Formats: - HTML - YAML - JSON - 2026-06-29T04:32:49.186337
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': 'dirichlet_L_6400.1253', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.6930873625456359, -0.7208535967029188], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5555702330196022, 0.8314696123025452], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.03925981575906861, -0.9992290362407229], 'algebraic': True, 'analytic_conductor': 687.7755186856001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '6400.1253', 'coeff_info': ['x^320 - 1', '0.999807240482065 + 0.0196336924606283*I', '\\\\zeta_{320}'], 'conductor': 6400, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_6400.1517', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^279', 0, 0, 0, 'a^370', 0, 'a^558', 0, 'a^337', 0, 'a^243', 0, 0, 0, 'a^476', 0, 'a^331', 0, 'a^329', 0, 'a^582', 0, 0, 0, 'a^197', 0, 'a^479', 0, 'a^296', 0, 'a^296', 0, 0, 0, 'a^53', 0, 'a^202', 0, 'a^358', 0, 'a^105', 0, 0, 0, 'a^364', 0, 'a^420', 0, 'a^115', 0, 'a^209', 0, 0, 0, 'a^290', 0, 'a^573', 0, 'a^247', 0, 'a^288', 0, 0, 0, 'a^391', 0, 'a^221', 0, 'a^274', 0, 'a^462', 0, 0, 0, 'a^387', 0, 'a^324', 0, 'a^476', 0, 'a^331', 0, 0, 0, 'a^118', 0, 'a^42', 0, 'a^293', 0, 'a^255', 0, 0, 0, 'a^504', 0, 'a^255', 0], 'euler_factors': [[0], [1, 'a^279'], [0], [1, 'a^370'], [1, 'a^337'], [1, 'a^243'], [1, 'a^476'], [1, 'a^331'], [1, 'a^582'], [1, 'a^479'], [1, 'a^296'], [1, 'a^53'], [1, 'a^358'], [1, 'a^105'], [1, 'a^364'], [1, 'a^209'], [1, 'a^573'], [1, 'a^247'], [1, 'a^391'], [1, 'a^274'], [1, 'a^462'], [1, 'a^324'], [1, 'a^331'], [1, 'a^42'], [1, 'a^504'], [1, 'a^245']], 'gamma_factors': [[1], []], 'id': 7569689, 'index': 0, 'label': '1-80e2-6400.1253-r1-0-0', 'leading_term': '3.89048484830845758999343886055-1.60925464662557141229674745679*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/6400/1253', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [4.210174921853447, 2.6147653750205886, 0.13012905704889333, -1.1740782274566466, -0.4443644016845507, 1.005847779239835, 1.1529304506952998, -0.15937271716130633, -0.9203781505280164, 0.19300371781427178, 1.5563601237647249, 0.5910811912489982, -2.235219006745353, -3.338108999842011, -0.8489428004204465, 2.2306538707144106, 1.711510980806057, -1.8994231049500474, -3.9318839465244584, -2.153053359339834, 0.2000508811413598, -0.4524914692792885, -2.6399103377534474, -2.525138430765243, -0.16349112617485934, 0.8679872815536372, -0.3757796977680369, -0.8309509288725369, 0.8515287913525903, 1.7037800118566062, 0.02437363523915267, -0.6168498909755953, 2.9834825464763135, 7.232882383104238, 6.272299501842983, 1.1450005919476571, -1.5416044029498441, 0.29193661293430434, 1.8301735149682399, 0.09941582330489622, -1.5307511176691462, -0.2682881586617102, 0.8990912588349471, -0.9294583620788361, -2.8913245761495636, -1.6159608609729024, 0.4972481199950665, -0.04915923802974953, -1.140902800276733, 0.456688193767497, 1.7202721970754609, -1.816304226383974, -6.731331261412558, -5.826462824805644, -0.002957933203338221, 2.9448031020983993, 0.8580163878459877, -0.7127741598763617, 0.6802969692321634, 1.0644925486435508, -0.962292130629882, -1.34901450121831, 0.9351964618948334, 1.5243761123267714, -0.6836309940215859, -1.404651878858704, -0.024506089432321448, -1.3618314289054458, -5.556782251271406, -6.188500735586479, -1.905503847371382, 0.4182142117937184, -1.903733718886699, -2.5340415689822824, 1.6820335246216127, 4.544171965632932, 1.8867181164695415, -1.3356351108948261, -0.8155429415984112, 0.3884699697379685, -0.051708741729444826, 