-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.128', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.20791169081775934, 0.9781476007338057], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [-0.9135454576426009, -0.4067366430758002], 'a5': [0.9510565162951535, 0.30901699437494745], 'a6': [0.20791169081775934, 0.9781476007338057], 'a7': [-0.4067366430758002, 0.9135454576426009], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.128', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^56', 'a^34', 'a^3', 'a^13', 'a^19', 'a^51', 'a^52', 'a^20', 0, 'a^30', 0, 'a^36', 'a^59', 'a^8', 'a^28', 'a^9', 'a^1', 'a^37', 'a^15', 0, 'a^50', 'a^47', 'a^6', 0, 'a^48', 'a^53', 'a^14', 'a^16', 'a^27', 'a^25', 0, 'a^45', 'a^22', 'a^26', 'a^29', 'a^18', 0, 'a^54', 'a^41', 'a^32', 'a^40', 0, 'a^55', 'a^7', 'a^21', 'a^4', 'a^38', 'a^23', 'a^24', 0, 'a^12', 'a^5', 0, 'a^10', 'a^57', 'a^31', 'a^49', 'a^33', 'a^58', 'a^44', 'a^11', 'a^42', 0, 0, 'a^35', 'a^2', 'a^46', 'a^39', 'a^43', 'a^43', 'a^39', 'a^46', 'a^2', 'a^35', 0, 0, 'a^42', 'a^11', 'a^44', 'a^58', 'a^33', 'a^49', 'a^31', 'a^57', 'a^10', 0, 'a^5', 'a^12', 0, 'a^24', 'a^23', 'a^38', 'a^4', 'a^21', 'a^7', 'a^55', 0, 'a^40'], 'euler_factors': [[1, 'a^17'], [1, 'a^56'], [1, 'a^3'], [1, 'a^19'], [0], [0], [1, 'a^28'], [1, 'a^1'], [1, 'a^50'], [1, 'a^14'], [1, 'a^27'], [1, 'a^29'], [1, 'a^41'], [1, 'a^40'], [1, 'a^21'], [1, 'a^12'], [1, 'a^49'], [1, 'a^58'], [1, 'a^35'], [1, 'a^43'], [1, 'a^39'], [1, 'a^42'], [1, 'a^33'], [1, 'a^5'], [1, 'a^7'], [1, 'a^32']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.128-r0-0-0', 'leading_term': '1.14006281639752420259709024259+0.715554218788751526387985295977*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/143/128', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3460167403708747, 1.65581618561328, 2.096808508714924, 2.2726681311247128, 1.9313069798232099, 1.0340583716518688, -0.21874218258613382, -1.423338543469439, -2.0989598041727615, -1.8821831363726482, -0.7149413830442435, 1.0700051213405086, 2.8342684065555614, 3.88255261069454, 3.7771485338071944, 2.5646305255377304, 0.7818797703243953, -0.7895452439982746, -1.513420069232207, -1.2288418320473742, -0.32713439212440104, 0.4864560815825928, 0.6219535328013206, -0.030080555197000702, -1.0334681791908977, -1.7018465184785996, -1.5785216398033395, -0.7809394959782961, 0.04910504367122389, 0.19758874989894498, -0.5486479944903233, -1.6160546806276046, -1.904155721213821, -0.4915635705714822, 2.6479502898510665, 6.425477413794907, 9.136946068392602, 9.431334859306087, 7.145116693713792, 3.439764707043775, 0.11610308167621013, -1.465369192470665, -1.1454334989890746, 0.09527723523027823, 0.9490488631575547, 0.7400342787318719, -0.17178713352561484, -0.8156723966047738, -0.4997904245934799, 0.5598025626377083, 1.3881595679976262, 1.067124867471358, -0.44925672119416166, -2.2116615279939547, -2.986210914416238, -2.2439331506031457, -0.608178833448713, 0.6458569464935138, 0.659814957811424, -0.2606173102259054, -0.8883597753323781, -0.1620908922030927, 1.7750609606555625, 3.5086970658643004, 3.413742400002873, 1.033847383256818, -2.373009945827363, -4.6579761235836346, -4.39264311348498, -1.9924079170487194, 0.5823841542490414, 1.343122003477245, -0.20137018215190333, -2.736198511221961, -4.26948229523855, -3.7316246413792085, -1.7172494853787716, 0.18485254327714493, 0.8033452731832842, 0.26752436370560023, -0.3631162910227631, -0.2706677221948818, 0.32301693837706175, 0.5051247360763517, -0.20605361888240387, -1.1370163658790875, -0.9599695600727202, 0.9567573671401434, 3.6478663666646374, 5.105585256056644, 3.97005001322859, 0.8838729309200876, -1.8080886274986285, -1.910973255311765, 0.7596292392377013, 4.161338227062389, 5.703198425127844, 4.383220012870732, 1.5229949168794716, -0.5087144590417332, -0.385837253120094, 1.1658722763011413, 2.2819050338254465, 1.831275160756828, 0.43313213264603223, -0.3053436891937764, 0.49934498048133547, 2.079275181056947, 2.7888820426844494, 1.7813069516798155, -0.11714566965978006, -1.2258108821415825, -0.6939633667859748, 0.6652458820521134, 