-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1100.459', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8090169943749475, 0.5877852522924731], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 5.108378523927094, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.459', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 1100, 'conductor_radical': 110, 'conjugate': 'dirichlet_L_1100.139', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^8', 0, 0, 0, 'a^11', 0, 'a^6', 0, 0, 0, 'a^6', 0, 0, 0, 'a^8', 0, 'a^0', 0, 'a^9', 0, 'a^12', 0, 0, 0, 'a^14', 0, 'a^5', 0, 'a^9', 0, 0, 0, 0, 0, 'a^9', 0, 'a^14', 0, 'a^7', 0, 'a^5', 0, 0, 0, 'a^8', 0, 'a^2', 0, 'a^6', 0, 'a^7', 0, 0, 0, 'a^8', 0, 'a^9', 0, 'a^9', 0, 'a^7', 0, 0, 0, 'a^6', 0, 'a^0', 0, 'a^11', 0, 'a^8', 0, 0, 0, 0, 0, 'a^12', 0, 'a^2', 0, 'a^13', 0, 0, 0, 'a^13', 0, 'a^2', 0, 'a^7', 0, 'a^7', 0, 0, 0, 'a^7', 0, 0, 0], 'euler_factors': [[0], [1, 'a^8'], [0], [1, 'a^11'], [0], [1, 'a^6'], [1, 'a^8'], [1, 'a^0'], [1, 'a^12'], [1, 'a^5'], [1, 'a^9'], [1, 'a^9'], [1, 'a^7'], [1, 'a^5'], [1, 'a^8'], [1, 'a^7'], [1, 'a^9'], [1, 'a^9'], [1, 'a^6'], [1, 'a^11'], [1, 'a^8'], [1, 'a^12'], [1, 'a^13'], [1, 'a^2'], [1, 'a^7'], [1, 'a^3']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1100-1100.459-r0-0-0', 'leading_term': '1.15029701417087114739610921572-1.21674570861059429701994500455*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1100/459', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6744113414070982, 1.1620561954134088, 0.3008847243299742, -0.8234378782450147, -1.4775838944716475, -1.1090759657291591, 0.009646934440206095, 0.864928616650128, 0.550900139849201, -0.7816725223986958, -1.8158621447020078, -1.1217616412042, 1.4274573550281626, 4.242355142209721, 5.228478302058435, 3.681996188194074, 1.0590727597207874, -0.2950098765694632, 0.6336598447143392, 2.5558540642662777, 3.2276474429123563, 1.790327375150929, -0.3753361208705682, -1.2386889165309807, -0.4081641127804398, 0.4967336399250378, -0.123927335500174, -1.7846809073767087, -2.3828566894838414, -0.8341213206675248, 1.248621105206335, 1.0960783933734572, -1.9738567578794755, -5.4130846005918665, -6.002269301320638, -3.3469114898007803, -0.24556774352481828, 0.548997181341631, -0.6605900212118022, -1.3003611390589742, 0.00990950706226394, 1.7406373932086359, 1.62629409295717, -0.1945955878840063, -1.2905102626599552, -0.21808656543022506, 1.4411193810795866, 1.2019944317976472, -0.7340179755393659, -1.3713825412439256, 1.184692158427186, 4.821373282024087, 5.583371071258158, 2.456640299923633, -1.321434459955459, -2.188163480260457, -0.3875339378044568, 0.9328518717037837, 0.16132346441306228, -0.9132910541000712, -0.14342422488876871, 1.601325211048045, 1.6593089724869294, -0.3764239297162383, -1.7983780774951361, -0.6329449758206528, 1.254396241960818, 0.5488791648640782, -2.6769959913008705, -4.594477445698962, -2.63980545590976, 0.8680434646731598, 1.6685128051599247, -0.8404275566735161, -3.013630711535809, -2.058561027062609, 0.4022904190382575, 1.0928549425506084, -0.20203733927532547, -0.8788391092738684, 0.02713031446169469, 0.24914598383066217, -1.8734131486699956, -4.13254823894965, -3.232398638773126, 0.1397713421625331, 1.7172992328409507, -0.485654022826709, -3.2193969804156453, -2.4874145571113324, 0.8139076022931385, 2.2427330648449235, 0.14470128326482426, -2.2563157155032023, -1.8182085384823954, 0.11404535173074896, 0.27065801144535884, -1.3491125517677884, -1.7598799632405056, -0.017677175623194444, 1.2454842152252217, 0.34258491533909813, -0.2665924993381891, 2.276835287352992, 6.0487935232389205, 6.222211502399456, 1.9324494572646966, -2.058312200396213, -1.744465087784149, 0.9060274109613411, 1.414881369875511, -0.5835215129896703, -1.5075823652887443, 0.06646601511440588, 