0.8691993427446896, 3.4308776838561448, 2.9642086451609426, -0.39140069634889013, -0.5794313429242928, 2.623974780829873, 2.4926602797878945, -1.4972809727570109, -2.1612543068050636, 1.431860923989573, 2.011267224421047, -1.6421716346820339, -2.375810729257297, 1.3311177668926746, 2.850693945564975, 0.4428619699587759, -0.6099688648618959, 0.5884342156106448, -0.003079127500741221, -1.4542692100880414, -0.017258298993587474, 1.5358591508133008, -0.9473436227150673, -3.3041379500589065, -0.7895199924643874, 1.3510729984327554, -2.4110087284698474, -6.109232276221662, -2.9190922456812265, 2.0085417952943385, 1.5917380459299926, -0.8211147097149185, -0.33206713095955115, -0.2360475607031029, -2.9976002361603147, -3.6667188891995997, -0.3341853391270757, 1.4435902394389284, -0.01771675466190099, -0.10853863566155478, 0.9666646992105912, -0.8681203193748863, -2.239971951290682, 2.4549412432881086, 7.729964004576065, 5.094293834215218, -0.9902905862559123, -1.301128754235554, 1.6632500235685137, 0.8294472510307533, -1.3979951580949397, -0.3806937754519973, 0.4634650620626147, -1.5852438819380898, -1.8618147497288604, 1.0261531310427383, 1.6393886056238074, -0.2703312980017202, 0.7081539391058519, 3.0285337302299125, 1.238084629957372, -1.1757858365238696, 1.3014141080552206, 2.9989489625241967, -2.4332454654990885, -7.956099628744249, -5.549522608564715, -0.591778689596235, 0.049079449699475836, 0.013608371209180865, 2.4705612407558295, 2.902867620980679, 0.4065337000956144, 0.03598221294629684, 1.077418487473752, -0.8075025353228468, -2.2444947842545124, 0.9974126524412525, 3.278083001364638, 0.2520975626759592, -1.207916277476268, 2.600155173181169, 3.7825975098103255, -0.5656418835264855, -2.026931837701344, 1.5342327226754868, 2.166563973042795, -0.9907852342949591, -0.9648780585380052, 1.6281943871778934, 1.2594500708645917, -0.036713460231187565, 1.1575317226636612, 1.2624714156184031, -0.5619657611528872, 1.0429175864448652, 4.183756941476074, 1.0891607754985477, -4.897529832551226, -4.152260649030676, 0.38129336464000757, 0.07580515552746284, -1.7631636784030886, 1.0119106360316326, 3.1962640134863083, 0.14858309580308526, -1.849425928117938, 0.5396970943006738, 1.4463980481871954, -0.27997243596760735, 0.18754084388595865, 1.2150183590974142, -0.7711964192010389, -1.2641914455847727, 2.0188147820105113, 2.166957158880633, -1.5833015976309213, -0.3778030913110432, 5.068856720084637, 4.383926028138769, -1.2836027923927902, -1.8600233684513505, 1.418795424643133, 1.0512631820824647, -0.5243866380330874, 1.0572155975954445, 1.7085067901660975, 0.0464688425210484, 1.4485886429757016, 4.489664922540756, 2.7894883821073866, -0.7190034806423169, -0.4404840458762957, -0.058651076851827744, -1.3466518412520871, 2.5463520197711462, 10.080353855206322, 9.488022829107543, 1.2078539861134918, -2.3624187869677895, -0.0494261584366832, -0.1148095946007354, -1.6660833568642082, -0.2073556559224739, 0.32024252494460725, -2.168352873249102, -2.1771628548172632, -0.025956602939072367, -1.3381877486190477, -3.106870642165272, -0.4919932983601447, 1.108021740246971, -1.3064766421419436, -0.16807295591849145, 5.023757122089577, 4.467158890724326, -0.8932483516038752, -0.8286325097259273, 2.6473379833024433, 0.9880379030419475, -2.2122172542379546, -0.7707828398062971, 0.7406404001905891, -0.7243963679264802, -0.299985525694205, 1.5695318188074814, 0.43557649373068247, -0.1526446717648037, 2.508786818983756, 1.687577538463296, -3.153164575587275, -2.4069444232734973, 3.125647175104025, 3.0214212612227187, -0.8087166411149168, 