1.2471775326893428, 0.33654050092380344, -1.1558317250028671, -1.6953805268081366, -0.8321834473917414, 0.2285140959114985, -0.07932142760998218, -1.772771749802999, -2.845714773215658, -0.9722100027348952, 4.08468061463883, 9.726675982006181, 12.369395337490822, 10.353663543442295, 5.293020872071704, 0.6367783335560142, -1.1907254772232392, -0.45634541833532494, 0.7647283506052747, 0.889654282263508, 0.18555488297573336, -1.755880772869757e-05, 0.9496310763386097, 2.137047220211442, 2.203729464900516, 0.951723907976433, -0.35637168718270024, -0.4087144920262764, 0.6088340855071422, 1.1398113099174445, 0.042797856991167935, -1.9029009768653617, -2.564921223232089, -0.7025286693431936, 2.441020492722885, 4.040239981587404, 2.377716302780733, -1.3570832133853759, -4.07884687177955, -3.7171665447897793, -1.1302413499193735, 0.8996767674405615, 0.528304139898165, -1.385405625258846, -2.3810441016110286, -1.1194698087329873, 1.1843382384893553, 2.0984899027586135, 0.5924424357067198, -1.8778680814943216, -2.9276640898326285, -1.7068521574982092, 0.3683856817751584, 1.286528150449441, 0.5686139409740075, -0.47505433636002453, -0.4831620941348882, 0.35261465766172073, 0.6934150987720171, -0.09171263497653113, -0.9551940138659291, -0.4128531843666037, 1.3646902053757062, 2.209883994862208, 0.1428930400352754, -4.114802120311578, -7.2184370265111895, -6.202089114620725, -1.502692312960124, 3.190668575483415, 4.295978595621958, 1.5984955123221793, -1.8245608561559181, -2.8004713542141046, -1.0088505496492675, 1.2180562408887263, 1.6764039565441846, 0.46586328169856583, -0.6378482560747919, -0.5214569585703431, 0.10005694116803993, -0.05916367334409994, -0.9197871730717346, -0.9507097400537298, 0.8621776924147776, 3.402383139889686, 4.297466992691112, 2.482028713080849, -0.4849031319575385, -1.9935362807540398, -1.1623074100798605, 0.3525073089452755, 0.48349756815052825, -0.6574155362359431, -0.8371752523596121, 1.5194463212560763, 5.0367493512450725, 6.429707948228131, 3.975546676687305, -0.4014897687822613, -2.891599013700331, -1.6383599029840823, 1.467617737265925, 2.942206070997887, 1.3856680532983503, -1.3101271875025122, -2.3370394601790503, -1.060725896362722, 0.6122206908953888, 0.711288730741317, -0.5753276513077278, -1.4593526799395617, -0.9417614023278718, 0.032579190957285065, -0.0004614345783767902, -0.9846449178747819, -1.400474146051072, -0.38592999396121386, 0.8885004591222774, 0.6132596224383214, -1.020480318815255, -1.3695542118957351, 1.8401954176703368, 7.394159427238, 10.988221345858197, 9.235145810213496, 3.1655704086852783, -2.6217671087913113, -4.353143928180871, -2.370544439878356, -0.008073694537087806, 0.31849576015048, -0.6906011019074481, -0.8826300091951829, 0.27732508521606464, 1.0782147078642936, -0.03809312512755143, -2.2445744551260565, -3.1481503385766008, -1.658788553376475, 0.6736775741921642, 1.5245448790937528, 0.5417897163987566, -0.42158087296983093, 0.18621786329561774, 1.5925307718976212, 1.7548299987649703, 0.1460833151774163, -1.3587986040827331, -0.7783071646277255, 1.3311908266328698, 2.363627742420777, 0.9247415866815916, -1.1467788681949074, -0.7777995914975081, 2.432634580267848, 5.134447014146414, 3.636451773939452, -1.861874467727676, -7.094296354536659, -7.967949801440334, -4.5609837323854645, -0.5754867052349594, 0.8177258997114385, -0.09604908122541256, -0.8475436846980615, -0.13419872290625, 0.9572680866970891, 0.9341083921882561, 0.07085145338157423, -0.14411087017548702, 0.6711218512570254, 1.080086828758397, -0.1343961710143119, -1.9282011067591736, -1.9680912326427726, 0.2879485308922969, 2.3803089682988867, 1.4657871053365799, -2.1436836965111192, -4.966934835883479, -4.237713217023568, -1.1889547878242281, 0.30502348622794406, -1.7255338513826548, -4.983590341250434, -5.563076410347366, -2.4631243163483285, 1.3807816830987036, 2.617434648552371, 1.1822751642969695, -0.16766296289427646, 0.4369491605743473, 1.8156603742892, 1.6730458077156571, -0.12179322857840467, -1.24688446565037, 0.04169225814712033, 2.5495737125719398, 3.5257416202473073, 1.993302312447373, -0.22306569053420292, -0.9501760231086439, -0.2717450261444283, 