1.2349853887164772, -0.2825936747731813, -2.3392473750522305, -1.8776390139236487, 0.11217647769002065, 0.44063170395915663, -0.6648451169410876, 0.28487205690024303, 3.8824278342541034, 5.739827934916817, 2.6632533065164865, -2.094499860739369, -3.004222254022145, 0.052005576941065515, 2.0877581094069546, 0.5614813865945651, -1.5106841932573705, -1.0726003587868826, 0.2318400654171106, -0.49934668164996165, -2.1444314533152995, -1.5108786306901354, 0.9025078924407038, 1.3864626939475042, -0.73195745200702, -1.65472919519616, 0.6105879992978174, 2.518434570824218, 0.4787654743686129, -2.9417555488412144, -2.4536084208455695, 1.8395422165438189, 4.416373315570284, 2.504536614951784, -0.3338393219682293, -0.3144233613349871, 1.080766056531051, 0.6758657073232841, -0.676114365051349, -0.09726047493863048, 1.5497199977963692, 0.7142551822937726, -2.43216966940115, -3.56928174848831, -1.2810511862842777, 0.16073698728028196, -2.4067912748094287, -5.510569679201925, -4.215809536910852, 0.03737239200107538, 1.6315570552790293, -0.55958940189363, -2.007908946457843, -0.26338972570060126, 1.4464630345062202, 0.20504698618888736, -1.721217173070977, -1.1999538587417837, 0.36479724733175917, 0.133355880525402, -0.4436640934686633, 1.9121598843706826, 5.5376973204056865, 5.191305420464566, 0.4675898966450129, -2.718200350860767, -0.8554372480045485, 2.0598964414992915, 1.2696726622270016, -1.3549821471799433, -1.1605931588110971, 1.301974358973568, 1.647898679299435, -0.6094253604642768, -1.537092926341595, 0.10069438196983872, 0.9513965319903094, -0.4881125074718611, -1.053194566951444, 0.9876968874329927, 2.1185631973134957, -0.3104728516284936, -2.4708573026782505, 0.3387772234908846, 5.480781436103175, 6.29383057033654, 2.138752277435044, -1.0882450523023635, -0.3995959224374934, 0.6773244938951913, -0.6365868524535907, -1.658076349625985, 0.14097729493499978, 2.0913174233735945, 1.1545003980615973, -0.4021382117729688, 0.8784369921692723, 3.1259427155724246, 2.3874995287744065, 0.08487422197881012, 0.8382114245412544, 3.810840037245339, 3.1359147842881163, -2.263732468281253, -6.0552079657744455, -4.044644103182033, -0.2151542071142853, 0.332512935433414, -0.9890579110122901, -0.4008840442526367, 1.015672899558292, 0.032374893199751474, -1.9848028808863853, -1.3445356942370719, 0.9158284328909425, 0.747328534753237, -1.1141297655707587, 0.07083793773245053, 4.2372072575710975, 5.575992541122316, 2.097254752786979, -0.7546808118828009, 0.8451287355611037, 2.838828265112684, 0.5749408524911778, -3.163503663100986, -3.106428219425078, -0.2267578733696425, 0.801395850510697, -0.18656207671944425, 0.12319278355830729, 1.3100333713815835, 0.1047316325450193, -2.4125825250255453, -1.7668738776022224, 1.52325047608383, 1.8476628020727157, -1.8230824241108743, -3.5051608527434115, -0.1301126580557591, 3.158959930876027, 1.6874628553798205, -1.206244517607211, -0.5845908645170628, 1.6270926244578805, 0.879189184290649, -1.5912281068310816, -1.4763613956034791, 0.537469822408591, 0.5139422641062146, -1.038241152128738, -0.468918285166399, 1.373875839539156, 0.4321783510224365, -2.0684243045407036, -0.4652739607079087, 5.125433865295761, 7.539898449534145, 3.7700233995008987, -0.2973066969679048, 0.28317185900996245, 2.2781171599615853, 1.3868590972553627, -0.17963434706319162, 1.0602086103047796, 2.7504606470848945, 1.2692727179255527, -1.1698264998406698, -0.645121612225054, 1.1047953028577528, 0.3346182481248139, -1.1154380532652277, 0.6041923301563403, 2.959024228275178, 0.5242443771006522, -4.739074909745762, -5.4519880940625365, -0.7799555849067873, 2.3274726362347407, 0.7025982282022345, -0.9272883150310349, 0.6184900975091462, 1.8832479737941221, 0.3036929217117445, -1.0028160531612538, 0.030766306352667087, 0.09604988591395755, -2.596172490745896, -3.8954594040910058, -1.202784460767903, 1.1348173015820309, -0.44052156836725614, -1.8820406358234638, 