-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1001.236', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.5877852522924731, 0.8090169943749475], 'a3': [-0.6691306063588582, 0.7431448254773942], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [-0.9945218953682733, -0.10452846326765347], 'a6': [-0.9945218953682733, -0.10452846326765347], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.236', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.878', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^22', 'a^18', 'a^31', 'a^31', 0, 'a^27', 'a^44', 'a^40', 0, 'a^40', 0, 0, 'a^53', 'a^36', 'a^36', 'a^53', 'a^47', 'a^49', 0, 0, 'a^30', 'a^49', 'a^2', 0, 'a^6', 0, 'a^8', 'a^2', 'a^59', 'a^45', 0, 'a^45', 0, 'a^2', 'a^3', 'a^56', 0, 'a^58', 'a^47', 0, 'a^10', 0, 'a^15', 'a^39', 'a^37', 'a^58', 0, 'a^11', 'a^58', 0, 'a^44', 'a^15', 0, 0, 'a^9', 'a^17', 'a^33', 'a^11', 'a^26', 'a^8', 0, 'a^54', 0, 0, 'a^25', 'a^54', 'a^52', 0, 'a^1', 'a^11', 'a^53', 'a^12', 'a^24', 'a^5', 0, 0, 'a^4', 'a^7', 'a^28', 'a^56', 'a^51', 0, 'a^7', 'a^19', 'a^30', 0, 'a^45', 'a^24', 0, 'a^48', 'a^21', 'a^46', 'a^18', 'a^7', 'a^19', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^9'], [1, 'a^22'], [1, 'a^31'], [0], [0], [0], [1, 'a^36'], [1, 'a^47'], [1, 'a^30'], [1, 'a^8'], [1, 'a^59'], [1, 'a^3'], [1, 'a^47'], [1, 'a^10'], [1, 'a^37'], [1, 'a^44'], [1, 'a^33'], [1, 'a^26'], [1, 'a^25'], [1, 'a^1'], [1, 'a^53'], [1, 'a^4'], [1, 'a^51'], [1, 'a^45'], [1, 'a^19'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1001-1001.236-r0-0-0', 'leading_term': '0.799896314904408346190418296102+0.413195384244016613767028584495*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/1001/236', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9003135787925296, 0.5509726887907643, -0.7266135219514042, -3.365014166459111, -6.746946687215507, -9.359093861024931, -9.672629569952818, -7.237704713094931, -3.1856080620215472, 0.39039494730879715, 1.8523918992768738, 1.1511826276581765, -0.30295491404566566, -0.9658057409748082, -0.4993525648359929, 0.1291627053734569, -0.13624120695639297, -1.1850805979646608, -1.820074629130628, -1.1441619316156095, 0.27246687030707445, 0.8705674531765388, -0.13712140408090512, -1.6772290340391893, -1.8268427624678107, -0.022849445781029966, 2.0253054199233325, 2.0319951428329115, -0.19687520153268026, -2.177482775435113, -1.2451638803339924, 2.38860044408615, 5.506419533334961, 5.118404337519955, 1.6372849334317734, -1.5843397510088293, -1.9154246031432676, -0.1694209163613622, 0.7082698850664597, -0.6470796175748106, -2.3926855410238645, -1.8833738989488413, 0.886378635405878, 3.0912356770411935, 2.4014511179464915, -0.28179936176975784, -2.02433480219641, -1.3782721476583928, 0.21673069269945264, 0.6916850156661236, 0.03260595413659851, -0.17799026526936845, 0.5538920986962329, 0.7647403620677999, -0.6253019711981047, -2.199859123049207, -1.6710772881700255, 0.5256170980807561, 0.8622383905671109, -3.007077430058003, -8.456879661394282, -10.01758247198304, -5.597763370199877, 0.7250106528824736, 3.1248236211788525, 0.49569129370697845, -2.847094450819639, -2.777898181377011, -0.013924288475479028, 1.7146735051753914, 0.8346283704641706, -0.5948541320027618, -0.4331286038777467, 0.5470756423487396, 0.3600239880059963, -0.8449193391748911, -1.0865685120072053, 0.016897553002948693, 0.21465405690435704, -2.0082570931966863, -4.583623032157022, -4.200539126350935, -0.9237348982755623, 1.6068637281467975, 1.01124995774726, -0.7617943286298681, -0.5902078916398782, 1.0866693786790773, 1.08695885374355, -1.229551183757689, -2.302326166802767, 0.5735469856163184, 4.578209365512457, 4.400683072873233, -0.575925623424437, -4.947441673668291, -4.054338639120662, 0.23863584925492587, 2.4768747214909714, 0.8452790994343128, -1.2880582425902332, -0.8622102626399756, 0.8307384605998375, 