0.3092827671165081, 2.3850538854766805, -0.5645304097608507, -2.1513051702113497, 1.3251671638406681, 2.523309146278706, -0.08634192624078676, -0.3111347757686356, 0.672720919572286, -0.8373320143438717, -0.8029695681566911, 1.4066126322412116, -0.4556601892761572, -3.658049551276607, -0.7441455859939076, 2.2234635725012484, -2.680434817924658, -7.062881173962152, -3.1577702236216583, 0.8707458741735444, -0.2878190023889966, -0.15635672316502558, 1.701769990071702, -0.3747404350565209, -2.6141300625573285, -0.010241895027851045, 1.8591502736489693, 0.013097453911244832, -0.24769895964442573, 0.3060339061726809, -2.2474969456585487, -2.267366028349095, 3.1018931731837673, 4.476699220367113, 0.10368105070637754, 0.6630431328385843, 5.588340242983534, 4.163480323229214, -0.8805509630114863, -0.2616702686408919, 2.2079726164895366, 0.7629779177956102, -0.2647549932333426, 0.2513755809879375, -1.9334271170462967, -3.113770860307502, 0.7158308655334256, 2.746763341303906, 0.07888122120585249, -0.22361342326778075, 1.194773963144172, -1.7967222667976115, -3.470103591243929, 1.7443189435255413, 4.131816874416404, -1.3413928318717876, -3.7360535260724257, 0.46662559843571855, 1.7954288222893233, -0.5745646207299367, -0.3862369903676679, 0.07622420310934665, -1.4244003327800694, -0.08796952657971222, 2.328824587721657, -0.09083603332752507, -2.4742394959778697, 0.0579513196710634, 0.7122416746644603, -1.7836514282760247, 1.0990064530201213, 6.254131930498544, 3.539115585208263, -1.581948069685967, 0.11071014507458424, 2.3781533693521166, -0.14072664761887793, -0.6486064137959963, 1.6725198476503038, 0.23668110807229076, -2.1344208777434233, -0.5097987229374272, 0.41291119508266616, -0.9030937041174998, 0.25125202846083866, 0.6188528964352717, -3.081701256999418, -1.9602243936303239, 6.1591646326948934, 8.286308524100129, 2.0532543481854173, -0.6766631745070364, 0.6527277495470809, -1.2763457562523957, -2.2823737572829206, 1.4367178200991841, 2.247531794182511, -1.152953369240579, -1.1676533840126588, 0.7555686644498923, -0.2664905935392744, -0.10694998325832755, 2.080896819153914, 0.7054918295333696, -0.6645477788857791, 2.8556821284007823, 2.8226231903656123, -4.114487633432166, -5.769156220690219, 0.0988361782189155, 1.4849604955975648, -1.5461282395111258, -0.14552980721467773, 2.194322940244487, 0.3892124237090362, -0.12423254569836134, 1.3040457691524128, -0.7789842705192852, -2.5814323338524465, 0.0594886165084174, 0.8746132613896618, -1.1352189724515789, 0.5708739925903887, 2.4329096955854044, -0.6532021820988955, -0.554161849309032, 5.1931926277714755, 4.966486165171083, -1.1975324930968716, -1.0414872121834455, 3.3244773250904656, 2.3734956488710366, -0.01697938879920764, 0.7688835503589737, -0.17944635481343005, -2.146785847313485, -0.4803606348247199, 0.3266252095927075, -1.6412287448557366, 0.3586150749439371, 3.8055625871480325, 0.8906492614225706, -2.3654918300132177, 0.18519966749427177, 0.5063709237590788, -2.7368464843644453, 0.36508053280089897, 6.258829421603921, 4.035591823298425, -0.8883143762674961, -0.3785915737935206, 0.03298948812789536, -1.9786770247122014, -0.7947693574206108, 1.1910742335884599, 0.12951029087851074, 0.7245130805660049, 2.0702224642148273, -1.8042430214080178, -4.810201833151519, -1.124992584589635, -0.07183886750026502, -4.692033512662823, -4.221944680529186, 0.2794799741286244, -1.3059776466172344, -4.0856671553914055, -0.6448445686318485, 1.809376458970162, -0.24071550796228625, -0.15953852012075753, 0.5136275179930532, -2.5550251586584345, -3.385035977576784, -0.13866858722804115, 