_character': '105.17', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/3/w/a/17/14'], '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': '2-105-105.17-c2-0-16', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-105-105.17-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.04302390227654649, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11652099762157364958750364124', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2683009113030638730386165685810', 'Lhash_array': ['2683009113030638730386165685810'], 'label': '2-105-105.17-c2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/3/w/a/17/14'}