0.9593756958593987, -0.2800970622395069, -0.40988375026028046, 1.0325440897559137, 1.7954518200811274, 0.7465869658273865, -0.26554521582999135, 0.3635332563888816, 1.1713557809042965, 0.21677041896489457, -1.1010283640012541, 0.053473629147049444, 2.532000567048279, 1.329496421141232, -5.258915584670399, -11.534198186242172, -10.551687714402552, -3.060390364600623, 3.1873184181410585, 3.0818085295719655, -0.3845608279067589, -1.611774431923962, -0.02096317221196671, 0.8360522215581563, -0.2464233892445284, -0.6973099110403507, 0.7646969180217495, 1.6231556353897716, -0.12177954615122599, -2.1593110060249066, -1.1931656783169662, 1.7880386876197907, 2.875992699242925, 1.1674996185865347, -0.18722409097273177, 0.7287807472000747, 1.7560318377041053, 0.733187237986216, -0.667128538887354, -0.00015574042517823964, 1.2609705559955335, -0.1265782046953195, -3.2751066793690993, -3.767572965693161, -0.8193491754161984, 0.5424551304954427, -3.0768172340633, -7.430168122152649, -6.144207826993458, -0.24332531156224316, 2.7784203590082437, -0.6115746411632964, -5.359423899502839, -5.4152631641350535, -1.7660933667638923, 0.40948091774981576, -0.34397886215407303, -1.0325160813732748, -0.10643492447600471, 0.5379790201709318, -0.21621296067882684, -0.6707613938611183, 0.05272972582438215, 1.989635207938748e-06, -1.7122731362418757, -2.1912544316098117, 0.7899531260956272, 4.122325578749621, 3.291365758397819, -0.394126920317662, -1.3173103827716477, 1.7038602427357867, 3.3859563621747935, 0.4434826226130676, -2.8868934282271024, -1.4703440418916676, 2.387961423706922, 2.4030020550502056, -1.8617235816448003, -4.447121882417657, -2.2755601286407474, 0.7538430572868299, 0.7174448861428206, -0.4438541927194094, 0.6296643811282865, 2.435046223686525, 1.3972751468447977, -1.5164189384816242, -2.094666592419391, 0.11976801049169776, 1.1960921605064943, -0.5133939993145276, -1.9193244201158643, -0.797301693855642, 0.6449671282675234, 0.13698913909600904, -0.7409018567169785, -0.157923987188103, 0.08412902183650531, -1.6098644740564336, -2.033006150960575, 2.06336030463281, 6.427795496352468, 3.2534276588946973, -6.826047325993072, -13.358039169536346, -9.377627462616559, -0.4265559835350197, 3.7845861310074067, 1.9661415200521164, 0.011090492268791021, 0.55885056216695, 0.6510721220079632, -1.1290227925630054, -1.9703797396928953, -0.4885778354244524, 0.5990647186017606, -0.37431737128830683, -0.9810238659232818, 0.5104751535861362, 1.6340226020337694, 0.34411035632790116, -0.7829799944845511, 0.9269821176423705, 2.901279374383815, 1.4753617083534238, -1.2032589018301323, -0.2815598837602593, 3.240179471170774, 3.6018333609914306, -0.04090456265161066, -1.9095079168721605, 0.7288309785704271, 2.9553170037148195, 0.7344600891664612, -2.091413993485013, -0.5274535385340492, 2.796558212178143, 2.160399020511485, -1.171596660944283, -0.8505966674641126, 3.791921061849676, 6.391855341275079, 3.647799349506725, -0.1472349223570922, -0.7079707608528425, 0.2870498974151207, -0.0836550158821033, -0.6844231466725175, 0.345311292481846, 1.3550648274339256, 0.5409046387326727, -0.15199292153302263, 1.108405454568367, 1.7521330984911678, -0.6753998075715846, -3.0029605209064307, -1.3845985659509783, 0.9810257847741404, -1.6655934499055662, -6.876727353485013, -6.1024280926009675, 1.687405110919819, 7.031251029723437, 3.6512856477407927, -2.6661426723275348, -3.650752437802647, -0.34690899493803057, 0.9457937703669843, -0.596981634213368, -0.9782401312426465, 0.396151958547565, 0.5576856254525747, -0.5250026930496042, -0.22867047646390903, 0.6475439962329559, -1.2082472504381467, -4.668061908918035, -4.794173257845863, -1.1645402092707278, 0.9863355823246723, -0.6221438340955493, -2.0745213626671664, -0.7652886075018466, 0.39661447008286516, -0.6757909900741501, -1.175961106586322, 