0.42830742013111256, -0.21706158969150105, 1.3037457593946398, -1.2357001288704086, -6.035140234225299, -1.6773672976373426, 6.489554481347492, 4.525516364198654, -1.7739149157692962, -1.5191045073573122, 0.14459767054730205, -0.41274874961713914, 1.9247578605633209, 3.617330100180755, -0.301979773576974, -2.5633795598879088, -0.08750741229913292, 0.28194896166162586, -0.4852345708432298, 1.224324230744918, -0.1974260833210089, -4.019369242353633, -1.8980354270990123, 0.6256732372727413, -4.764239695222875, -7.976615900068854, -2.081037021377104, 1.4984581052973849, -0.8720346789694721, -0.05931056499629734, 2.368841271456807, 0.6233379670134953, -0.1703699735774482, 1.5184922055464862, 0.1650942179807621, -0.9707470921407547, 1.4709385275610198, 0.6756529481334572, -2.7319908801667414, -0.8313135018362895, 1.3415415383878857, -2.073132898208225, -2.080983719863901, 3.1397411728731024, 2.5739867261588554, -1.1317851003955433, 1.985648636405162, 5.20244793391411, 1.418202906509514, -1.235512944690282, 0.2691377588894874, -0.043353105513106595, -0.5498378517822109, 0.2491651855690724, -2.699166939958846, -5.437580217689383, -1.453426468585194, 1.5840821268675127, -0.7722252137369096, 0.1683323342256031, 2.746348006230548, -2.1286110241643907, -6.813372531211092, -2.690580645246852, 0.9188970656395794, -0.4148868283273698, 1.3991064506760584, 4.149252631194318, 1.2592114545455468, -1.1559815760276637, 0.3635509462161135, -0.028113167830673212, -0.7491876050945412, 1.2794870250546286, 0.35704526419048266, -1.8469282720426197, 1.9462744982362679, 4.303740054572271, -1.465418057923359, -3.903825105228584, 0.9552167427308554, 1.1537884041471458, -2.6984992625513917, -1.030573068577795, 1.4358190960180504, -0.25548539589282293, 0.4328449284202102, 2.719674883204525, 0.7625868084061823, -0.18761462571888332, 2.541020855261984, 2.009428319888655, -0.10958382427420364, 1.157268399589185, 0.17641382439266243, -2.564739805675438, 1.5791537377321667, 5.609636038400016, -0.5786012025536023, -5.90359085084339, -1.5736591360907144, 1.5344058739503008, -0.6344794744585006, -0.46982507512884963, 0.18608919205564164, -1.5404033830456563, 0.18783877444690283, 3.2038314215309405, 1.0496222051417043, -0.5181261612767438, 1.7935593014578752, 0.967965783273886, -1.0781249624403755, 0.592190603851335, -1.6038603436445844, -7.820515048623097, -5.407137099163487, 2.105815053261137, 1.5726706809426823, -1.3427968518762192, 1.4752163806929326, 2.4479300701537605, -0.38331965944656665, -0.031956197107514704, 0.4819129153207158, -2.0420930952663574, -1.6936673253319836, 0.03684085721208696, -1.6475332678152736, -0.851935919787114, 2.594832462577868, -0.18852472392217923, -3.7770222949748544, 0.855277377242768, 4.261903398317942, 0.5239651955083064, -0.47751521767950206, 0.6990955266485304, -3.970259502063961, -7.0187840094482095, -2.3996463873137355, 0.5329423030881775, -0.5459867650727477, 0.581516356465089, 1.1100193105387124, -0.6452956300499965, 0.05672472404524788, -0.8209521623137039, -5.935479693334173, -5.061358508087424, 1.495885838758646, 1.3732726825002897, -1.5879817532260563, 1.5510810196245592, 2.365712252119187, -2.7127237647719804, -2.799153453781648, 0.9004315486847759, -0.2208609447284965, -1.066509649464551, 1.6752395840836654, 1.3019429346830582, -0.14264827086859772, 1.8024653223471767, 1.1348861234438024, -1.9779204457998474, -0.6945405619361741, 0.6538294381042327, -0.012432334777721397, 5.928566317595561, 12.922232059487166, 7.779400513937581, -0.6386163756119349, -0.16400041117359848, 1.0921086731387855, -1.3760921786892062, -0.303102969256785, 