-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_23.16', 'a10': [0.8412535328311812, 0.5406408174555976], 'a2': [-0.14231483827328514, -0.9898214418809327], 'a3': [0.41541501300188644, -0.9096319953545183], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [-0.9594929736144974, -0.28173255684142967], 'a7': [0.8412535328311812, -0.5406408174555976], 'a8': [0.41541501300188644, 0.9096319953545183], 'a9': [-0.6548607339452851, -0.7557495743542583], 'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.16', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2', 'a^7', 'a^1', 'a^3', 'a^3', 'a^1', 'a^7', 'a^2', 'a^10', 'a^6', 'a^4', 'a^5', 'a^9', 'a^8', 'a^0', 0, 'a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2', 'a^7', 'a^1', 'a^3', 'a^3', 'a^1', 'a^7', 'a^2', 'a^10', 'a^6', 'a^4', 'a^5', 'a^9', 'a^8', 'a^0', 0, 'a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2', 'a^7', 'a^1', 'a^3', 'a^3', 'a^1', 'a^7', 'a^2', 'a^10', 'a^6', 'a^4', 'a^5', 'a^9', 'a^8', 'a^0', 0, 'a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2', 'a^7', 'a^1', 'a^3', 'a^3', 'a^1', 'a^7', 'a^2', 'a^10', 'a^6', 'a^4', 'a^5', 'a^9', 'a^8', 'a^0', 0, 'a^0', 'a^8', 'a^9', 'a^5', 'a^4', 'a^6', 'a^10', 'a^2'], 'euler_factors': [[1, 'a^8'], [1, 'a^9'], [1, 'a^4'], [1, 'a^10'], [1, 'a^3'], [1, 'a^1'], [1, 'a^6'], [1, 'a^5'], [0], [1, 'a^6'], [1, 'a^2'], [1, 'a^7'], [1, 'a^4'], [1, 'a^9'], [1, 'a^0'], [1, 'a^10'], [1, 'a^1'], [1, 'a^2'], [1, 'a^8'], [1, 'a^8'], [1, 'a^5'], [1, 'a^1'], [1, 'a^7'], [1, 'a^9'], [1, 'a^4'], [1, 'a^7']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23-23.16-r0-0-0', 'leading_term': '0.454282089098082308028549278127-0.459663663526187850193279312919*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/23/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6462684427090917, 0.6649928322968179, 0.7567482715005851, 0.7935402467369304, 0.7207236981730752, 0.521800881608568, 0.20720187467459614, -0.1856293406837523, -0.5925380714869507, -0.9280828575543781, -1.0976785295589568, -1.0157838357430429, -0.627323696737357, 0.07227077583860833, 1.0240036007690252, 2.1044850006676983, 3.140612410715745, 3.9395851786484943, 4.329769424802164, 4.203860650847718, 3.5532726474835084, 2.4828718147670985, 1.1986565662641644, -0.032591870158173726, -0.9446725431630851, -1.3399854484504092, -1.1456332823802065, -0.43988358400516464, 0.5621489262552256, 1.5635915484633622, 2.2688759704230335, 2.471560047656994, 2.119547632241694, 1.334824104001861, 0.3776335001925302, -0.43714649059973376, -0.8464398303387625, -0.7328233964918687, -0.17147499636750851, 0.5904821402124828, 1.2202325032341603, 1.424656232515368, 1.0711520071010916, 0.25755815004372323, -0.7004940936557839, -1.3681340132328033, -1.3464778651691378, -0.43066482511189613, 1.2893816756203256, 3.4290146634501153, 5.418240769765155, 6.6874386762952005, 6.8644682659411105, 5.909361120573232, 4.132532532022715, 2.0850832984243204, 0.3596130127732923, -0.6228986049671142, -0.7563740357934093, -0.2652762278206579, 0.413955146259978, 0.8360350980676784, 0.7476457124147151, 0.19795841610817205, -0.491571927961078, -0.8869707655830816, -0.6604962011122503, 0.23235963115283303, 1.5037995747510435, 2.643449073455584, 3.1447601039304933, 2.7481704925938013, 1.5865467323521316, 0.15685826005125952, -0.8811231710634313, -0.996747840995523, -0.040685513265645276, 1.6624727551036238, 3.4333859728780984, 4.524846691319059, 4.451643589973056, 3.212871132621088, 1.30041655751737, -0.5160852529447447, -1.5326724567050396, -1.4247179061687003, -0.38370814570071426, 0.9877241071747767, 1.9718059127789138, 2.0789856752831506, 1.2713042572115203, -0.042325382267514075, -1.2327008433055249, -1.779923793048074, -1.534055115315054, -0.7703171854743176, -0.010196252284846042, 