-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_111.98', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.3420201433256687, 0.9396926207859084], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.766044443118978, -0.6427876096865394], 'a5': [0.984807753012208, 0.17364817766693036], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.17364817766693036, -0.984807753012208], 'a8': [0.8660254037844386, -0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [37, [1]]], 'bad_primes': [3, 37], 'central_character': '111.98', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 111, 'conductor_radical': 111, 'conjugate': 'dirichlet_L_111.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 'a^1', 0, 'a^28', 'a^33', 0, 'a^12', 'a^24', 0, 'a^31', 'a^3', 0, 'a^8', 'a^5', 0, 'a^7', 'a^23', 0, 'a^35', 'a^21', 0, 'a^2', 'a^6', 0, 'a^14', 'a^15', 0, 'a^9', 'a^19', 0, 'a^16', 'a^29', 0, 0, 'a^18', 0, 'a^34', 'a^4', 0, 'a^27', 'a^10', 0, 'a^32', 'a^30', 0, 'a^20', 'a^13', 0, 'a^17', 'a^26', 0, 'a^25', 'a^25', 0, 'a^26', 'a^17', 0, 'a^13', 'a^20', 0, 'a^30', 'a^32', 0, 'a^10', 'a^27', 0, 'a^4', 'a^34', 0, 'a^18', 0, 0, 'a^29', 'a^16', 0, 'a^19', 'a^9', 0, 'a^15', 'a^14', 0, 'a^6', 'a^2', 0, 'a^21', 'a^35', 0, 'a^23', 'a^7', 0, 'a^5', 'a^8', 0, 'a^3', 'a^31', 0, 'a^24'], 'euler_factors': [[1, 'a^11'], [0], [1, 'a^1'], [1, 'a^28'], [1, 'a^24'], [1, 'a^31'], [1, 'a^5'], [1, 'a^7'], [1, 'a^21'], [1, 'a^15'], [1, 'a^9'], [0], [1, 'a^4'], [1, 'a^27'], [1, 'a^30'], [1, 'a^26'], [1, 'a^17'], [1, 'a^13'], [1, 'a^10'], [1, 'a^34'], [1, 'a^18'], [1, 'a^19'], [1, 'a^14'], [1, 'a^35'], [1, 'a^3'], [1, 'a^12']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-111-111.98-r0-0-0', 'leading_term': '0.935022783124484967864673286795+0.238685908160776508438267923239*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/111/98', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9650070298792609, 1.0565818038960164, 1.1375779873092664, 0.9024752606460175, 0.19669382933803034, -0.9553470666161858, -2.34335259057326, -3.605599260001517, -4.327045601307283, -4.186168627414513, -3.1006255910759064, -1.3050453391438934, 0.6914609082949854, 2.274353770180553, 2.964085159424907, 2.6255097943916508, 1.5405317430803962, 0.29061366822027457, -0.5132480172514866, -0.5293291641931166, 0.14237210675772918, 1.0179248093576896, 1.5033568151753205, 1.2446634329702915, 0.3544339024378566, -0.6314756178795791, -1.0645127536579417, -0.5920695083306577, 0.5860810403006625, 1.7958336913583501, 2.2893967118050105, 1.7447951392366297, 0.5470031608977061, -0.3640358134541471, -0.036071056873520815, 1.8665001245731885, 4.74541128045625, 7.303669782879807, 8.240767622171424, 7.009555810611065, 4.163649425997785, 1.0550219369972202, -0.95315039184737, -1.2724293846796093, -0.37370918195065134, 0.6095026816829316, 0.6867167714624852, -0.3251881038409143, -1.731336755642953, -2.516845474316949, -2.1193237801918494, -0.8459801842340204, 0.3732998085312643, 0.707862108270108, 0.0672389784773377, -0.8450045650087493, -1.1237118463527636, -0.44508718866377883, 0.595791826030118, 0.909200592447553, -0.1861025408881722, -2.2824556460336014, -4.0141964720692895, -3.9901287364444036, -1.873020949147283, 1.2280408891725123, 3.4207807030022557, 3.3256050556526904, 1.0666998424638994, -1.7958114200574762, -3.3711895753739327, -2.771625758243402, -0.6810455082969236, 1.252020741611952, 1.7032019627725874, 0.6306619515458186, -0.8240357593367057, -1.3589451030781015, -0.5865179497423143, 0.723874717569345, 1.3980903963889324, 0.9188652593482858, -0.14127077478203126, -0.6915726597313768, -0.1777339976449253, 0.8489657994012657, 1.2026112804172426, 0.19247270532772115, -1.606177065718587, -2.7019151386652824, -1.9472344420509817, 0.3566562308116425, 2.5324386531810466, 2.8312555469937934, 0.9319913279066008, -1.6552991841367102, -2.709279830941761, -1.08133069595015, 2.323898887958825, 5.21096996249451, 5.675306263724485, 3.6394583151009847, 0.7790875623724103, -0.9367141443609549, -0.804635280837464, 0.2651425726476125, 0.8086673855754944, 0.22560356074990726, -0.7549794948104664, -0.9300688418184317, 