0.32362898200474355, -0.09818550445860658, -4.162654072523909, -5.918635802885973, -0.6221992509212941, 5.939003953992237, 5.126019013128062, -1.0645787606057902, -3.1612053420271153, 0.9892487470512158, 4.080819926870608, 2.078516505149933, -0.37227762109208107, 0.6204301027403378, 1.957605268278156, 0.41439940291054034, -1.4751925074703298, -0.7778177845963361, 0.520088829473063, -0.02897654433320412, -0.7075355615965341, 0.2659054504299288, 0.8745056643845499, -0.2714120115692456, -0.6659513665817389, 0.4926601178482885, -1.0546742298511889, -6.894091406508943, -10.460938742882426, -6.333377900746155, -0.11915644842975676, -0.6942375691676038, -6.2748335657672945, -7.646429078162582, -3.0800728602493583, 0.13382965240150874, -1.3045814178506716, -2.458273214924714, -0.4762488519273692, 0.5900722639736365, -1.5548910937931333, -2.7191087796958024, -0.30124835110976683, 1.5916382933209787, -0.23206201221122333, -2.2024475736519706, -0.7839600195550315, 1.161158486824094, 0.15026618618943885, -1.4950602674232822, -0.5910805402477353, 0.7803746978553374, -0.16362588780771095, -1.1352702548859979, 0.5128390128716845, 2.065794623336048, 0.5912940632340234, -0.9923124289672249, 0.4075385984628015, 1.39001882412234, -1.249096906190739, -2.25658153706485, 4.151685702844189, 12.049534928804981, 10.48181805405709, 0.5453452193452833, -5.5310705893552665, -2.4114288976772817, 2.3747473197294573, 2.108630011612717, -0.23758702759996947, -0.2005046598155384, 0.6389209402383166, -0.12641911024179184, -0.7533327370763385, -0.022961762104686565, -0.2497687856641332, -1.887130725619416, -1.58605459037184, 1.089885397986768, 1.8059987774989148, -0.46745166196873617, -0.8411330826987228, 2.4328481570025438, 4.084961235171011, 1.300940022915438, -1.0560353204751551, 0.15885343511887798, 0.17909188659174669, -4.051297822253094, -6.3797899918462235, -1.524551273007062, 4.743339779224104, 4.436068288253701, 0.04748288864437441, -1.0479115264826144, 0.6157806278739554, -0.4447385228198279, -3.286744480953865, -2.7037377193894208, 0.19451218549008106, -0.09756130654067476, -2.8899586929819705, -2.4928333195708197, 1.204902754585754, 2.7128088087998234, 0.7714460198047721, -0.5540175992075992, -0.024530011145314792, -0.20185299795405054, -0.9832644838317146, -0.07544620037596983, 1.1777428507384555, 0.20671523967215824, -0.5295994429850098, 1.855721932706787, 2.5897636768308496, -4.049730339507253, -12.240294464566517, -10.70803560759043, -0.5908170890862129, 5.31121847705482, 1.939626107778233, -2.125993552244441, -0.494942818897257, 2.0514021463576437, 0.646676960965212, -1.223729760976474, 0.06782753226707956, 1.4657865345299028, 0.21831130772386484, -0.7409061998990641, 0.6505724699233313, 1.414085377529946, 0.09982064044756842, -0.15471025504665759, 1.313453880373797, 0.5947009559596695, -2.565774843048889, -2.941583118603551, 0.4843311977112039, 1.8959264657000185, -0.884480523294844, -2.589518394071305, -0.7516846347456895, 0.019701845558896494, -2.05464737216458, -2.003696940766346, 1.4123390268426703, 1.9880388331868093, -1.924665458365037, -2.7439959999408208, 2.7110068414131265, 5.9701493168154, 0.8769419195146416, -5.587715729128912, -4.9769222827607065, -0.5123492945305628, 0.4313983528287046, -1.3141436767886923, -0.9848705699743148, 0.542751711598778, 0.10367195300689204, -0.8165697477644325, 0.019165336113668035, 0.4432611002181494, -1.1397960205095838, -1.6954435098474996, 0.23453469526199935, 1.0914822375780924, -0.3483202739107631, -0.12670153318127111, 2.122309596156551, 0.9939286735304933, -3.363190009302052, -2.609307805551304, 5.036485969610465, 8.933767196743844, 2.6120221381544266, -5.029774111040057, -4.078281284615517, 1.3800555032954989, 2.4280180865162477, -0.06994925061590733, -0.3771655559805095, 0.8235488670990403, 0.14009302877088428, -0.5682490183582067, 1.0039496258873404, 