1.5122732598212567, -0.6399920602404339, -0.6074163701387107, 1.1395587974063592, -1.2705995207279392, -2.1838527014782914, 1.1812372301343292, 1.0930935828358384, -0.41021674747833536, 1.9779191877901987, 1.2314107841965796, -1.8147826506861966, 3.76173302466686, 10.504204135696162, 5.773694630052255, -0.62260803851815, 0.47076161714284565, 0.9352732888897426, -0.5590161872942492, 1.390495870705652, 2.0021961440837592, -0.0451387953129946, 1.4342774111147112, 2.5775315509353582, -0.297500105588529, 0.06486759895218948, 1.9898253108778075, -1.8317680198900996, -3.889666316372455, -0.013353430633366787, -0.7413087739267612, -4.193389494394036, -0.10015331747519657], 'positive_zeros': ['0.643824217487586994477586366509', '1.34021125550241869583017331945', '2.15354211469807140476889968565', '2.7770772910081067558598648572', '3.50951563847412682510475450441', '4.44773079838489371495434474866', '5.15875595084853147242768946676', '6.20367808975691103196477196219', '6.48522166387460142134390523002', '7.52310930683967015022869572164', '8.04802975984749778722505073447', '8.616240581857518025517515598181', '9.378736453100179638367289365414', '9.77705744325965679690367677767', '11.01679842517052806873527579504', '11.52875076356840618209482398120', '12.19979418065711379690085179709', '12.85420857700536218384931399117', '13.32531283515341655774591036731', '14.27053574840533226169863174046', '14.67787477080718393110157323210', '15.25348858658053440321890156248', '15.82470349198681761853983709853', '16.87516496585004159148553046451', '17.6023276651250336711211941490', '18.00684513689799441426721107327', '18.61438328301813439582199076508', '19.25695373109242151052532836685', '19.911168655337435454115831004196', '20.63524045882725849594101241415', '20.74534548864694701489395657441', '22.040703520820475573023228408367', '22.28579999035182750074585551792', '23.020280258772988084208132398297', '23.897370490632359858499194982586', '24.53244040588031304876038366326', '24.96500818608202521977101961544', '25.13766627098699006054881559280', '26.20825566738601488207393523256', '26.62759343021017809159949744513', '27.3839462864480460545127725105', '28.006483243837764658174572310018', '28.61812982349158092393708342966', '29.272608531865537028321192060992', '30.05774673250590297816297552278', '30.47510344887657431720484794367', '30.93696211978894942635636432699', '31.56462368650270019361951190026', '32.10580715496596180067639745438', '32.878179985943783094589752803987', '33.28803782040567345418095856356', '34.22120725199677186839193745423', '34.86317762838775857100011408079', '35.40631302842914162816677187977', '35.56916746437156621489543595858', '36.59243671833450633727595322788', '37.183810962594626487697174599545', '37.525768707582508263631806084193', '38.02806894148519409706254084419', '38.62958878695597145731959719004', '39.62185517148445156545857959019', '40.1246998657234606221500576305', '40.717021243430054900138598612339', '41.31299536950149447768257678717', '41.66188478793541935689356922556', '42.3934392822309522941130170046', '43.066382715614111930797355914873', '43.343974396183637320559980342196', '44.1748263405398992724467109413', '44.57812530266364180747324867315', '45.207592366395454042916707343041', '46.32943849529754065703515400100', '46.58000271579919131214761080288', '46.87212955723029431814334517920', '47.88444919079202600837666335262', '48.11555104593659810437387722080', '48.66017068649192512627067514245', '49.30264942454963128625680846545', '50.02082942770286829105822673209', '50.43975959485088269328188855893', '51.21199075287177733987