0.08374438127945655, 1.3976527636842428, 1.6896910663751141, 0.5213440104735261, -1.1709100310230665, -1.9339442499565784, -1.208868573538661, 0.09373877964154337, 0.48731078759044594, -0.5246713681149271, -1.7428886198125288, -1.2353380229092386, 1.7976913626850108, 5.978219433869484, 8.61576514360131, 7.860290687265854, 4.28435397470427, 0.4628880249344206, -1.1234002578923616, -0.036276196749586376, 1.9987505184647052, 2.8109481319014638, 1.7111773580122562, -0.10873128853715949, -0.9404531359256698, -0.26888426386110437, 0.831919337146521, 0.9151647325689156, -0.30843385364733344, -1.687788911567218, -1.8522719083869095, -0.6503091069001055, 0.6958871473484345, 0.8867912682162851, -0.0649587321841413, -0.8461172466451193, -0.31058968115604646, 1.10952616134603, 1.616936650519313, -0.153644253936339, -3.4893938192959206, -5.863984652644067, -5.080752195386979, -1.3605364813478493, 2.655271957779087, 4.109544762538996, 2.3545118815461157, -0.6385683686045609, -2.222826615739361, -1.4891551076021823, 0.12003786376579476, 0.4613459844732827, -1.1254849406860732, -3.2542472893976897, -3.9922866674664634, -2.7939554456307776, -0.8983366781550768, 0.10207434211084657, -0.08830190864628104, -0.3570298754268882, 0.3496668431591103, 1.670429314065156, 2.142970007322579, 0.8935916562074286, -1.1744626715153281, -2.121215800331552, -0.9912620396395451, 1.027704892937725, 1.6867363181991624, 0.03592354471866929, -2.3738098132227896, -2.845701523212606, -0.24430454949672425, 3.6515352174124835, 5.6218220991287895, 3.968596158125026, 0.09381400151375968, -2.846767503007631, -2.864301167399569, -0.7703089013006325, 0.9598986518950934, 0.7655414670205285, -0.6491451672643496, -1.4184272396197126, -0.6824851437892393, 0.5762060460962182, 0.8269258306985718, -0.16341531413694238, -1.0599019277472914, -0.5532873765171669, 1.036415524766879, 2.034189650121319, 1.3160231451767102, -0.31214518293875826, -0.9165121007409092, 0.370064596750056, 2.2248518142832054, 2.494244747965785, 0.697472777649317, -1.0981442912427235, -0.2185463845975216, 3.7086235424558924, 7.950425623437953, 9.006051161101055, 5.869171213919951, 0.9627877295523359, -2.1741353352541255, -2.0841293501194067, -0.30829836595171284, 0.666460292024611, 0.05462775767963844, -0.7724546454842597, -0.25344108758303113, 1.3782329575970085, 2.345613274501276, 1.4250896436205363, -0.5956400245466157, -1.7831801839730028, -1.2156403413789767, 0.08660342756758796, 0.519131442472234, -0.10213682699486541, -0.3254198882348594, 1.0289628648667872, 3.0968165737749564, 3.608517727787027, 1.4751380643137182, -1.562584571942677, -2.3312589478361585, 0.5361186632983226, 4.937698998254811, 7.158368543868214, 5.4661092546678045, 1.7383490924087173, -0.5617759032203183, 0.1109324385949577, 2.073531358658949, 2.522928586848182, 0.6120148334376204, -1.8392025508668586, -2.564514956818744, -1.3428457166496945, 0.006296988283077729, -0.09512479387185477, -1.2062879011824328, -1.618232074837573, -0.5852853796677626, 0.7299191875707655, 0.733634645643693, -0.5516198732339384, -1.4549471412838093, -0.7787395178379692, 0.5039877098454049, 0.20911813159485873, -2.3586880271296393, -5.150297737059919, -5.304342613320829, -2.3322895460778974, 1.0553656375217688, 1.6471244601171675, -0.8445196558812158, -3.4042664640868923, -2.8987151320352247, 0.5860924479575014, 3.8573104426616096, 3.9936570816512784, 1.2722413305154978, -1.4327652161488809, -1.8686042479532667, -0.5553100540669427, 0.33289474184864365, -0.27991649433298954, -1.3155911358688805, -1.2365533174025853, -0.17673322636516603, 0.21075070210764782, -1.0340022344689073, -2.7487700094491356, -2.9066341097797923, -1.1005645174533312, 0.835066421995052, 0.9580674010673642, -0.429637788148546, -1.1748310831933328, -0.10220074194489599, 1.140935539164461, -0.27893332220915545, -4.869286540585352, -9.513590477796814, -10.224883359877657, -6.190794580630007, -0.6993556171547157, 2.1346310461674314, 1.3162293803802467, -0.5903231604572389, -0.7103553708933401, 1.0503893149340384, 2.4236503570998478, 1.821598954694451, 0.20516980533971027, -0.31850054635269465, 