1.501510258114939, -1.4042735215290778, -3.1344628931345833, -0.3434632455742834, 2.33330568451139, 0.6128038600998806, -1.9073465761239645, -1.1351339887869598, 0.38563183147195035, -0.12484303037948496, -0.2139597264069398, 1.3029385545924212, 0.9160996177305794, -1.6156354303132505, -1.341152217385627, 1.4289426747418872, -0.3709857324515447, -6.907871500176737, -8.520275632906829, -2.1562590435845577, 2.15230478665312, -1.8130808755886965, -6.0542542604957745, -3.004991493427493, 1.825187836233606, 0.9918304104654616, -2.268486940339519, -1.9419419622864296, -0.0462551765063556, -0.7285139336574573, -2.0068501508766663, -0.9932783789384747, 0.26237618631594706, 0.005978770754949608, 0.3129867913488001, 1.356938098849362, 0.3265736353731879, -1.4300680478833006, 0.4893853284641004, 3.849006998927328, 1.9154513918662597, -3.745260049094793, -4.6537709044783, -0.490343753588297, 0.38134117312828836, -3.43431814181869, -4.271259835223256, -0.5991886296786287, 0.2531077134728844, -3.139714672129079, -3.3548834517841577, 1.2975289698419452, 3.3811760650159526, 0.4076047028134663, -1.2805635230787429, 0.6263434952013923, 0.7853138756981795, -2.1546915586766744, -2.868624155016337, -0.335162414746616, 0.3368131601146149, -1.6723200535302842, -1.8535920027653845, -0.051994303186267424, -0.42962385889756805, -2.3977679113792685, -1.8491732313995823, 0.2715949716666931, 0.2975339327027724, -0.45031206868441737, 0.48294000852235885, 0.18432452823013354, -2.9795263791055793, -3.4068746849570557, 0.8123661460626823, 0.04455160288850206, -11.589853322725363, -22.47641686329844, -19.0507312789892, -6.546007477227791, 0.2483506763571311, -0.9321779908464086, -1.646081113534381, 0.3994182938286782, 0.8822680293526411, -0.14094885950616876, 0.426658518493819, 1.0301133164438678, -0.722538419805868, -1.9790427952494447, -0.4983244614155815, 0.21699830146685067, -1.617639510025583, -1.7012446707681828, 1.4496051306789899, 2.6500347391649424, 0.09271265466173531, -1.1886504542007457, 0.041733544597431366, -1.2548763768290152, -4.885034888534117, -4.240418828415576, 0.46098162323156133, 1.4276119455830685, -1.7703849265692544, -1.0451824630414548, 4.30169170490948, 5.742160007398796, 1.6349273544125325, -0.3020386745767583, 1.5838076700167663, 0.628221809736554, -3.3639890678232374, -2.701998267167742, 3.095755891828053, 5.614402765749775, 2.3659575956259276, -0.34863667757615, 0.09876539558475594, -0.008120779048763646, -1.3726211301734947, -1.0894647080224629, 0.1274884844202713, -0.09962337190506272, -0.036184671241443526, 1.646663895386768, 1.4604815442954187, -1.245086945144032, -0.6661256325335357, 4.09289628509193, 4.937341060874324, -0.2910032960587072, -1.812553807931265, 4.628406846256649, 8.637116143533033, 3.1270082734493454, -3.2580033834404056, -1.9716623278765604, 1.5285703993056372, 0.11574689800665483, -2.3705174133271636, -0.8087941465962003, 1.3066389822546585, 0.2814949817324598, -0.8073406144619271, 0.02881151850128046, -0.19980834586607826, -1.4743310313182247, 0.0004515770271333444, 2.716570430084715, 1.5002093283668778, -1.7827699507873604, -0.9954078490408921, 2.4304225445569356, 2.428357684017988, -0.021895190081489872, -0.012676950387572078, 1.0612256590202773, -0.2096476864970688, -1.0170535348466452, 0.8329845051463589, 0.32269301350893237], 