0.9927275386942792, 4.096110398458158, 1.7838632921385795, -2.906917163476903, -3.106086973958888, 0.5048904826325964, 1.796764667107619, -0.039085081467610736, -0.6190646289641828, 0.5474558936951849, -0.06819574050102131, -2.023819683183156, -1.481687579833744, 0.6246117363285207, -0.3445246797365607, -3.4905079750661527, -3.120386596376907, 0.6376547570979786, 1.2450579420550794, -2.6438422041254475, -4.409008375276418, -0.9706248348919861, 2.173859503795491, 1.1243543756767513, -0.07082511779539559, 2.1028272440065705, 4.029861058837131, 2.241576706784277, -0.12182364278938337, 0.26339614605920564, 0.9162804295498662, -0.3665596697506514, -0.33221222253806654, 2.7518218235063547, 3.8244592487867712, -0.4400106117113338, -4.378482202610977, -2.1338998127533855, 2.3670239639591335, 2.356550996074825, -0.41978253588428555, -0.10169918682997231, 2.327581058191983, 1.8229846492280035, -0.7382018355051345, -0.7275578353717238, 1.0035458400279236, 0.18361065273999222, -2.095714348351643, -1.5891809954017313, 0.5025909764336872, 0.15504797746125326, -0.6762853704338688, 2.5673276091849146, 6.949587679761515, 5.538157610656311, -0.25292678003183466, -2.2804418676938107, 0.8433330344210876, 2.409578304180245, -0.020225741368241942, -1.4751362284952323, 0.1519604759517251, 0.9778084582132891, -0.0680483822927608, 0.8467309674733343, 3.8250760588553314, 4.019598776263809, 0.98682610281262, -0.12169376927243773, 1.494420476651165, 0.9207507631296603, -1.9443524156478253, -0.9232928723263235, 4.591503541815371, 6.88793191306556, 2.7441164942057528, -1.2207697506287718, -0.22395300153442405, 1.5852961416380755, 0.37412636689886236, -0.6658092025209899, 1.008893611627492, 1.9603599580601356, 0.255837235255464, -0.33420074375484626, 1.5824805294685076, 1.5133353161600447, -1.6647445646311694, -2.1417236461033267, 2.136804220377649, 4.676194852884423, 1.7900474350447657, -0.8366243337253207, 1.0478488787668387, 2.5002240763592765, -0.8222446092789768, -4.276379062736485, -2.889000873138383, 0.033125575846101186, 0.07658879299898624, -0.5183834038524531, 0.9037734241723903, 1.3730967629680129, -0.9112069746860072, -1.785370768827951, 0.5269617575190733, 0.7116067768123467, -3.5743754485526877, -5.871413450623127, -2.0463371486329094, 1.8221884384105702, 0.08936117709231786, -2.907746810440141, -1.7623642645771307, 0.30934090219165494, -1.1246547971436556, -2.8966244136037673, -1.065471817055915, 1.1730706626423884, 0.20076133056557482, -0.9517611403794354, 0.5607294742570933, 1.3575399329837041, -0.5786452932933179, -0.7411909937732816, 2.6809732005382267, 3.5052365843371214, -1.3350805670442936, -4.748258724282914, -1.237115633941533, 3.564906993613852, 3.034008807873275, 0.12817599933960144, -0.1966520041974859, -0.17112385249619033, -2.676901982632656, -4.08955759451508, -1.540311542925699, 0.7949661707423671, -0.3056264897617909, -1.1942387629520084, 0.3308841984592801, 0.011384841821024953, -3.483598247158996, -4.116682979723846, 0.2515400908110931, 2.516701373445979, -1.1734644574107094, -4.144212827803905, -1.2546811150394812, 2.3068365225262664, 1.2952512856565321, -0.7966589349799401, -0.09854864302976656, 0.429970824853092, -1.4121255887293187, -1.999967625528583, -0.09086666634128505, -0.26539928602693663, -3.3122151789958854, -3.5061348308983487, 0.2817992884911136, 1.7823391987283455, -0.5089819447872931, -0.18131117185243617, 4.175327446864076, 5.272667477731336, 0.6134276532452765, -2.6412605172641115, -0.6508685839063522, 1.263815876243054, -0.184374167949798, -0.9721068852318483, 0.6911844035295702, 0.9681156840564443, -0.5771285328821918, 0.2630905248541323, 2.777963705121382, 1.9328921263743093, -0.7738421438636796, 0.90949333473944, 5.320136653521599, 4.725973811103905, -0.3894265403613341, -2.024962983225265, 0.7476487891784562, 