469832157', '51.75165280885709821273347356847', '52.39799417214814581231265611669', '52.92232326001114087348011555180', '53.70275228089228873005193342211', '53.79468817080595713153166634570', '54.57111671077648177609572841770', '54.89859357203339179294390882993', '55.67663757184309718621538279936', '56.52495628477241851978194905457', '56.883921881005747683134882865853', '57.421129882540050423275522803553', '58.13673747822435573952690546537', '58.69162875882322215927909953341', '59.3144584314620006454993388437', '59.65209687390699445255917890251', '60.21818378892995389055628372733', '60.760729604245042726806425672087', '61.424851934488848457625905434368', '61.89818528453543042357796278894', '62.732834794836429236246502053145', '63.290985848009974416527433303678', '63.89911842645026504763655800847', '64.22119380714463058734172238274', '65.01881550970329417890066820227', '65.107107211150592293776196986817', '66.15981713441503766900963409021', '66.67046010010561095690732188713', '66.8582956182133942843218824720', '67.370077023560684607628709352278', '68.490551693060604474720279739843', '69.06999359156814552346555887552', '69.35564376071607590154092535208', '70.03207169281299367480745671341', '70.36616426628677430910662655597', '71.25963251396130908143321391033', '71.35857959195456829927786014392', '72.2324773391921311064385077592', '72.66033391664898031236249956800', '73.136429373824018231840498190135', '74.00000727233751938743887839095', '74.44263153665092877833911118676', '75.07446186631560073426440293017', '75.71683200787231310197095711193', '76.1161144308479181336042700172', '76.60541994881929213616326968716', '77.25935641446135244055176253020', '77.52725966696214349948659051975', '78.23436275969873035763920097327', '78.88215494531378220768638861008', '79.59923336319118911290260638227', '79.970029616678052576955600926836', '80.580893037511890581822817206598', '81.147211441016607877982356045438', '81.862955541168917577785455278497', '82.2527515199363182909045154292', '82.67542307333647071295068923059', '83.22975799831671945550291763291', '83.714298348275598208727259874183', '84.42099521012002692124320060792', '84.87556065731513632265337139958', '85.81774993480360051938806705183', '86.201148247887861667731458224730', '86.58556422787142383445343398155', '87.15481239394203595517638944607', '87.81338208448018246381814914953', '88.43969328571752917683584654915', '88.81321906024518994875540418027', '89.12638965561968768858796960497', '89.83365279321392519283599883610', '90.63448685042613874979329450723', '90.88557300689873408943345663274', '91.80072692411056124129866856621', '92.21271300766737831344140034977', '92.9359797944182559339864991645', '93.23539170308706504231445531849', '93.51519849942019249803574665071', '94.32660931085454856980569851425', '95.00967526977993946679434751374', '95.34820414244879944682124886481', '95.80024129849541737171008513143', '96.47654111416722016775444650905', '97.12192320060281822427997983874', '97.779718948619519486750203743510', '98.35100834936850824091876567274', '98.844858919576381282099768562940', '99.08420680817348981320673332153', '99.69617610354322654177320627378', '100.30545896669234945228551156477', '100.931644912925241004490994399478', '101.335672177010035071120280725693', '101.81412873377938503527248913144', '102.68008386224364157233454818598', '103.11614528325588183282316145943', '103.73490979891203167130908744293', '104.14687102434940528391494251600', '104.70981158760037312458691101936', '105.38425343845135362675676363414', '105.72358776541198592529377258201', '106.21256784750582524881686