'positive_zeros': ['0.48697104196929593976920888', '2.76943958706336336674063430024', '3.67922898361328816939964775349', '4.59301290586596054923292589787', '4.939732549967233629566295945296', '6.1867080539186315679030056041', '6.847588475717948899022975060274', '7.815531841926399515544712445524', '8.72687006324037237696662145560', '9.498188683873703459432865736530', '10.759720608793141927174381780135', '11.59298730784438524015445645247', '12.08209087008769319393525850706', '13.03544002629764120335543602809', '14.030370697408271377230797151582', '14.95017177475038554516438751299', '15.63994689325857362010206000842', '16.03924095484361241741178777300', '16.76707506046233969358465222799', '17.73575457964815870359211052342', '18.2312686164202288461852294501', '19.645399955821782111680488401981', '20.35169618176006712572764090170', '21.25153316609768052806967025461', '22.03160490954695846732491924092', '22.628458880116074251117014611087', '23.22464904881305835986549842750', '24.05781423619068742816524675053', '24.427676845715063478666734613367', '25.70925343361562587882054495094', '26.4118789655445122805225615100', '26.98812832533547324739822140336', '27.6636019636852004036738376440', '28.39529121450324971702956134342', '29.34413608845357305667779034039', '30.29450284461625928026917857227', '31.03757770422503244541130218776', '31.71282414542508267557950874697', '32.42646918480533189536180001757', '32.921301499349880133257423114302', '33.92853631946919250599735729243', '34.2693532683661788732834972416', '35.039937681158844431258915464313', '35.61824495671267052457283591885', '36.33245800165990295161873258999', '37.623060696058595917519174904748', '38.39959723309739476273313516320', '39.06611610766250481828750749433', '39.63006979159149246946756871655', '40.177521710037417578304060550721', '40.92268097259966217336620129492', '41.68997370424785478073525374118', '42.71365162368319243014223398176', '42.95347902513855646250907142430', '43.880787796736541567198793239759', '44.37503107445929522596956702166', '44.98613045045611550496146285751', '46.02711838341898538442286263402', '46.33638337245855106955536129097', '47.51339747814566468921628368973', '48.08879182908237173120201720900', '49.25825670010365242710815610784', '49.60412791892645724900074953132', '50.3404343483986853664486776326', '50.87037534132352864987346825930', '51.54160061055332179336019092239', '51.87500057561908960342636275922', '52.750547088705007241240249963352', '53.71301269918976194383774134762', '54.22364009705448954784717227921', '55.03213402218828442864895137624', '55.73837859638793410323210819644', '56.439214438410943513326609995576', '57.396215265861495544615048821387', '57.96804728640803956995793461770', '58.33276761725826112498858376999', '59.20907136754874078718417328514', '59.98430796938190932660395205130', '60.553842672798501108035132766508', '61.3860849577429582980833588061', '61.910340665047365308881428868073', '62.555431464421221593346134511791', '62.840364802878672662782602274698', '63.62764691346139152146660452988', '64.48716239599881581427142560361', '65.64255456455457432331575605407', '66.56971158471962527833697690107', '66.66721332962655801850816658559', '67.32278451959418927551266104986', '68.2116549702190346024644895100', '68.66555929159013597200681604763', '69.29272358619089548921403962110', '70.0571556270633364065991819380', '70.50737473792632111407616946931', '71.39968026560989740686329930063', '71.90252951128649380823209104557', '72.80918673215565918486951886608', '73.37411678038235513700305336329', '74.124551565294615043567971927025', '74.73256445648849632778154510530', '75.50551053410914488056425613675', '76.00882727679765926612230151374', '77.16920975957761710365757507166', '77.69947615918133408383216374049', '78.09741874357863893792864806093', '78.677931038133003625573311203855', '79.52282379308702952671053683483', '79.76330352187719131582368479092', '80.560321616886911472941669760330', '81.38899912482709411151953402615', '81.75805502404180306472930854980', '82.75151575131542442457729903052', '83.603379417705043075653598440046', '84.41151052492879573816980583715', '84.8933873442577856118107745013', '85.53531081349076851135057980444', '86.09226477792014658347194656169', '86.62152912759535981355575901041', '87.05443050753598453908519035166', '88.23150645247164097718161796390', '88.66811399444698795354720521691', '89.51126932