1.2225805532737757, -1.4230862515598348, -1.3831242802592991, 1.5280317849654033, 1.7522388236854276, -0.6829609217536349, -0.8053061178586669, 0.9601928342105303, 0.5364245660695204, -0.5704608126860738, 1.0401994802597216, 1.9145527131325948, -1.959932037684677, -5.33869597691629, -1.9329208688103074, 3.421153346730995, 2.7340219480949353, -1.3193248404070215, -1.5206943763000784, 0.6444769347630883, -0.19901026823874818, -2.0194618012107064, -0.4098318822953207, 1.835518103882147, 0.6825074196868497, -0.7652417433684184, 0.8439114956955774, 1.9066141521353661, -0.15327852278645118, -0.904094769576091, 1.5458128349574742, 1.4686193224544994, -2.839597203619857, -3.8572937876106073, 1.5818537125492098, 5.5749449328798075, 2.9982260255105118, -0.19178414070377256, 0.9495666619054101, 2.295082199229454, 0.6438334645730086, -0.3794826532867832, 0.5483375114490812, -0.6531935622996157, -3.7708309541607674, -3.4186514462008253, 0.006799197775353479, 0.6424630865056331, -1.0939826333246754, 0.11119780140511981, 2.2450500483596363, -1.0707032069391744, -6.922233718986151, -6.683489671852282, -1.3614783186051196, 0.7407534084384086, -0.8950860264528437, -0.16715989327477954, 2.6192977837119136, 2.368229908364184, 0.1656960622189574, 0.29274800360862885, 0.9822262898226316, -0.7368600001601, -1.3252223533902647, 1.7921369058899352, 3.038149067496767, -1.1524428823626671, -4.369703686686068, -1.873525532286028, 0.45098700918706136, -2.064324004913316, -3.7076975659555655, -0.05901535160464227, 3.1770566143155765, 1.4826635665236803, -0.31299472709892645, 1.4384105133245912, 2.5237826334643723, 0.6776006136815361, 0.019586207334039495, 1.4603008184332475, 0.9103412112230101, -0.7166796726937179, 1.4172836644003421, 4.616233954216713, 2.0001557362208624, -3.657999014940387, -3.796706623319083, 0.31185955675305327, 0.49100672643133475, -2.8296084966060255, -2.8032332078115063, -0.12233191083949238, -0.45273138176074945, -2.3369875560307047, -0.9818802234543131, 1.2666387621652182, 0.23061627781655675, -1.0569093663788893, 0.7914360211580267, 1.9464673095005516, -0.1174588557037187, -0.6671077888414491, 1.596558665154283, -0.1114288227173493, -7.052071595776784, -9.972157502957323, -4.821486485828333, 0.30854059296474756, 0.04255871815576373, -0.6819877993374157, 1.1820162612447336, 1.434657481806573, -0.6318856203506507, -0.11797116569347735, 2.6250991427748356, 2.3313501429776498, -0.08713819719781367, 0.20187904311633162, 1.1776700918671104, -1.4533468650452699, -3.677458991146431, -0.44746614921545425, 3.0178361958136053, 0.46728695355689015, -2.90385105073746, -0.27509727843107623, 3.693619959947292, 2.1785424361722776, -1.255236144052539, -0.94389424349878, 0.4237165034217287, -0.5058348545215658, -0.6497860310353375, 1.0985582031595789, 0.17722500364526242, -3.322938853288707, -3.36783704690062, -0.29518694180187144, -0.605157566074983, -3.289499768469479, -1.3580679752475153, 3.4481599609729185, 3.232190432783335, -0.5441328373556191, -0.026046523487568307], 'positive_zeros': ['0.70891242410472822688023447438', '1.8724560306882041983904773729', '2.64484439747864748622590081884', '3.59530690893811317490016393448', '5.1816357247016517585619237187', '5.49335441176364585479616312504', '6.813543792350400664353190151262', '7.606641966005336621623478093006', '8.09668025030888224472774684431', '9.17404652489086981184577415611', '9.82654968512597864596162211853', '11.2876067538676441851140072849', '11.73020679330827421393828398035', '12.49842011590756211983589491618', '13.40621575101627553672151116444', '14.09891883672328445141491794415', '14.886766126886539629942880353156', '15.518151766378341584265936952890', '16.74856132961733065138346931323', '17.559865014819137636752275685533', '18.16049582042837503441307074042', '18.77597425750405115779190557379', '19.63697036326416423934394490070', '20.40237039