0.7915150632438442, 1.9092696654958616, 1.402256968399906, -0.2583701966475413, -1.1132397100986293, -0.24123287598036225, 1.051578467445667, 0.9324391951475297, -0.529134635927701, -1.3885566617011353, -0.4224237567226844, 0.9878550424498462, 0.3227267948486041, -2.7511094950208306, -5.288841881157281, -3.9495990590085084, 1.152247005902908, 6.096982596455161, 6.981081896853931, 3.8020690367439633, 0.15069723307096813, -0.8120074702491624, 0.5100839640429997, 1.262505151268899, -0.15533820185142427, -2.2867369357853686, -2.648186612634723, -0.8621069436523139, 0.9643145056149517, 0.8946981866004395, -0.5759930357677818, -1.3926835402728477, -0.6360525724788206, 0.48447712404785764, 0.5223668451031704, -0.06312619669420239, 0.5192545430319546, 2.748860365869268, 4.622959432017123, 3.8091105907130935, 0.6552304660971773, -1.832586670787905, -1.3878778904214888, 0.7073821972003808, 0.978605355499402, -2.0641564668418866, -5.84551945985414, -6.391750180152645, -2.808629759494987, 1.6057817014465667, 2.9182678722952886, 0.6809602317446308, -2.0198514006257415, -2.3409849920341386, -0.6823137617754652, 0.40771578571328815, -0.35605426690572767, -1.615806496607354, -1.4757924771111202, -0.08371703272861503, 0.6977449258286712, -0.05853671177636001, -1.0138351903543732, -0.3816626752678778, 1.5248409875609814, 2.497835439713226, 1.2766379664475387, -0.6820102042715912, -0.9966230127981508, 0.43628087906368335, 1.0593609210941886, -1.0950382434845953, -4.484025725237197, -5.3923213434581845, -2.310450259465658, 1.8649575844011048, 2.7272014140345706, -0.7823734463518837, -5.165765352001147, -6.208209346107839, -3.3915386980199553, 0.07843362827012407, 1.2442760305659402, 0.41516147639632084, -0.0944432656220622, 0.6345507054019949, 1.0998140005216126, -0.20118924754722717, -2.386885204274736, -3.115520330375872, -1.5805835605997367, 0.4324570206771597, 0.8459527937336239, -0.11140156757840244, -0.4584055280679329, 0.6270275985354911, 1.5715973611015195, 0.6891087553714692, -1.0298530747701138, -0.654528894202753, 2.8732657378351636, 6.6400305032039615, 6.50562705651511, 1.8490186839223115, -3.3657930725072944, -4.739625873888202, -2.0870931705440556, 0.7866032767786137, 0.7216744235188792, -1.383723290203057, -2.2556374910784798, -0.555181318382983, 1.6267448097228026, 1.6686936593063322, -0.2633799690669821, -1.6716208123897225, -1.0672374032208667, 0.30758387065317916, 0.46974567000003364, -0.5153998084528251, -0.7667097571307393, 0.5947628525037841, 2.0529212491474356, 1.7624778620145414, 0.25410362533361613, -0.11013841515623737, 1.541716688952239, 2.9812679056241715, 1.5275012640699734, -2.17210998932554, -4.284081532176179, -2.1826170778045944, 2.160499153386048, 4.179813130760161, 1.938597075048547, -1.7029673822897906, -2.597781167172071, -0.18835322414975192, 2.130498566205598, 1.3565113259581074, -1.5900781024812676, -3.334289295109262, -2.2871209128230365, -0.22292501172699833, 0.4298710707164414, -0.3359973575816765, -0.6491962693958979, 0.22780697519624543, 0.8090567933349221, -0.29290109298509154, -2.0328445956303702, -2.0680256094504688, 0.02164199460370686, 1.9043245250853669, 1.4382105647173078, -0.46120413824034867, -1.0320251126352147, 0.46840167814628586, 1.4900895427668654, -0.4215674270349197, -3.808270866068108, -4.327378061676347, 0.10470930732193919, 6.300928573933087, 8.908082746213081, 6.149124654831737, 1.437991817335684, -0.8287744470117251, 0.01003992442124401, 1.1560442622236617, 0.5807489571969118, -0.5399675770452007, -0.01416175022683258, 1.9930709519725864, 3.10085790405531, 1.9938330994873292, 0.18290689575772565, -0.15884690139101526, 0.8111225743101139, 0.9811365812469557, -0.5400226001373736, -1.9879129575488812, -1.3728724796075433, 0.6043453414875796, 1.410850654452981, 0.36171546836769763, -0.04503697997906807, 2.556767813740099, 6.5762407010531625, 7.538542034733764, 3.349191854866367, -2.6965956073677897, -5.224669180312418, -2.6627354784229684, 1.3559775511139234, 2.5765736084865973, 0.874381777316507, -0.4768282602157974, 0.5081581392520853, 2.1765308654848656, 