271337', '106.63074948676592766360226382131', '107.27351319100260820784697926549', '108.25621138402687040832819630086', '108.58036575137154859265920675137', '108.92370118075830199869942028196', '109.57988091873704469750273941457', '110.20296390991944345991258739190', '110.77659379956180752653801096933', '111.19761945705877885897436673424', '111.57826610474540584056099176337', '112.265399548452709189758998707009', '112.58994185098589760188189713078', '113.264896595767136678903336357260', '114.05680191644862520742747449896', '114.516877834658556946485368749350', '115.01306987492275098564660038990', '115.68327042019009571837455310400', '115.96279960415617030639756094848', '116.48879219318083770451987209458', '117.181424941845472753248217191444', '117.62517227314430364511646012787', '118.07086409730816558143530935211', '118.694119307406449605833232020011', '119.099675415444451887859467273585', '119.929435002542552829043668394483', '120.382033094213035573328814347446', '121.24060429139229269463122663824', '121.33433866674562020214451733187', '121.85226625416538882864767244593', '122.56477704416629875304042827729', '122.87141108723423208800971568454', '123.41146906889500948471083723123', '124.117271263118266427696762662820', '124.66969848494941365578638698797', '125.04890165672671304834996424786', '125.6077968137025998871172440938', '126.47735456521997149302577698344', '126.94166653082759052278816519078', '127.19384446167457142409784056617', '127.9002017983258074298824512254', '128.47885479537460835235718268083', '128.6098082555656305296926083314', '129.26863365391311564731909413685', '130.094342844362067530235549400398', '130.30493445769811196852975901399', '131.217519913509389291956655868349', '131.453499356046005892062854297007', '132.23130754186788571968772411554', '132.7761331944955009293083712924', '133.15493442372141558125004109422', '133.51715781475455029262802509562', '134.39125487227766466395109293593', '134.79085732826692370664077138877', '135.059122706264008400845798025870', '135.54757039541957050528589927068', '136.3057277318158721883674644999', '137.07496150875543472195634316222', '137.71966160125383163408495670073', '137.90396243296776868005095441647', '138.23871937500632898095020381740', '139.04302398828431325571562590029', '139.6992754476940023877079753613', '140.06217477834359449165125468377', '140.424309214782871516636329925', '140.92205263058249026784373012769', '141.70137222236600554781315166539', '141.94735674301092246865598303118', '142.91709102634758284054489998562', '143.331629383715038619550006427753', '143.75590055120918638517445289229', '144.46187690807444039880952901222', '144.7229224686322688627008716997', '145.33251899262575055073840845914', '145.76758530653287844861839353506', '146.30508093306953127518869507734', '146.94095008733317137179862547261', '147.34286400915590420660676199715', '147.93827707571419606966270595512', '148.61271634195789143954011245316', '148.93962017559393308145797359038', '149.78547906709736056873248122104', '150.25622638367985846438424631039', '150.6149912976761904977427831973', '151.09031121207268022225938638040', '151.3210288503708139747632601888', '152.2751089609672364634742512530', '152.720852049556421286106887629295', '153.11031229867723659659973921983', '153.656644298068567026079765710024', '154.53786891242749295339404311471', '154.907928944942306947452806746469', '155.179978116194900958600069676241', '156.036305413627896016585041640243', '156.49288150340046744885214027619', '156.86976780427739216868539291003', '157.318681164521296750176932609763', '157.84720991219580613