0.2946120537806535, 0.04135637579487363, -0.4410819511234638, -0.5634180822978312, 0.1798996603557752, 1.8760837861148838, 4.0586570782009295, 5.865089009804047, 6.428196898560911, 5.31182043711897, 2.7652676356563535, -0.34643167497487354, -2.9168767077410362, -4.0985820518694664, -3.6801054296684956, -2.149834557662151, -0.41675059438622697, 0.6630380779625193, 0.7044449714345307, -0.0606592689557596, -0.9767611834769001, -1.3783211160575826, -0.9852129461325042, -0.055638401124464394, 0.7868849891282086, 0.9469467908240645, 0.23640825454717704, -0.9891433668469867, -2.02451385126166, -2.23176386167336, -1.4349710084578842, -0.052579608150409636, 1.1247247653438217, 1.3934787390007177, 0.5690533795333046, -0.8719462526904564, -2.0398496075136316, -2.1441214103982094, -0.9796522688152485, 0.9020152758890227, 2.4541839558817258, 2.6989814016641, 1.2823652054388475, -1.2970324464215164, -3.923855104583766, -5.442242075120103, -5.252215951515329, -3.5938236635084024, -1.3670061989764886, 0.3964337611522963, 1.094293082669025, 0.8242390663635818, 0.22151275420470967, -0.012276641587487614, 0.41922555761142893, 1.2346454959929187, 1.804178312989348, 1.6216080043131686, 0.6992965290867094, -0.38874295674452247, -0.8643002357790994, -0.28494903856428166, 1.0868367524146605, 2.3495751734297516, 2.4612642590836824, 0.8873806440285973, -2.000181372106604, -5.040477193939763, -6.878211361440477, -6.70125748233899, -4.687276412091605, -1.8909777776135743, 0.3627344308653067, 1.2164495416119145, 0.7088797890926213, -0.35101523222371017, -0.9647513657841645, -0.6010025641447156, 0.4879788513177749, 1.4792853272934594, 1.5658446607083039, 0.521004102498261, -1.133649048172666, -2.4653536773190234, -2.74317008921767, -1.9137845341399442, -0.6193567242915832, 0.2540985634408643, 0.18906837653015995, -0.613466888838196, -1.3959876123611092, -1.4178468558669681, -0.5475656693235471, 0.5503628096766087, 0.7982441821017576, -0.5647982447834962, -3.3823335472290625, -6.530234252192963, -8.494369122652541, -8.243285807195843, -5.854649258845618, -2.4935240447204228, 0.2551888877988688, 1.2887567250652574, 0.5653784984716682, -0.9844165994608135, -2.124929811152446, -2.106026070620652, -1.0638893080240985, 0.1991564734057539, 0.8594383063498788, 0.6658011453772533, 0.06455955421479337, -0.21340793389984014, 0.21999936794387964, 1.0486953874741936, 1.4451595246781546, 0.698061230949421, -1.17708474834991, -3.310086018510386, -4.470491399362853, -3.8786046490984396, -1.7785865542253767, 0.6466983236565422, 2.0007531449088223, 1.5740766208914345, -0.1843736860533696, -1.9556703677788927, -2.4201515545764316, -1.1299385577281533, 1.2014177414803395, 3.1854382084875352, 3.6872279879348486, 2.5634520248025705, 0.7147075187184313, -0.565455470309559, -0.4790145450088151, 0.768841452657631, 2.1791082811176254, 2.7093111669543495, 2.0120923998337337, 0.6353349827353671, -0.4383667839156264, -0.5494658138217611, 0.15831452349933925, 0.8928232336181792, 0.8762610535529542, -0.0025128580352386707, -1.0664719378638996, -1.38255377491171, -0.5630718238543907, 0.7838645099225652, 1.3491921859857465, 0.017544208822741436, -3.248669626675282, -7.186972879157022, -9.891745242231142, -9.954830415894662, -7.338293323090766, -3.391408081835439, -0.0015992017638114583, 1.543624109620752, 1.224667819543185, 0.07793991658689867, -0.6804865373554714, -0.530004285032163, 0.10242117662555449, 0.3427919762023708, -0.3142241334028687, -1.5312633754763934, -2.3670893300314786, -2.0333355818767918, -0.5635210485794965, 1.1497068422833825, 2.0034855137994643, 1.5313484882130843, 0.28508445452835035, -0.5705875743963323, -0.1683531769246168, 1.3364876845787006, 2.804135025890572, 2.925532094458954, 