1.9446862911146297, -0.003084362386192024, -1.0580433061045642, 0.15118690986434954, 1.9389076503059985, 1.9705688849773808, 0.3959919881964025, -0.6200593508210084, -0.09640754165218918, 0.5254891530121316, -0.1402340805615694, -0.955535186520556, 0.31520845849902457, 3.4093502957399666, 5.03931282896113, 2.8018763845916217, -1.401372747450011, -3.2892321906141526, -1.445186988219949, 0.8300787952080403, -0.3039224135752068, -4.204121609109253, -6.34911929619322, -3.9022267089496547, 0.7990561466087286, 3.1545038060831723, 1.7565747048695788, -0.4650299340343261, -0.4138225644863825, 1.4289524339587276, 2.314847455747379, 1.2357007725289826, 0.0016298375540348292, 0.279211068029682, 1.1375443007274857, 0.6155607846298161, -1.1333881263456658, -1.844880842010976, -0.4068974203690715, 1.3552260040415072, 1.1431856383176782, -0.46840546676795664, -0.7036305743030868, 1.384529889689772, 3.1845191892430025, 1.9137700893387763, -1.2258443433520694, -2.043054267492467, 1.2605787355158196, 5.266392468451725, 5.121293498716391, 0.4365260886067185, -4.1401596445035, -4.4222776270827096, -1.3344435556867722, 0.8720560050802504, 0.06645914757241018, -1.7331768425310234, -1.7765308916131852, -0.27569159030167434, 0.515382198718745, -0.0457758763828915, -0.09448051477163197, 1.711464587832604, 3.8451930950793654, 3.81539085822619, 1.6586638670847276, -0.03150462008575031, 0.34762744826239267, 1.3568078997196316, 0.9231926095821027, -0.3452627040327094, -0.00621684218291489, 2.1234910262317324, 2.6541694427599163, -1.2723873186755252, -7.523696603912323, -10.499853542003, -7.428736789699033, -1.6796761783199292, 1.1974429230928663, -0.21403849417523116, -2.330174192062482, -1.745698793070788, 0.5875021870698057, 1.3437206721414847, -0.3170991169753226, -1.775400037380188, -0.8312348828286013, 1.2629473991023068, 1.7445389314832047, 0.22944113518120302, -0.999253420235803, -0.4472758881803857, 0.5777066222803573, 0.23994228107944982, -0.8363033770082491, -0.4817610438461911, 1.4681552810100489, 2.420936712932651, 0.6072444186614017, -2.024413549491057, -2.158467209971388, 0.09920847828216892, 0.7741769895780282, -2.8405497248166207, -8.077790484081516, -9.60844442297561, -5.853930952148531, -0.8753176630628962, 0.7035240101215413, -0.8809828939963961, -1.622172809144625, 0.5476126491947906, 3.1857910966701293, 2.983181322092725, 0.25995754373015034, -1.7337598372471823, -1.276327162395275, -0.02130804757488671, -0.05402103068398541, -0.8449359339177485, -0.49960774229356825, 0.9129265730061302, 1.2246454892185283, -0.44202597077769146, -1.9406530212017734, -0.9642776612140282, 1.4485178179512035, 2.065404978607497], 'positive_zeros': ['1.31186463455208164890533249377', '3.63927637013291257924647021823', '5.39957631924920266210104238397', '6.19793396804247133928522113172', '7.6049791568537501286454569312', '8.60830034912123152872194438424', '10.15248924170542699082358172405', '10.63471013609497503787385195864', '12.94659148030732960896613945170', '13.85284071120848546063988250945', '14.610220480864379318708902920712', '16.1364061393242948544972562810', '16.89717457282250076643807497185', '17.94130282369392822010759042752', '18.71583886691997101710447765959', '20.18874750537895133010487421613', '21.36242371576378378017549038467', '22.594650252903091366276597963', '23.56484343537019556671133154497', '24.513243624893255167960904267955', '25.58136581950353774070827857893', '26.305925988143552454820497633765', '27.22379989711012017350504901540', '28.394363193074524748283955054332', '29.48302129689141807672104718672', '30.42076999837696169647251349126', '31.9805309182297931364099377603', '32.73568425238397966923186205144', '33.50619335017836786027607306008', '34.35606886025788228739611853966', '35.406170772360324617943261081390', '36.5359388690444608534198060', '37.06419384609182061893538173548', '37.968658082709302138047614806960', '39.73955016262722530483721662328', '40.31825251286087971399156779789', '41.54115212474303787276733684014', '42.257938990883025746713824728197', '43.06240767065550835930776543469', '44.19592695656569788503865130552', '44.98