0.06554952821380233, -0.6109231404890897, -0.9758779781045646, 0.010625323645455622, 0.859096810805387, -1.0658572836388944, -5.740104987451057, -9.220550971637232, -7.32395611020695, -0.46775248622365473, 6.116506260382314, 7.489722692264788, 3.8485540104468923, -0.2570105127788192, -1.1452872096230289, 0.48603338858998857, 1.4189207389227425, 0.2233871155972032, -1.402234888440497, -1.3927149210021834, -0.1023293913887683, 0.49687600978712065, -0.2591434921572941, -0.8825903026423639, -0.0726984377030703, 1.1833543163215354, 0.8626441353058479, -1.099649748668808, -2.320262639887205, -0.9847269138514735, 1.5224172396366522, 2.099173183719515, -0.0963892505228148, -2.330638868960282, -1.6126743987141172, 1.4199329484145067, 3.1024061801014398, 1.2650583519587715, -2.003334402598725, -2.9300005365548656, -0.7625410303807904, 1.378825217844734, 0.5936244084675507, -1.9975907379032645, -2.6120804318830646, 0.39790458424227926, 4.377775925310596, 5.491371878117133, 3.1208381031051733, 0.15860731534780234, -0.7679155170585552, -0.10304161025367461, 0.07284198892160973, -0.7792734617047611, -1.2090106165430925, -0.35158646590324766, 0.4773080218053945, -0.3763209862317827, -2.2709983017539215, -2.8473603085861856, -1.3225688842559125, 0.13613673917957816, -0.683346056654511, -2.4977672246284333, -1.4828103521769744, 3.7784913409555276, 9.506940580833797, 10.185106759651216, 4.651459195727699, -2.3929289203555824, -5.3619245978818615, -3.3935641347519834, -0.2393811503797869, 0.7344474147324896, -0.03322361394812854, -0.1519548214366147, 0.9185870912066079, 1.4193380458771725, 0.3322158791814978, -0.8168931683109133, -0.09960781862118709, 1.8204267272717027, 2.273905895754431, 0.17540737539103082, -2.3073657386472757, -2.4479191375637837, -0.46963879487312377, 0.8885745447546001, 0.14138635906008878, -1.046854161481654, -0.4529499378321987, 1.3222720652751248, 1.615631830128173, -0.2313092504105462, -1.264221596393618, 1.4577530979535112, 6.458903363546918, 8.76428378100504, 5.591899759713058, -0.1433195847966225, -3.048012948120194, -1.3278946235087299, 1.6821867112275544, 2.076843484820624, -0.007866471381116234, -1.3297713565548162, -0.16691778449850192, 1.6778214837988352, 1.7323360940896575, 0.213408540080024, -0.6561149266248463, 0.036161753951705934, 0.8449916012255634, 0.44138886783361475, -0.37040604426974566, -0.238775655768025, 0.02324252120364472, -1.8772762150450284, -5.994421656728351, -8.739697316703431, -6.660715210585833, -1.0815858015320383, 2.6964724200770074, 1.3017053380857315, -2.8540364227680226, -4.667537644191937, -2.5069696953893406, 0.2853289116609595, 0.1334375055266819, -2.217537555915751, -3.1315798615767503, -1.1556843065770313, 1.2145465110058684, 1.1714767923437457, -0.6408098032138052, -1.3463537172786229, -0.04070283285239738, 1.0359674735465745, -0.1232440027797455, -2.29744084100757, -2.6940712834166964, -0.846502857270018, 0.7979713252836602, 0.36391284590161815, -0.9334313966578515, -0.7978267155787351, 0.6462813861928973, 1.0663616964670242, -0.42274400382686667, -1.6666416190675695, -0.6455106852353855, 1.0090812274541414, -0.31160997462158313, -4.910877132820972, -8.142800116267775, -5.480565814575527, 1.6400515763240386, 6.8128822179644795, 5.680675607750455, 0.5019965903817982, -3.057166448014902, -2.4626392379649946, -0.13313522436895917, 0.746185973364409, 0.13223034598740108, -0.0507152855569442, 0.5731159464065807, 0.4634458335274696, -0.9053819865839614, -1.7447781913087366, -0.5643057891347965, 1.2272393044921306, 0.9705607812179248, -1.3839443761442294, -2.8702963984739864, -1.5140447960825019, 0.8184901605240475, 1.0251868515545033, -0.6117932509894299, -0.48045212901016193, 3.242776258506368, 7.367073188986726, 7.192966129325117, 2.471308451079791, -2.089598293036371, -2.559567657418391, -0.25365455403832693, 0.741543061948244, -0.7496921802511519, -1.8866204709096723, -0.4107920310264149, 1.8214124688637974, 1.3647379390183358, -1.8993344186331755, -4.402375937144504, -3.5254128531754247, -0.7754905879804881, 0.6342059641840126, 0.04530380138330759, -0.4677226760248661, 