1.2294985330729897, -1.4789201045903277, -3.6120657267223377, -3.9005381483858237, -2.309693486276329, -0.09215977991601085, 1.082274200853299, 0.30209406983805304, -1.9508819301501403, -4.159745165234202, -4.852250081662418, -3.6115326289669842, -1.2974161778639368, 0.6431004673957778, 1.2260749096953718, 0.5521652282116499, -0.42764686949039327, -0.7574054512358979, -0.23086831077778716, 0.5387648848220384, 0.7526549846492988, 0.20272083330843282, -0.4872582804729992, -0.39023606543310263, 0.8426184296189839, 2.494786284431764, 3.1644221466139477, 1.8004220567681748, -1.376242644210297, -4.81463874227876, -6.570098317618215, -5.607660344096491, -2.532884221977237, 0.7997248885219466, 2.535190318210791, 2.0287484227016863, 0.15920060145341186, -1.4402418340349121, -1.6183726561617533, -0.475427272955354, 0.8729963440909216, 1.285029769713521, 0.5155938626074138, -0.6533007586537791, -1.1399170923655624, -0.5185673214302244, 0.5967943558799103, 1.0596726333069209, 0.16827563881540214, -1.7004291369799795, -3.3372549845206807, -3.64230209175131, -2.495455115898867, -0.8331274806780484, 0.1478200149927763, 0.011576710811583337, -0.5278295244245899, -0.2127100459328318, 1.6131026223911145, 4.255069511294681, 5.982440992797381, 5.246839491647254, 1.9048892367949566, -2.5106275049090967, -5.729933692267639, -6.235670629484748, -4.2172713921266665, -1.309310059697589, 0.6470864437023983, 0.8622062791768266, -0.04649033822929115, -0.7802696550514697, -0.5019778311069503, 0.5448014430895948, 1.3908611524955634, 1.2909602686440205, 0.40978268926367134, -0.3526335104312346, -0.22640022018574854, 0.6561695396564481, 1.3005993602477828, 0.7207524264449254, -1.0869869944740584, -2.9388747862872564, -3.2954742670420054, -1.5210615753354606, 1.4529321166422418, 3.6644099243734076, 3.5157976374816737, 0.9737616999140262, -2.368726442407674, -4.438878316539737, -4.165448779692616, -2.1612093393840093, -0.11013889922276254, 0.6129454091651065, -0.02508056037195247, -0.8308140935660153, -0.4971805218224869, 1.2388527572219905, 3.3514554806272683, 4.371367593866017, 3.592013550707997, 1.6263662439911701, -0.1282129026038553, -0.6353124402389916, 0.005207160095840111, 0.7890745015213141, 0.8022463940289981, 0.07516550455291385, -0.47290968524018956, 0.04453215250214599, 1.5269434203043244, 2.8010743446881943, 2.5682434432500125, 0.6225284360322947, -1.732765359008435, -2.5340692410451933, -0.683212272984968, 3.058407885576702, 6.457050212069993, 7.347634099138817, 5.171136574018879, 1.3338854934165434, -1.8651875202191208, -2.8784685067011697, -1.8556570431964217, -0.2355582713626789, 0.5651313054068863, 0.23266986041494805, -0.4414743048919869, -0.5135291850772354, 0.136916356547988, 0.702032452154252, 0.28004047872390586, -1.1507689712596172, -2.555797491564567, -2.686200407697167, -1.2216367356497018, 0.8227375381286433, 1.8543936854262604, 1.032675011627995, -0.9689019335622303, -2.4680959915144776, -2.174169673227603, -0.3146202628493807, 1.4936699235692965, 1.5702248885420822, -0.3903955915011623, -2.9813506292452043, -4.163751199224717, -2.8972580625682465, 0.016639737592605394, 2.5704006975079827, 3.1338285524405802, 1.6816534550649178, -0.31515862898256414, -1.183517543527077, -0.40411340859788175, 1.0925309282869817, 1.8643532705701151, 1.2493851392055095, -0.12446771200839273, -1.0057980815981555, -0.6992022247727023, 0.33614455089532563, 0.9963389661845612, 0.6398317371209208, -0.2807410593326774, -0.6980204651790489, -0.10671220407140355, 0.6836319716074715, 0.0323515817320153, -3.0948257031176296, -7.941552787021658, -12.139823449576333, -13.266680569030202, -10.609832315618899, -5.727783774444758, -1.3286093727587995, 0.6536586225577286, 0.2717222650461367, -0.8288244559765988, -0.9684777962728096, 0.2024507431367327, 1.6358891817562355, 2.040173531227836, 