216214046596033250002185713', '45.69900662545566312950101410162', '46.54549547646147417231700688610', '47.90877670148875551545344505209', '48.99140492907673929147297745323', '49.97174950897723968193638411974', '50.441173723927244912361691568888', '52.11798615749296124350804407026', '52.43945150474098085826769586785', '53.02296936139448468798608031310', '54.19604397962041509332453729601', '55.14893938334882871951159105465', '55.94203379058112148542864851258', '56.89507870351619314699953877760', '58.13247987544534112075872937143', '59.17191369606168885408828771741', '59.86334830048493559182766925985', '60.78373683870632792137841594393', '61.52117869683830457671138116425', '62.30616138460901787549924192247', '63.37352353397604267429758679974', '64.00045366130182830291319389994', '65.09672199245285854285701603669', '65.64972868119270451128314960003', '67.25784923668464473432023376603', '68.184917202969040331552993595607', '68.76615084089200490634514971942', '69.43147937089483778727761229589', '70.532811238338235476706189774224', '71.538015427256411186537644217912', '72.14480294802428184006682969666', '72.61912073173800881018910043104', '73.8933507053637826353023707278', '74.64678563077005822058267962544', '76.12689476312269851294282943585', '76.54279596933266135701621640952', '77.57169435988499355143827984868', '78.74736638021344422026588041437', '79.02443221635563304135555639047', '80.12223634814470111255438051952', '80.81863181053978874174331370248', '81.73576698875269811795941279956', '82.22573212652799614772748445406', '83.63511591014174815634378106833', '84.29037677215338177128415564983', '85.26703028402842281812041079590', '86.37620683325218869856577264365', '87.32395418648395705772841498135', '87.7288028757681932070724815435', '88.80842869758213353363146275699', '89.15521167410362818314151695568', '90.46787704319392106318207268767', '91.16171816460500804090700748841', '91.89433974157433291362278956959', '92.471785703633374151311060284625', '94.11177253690426145078298140779', '94.887558292288233906481124486329', '95.45990269096165343901172316853', '96.61357301017417030568673920396', '97.003974152744303011069493718216', '98.07595818208035382975528434618', '98.801353127946194177671400091318', '99.5838476729322181330052976681', '100.39196444097803295936204901902', '100.981196382910880115821905900847', '102.12568985251573246314144058616', '103.45645158058118984064508608792', '103.96209262823759601063021364572', '104.6653383622005961555963425734', '105.748225791126742953554444293897', '106.447687061172942734565459482806', '107.344492018285875076259453560466', '108.07316882103946561608017001251', '108.28592042422684942740337361651', '109.74947586722430040755389986055', '110.51531759417946831276015382050', '111.07301721503992766731171556034', '112.37236386022429904483134386811', '113.19299962031988571275915070275', '114.19835089133993376230373103458', '114.60102901162837577913685180780', '115.64381003969764333920294167147', '116.234907643460765352169077806198', '116.94523530027967889253602656517', '118.00257431013982725664662515535', '118.66596233246841508976505210044', '119.260775366854770237106150150073', '120.47282752340827260558316696863', '121.19764120798912644604623335324', '122.49061656482468914073142001973', '123.280097910149043720963695041300', '123.516370309994289620065753566200', '124.34432539753445288406320796182', '125.54259877950189577035456492252', '126.21589149823074014140390886556', '126.729379892935209902597531520256', '127.61612690591205423965635801851', '128.205056495848589833945257769331', '129.474136675881965506541092355008', '130.512732240748387371224594389816', '131.054973430600302541449339363250', '131.94415280810559632160224438008', '132.77424282193101536576502597177', '133.66705135459177699080764986025', '134.22354607315804256604864850684', '134.892679839426362152209191288275', '136.00572003987468617431933663943', '136.28764317672490602099557181156', '137.32380799702543037493703963481', '138.28168194557546402394982279320', '139.21841526015064180687917082613', '140.01917480982598136053982446871', '140.