-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.1469', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.5, -0.8660254037844386], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.1469', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.269', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^4', 0, 0, 0, 'a^1', 0, 'a^2', 0, 'a^3', 0, 'a^4', 0, 0, 0, 'a^5', 0, 'a^7', 0, 'a^5', 0, 'a^3', 0, 0, 0, 'a^0', 0, 'a^3', 0, 'a^0', 0, 'a^1', 0, 0, 0, 0, 0, 'a^2', 0, 'a^4', 0, 'a^0', 0, 0, 0, 'a^3', 0, 'a^2', 0, 'a^3', 0, 'a^8', 0, 0, 0, 'a^5', 0, 'a^5', 0, 'a^7', 0, 'a^3', 0, 0, 0, 'a^4', 0, 'a^7', 0, 'a^4', 0, 'a^3', 0, 0, 0, 'a^4', 0, 'a^4', 0, 'a^4', 0, 'a^8', 0, 0, 0, 'a^1', 0, 'a^2', 0, 'a^5', 0, 'a^4', 0, 0, 0, 'a^3', 0, 'a^5', 0], 'euler_factors': [[0], [1, 'a^4'], [0], [1, 'a^1'], [1, 'a^3'], [1, 'a^4'], [1, 'a^5'], [1, 'a^7'], [1, 'a^3'], [1, 'a^3'], [1, 'a^0'], [0], [1, 'a^4'], [1, 'a^0'], [1, 'a^3'], [1, 'a^8'], [1, 'a^5'], [1, 'a^7'], [1, 'a^4'], [1, 'a^4'], [1, 'a^3'], [1, 'a^4'], [1, 'a^8'], [1, 'a^2'], [1, 'a^3'], [1, 'a^3']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.1469-r0-0-0', 'leading_term': '0.0156822181556663397637456767401-0.212830737880653883272105819984*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/1480/1469', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.21340771999415933, 0.5948560844455134, 1.4243572574084378, 1.668457428361709, 0.8708293972835454, -0.5261979975453138, -1.3780033161634164, -0.870326521216349, 0.5109666540338157, 1.1410616904219348, -0.3114102438324066, -3.395406903168641, -5.914888002584335, -5.768799482707784, -2.9665725326638923, 0.26939579716065937, 1.6139027113474413, 0.8810893233055861, -0.004633737548033882, 0.6708332526582976, 2.3937494636194288, 3.0718566841067965, 1.6379708596212066, -0.5336873237277324, -1.2494299700305076, -0.27492005156399335, 0.2602956804554448, -1.406526001907622, -4.093455841016736, -4.702731734714485, -1.95344551795863, 1.7225232900445238, 2.7350026947536477, 0.4656475019905177, -2.081224402682131, -1.965259308943687, 0.2689557461272981, 1.6884854117800183, 0.9599695503101925, -0.13246853242313206, 0.4508721366623667, 1.9074588357474203, 1.7369956757671958, -0.41562972715663227, -1.8128657281579499, -0.2956989429756475, 2.3934542415797115, 2.5763972909410584, -0.3999024022197406, -3.015131165762972, -2.127497299115956, 0.8116551380781295, 1.7031010357117717, -0.6928343468767381, -3.2444554834374886, -2.8852580267625454, -0.6317331509577365, 0.3531227467291282, -0.5391037968440087, -0.9398365085140441, 0.2563994652396726, 0.7822885593013148, -1.4317991531243188, -4.409906241338398, -4.3455698810419205, -1.1629865727841713, 0.8752327366575855, -1.0398566158685048, -4.226459716692116, -4.2267485240604366, -1.0307432558082854, 1.171538760817472, 0.16141190567999134, -1.4219193168832325, -0.505250045859706, 1.7274825252480175, 1.9908420542869765, 0.1873310081602563, -0.6409337871105977, 0.5437338053606586, 1.0643426028682559, -0.7434378661303529, -2.0730846456160177, 0.3459271499014491, 4.5709364785115945, 5.351132875102902, 1.4994140966472416, -2.236045108324683, -1.8353386180900353, 0.6719402968873226, 0.9581700384479508, -0.9860329336895248, -1.5501615358720509, 0.24689442946232648, 1.324448815296236, -0.023294564239804184, -1.140305960995689, 0.4478862287547556, 2.632619091057872, 2.0937169822139694, -0.0027148638322268192, 0.2231269428899651, 2.5662329482192794, 2.277724061854084, -2.4805326065138447, -6.910936121582278, -6.001036462786747, -1.5265392183051532, 1.0034088446483822, 0.33197728345496536, -0.030011439225134072, 1.4540782056943258, 2.0185438234553716, 0.09232491085438918, -1.442699825892082, -0.13291256260742365, 