456351206668993794677', '21.0016103138272626280143748933', '22.09967146500467731404512354450', '22.72731761673997707551687442797', '23.69163230244860621544557874240', '24.33238450105377885079942149367', '24.99215810551781376260385125553', '25.3748138688599237648097214175', '26.54907731033117671890352617925', '27.14082742513397094606593711829', '28.047836487390578469131624182074', '28.76498852286922666171361614468', '29.66400192889102238896243923641', '30.06432022839480625951572884177', '30.94017968409714860103650818762', '31.64198610389542540708208736622', '31.94399664919915883765455034897', '33.24786385938128465046605586994', '33.95000451858242076492402800400', '34.6050540302980865078418131772', '35.302305063121777884026675748188', '35.90061904957139869828168950016', '36.85338326304162184058449794805', '37.31038026275718009140049302882', '37.77683973693121039280868029648', '38.91221616835193318224986069025', '39.682786461516992301550399214487', '40.38026955210460491671244233182', '41.16378841099616227221514558094', '41.45837750798273121270207421788', '42.380049692984183829223921264258', '43.02964628193358143340309613994', '43.685880736084771004056467214822', '44.41473193484172383509402359507', '45.18873603551868519060697200258', '46.19590045927548454297993271877', '46.62890531106497655589475472124', '47.32458302937702602647162378335', '47.83021058200086429854101963368', '48.51607847795999324511173504985', '49.5572248809835143437914396453', '49.73955721485470109266682864766', '50.93438716758312338705531591721', '51.49901717205534653701412866995', '52.220218349454945341261990735182', '52.84001657297414103376822066168', '53.6548375162246747687419343518', '54.10139591196014051430238537769', '54.486452704417573138446476089368', '55.65421063915816015883859400403', '56.32526621321688245400019211519', '57.01455924268966823409046722814', '57.64851954762255210075292386801', '58.3589459818665995999327988968', '59.04620688690537215167601742416', '59.601378289204497546492339134086', '60.18746072037512869316225451970', '60.90865960450263532039529884840', '61.54130246141008669960253013800', '62.6604887829055716060478831309', '63.19779497762517839218465966734', '63.64303698156577363678117351495', '64.35829541613537968383707537820', '65.18650727662152246934360766394', '65.498283261302201880638644363142', '66.58478211528783310778851145523', '66.740249698371259609654775761809', '67.6950425310437147255897550932', '68.77815540660757811478240174472', '69.139587063806219554049662820315', '69.76029879056611783187584410001', '70.317106870770294157300750426588', '71.11083671211019365316811514853', '71.67878684758472953914056945966', '72.1808912439443093115127565117', '73.30021735954273164653521790354', '73.65388116588906393904280922608', '74.41835739833535451334264961177', '75.34165675460230816709618564365', '75.87404121737079025641869665462', '76.21856066858864705781234072831', '76.88753144404276280243303279695', '77.6667650584474217559429018987', '78.298169174375533428643041789', '79.071370732387955156810077387159', '79.844058666323133608904687275072', '80.3862641026836565802550602208', '81.04220062512738089036570221627', '81.78133968584198863238075420081', '82.2865482964212333917974044607', '82.88442751898732399879725485133', '83.48702975535794940598411949180', '84.09353119154905809147959425253', '85.27097528225106391128685596637', '85.58496878540108711557467212730', '86.48606927959033418492743508130', '86.69558078165749409707794779517', '87.63828691923051100009780247001', '88.22287270890503706248221116983', '88.80287120136675256984106925842', '89.31046038253854390461472665662', '90.03176636275438821456944272243', '90.986631612501093264705782701185', '91.64775086436048831583138703023', '92.10140825479473130539607773641', '92.85643793216069086898890388629', '93.430237729354941342661921459260', '