1.1372281234283323, -0.11271663011388416, -0.4672934043650764, 0.39337766023529475, 1.5494765973836726, 1.7076871736636265, 0.4422433521210271, -1.3536665583596872, -2.2490289112554396, -1.5888030639004784, -0.12589866416469706, 0.6423262768490469, -0.14045437665194443, -1.8489395888541147, -2.8924387626955435, -2.176766793585366, -0.20437443674097047, 1.2316066270044874, 0.575429637283765, -2.0436342041945377, -4.744402892494527, -5.347689934801221, -3.166715989628104, 0.37660053763641643, 2.845293730905116, 2.684992345128972, 0.35641958345439667, -2.186685927328441, -3.1495548412236327, -2.241217283544585, -0.6339194625018366, 0.27613814682640947, 0.09901910463109892, -0.42002104900692444, -0.37135617819902367, 0.2820493536625691, 0.6505664999721719, -0.09788564104027285, -1.7078487042695911, -2.8463686842050753, -2.262618980498789, -0.06366814432704829, 2.14272575701324, 2.515881950703371, 0.6279714982225477, -1.9863587655543817, -2.9650569526452015, -1.0556626088364751, 2.780500126314642, 6.06527174299795, 6.740110415250186, 4.721920510246953, 1.8022383394779893, 0.05356400399654862, 0.1687209899111766, 1.141581190154639, 1.4506144970419033, 0.5729932776875087, -0.5707950956376049, -0.5955412321209984, 0.9240114165557616, 2.9488483856523455, 3.8687983258582035, 2.9504904876797586, 0.9830716283909283, -0.4722063381925013, -0.5070932861440143, 0.3817924591769668, 0.9083721670675368, 0.3569112719834004, -0.6640522589663173, -0.853096869007326, 0.3392782071743947, 1.876556276303513, 1.8441822848563771, -0.8020679576278489, -5.006414991763753, -8.121709286742233, -7.87979614619319, -4.215832257505354, 0.6107940362286272, 3.7299232827558377, 3.7829464084430637, 1.7142376529000325, -0.3174880386919502, -0.8403005551636579, -0.10674223134896313, 0.5145111208311943, 0.0517394585394332, -1.1407764110209653, -1.8569288443663496, -1.3413258434044624, -0.07147927644987898, 0.7642364491891495, 0.5495987745157103, -0.042088718609912104, 0.3145654813812381, 2.1677780587126123, 4.481879117023842, 5.353897152884032, 3.7133783678527563, 0.45487870939763614, -2.1270488596234136, -2.2077705015923157, 0.01933041892843758, 2.518316029569554, 3.1872548675753705, 1.66532255512036, -0.4380367544882885, -1.0762129700079206, 0.3464816668002865, 2.4433033006925626, 3.126693015961692, 1.5066679173309054, -1.3239783121418043, -3.2925333966696324, -3.169181622040374, -1.5351245592557963, -0.07592933131499179, 0.044147498529288495, -0.8352198539454239, -1.4007374412408018, -0.7930657674092783, 0.5200787030994674, 1.2740687897474665, 0.7629401782026696, -0.39344795126255555, -0.896244825438457, -0.209365756041889, 0.692872715298794, 0.15457248316036, -2.425079670604512, -5.617389035644967, -6.845644586045122, -4.520849020874716, 0.4194799696641547, 5.0115784165830775, 6.485583789765431, 4.35413238229761, 0.6190876446841082, -2.001561525499019, -2.2219868303135804, -0.8848975319115424, 0.21488810802514774, 0.11085266487520264, -0.6360204236152296, -0.834083650414174, -0.09717864581713019, 0.6916824223416277, 0.346579877155466, -1.2491852475497538, -2.8190294726794627, -2.8241300469208643, -0.974378150121805, 1.3909656071864989, 2.490639425057825, 1.746407302776653, 0.28084276427625876, -0.25364105685876204, 0.6026829258485241, 1.5521105785801668, 0.7659083240708411, -2.212355950977283, -5.733227947372499, -7.2886364266148, -5.6852970108215874, -2.15935382878653, 0.6328725387057486, 0.8731513517057269, -0.9372166241180069, -2.579755441767595, -2.1974848985518074, 0.0765284397385439, 2.378810967282815, 2.908535176328786], 