-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3179464562507075356533286263781', 'a10': [2.3973053413815166, -6.474013513125467e-61], 'a2': [1.6466436728731948, 0.44121684236819037], 'a3': [0.0, -1.0], 'a4': [0.7847122758550912, 0.4530538437013407], 'a5': [1.3583487251496358, -0.36396844394368993], 'a6': [0.44121684236819037, -1.6466436728731948], 'a7': [0.5018232593311711, -2.5977246613900866], 'a8': [-1.3186071432879753, -1.3186071432879753], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [-0.5018232593311711, 2.5977246613900866]]], [13, [[1.0, 0], [-1.3719107485025057, -3.334345647671113]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.19', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2090052114214170187189805794582', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6466436728731948, -0.44121684236819037], [1.7320508075688772, 1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.3583487251496358, 0.36396844394368993], [4.330127018922194, -2.5]], [[1.0, 0], [-0.5018232593311711, 2.5977246613900866]], [[1.0, 0], [-1.0723717616656339, -1.0723717616656339], [0, 11.0]], [[1.0, 0], [-1.3719107485025057, -3.334345647671113]], [[1.0, 0], [2.5851293752034237, -4.4775754219911175], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.4297994929810143, -3.4297994929810143], [0, 19.0]], [[1.0, 0], [-1.8617819169515248, 1.0749002909243404], [11.5, -19.91858428704209]], [[1.0, 0], [0.7443069917361966, -1.289177526115841], [-14.5, -25.11473670974872]], [[1.0, 0], [-0.5065436436740975, 1.8904466144427972], [-26.846787517317598, -15.5]], [[1.0, 0], [-2.455628236970549, 9.164529344874875], [-32.04293994002423, -18.5]], [[1.0, 0], [6.347616576812721, -1.700838735619376], [35.50704155516198, -20.5]], [[1.0, 0], [7.273341702606209, -4.199265789907826], [21.5, -37.239092362730865]], [[1.0, 0], [-1.6621183622450213, -6.203110176091592], [-40.703193977868615, 23.5]], [[1.0, 0], [-1.875793364187215, -3.248969411272807], [-26.5, 45.89934640057525]], [[1.0, 0], [-2.191040372993902, -8.177073993447907], [-51.09549882328188, 29.5]], [[1.0, 0], [0, 3.2328025499489765], [-61.0, 0]], [[1.0, 0], [-9.210007800229619, 9.210007800229619], [0, -67.0]], [[1.0, 0], [2.712128256988617, 0.7267125762297283], [61.48780366869514, 35.5]], [[1.0, 0], [14.287937696747743, 3.8284413673497535], [63.21985447626402, 36.5]], [[1.0, 0], [-3.67743908204773, 6.369511331846122], [-39.5, -68.41600689897065]], [[1.0, 0], [0.068476513865412, 0.068476513865412], [0, 83.0]], [[1.0, 0], [-10.780091218611416, -2.8885167363607662], [77.07626093681505, 44.5]], [[1.0, 0], [-3.394149346965525, 12.667137811352065], [-84.00446416709055, -48.5]], [[1.0, 0], [-17.195520879029544, 0], [101.0, 0]], [[1.0, 0], [0.17647358226303766, -0.3056612106732671], [-51.5, -89.20061658979718]], [[1.0, 0], [6.704664780082381, 11.612820046820296], [-53.5, 92.66471820493493]], [[1.0, 0], [9.503575843656048, 2.5464754725155636], [94.39676901250381, 54.5]], [[1.0, 0], [-0.3257995155927514, -0.5643013140879741], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-273-91.19-c1-0-16', '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/273/2/cg/a/19/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.277253412681058, 2.3504854139443343, 2.4411777061180215, 2.5465618114584183, 2.660690270839985, 2.7751805818872524, 2.880044131540218, 2.9644808363673874, 3.0176170389688526, 3.0292139964186204, 2.9903767714726563, 2.894270327646078, 2.7368202238667676, 2.5173497578318447, 2.2390878355991344, 1.9094736692090286, 1.540186205345687, 1.1468382426072863, 0.7482973625678081, 0.36562721302409457, 0.02068146133108695, -0.2655741650811592, -0.47489310548672803, -0.593575565529098, -0.6141079237855308, -0.536417760529993, -0.3685573677319762, -0.12666125054050875, 0.16592008129112415, 0.4803292788072259, 0.7846791682379413, 1.047121216625042, 1.2392324220402233, 1.3393688090586766, 1.3355860166420015, 1.2277224174337182, 1.0282857142277475, 0.7618825163190288, 0.4630777406501197, 0.17275515433716943, -0.06674675315259586, -0.2172525115350615, -0.25048670212889146, -0.15319370131995955, 0.06911443237223355, 0.39045512946268685, 0.7652066237124893, 1.1316862788095248, 1.4183458530920188, 1.5520826179469682, 1.4678144797947934, 1.1181890234677874, 0.48213981945528367, -0.4289933740779344, -1.5688806851557264, -2.857895186372745, -4.189317954744657, -5.439693663723087, -6.48236374522751, -7.202664908357721, -7.512900636058019, -7.365045287499053, -6.759271033293612, -5.74680647277139, -4.426309124699616, -2.9337863695919166, -1.427019973083995, -0.06630559380035231, 1.0060246697065363, 1.6844886674701103, 1.9149964671390145, 1.7027684889618915, 1.1121996273369106, 0.2583623340772645, -0.7089192738241457, -1.6263244286993959, -2.3406138228959446, -2.731042023701218, -2.7271600030681604, -2.3191596886791728, -1.558994115320658, -0.5519225136316135, 0.5603378689595927, 1.6222727931354666, 2.489442226495629, 3.0515048779599394, 3.2495569961849036, 3.0848280531227634, 