131853594409289623287', '89.85421857538812271683538807371', '90.5603484654753106199460426752', '90.92554008572366019631669181963', '91.900153838723764988222571489260', '92.75644355401988308688299040096', '93.3771356733502901829927529750', '94.28769508231448369441439631056', '94.585098435172143268560846833183', '95.36450530842629862086840231992', '96.08684575996331618673885229269', '96.55461754378848223148645233875', '97.12534147764633288361474095060', '97.75149802709824456811231032567', '98.3006147919294570872588079723', '98.65027017910222726817276993431', '100.01045432726734167038925173119', '100.25709457571894156224749403636', '101.51865205259289300460980226882', '101.67486964004353634825225249524', '102.56534339537571138127139661197', '102.9348694868805108695066470237', '103.78031182802973495306841549434', '104.34956386725779814298712574059', '105.09571547922240198488221417462', '105.64700547932666020270686577366', '106.34947856150329749751692498146', '106.8443814879597937931722780211', '107.43232531477775703874811555410', '108.20355438091114433553807222118', '108.69135672184787393812553687258', '109.25842836114881748266790860229', '109.840159003745057779203386525645', '110.95463158229993280410473018477', '111.694399902774040205309141045388', '112.454484369371394556469586282764', '112.86752825698731805505296768155', '113.40455362028101802907506743671', '114.07271749097634785536246617146', '114.30165865837587161660521112912', '115.18976645688307763102252948932', '115.87733539740382573743257399786', '116.35282793140342508776967693945', '117.30725196099763007077341280113', '117.78511909232129070931026875900', '118.1465744151810261261105069392', '119.12703004188311170933051967723', '120.004193009909750113106386007325', '120.49703005125406300318560276561', '120.88451979717523796994656129978', '121.84664490460513706832154934220', '122.174513361129329066178366173290', '123.025605272213725050526174564193', '123.86758024846023406394954405400', '124.38914491621831136802712511400', '124.60187717177226435706554129500', '125.32646404682357604258349042250', '125.97667455301838198517119718140', '126.357063923786807569542623212159', '127.038024199163903081247157523', '128.143464009755666430803887564059', '128.861413478573525196747870857068', '129.41951519275504782402621422937', '130.07596466036421653874738676013', '130.61537450908393862350960867203', '131.287622992358365383845099648264', '131.76156502208741761861819866479', '132.52329790614340397080541143493', '132.85313724474051523955869675496', '133.502577741998904355180722262204', '134.33338725399631102148809258380', '134.91896453303627127989566183348', '135.75655286704202427600920463269', '135.94291559348966008165768074656', '136.752014000058763513046366312931', '137.3602508025126995076809869744', '137.99244575123610666844838398758', '138.78513791360087831895218190537', '139.74024044765299384629138179107', '140.08287228766404935005574216873', '140.801191341819105070355599658', '141.2748209123766407353258139028', '141.87016972861091626902476003987', '142.30359082324921912837456496110', '143.09136559703586596789066578508', '143.6781593657291856333812149949', '144.082515525350282634999222151789', '144.76183823947706151859870726225', '145.43571871849239577583649642195', '146.337447964162239218896512851260', '147.09845474692518476623480404743', '147.80186069240172561350160437889', '148.21209734410186544482215034780', '148.781321816166269310343608069935', '149.21321093666257823988731274251', '149.87378710058178195212124069097', '150.6523923496125433355966842385', '151.30937565281723332117028621350', '152.06586033507045446350823179367', '152.45923435730144849048028933469', '152.86727911304077055437102578274', '153.55260637486597559176289791165', '154.20424014985220374904870245252', '154.664681805097878768380814916034', '155.72367143617223600