1.5414918950445624, 0.222822982402845, -2.38607942875968, -2.1866177356169896, 0.09203443116506327, -0.4513605844654283, -4.721438245023081, -7.374929150035496, -4.769432765634918, -0.5584538569968771, 0.053435701932201256, -1.9955699266782296, -2.1412256317442933, 0.03799783955812473, 0.8554854212241731, -0.5701860742555505, -0.9813479832229415, 0.7896416267497048, 1.6138956126009736, 0.09178323393925, -0.19738564892311605, 3.1379872104126423, 6.097389557791068, 3.9046490687689968, -1.140821905495303, -2.8769432088122313, -0.6981039706245873, 0.2218506037083406, -2.0546819758869366, -3.268024707608072, -0.6421493488734374, 2.2962109703210225, 1.7594517236520817, -0.28381355863692553, -0.2763532586074604, 0.6980146006933652, -0.17494400517578462, -1.3417369487610382, 0.4658748501104286, 3.26027900850946, 1.916636211700935, -2.9975491606701166, -5.066975650799893, -1.9088405411882017, 1.1567395985307702, -0.10147728475612766, -2.355120344119608, -1.084845336801704, 1.734092396270343, 1.6413526219017807, -0.47611213308911376, -0.6324596304183486, 0.7313079274037423, -0.0665278972328273, -2.579710826218457, -2.711427771329465, -0.33313685168748075, 0.3535682400791388, -1.0791433460874615, 0.1898853257166929, 5.30661950809881, 8.153231539065285, 4.595281667500433, -0.6201746805713275, -1.2377033199773753, 1.2243076128397052, 1.4520673104082737, -0.463859050095675, -0.6007900279310073, 0.7701292967723081, 0.021407722085448527, -2.2996297897379816, -2.0623344269995645, 0.5756775749386784, 1.091792350917512, -1.0205915789829678, -1.1306939863438026, 1.6861945664860265, 2.199447504032863, -1.6066345232543755, -3.983148919482918, -0.6872183313746361, 3.6738868997677714, 3.1353604798705734, -0.2847921737543033, -1.0897042780670196, 0.3963257289038906, 0.25794657033763374, -0.96422401365193, 0.05695977051586961, 2.0853822062598293, 1.2630659493100511, -1.092872886075491, -0.3732006553205576, 2.446928455110214, 1.911318313676981, -1.8326647624763386, -2.5172366350863165, 1.342914713026281, 3.551281980301203, 0.8858490776128822, -1.5849282035339831, 0.25762156563911315, 2.6930978162805563, 1.4839040672584973, -0.7621165492551508, -0.2519916516809281, 0.9895027626829617, -0.09541809259128868, -1.209357142802774, 0.41844381324749447, 1.7493735448597398, -0.46987147957797626, -2.436593788322436, 0.6336661926809053, 5.108354954757221, 4.107697624192457, -0.900666447342285, -2.6161348246600618, -0.003182970167099664, 1.3911060582363994, 0.19762127639551896, 0.7583191837005279, 3.6606310014153705, 4.070709774976715, 0.8571526074522129, -1.2737064744718567, -0.4304187418364306, 0.04546437092977676, -0.4460586578077661, 1.8577968291132176, 6.306456237203625, 6.486658303167694, 1.1305809272577831, -2.438900088974261, -0.037448436799949164, 2.8013072288413103, 1.0119262085862255, -1.639175703288596, -0.4228602548961105, 1.8783578061880422, 1.1585783125136748, -0.2304513699536742, 1.064614686020155, 2.3917974776902464, 0.6369550808672841, -1.1061564772098167, 0.44812751866751754, 1.9007874883949882, -0.29090601551445855, -2.2700109345037998, 0.18953382379209285, 2.8340791652136152, -0.015794109953284608, -4.707024573064605, -4.077643800148259, 0.27119786251370775, 1.3466444343606727, -1.122594582120676, -1.827520180535842, -0.24774355296011633, -0.06417602074125853, -0.5973325447476995, 1.504565238147378, 4.121573717174019, 2.7191803806736368, -0.5070919356924969, -0.06301876231470882, 2.4914049799317444, 1.5840610409176652, -1.172125124068724, 0.4276428706508182, 4.949891581335692, 4.911241736514091, -0.03686290891366717, -2.6426886115616646, -0.7631499585033381, 0.3684888705090924, -1.039270286856694, -0.9790895708735623, 