2.6171961173974214, 1.9537168582556688, 1.2291075768850324, 0.5815794047741212, 0.12829360789970742, -0.05514999715841738, 0.052545358824841334, 0.4157629275328966, 0.9500034341958326, 1.5390754807394706, 2.0582033973778873, 2.398628713225955, 2.488926089872579, 2.308823548328826, 1.8927301816570599, 1.322181409592983, 0.7086317848415198, 0.17001836399219045, -0.19412987437450419, -0.3238505543207155, -0.21164127985967876, 0.09582184378129815, 0.5077560122468874, 0.9092389782475201, 1.1869733191827805, 1.2553367472019907, 1.0769267514204663, 0.6727752439984056, 0.11947843376122182, -0.4667333474543805, -0.9560401138560648, -1.2358147485510818, -1.239389568404683, -0.966093316645627, -0.4873801485995394, 0.06334496945980442, 0.516106524035606, 0.7003695729966227, 0.4844161547204451, -0.19043839218926056, -1.2887735432270047, -2.6787827230825263, -4.15069644474228, -5.453426855951441, -6.342818754563787, -6.631946600281958, -6.232855699222271, -5.180348595238524, -3.6317300199496545, -1.8412386183902076, -0.11324004554943863, 1.257005802884801, 2.0431251904212946, 2.1354365438255654, 1.5662891598243056, 0.5068172704510179, -0.7651443414957579, -1.9201083752363057, -2.6440082326472414, -2.7035034534638456, -1.995773872748103, -0.5720853892183633, 1.3701737554439726, 3.5256185592711695, 5.541312324940315, 7.086845609839237, 7.919253115210941, 7.929100521550804, 7.158219601785879, 5.7858246044634445, 4.086702628833171, 2.371255957126873, 0.9209947058349521, -0.06623894765383445, -0.5096311098447984, -0.4509058938523282, -0.03219080852439259, 0.5471127521559961, 1.083101438240752, 1.4165853629975034, 1.4669726048385214, 1.243348949854898, 0.8313443016100134, 0.36065331377610266, -0.03704177330844664, -0.26776334232192023, -0.30154225701401444, -0.1782553248059719, 0.00825620923813907, 0.14287492612982108, 0.12895797019547406, -0.07675275284017197, -0.4448061586136348, -0.875819046783153, -1.2256601870413064, -1.346823792161393, -1.1347482437568779, -0.5657698459800897, 0.2849991897994876, 1.252590856017859, 2.1174678192268774, 2.65930168200482, 2.7156829033811185, 2.22993737731977, 1.2741885857210542, 0.039687951900254, -1.2051564729025366, -2.1798472907439184, -2.6639777243540697, -2.5577049719019644, -1.9137761669242, -0.9310508641183513, 0.09081262826750476, 0.8255398268594246, 1.0051811855982509, 0.4939942245157146, -0.6686316475786218, -2.268827067195003, -3.964166105305471, -5.364744842026566, -6.1297070646867, -6.05476622418596, -5.127808719774664, -3.5372805603657533, -1.6299292062839066, 0.1724265008555068, 1.4765329534922462, 2.0154416484620246, 1.7151105030754459, 0.7123514718132102, -0.680921057544154, -2.0582079376027265, -3.0229888841113985, -3.290192306315033, -2.758159031943809, -1.5324381178968616, 0.10449779863500619, 1.7691822914001423, 3.0782128837278817, 3.7473791577622997, 3.662585373752269, 2.9041775266580085, 1.7191032273276394, 0.4495488809056966, -0.5616100045125988, -1.0622592654041398, -0.9545092048746727, -0.3135716598592815, 0.6417613350674783, 1.6172193312347687, 2.3293144473554244, 2.584745157236109, 2.330575420484347, 1.661851826118265, 0.786026050403089, -0.043827834835069454, -0.6061751326604906, -0.7752428522922656, -0.5534930968711527, -0.06361124410475677, 0.4961902300079613, 0.9185808985520105, 1.0538609624848192, 0.8559784203400765, 0.3936241213616023, -0.17649218671818648, -0.6649203391063878, -0.9148490045005896, -0.8558526046446145], 'positive_zeros': ['2.50815529289745973786034629717729', '3.43109959976787521840668930443474', '4.96104038877219376644941513668149', '5.46731234857583119391220391201401', '6.57048923987942053478172227721822', '8.381739308859411948499434537694569', '9.158959844006378269391162036744511', '10.18741667940242982682207212783850', '11.56260470355742475729553618067493', '11.71920810592766783683107306965216'], 'prelabel': '2-273-91.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.15579801576916386, 'root_number': '0.8825897349890649 + 0.47014397761955024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0778990078846', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50815529289745973786034629718', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43109959976787521840668930443', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96104038877219376644941513668', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '91.19', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/cg/a/19/7'], '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': '2-273-91.19-c1-0-16', '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': '2-273-91.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.07789900788458193, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50815529289745973786034629718', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3179464562507075356533286263781', 'Lhash_array': ['3179464562507075356533286263781'], 'label': '2-273-91.19-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/cg/a/19/7'}