0.3263156178139446, 1.0946254397461461, 0.4417656228452489, -0.5844937078655874, -0.1217006154984544, 1.221852602814403, 0.8997746168214354, -1.3675818754223785, -2.016282187785759, 1.976462521941464, 8.107169735772468, 10.0800053723569, 5.054158309073982, -2.6113592929985954, -6.170664301767847, -3.978069765530154, -0.4229063953619616, 0.2249695145164118, -1.329102535512081, -1.650075956681379, 0.14887638448146384, 1.579162789703934, 0.8465335881245177, -0.5907397060811099, -0.5144907704772133, 0.6703224988256977, 0.8492337546687019, -0.20834525031134557, -0.34499980827032967, 1.4242001242400273, 2.776231280547953, 1.0533287415154755, -2.6597795062343974, -4.468443195830673, -2.7079732762408737, -0.07299395293204489, 0.24623123581207504, -1.0903992879080975, -1.017236655764897, 0.8716727822873619, 1.2869132531290275, -1.827545573009858, -5.412794301133025, -4.5671780022964095, 0.9115529275766047, 5.646872975213427, 5.0417290535394805, 0.6584406475788295, -2.2567136638356438, -1.428669484429933, 0.45120683426467884, 0.2841302994084241, -1.2736999201734913, -1.5448775762996454, -0.13129997809804936, 0.7416069718167082, -0.10971960507191901, -1.062728418699515, -0.4231978140297846, 0.8488316609085731, 0.8080942600923905, -0.09985883788179632, 0.4230370901763255, 2.531201857125011, 3.1502726344811607, 0.34849467707545023, -2.83548674720141, -1.4259956488581638, 4.746488218933901, 9.786618311980549, 8.439050381800408, 2.4083994583221173, -1.9036216822289267, -1.1685004682514415, 1.6845463866848187, 2.3083143369355383, 0.5204641677913733, -0.6779539943566092, -0.12260644077639662, 0.20472652828878607, -1.0007806379927957, -1.8258999710011046, -0.015476083978092116, 3.1448799645049466, 4.080666477876555, 1.7703412580104363, -0.8559616025525743, -0.9997669023692877, 0.41850544606842693, 0.7217407827672373, -0.3297721744857657, -0.5815363133662441, 0.5365278407839152, 0.6627781541671673, -1.6723467171830575, -3.883968178036434, -2.348451562785605, 2.1249414194146015, 4.563484561018855, 2.32350084815704, -1.0020889067184304, -0.1371176248263841, 4.692790112971579, 7.769903747659932, 5.22112775523693, -0.15501092444725964, -2.7819745635140034, -1.2368494407252795, 0.9694512192891092, 0.8388509975710187, -0.584007714527945, -0.8584620913405344, -0.008119232077802786, 0.22579799088365798, -0.24044663941955466, 0.28380025269395337, 1.9772434334054425, 2.546553438524291, 0.7387760435305357, -1.0663152538850735, 0.12520267433288582, 3.2064665635229357, 3.8615004255322023], 'positive_zeros': ['1.82279149630850601399151430257', '3.2577478116501233589641817640', '5.14112145238937495590368952026', '6.3577185519683641941623332915', '7.17739276908315843629318304569', '8.724933462221219094925525452647', '9.18381569458704404835318231700', '10.372925397689188216642373745803', '12.51422681478951470705468241237', '13.41378001889767814792232897781', '14.319518086984263197426286782980', '15.15971370829887164220947971627', '16.17234965627782545015370433367', '17.62313295500708134924906223451', '18.35852121006085916598775433857', '19.09520700818390511413693397509', '20.4085701448543151157634606891', '21.790567182564569132589753956703', '22.47290631433394861830146467245', '24.02252757086003344047955153400', '24.79623912395483725526820577165', '25.460757567190928668449275292325', '26.18477923788875946184184166729', '27.06158955932304646023313217344', '28.522396858998126102411439552522', '29.30495008285359602555520352454', '30.82525543042033307815581866692', '31.34192299549194930344632413682', '32.61681744788064225272094900516', '32.99817601502761138221083628615', '34.354612223848185644329486660382', '35.15972372421988096549540198011', '36.00664450883368313069308521471', '37.09444268307632002994454366396', '37.47813213380045679914040561819', '38.51196846811545799645673769764', '40.37643132617124885578513683720', '41.04020034864175215426232993238', '41.983174973345797660851356147041', '42.18751330890875042604925991973', '43.64187271237178507291928071516', '44.204965454293635356325300518306', '45.007289813845601135710977982306', '46.009278614496964897458524821365', '47.