1.142761493613556, 1.2791462760587478, -0.4873729776928024, 0.050576222424886706, 2.0655494977234996, 0.7545158650889823, -2.3278888315159154, -0.8104237756917609, 4.280338930313572, 5.109841455549285, 0.6201808967631225, -1.9350740260550203, -0.20913644803348724, 0.12352416828151064, -2.8176172501206067, -3.75641712720625, -1.0065749988345192, 0.4290882254106267, -1.138551232144847, -1.443913823885655, 0.44683684122081146, 0.5270864498257621, -1.0860917525063587, -0.0336675075006391, 2.396121616045177, 0.3942750812546373, -4.4661209168822005, -4.1729689296855685, 1.6654682508224092, 4.645073950323441, 1.9373423466272348, -0.17269722936033974, 1.1955341887783175, 1.518009732455639, -0.6000240944549476, -0.6345048301303298, 1.9709214797032948, 2.248983113115138, -0.2892349872060854, -0.8198286673234321, 0.825873992611027, 0.22508488118540484, -1.62927209747067, 0.13870246803058173, 3.1900133644118003, 0.6097481893977155, -5.709423730252018, -6.890988421311405, -2.1099525454709402, 0.7788169112642286, -0.5642926074116794, -0.7750419397321899, 1.3574128933876168, 1.3209813240404056, -0.8771007970445637, -0.6987194734841511, 1.2341602571566086, 0.6101858978529138, -1.004726486754138, 0.8150416041379199, 3.3745846719183787, 1.3035894686920715, -2.3801586898854485, -1.4386652164521305, 1.3154158290441327, -0.800336522693651, -5.108497247550502, -4.199022444882214, 0.3207990765392964, 1.272709457068642, -0.9513746132192263, -0.7858733399952007, 1.2198331653661945, 0.935734720869806, -0.21365691771759804, 0.7575864862180556, 0.8466174151526383, -2.524162341036322, -4.249626856925116, -0.41682805238535653, 3.2686120628442312, 1.4956140807971126, -0.9011915983376626, 1.166397586251484, 2.8975107714029003, -0.6595803351554185, -4.378564400406721, -2.5526642608105847, 0.7981744666450864, 0.39871814125980126, -0.9690349457714059, 0.05329882651429992, 0.3719550016213754, -1.778450315572602, -2.1127898420563818, 0.5704407312700457, 1.2350233801063288, -0.6983925401724039, 0.631600840220814, 4.940764383065417, 4.292595313880854, -2.140496943786979, -5.392122463824839, -2.167731084841407, 0.6814775766864059, -0.1136728312630355, 0.11888611423485337, 2.4069563275787447, 1.8617461889544615, -1.356239042599245, -1.7212953106485487, 0.6190387794827736, 0.7393954289814433, -0.5579045105217486, 0.7647941691655268, 2.2180341435333717, -0.14823263323788155, -1.6827126212600665, 3.1017710829051612, 8.522151663709398, 6.488268352181376, 0.7651531584998916, -0.328410909604152, 1.7323930490026667, 1.0712274699360285, -0.6302776790539734, 0.5830100752159748, 1.7650032040053583, -0.2093773109261259, -1.3548839873286347, 1.0220773769435503, 2.2621727199249335, 0.045637161634228936, -0.8268007271679646, 0.7014677390677715, -1.2067354229370602, -6.525730140836544, -7.170345637315315, -1.9656249633723069, 0.5325760974395287, -2.227615199271421, -2.994083008006905, 0.5908096567486611, 2.30070246418656, 0.27572130770488945, -0.5493845250644791, 0.4730888995405321, -0.3607168492491075, -1.431303534828169, 1.0519026305849846, 3.570062223179866, 1.3691773251527741, -1.430891516006837, 0.13913690961835068, 1.313663091086184, -2.883755564758644, -6.639832327749769, -3.918273362136896, 0.017837177075406, -0.8983727854030851, -2.3760388209904897, 0.31406026018110156, 2.689684923462978, 0.7557466755249492, -1.2502893646704294, -0.35278235661506774, -0.15855559566996205, -1.52086968520246, -0.5591016612139006, 1.1586838139999855, -1.890166529335708, -6.717722449688915, -5.385389834276117, -0.046568076106888165, 0.6754679365234819, -2.295965301970317, -1.600245085172102, 1.4329386454647275, 0.3057402626043688, -2.9075143683272935, -2.0686029401496144, 0.6858847715519497, 