'positive_zeros': ['2.044762235917227441005602451891', '4.03528117503497395606199794164', '7.178383719762419099693442656676', '8.580891341384805742436590726156', '10.75645338483036295494981316768', '11.94789351008338603970116213884', '13.52059537639149946355024865231', '14.77864637462672441075329062038', '17.5871153342747464320750956621', '18.55761841830637896742463096719', '19.77526761173815985849828230239', '20.87208035387172726679522644384', '22.84970431975498903297629724134', '23.75888055708372168717217522032', '25.83869469482731532443275203768', '26.96277899701958235711638522869', '28.42778028807417555980305445107', '30.00548137405077635256440342745', '30.65281967237935792977330619243', '31.51461797195130987311578820832', '33.71450450824251765414541776951', '35.405010925966572274206402222', '36.23026982523501020290933788759', '37.5173950391724365292793859954', '38.50340307558800926550590898790', '40.0115938491426742525531797554', '41.06705533972395857141697833785', '42.35488931284359335469464844803', '43.60287110990340675828927673499', '45.53820098404228229341669958964', '46.7590853490313388440618548925', '46.9040335398601005685289390515', '48.62925083275080220543891039128', '49.45052043584135594082125408411', '50.73203859553670324152336353791', '52.748653794904743670200007872820', '53.64526035286439920689667439307', '54.5594913218131234105606910850', '55.72805497863458146061033786463', '57.37391737460090908021507065018', '57.905408196260331130026532446724', '59.20829772631183906037692610943', '59.91076331076762443848408699732', '62.14959692510045542408354315580', '62.93216107201806307610539728240', '64.31943567898979798227404293735', '65.35062208562333924391173607865', '65.832708877661245302432143187995', '67.008688800971759401199271401372', '68.65968364784391346239785054795', '69.658918756513204943981112765241', '70.78298226170665963336229422264', '72.328159854112426972282683237367', '72.95631613131233254846732525461', '74.53224299333485450711449746364', '75.25567415811813103207172199600', '76.249306187878157478152005061770', '77.31741355864297136726472818609', '78.12726889513710564735400725722', '80.31269338515086504673936978951', '81.2720945787073075941623369893', '82.13493728957998106106527394759', '82.7089199604668170841049830271', '84.15986393775136321110422561318', '85.387290035036922354855521437149', '85.98278388476168959659051501394', '87.33353954400616622205483436952', '88.76500387468111950600224828989', '89.42644565772164456033974091513', '91.1256717568135052059250434642', '92.04034752965482024467068554215', '92.90059579349639742899106331923', '93.83035117889406465899087019635', '94.50464768246322924521610269114', '95.815779907242289065659355682364', '97.41620974875029768484373605367', '98.46247677920602335921296260642', '99.475302750489236229266513323814', '100.44534443080716287038019723114', '101.39352919676568769537377979387', '102.220569743080513248438987094699', '103.979772474038021246110748542355', '104.38167343972351439445744612716', '105.05501965298854416151530937887', '106.69726276513539685030480773070', '108.30193375404820572456891454933', '109.04851869264413105148142528235', '109.84971127718939252723046080766', '111.07493832366175793151361999485', '111.6589370334592535310903630565', '112.64249508065649062727251255191', '113.913506514756452774685272179649', '115.089753308845203630448285656474', '116.58595971309013291624655713899', '117.17945313231976070333882903049', '117.9256284070424230557304987519', '119.6563497599343812566306253388', '120.3107116433973021514623896271', '121.27875072923502506339295779015', '121.86236240104036293397036652128', '123.20256993786350249856459683405', '124.127561915224730713781761773873', '125.73720516394774378908046335839', '126.932260327705440627311309068733', '127.60031556368208212913187903288', '128.38327273126996693709988162585', '129.138449078745143311513782489407', '130.49403500475956414519585584051', '131.418736213840064770100085894632', '132.5456