491987757548', '158.32379281424952133487896195660', '158.996395207580810385727230693707', '159.626231172490344567428921209592', '160.08497272758563590826961460719', '160.70889976496191455421888249888', '161.20694939541663373606331522079', '161.51010298093597288673395794655', '162.27858533148274083227449384394', '162.530231643461520554825202397733', '163.387753754053589163188075781481', '163.527786965186698893872837711901', '164.0784332417217207739894762018', '164.61246808139952718229341195475', '165.29206914699504729789491689803', '166.02669766860471935296940682544', '166.47679009651028840231857696153', '166.96736387575415217259097851892', '167.23117990190255197040706884385', '167.79723080315139309189500154170', '168.541394553721862632956919285081', '168.83909908667543519220233127921', '169.47620157704186870398372014716', '169.90480910897660187430908534451', '170.21008370089063463911832642315', '171.1422847873285458962520279530', '171.678434194748983315397683075523', '172.06666445189215750058312581636', '172.75946202006230589932321715300', '173.1305872772907463373504967406', '173.51170245765572180304967963508', '174.329655691444931786850105718409', '174.40720146334106759592715023573', '175.068141730562453625936260485653', '175.61440632625680735083869833887', '176.209664651219132480241743947055', '176.91934033066991970780607767296', '177.25899679690776313278364289803', '177.58550926021267217148584651638', '178.61083474435585652302680943403', '178.91098191822205867828354724806', '179.28112749269555715712379722963', '179.87047433883001092446247800823', '180.29995379588732277438523958102', '180.54205645765523886240443665152', '181.47920950072686494896396592819', '181.97864201231463762024670851378', '182.38939067440251910922352583285', '182.96485487571499461993859016584', '183.64715582313722076211992294356', '184.03657241574874540446288582591', '184.50558343873946136016468245116', '185.19604851496445722328042021029', '185.36181309728725505417205034358', '186.03688616625612222450813636080', '186.643747547023521033888179165538', '187.04081191200484318650889532544', '187.18995282104312684098745119641', '188.396892774464011091592165563483', '188.7665968092218688901987455874', '189.2042165042116892387584951583', '189.71882731221526638189897915408', '190.23367494726520952816029617442', '190.70403068781607699000831078913', '191.13169850569143530154609266754', '191.76519277930103654580326662030', '192.331098092692299506150389207758', '192.58806049720267335407189916092', '193.217993627090165361602517015940', '193.60532326751312711566455631229', '194.62741619448000609043788163253', '194.941741661614844889043248876860', '195.459540032457172987252736892868', '195.771122658281707771060801681293', '196.54753704257641446262039815598', '196.676264798189566149093724332871', '197.46542508460084933078455771390', '197.80527233887773228929473301271', '198.32632687245726685991804486602', '199.063798226842565450123580913203', '199.31400096769207989865106167447'], 'prelabel': '1-80e2-6400.1253-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 687.7755186856001, 'root_angle': -0.12484375, 'root_number': '0.707800640769293608879436392449-0.706412240074149183752209417448*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(320)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.56516405899698982918624334584-0.347340044575812699743479296288*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.643824217488', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.3402112555', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.1535421147', 'prec': 40}}