07832757503552609871503139252', '48.26328034458727939208556792821', '48.84574204097244327632892178637', '49.83636828471784791813177686731', '50.6991699834753290394694540662', '51.81354487728429234378268137151', '52.6499816257845758844335689', '53.31353510059117428791894010208', '54.03650204752238357363237323945', '54.770064289724983465578200587707', '55.637363346064545350046259605469', '56.96228579624604512785182114332', '57.94591723409522013811129652911', '58.876279763240506563012093430748', '59.79066744642829418363637397649', '60.55833438362057966612646630592', '60.90886498603659343336263602042', '61.75963969516867577731227532798', '63.06969755258911237263925073789', '63.97426613460701865063838870685', '64.52049587389756981835157803202', '65.15179630098732555924280568779', '66.53207226494955087911202557036', '67.35236236279159369037792207442', '68.27937125032629099652400684397', '69.239576849777027572756793730287', '69.87511420180324041655471915183', '70.92213702958858527825794673764', '71.2497909766259160509382950677', '72.26779132846487888922628303351', '72.9395878910732977809303913496', '73.61528131266571161602389129204', '75.15232360818868115453140838667', '76.25169585849394943739672879951', '76.67309596565927127722223197642', '77.43725640386748017358905207151', '78.11905391298838872134471747169', '79.27548327353062986169341331633', '80.13253554695907026106584008483', '80.57859290545448947973993839454', '81.58548572427091609455435061778', '82.31086993787775588585413904084', '83.24779126259340346692844039950', '83.845643556814406797181268757317', '84.90617956584909070650841836016', '86.31845525898353009415412482355', '86.85112676368494946077792979480', '87.53395117699303384479341091414', '88.46785432180644406996496448084', '88.82983072418560455569291338764', '89.664785457738823595122600367291', '90.592329175693362979736680861133', '91.39126801689472393679969481317', '92.66192888665998489476390557443', '92.91445778814857963312170996951', '94.2487271305339549076351208051', '95.23749738855202643004426222272', '95.50957416713284044607843249626', '96.54293189494315409899225192813', '97.18189294387228139582717440570', '98.39864882576401177854293485793', '99.19237040688673746062169093332', '99.43147272335564834242302741055', '100.31009015249252805625353948451', '100.82995972094629487537177123636', '102.20630336980507481134203847520', '103.41012036114892682814257889307', '103.981383259886719340597034113698', '104.72470539269269488182989756071', '105.6512693837313434900993190047', '106.171031543112359044348464441927', '106.891249383192559142245403107163', '107.65189751617898772169955330935', '108.55608666051314737355273963448', '109.364452355189445099309376889768', '110.173884049635723155466406143', '111.05359162435560676493733831456', '111.960819519601309683972682041', '112.57561691957250615146014827836', '113.40753304208663748023075126521', '114.71155842508586392148654735650', '115.36094002414721767638893368287', '115.66647858845393551992685000745', '116.656707357752452730187228485005', '117.111405330542504950135773166006', '118.37758499189041039563642609820', '118.60428240125108750565538818552', '119.486534212367484310419127283296', '120.820726750207079953665438036718', '121.909149779671688439703683836191', '122.48706056628806728430714826816', '122.873593032795716864942480666495', '123.81824328077668539399148176132', '124.39295542688060435290325575758', '125.33169263252377164910389650316', '126.3218708860769990417146057789', '126.90535669067706822857016440722', '127.58211041790096278777170072404', '128.40392900435634239352932458740', '128.9478862308164616457672225319', '130.30377658792288240655347658556', '131.06297040449550322271186066655', '131.87391810253921243606930363363', '132.52561009762473304223715603302', '133.48207770893634342814981316054', '134.05216006440698313807176676608', '134.83514553975602896074223560716', '135.45033117465664788998229308611', '135.63830463375073505392969153781', '137.25026358247061314024001535465', '137.914017318786099732504063300000', '139.01493484783000248384500875714', '139.39742367638406229674333164615', '140.44317882287105460611200046258', '141.142784741438667551224674170', '141.882498903785749626999631138580', '142.48165449477365397411949483104', '143.56263636830436680455284475769', '144.144392931309116193413572066853', '144.86521933425817582848671206683', '145.554652232778324948366799666275', '146.35076156269035687085018946934', '146.84460225110572382326159266721', '148.05649709518234548451918190522', '149.09305859407619889922918414199', '150.02234647126373101511054549498', '150.69347707240957672781873831415', '150.97330670413599663434143385331', '151.68866272479971960289983359361', '152.58726683399067912682816581552', '153.269442672874450008578894091544', '154.24975563709210641994100473819', '154.88509242269000140127094391400', '155.374040680642645352788776524569', '156.70741655816143963358394920829', '157.53698442200165614468139351883', '158.00253377000491759783991352443', '158.800691732271889844808011273200', '159.52255092686869469805599979128', '160.73694730698356865865895362440', '161.26486718395255416197685979526', '161.78287443103746084333233590901', '162.61158067247176604640656559905', '163.15370721119521570309004163755', '163.88682836950281023860937679751', '164.57336632494753896407322646833', '165.82421385208689145654069817151', '166.93824048874805647337299416120', '167.24630068270059153347457922156', '168.10333723777016039825396039810', '168.91484624709904380794067099020', '169.51310971703872464298718024887', '170.25257459453274766153747368971', '170.71181672687192484476512441357', '171.65506591782730126971241828175', '172.8259208959889072468713443913', '173.19145607489051028136610029299', '173.9275921216386214173076923731', '174.54056855636567075640710309267', '175.579394068270746370445112824977', '176.61014400626049624652589441638', '177.40321802328826171179253797206', '177.874456362494847274422242638004', '178.7767731356027931844055137949', '179.34884758857190499741213574119', '180.09440323431871754725477863552', '180.88940373583247176330772554635', '181.146732488572672605172635840500', '182.21538501280105580603028915512', '182.90012309983169433244703872950', '184.196875934409038933829692928291', '184.81140242910359823947031636888', '185.71339515623914848542970917123', '186.29525307696641114708315288656', '186.648162697902124670487234951981', '187.501589840607958537722838445877', '188.62341393668319822407356670581', '189.28009352650122864228220511335', '189.90825940151120055730760155776', '190.49058424878294842731884765587', '191.05813548791082390456519731655', '192.04471030666866541847233179978', '193.00556032789606726542104605452', '193.449400524987214549263642555866', '194.677429834120265741256823126123', '195.46150074433363612355507422171', '196.115988921369982963693230595160', '196.87824539417082303723283919953', '197.33381539500749126655459380677', '197.73561508157120313537620140590', '198.84669035726609615590475825972', '199.36048473682427861435935306229'], 'prelabel': '1-143-143.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.35682459156626956, 'root_number': '0.434784365536603137884978626733+0.900534594274386255011605642407*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.178412295783', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15610029692469417278299740115+0.505577413583243464630168554186*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.82279149631', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.25774781165', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.14112145239', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.128', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/128'], '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': '1-143-143.128-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': '1-143-143.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.17841229578313478, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82279149631', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.128', 'Lhash_array': ['dirichlet_L_143.128'], 'label': '1-143-143.128-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/128'}
Lfunction data - 1-143-143.128-r0-0-0