93.76782027334887548487708523677', '94.799371938525651629282200372636', '95.25979796247713035204169761997', '95.86249635115480041715115262113', '96.67218126021802954580320105588', '97.454962274991099464148053719938', '98.118540045144388207435486767309', '98.600824951342993400537050625752', '99.051102177814062222423968253', '99.88603742168272363738508687111', '100.273057839244548833367768007379', '101.193685734683096591878131150355', '101.683256873801114245866989569692', '102.56869886091303350817240777232', '103.32665117139145587409268932947', '103.46772873920517775564523628673', '104.65626311537247420034263538488', '104.9307761604657269923534628483', '105.55036651406786115948367107890', '105.98501724026770064128216757673', '106.85034662999262440194098858330', '107.632665302810470208112203104105', '108.37779743149051289737748448932', '108.76376066342420955615622082541', '109.584962339385430785262066201884', '110.12000243974169604938292693246', '110.64906206823747029719267199526', '111.4674688859421737907974101025', '111.90629354125653351926417092790', '112.304288881869929135662593668010', '113.422339568469831290980058353442', '113.9911948905931969363693221000', '114.68533475056039541278165386156', '115.2888347729356296239452655996', '115.91077451550005375543057789173', '116.10778867109600694055509852128', '117.32757078758733653285648201604', '117.53633263280969914802940906920', '118.224510321681963281759563014150', '118.81233118778301409749951873789', '119.86091417561861768722177495577', '120.339929824883459480241838706644', '120.99791124014172541248587164364', '121.41412871699492565292994836463', '122.23134216513933909342580072890', '122.573227193278228971126587672426', '123.283634115233901491487925124662', '123.92674771153392222346138230719', '124.840077169842615076381824250385', '125.19809403828087095252332682931', '125.88197105467526339975724868549', '126.868985470767447895422270264029', '127.209516119859443201466387806198', '127.65164394156111617274564001937', '128.32960101441114791615689484593', '128.99801634126237587173799389874', '129.446365750634308755418308913526', '130.4373489204087087770802322115', '130.944989916254701454631646185498', '131.78517085769503852227368884622', '132.03186627852901508149595293187', '132.92503560137155292914052148066', '133.46968970222747114638535278290', '133.9770273607717554875984697211', '134.60575512409222070662539400548', '135.085686947033531540390392426116', '135.866280521687017699224850294736', '136.628842646028582996664740696398', '137.52266898006224996182127741548', '137.90249994269405712558236566713', '138.07333004217265092698127254629', '139.21614839936196544164372279444', '139.63726249863982966955380984647', '140.25069899384064854276381826904', '140.62643117397631583086920345329', '141.54631008507402949012929083516', '142.11284692600179976055241713812', '142.89744034009361818736302256261', '143.59256744028849029706751359646', '144.084023831607607948055626095894', '144.47552545343799671516173614515', '145.32991279387324478639973839009', '145.583599205143140059733080362130', '146.53961830589252245450501004460', '147.12130679104072402110150262874', '147.51745569814761811789715936683', '148.47378271630934650466818537218', '149.12911383481864811625281504080', '149.65918830894831865237165889813', '150.197211597332644731842391259701', '150.809989445956032071217214564', '151.215180839329346005631194950802', '152.0711702687090978044152641041', '152.42519838365700236535440584085', '153.41171038645072273945990428976', '153.983597155898718474374554210152', '154.52485697556105722040297164842', '155.15000090028188122465869681815', '155.84417979444210469309460688512', '156.383803031254134663385767183946', '156.97839238739924760137755252803', '157.354661381520674290384854701212', '158.0020244212235775897950517983', '158.84678831250948492931838