419401240519', '156.15414373464625356172655783795', '157.04083175875291866578575621799', '157.5855218418563011441512090898', '158.45706401696750381734734008022', '158.57362357112380082030713653745', '159.57750261888989691219705688241', '160.00468194409311767119283372335', '160.19084021881558313695267513338', '160.98302695331651000164800903676', '161.52045228499510522405131398267', '162.29303308059512626536679701788', '163.16842257141189523711102718344', '163.480768521048688194449282408533', '164.43489403048601645945129348623', '164.720695910092878569553733239322', '165.5441561323098403000240868005', '166.28738674911250756493507311453', '166.78754618139477251136941885034', '167.28512223581350758009839354832', '168.17174367284759477853298366504', '168.50442181297024625314715125154', '169.38866477165179710662798564405', '169.60016419154284319442086856149', '170.57227333064947305679396847529', '171.022833050707701924883230651', '171.44001132797570305763856961207', '171.90010319348951119447412067', '172.75272319533974973342985180871', '173.127073627357607694351205907296', '174.65278977144501896969437277480', '174.871367766478288936118779493248', '175.56453097333816407235133292090', '176.18568312896267324809685447856', '176.44282952783586059975666162435', '177.0886613381622192138757279301', '177.904217698905891691282683332366', '178.18237001610497672123042459517', '178.93140113433444587671740252737', '179.69776072420803215775081266983', '180.297196602459677993014661294690', '180.45438207044117408482675513006', '181.52850571965995277845544004279', '182.0202528607474290362716430956', '182.56986103732833466369323892263', '183.59201902243597269435168985691', '183.82349385608195267627517325601', '184.426688707208397462333346246767', '185.15472844695586843442386582712', '186.167820323436981065951913595140', '186.5273301197078684937114680306', '186.87281402536426071073706119728', '187.76020587730809493217095595262', '188.07781819389141670031425801009', '188.44727332763227286217278849863', '189.23149435290974868238909812623', '189.74021050700736303663180144225', '190.60822053762821755466571046067', '191.05447962314281712207388442016', '191.99711710389296104153952739300', '192.64363308993898240325143851847', '193.13592642362432981455783184865', '193.837167623142800747804960887311', '194.42297767214423481460665576621', '194.9897468893641313334475652013', '195.25983098468193386261158751170', '195.93745326316098936477364362520', '196.69080392577114534740738755993', '197.27585511649029630672050159220', '198.120993781179990436140882738916', '198.44039829037905053397762715961', '199.0284733848844907738759934614', '199.56336577570520185412180126508'], 'prelabel': '1-1001-1001.236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.3035457845183886, 'root_number': '0.578736998469644613258875543148+0.815514246719422166938602091299*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.151772892259', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.706422004469627672882300283029+0.468126784810793034219109572591*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.486971041969', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.76943958706', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.67922898361', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.236', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/236'], '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': '1-1001-1001.236-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': '1-1001-1001.236-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.1517728922591943, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.486971041969', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1001.236', 'Lhash_array': ['dirichlet_L_1001.236'], 'label': '1-1001-1001.236-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/236'}