77635835960744769836085833630', '141.92185287925073116016580173647', '142.38488996391623530267366507111', '143.06010259398164878874225211029', '143.69704911419098375548332079863', '144.68479147681535953824972389431', '145.54557569148678926577007182973', '146.171577266078376667149381153904', '146.83302981749639722138923217627', '147.80722817173111535897620945632', '149.19844905049991319525431947209', '149.68547319015059428607445145480', '150.45056808664011300712715868775', '150.94031884658143657662428936513', '152.23647996051470851163233836450', '152.5673310619022195744243575379', '153.34842235135781562972974594610', '154.27812398987425564037880536505', '155.099547111840707354831667321777', '155.32608029102222142655797771039', '156.72849234738928378460863300206', '157.69476484089441156999583644147', '158.582599672813126428500594509895', '158.96716850049272530140401619741', '159.9995092479083631470480861701', '160.600629478144804488261680724046', '161.64217937417528346159188720440', '162.21983732363517434614304357084', '162.7732748189684681427867913477', '163.39654419205791682439790681413', '164.5793318291219256663150958121', '165.47632878484692109042672232201', '165.904951693371241324893545958793', '167.13071164391416637958541249722', '168.0391118542305863094294169729', '168.51939293896444206798177450217', '169.68841459669193403582564397302', '169.8828823426856174224749730217', '170.74233013276860833030505851031', '171.6230382629274172216992539209', '172.40627314097413802610311167172', '172.94729173505846487079723228752', '173.937171496686268572486842255412', '174.5972165449080727597906335519', '175.64941905267344004479417805050', '176.703396999976548775281741075682', '177.19849756767383459976403839470', '178.186704977503696325588770191317', '178.730169125437490151877089749385', '179.0924714765803281521184982067', '180.61119713548612245514937992496', '180.82133441834351536569046688426', '181.77423913731593611622882247965', '182.188742866646735560901486504471', '183.05345770351277556385685293151', '184.49686212318336410579973283735', '184.97355765144471183408035333164', '185.85524454725565085293281787594', '186.516033419290822237547956254383', '187.30739943281936809056399981687', '188.165088660248558097290842689913', '188.86457450650245807768986693914', '189.44145306029751842733634063103', '190.09042951279632848103150028212', '191.002902670535451012125836034763', '191.86138024680884944176988436309', '192.29485568172062917882965071076', '193.83624458036832744509301573983', '194.23288450790480905818488258396', '194.943033969311823390766421027088', '195.96573892267497202984379413239', '196.8837670560277572251469142528', '197.163157745097118903171662962596', '197.92895432505558398768862504867', '198.684190661177989395391886310949', '199.499184876916109909129942488829'], 'prelabel': '1-111-111.98-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.15911364739600722, 'root_number': '0.877644752419908184742150688037+0.479311682050206310744129113099*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.079556823698', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.941618426720564168427806478187+0.249142479202814409030843112666*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.31186463455', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.63927637013', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.39957631925', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'bad_primes': [3, 37], 'central_character': '111.98', 'conductor': 111, 'conductor_radical': 111, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/111/98'], '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': '1-111-111.98-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': '1-111-111.98-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.07955682369800361, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31186463455', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_111.98', 'Lhash_array': ['dirichlet_L_111.98'], 'label': '1-111-111.98-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/111/98'}
Lfunction data - 1-111-111.98-r0-0-0