620987', '159.57277971376790462270873224693', '160.196826430396478069835118424437', '160.5975518457631834851668526453', '161.29300389298509535653521784825', '161.97076928548760596879193553803', '162.38359748497123019059298941143', '163.10538605792313692311598439360', '163.57246662777621676863783421493', '164.18390754237072546266105106536', '164.92434196237349552891031157138', '165.893817297366872482258820392506', '166.10612921899655708024888550039', '166.98166003158474134725625484959', '167.32689463660052224931551028374', '167.73250320967777310746061516561', '168.74924561483130068024391453348', '169.172490531816644692243115264119', '169.67519802158088422142445374937', '170.25410301726037353529592995612', '171.356152079874336895992612749810', '171.71764225138093601359644638265', '172.20688856563991421574702046500', '173.16981444518523382502203084440', '173.35019696789839197667626529283', '173.958234666382414839059758176071', '174.53367526956297263666347661254', '175.24436412767793995117430234507', '176.11409668493431996110776755246', '176.36028073671105401220220164809', '177.19128527216508523518015831596', '177.997474121130128701231317451659', '178.234948972906207170773307090485', '179.2000763400307760033447835159', '179.36815994872080620776626565668', '180.13603121469440256354620621436', '180.49481139148698905776470567265', '181.35312579401133617387188999776', '182.158709274954798701023636932022', '182.55133763768195289793062429682', '183.46111993327687897230485558472', '183.67000860718734590978629710641', '184.48233940424348410808084050322', '185.03329038186231129773125570799', '185.52686911254029646632889084440', '186.23439385919388702068958954358', '186.66333199275140779864908634906', '187.18081198152481964023412875220', '188.401380236284401581861522844319', '188.75785409200803655073355521311', '189.20162291250581826551831877084', '189.897408410231842654915490507250', '190.3271097472550712278251108666', '191.23301758896717860019261934894', '191.52196010115989251682514695974', '192.05995732226920941257029673850', '192.84074224674798491010102975957', '193.46876776561758171115007828439', '194.079882709521910951334054562216', '194.86031870273035502694631182942', '195.475487173792904215938496247332', '195.82169477971004311931806911450', '196.369825391179138267946271876227', '196.89264456007187048452392570837', '197.86185760120640219025072370189', '198.035184061705607355827331891292', '198.83357192656227347659325345357', '199.63070959171239303874830744981'], 'prelabel': '1-1100-1100.459-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.108378523927094, 'root_angle': -0.5178667859348701, 'root_number': '-0.0561006941745587682174778545315-0.998425115926644058843255722544*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.258933392967', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13238209442238735475837462288-0.469258180920647215909519672354*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.708912424105', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.87245603069', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.64484439748', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.108378523927094, 'bad_primes': [2, 5, 11], 'central_character': '1100.459', 'conductor': 1100, 'conductor_radical': 110, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1100/459'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1100-1100.459-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1100-1100.459-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.108378523927094, 'root_angle': -0.25893339296743506, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.708912424105', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1100.459', 'Lhash_array': ['dirichlet_L_1100.459'], 'label': '1-1100-1100.459-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1100/459'}