396984460158919777336116', '133.38978644391104212942732218475', '134.68581984716982278428701895447', '135.88129403481586955191009182662', '136.64856901960012494047989574751', '137.783690396046887134567115132989', '138.65238650956569627947385208415', '139.59093182271632249917964913419', '140.34774821564386296807522816938', '140.94291469871142422966664445864', '143.27943288354463366434384782946', '143.824262107398541471231589099853', '144.64598760664322668448759455777', '145.90285180758360417624020037630', '146.455899500540797661400577001', '147.57578992382655254032132787000', '148.77980915325117060067295598670', '149.344050178121472057244892732', '150.656735812309647061641725514481', '151.33535678148168892307738906097', '152.77846748241050786700201128576', '153.789559198537933410894042617555', '155.168511001009074953997011042515', '155.68079687597758391008904329606', '156.44072628984588536716392902441', '157.16392930847825595827965394377', '158.445302735099000582690707547072', '159.44743012560967495716219226680', '160.40698687251097946109096698039', '162.21162717351719906487691743546', '162.422745036687604976092550215051', '163.5785143220579206437098573909', '164.21749677044889164269893378955', '165.80368027737150041742938852712', '166.43893615793186311974270945867', '167.293299154156794842532854344610', '168.05880198478289898850479647776', '168.99236541040357050609435041448', '170.58259747402213808411418048', '171.811069220778398837166618896619', '172.53661488098002270868223486063', '173.14090854634137173155897262419', '174.3931404221338477884635783978', '175.27751083887298704768902753595', '175.50630624098732876640158361947', '177.230894170428072517691003608019', '178.122827725046145827587961360749', '179.29965816593405783648637774561', '179.94697727778050070205737554692', '181.10596576038121986233954372979', '182.52983075140187859226339455680', '182.8355413583940562691612911557', '183.94012598050717626410031066070', '184.89110969821796193156301813944', '185.68538393863733374441037001932', '186.27802548507161405090710946951', '187.78796381680876895893513972860', '189.1186824257692327805040388718', '190.21954994528486108441643047674', '190.6763842031647627611948174688', '191.59325366679712192254101293647', '192.27322583600016345994368534531', '193.56007793472747528009670302773', '194.76930453105567300180301245724', '195.13963676806108596018075112661', '196.03875702657151884648681195277', '197.716254117317931239557929579401', '198.29807254499967794420590909809', '199.36602163030518660839156476512'], 'prelabel': '1-23-23.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.4962514437176789, 'root_number': '0.0117761646785198112432888878915-0.999930658568615137944589185185*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.251874278141', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(11)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.712483014794648063958650874129-0.491005959336189497717681074989*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.04476223592', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.03528117503', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.17838371976', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.16', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/16'], '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': '1-23-23.16-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': '1-23-23.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.24812572185883944, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04476223592', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_23.16', 'Lhash_array': ['dirichlet_L_23.16'], 'label': '1-23-23.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/23/16'}
Lfunction data - 1-23-23.16-r0-0-0