0.3210802147028315, -0.7213541417975913, 0.9879162479442849, 1.9512468472493865, -0.046295153833737335, -0.43119929281923125, 1.8318087102453602, 0.8985306904514277, -3.164023437727616, -2.5735987928781587, 2.7723324514594916, 3.7284920941198685, -1.0978347258159649, -3.025990050848014, 0.18494961012973063, 1.7603887725921759, 0.14212185029693208, 0.05951025608470474, 0.8692218081682439, -1.3776585474033205, -3.726613914558599, -1.6651792925411673, 1.1187332456361223, 0.241475878466938, -0.530393029274296, 1.5871595146485198, 1.5109986627129028, -2.0731076108898487, -1.4951430485453994, 5.005897486202342, 7.883256444095508, 3.0575302827871824, -1.33367577758459, -0.5275734844395276, 0.36325981562099874, -0.8973001198616974, -0.2350446536591209, 1.7657825802642402, 0.5159433327562413, -1.87931131337777, -0.5355083242607732, 1.6683427042446932, 0.5111535475582144, 0.0978004092270114, 3.696957900057897, 4.975283854211917, 0.14090629263321716, -3.2958019106124534, -0.5536217452191153, 1.4410734558500138, -1.6651331906783775, -3.4485262162404267, -0.45134109279147006, 1.3778644235814235, -0.413614194635871, -0.7686418746543009, 1.1211363799130052, 0.9116368699985532, -0.3708766402158943, 0.80010349478101, 0.8788837422391653, -3.5988123554477376, -6.376745814415574, -2.366780260811657, 1.6492032501017686, -0.31495686238529885, -2.3238565172899603, 0.5659962463902882, 2.3732599850354, -0.7534948295423034, -2.5931706172702684, -0.0502412830292617, 1.0711073456807816, -1.1376593562735215, -1.5239628929947675, 0.23389463751693546, -0.3252030335089019, -1.6408483211983609, 0.13217958078556016, 1.370219008018928, -1.2162485697293506, -1.4060291129256821, 4.636591694481273, 8.571033516498634, 4.410588157158667, -0.5040209640659689, 0.09339535848636127, 1.0375578801194976, -1.3022924853988704, -1.7617166038860028, 1.170538965578312, 1.708929331320005, -0.7054600667828334, -0.8228176519289057, 0.4776790934978084, -1.2304377402664393, -3.1157189496255917, -1.1800376109763513, 0.13253888048514698, -2.46645514880301, -2.705895711833162, 2.171311467981033, 3.700147630222234, -1.8551923261880656, -5.524325995942865, -2.321719706553141, 0.8207583159716192, 0.002845585283057243, 0.035725594226833565, 1.810605156811599, 0.8314230721635059, -1.4681851643196178, -0.6037404401430417, 0.43328982392736554, -2.223606617345419, -3.7958990587132115, -0.6994299423710648, 1.1854348173488733, -1.0629076359159009, -0.9070479653343853, 2.9926938722039176, 2.3717120069038287, -3.6881091408399196, -5.52975248445065, -0.980768134325654, 1.6886542730991139, 0.22187721941445274, -0.02750388753408088, 0.9016086969274317, -0.46716102649199875, -1.1825640250196001, 1.6370414947381182, 2.9335081200924065, -0.00037543899149551413, -1.3447616614835547, 0.4048003860985994, -1.3035722097506397, -5.968895309253262, -4.917552618342162, 1.2586783707397822, 2.9755989163759686, -0.1314042301352934, -0.2265601040721783, 2.183662373768629, 1.1185059619321946, -1.002479627703937, 0.9386355268896004, 3.3052988952018634, 1.7470267247687625, -0.08566096891635741, 0.07794538659430231, -1.436185918846605, -3.346202840294052, 0.011955343158341923, 4.911332119388645, 2.7756784545060587, -2.8641739387137166, -2.4185043625593, 1.6800335934628445, 1.2812488031329397, -1.1508180130562355, 0.27158851551807284, 1.9003985375311316], 'positive_zeros': ['0.08661121336054289709167039628', '1.445553195537027892382377211340', '2.38681478199383243037582026125', '3.084531128333389644863581733642', '4.65575645993154591568612733840', '5.61927033474742861433503594315', '5.71091062764002344508347935505', '7.10085608996737396113032970931', '7.88961824676115342666958070376', '8.21953262699889071388104162460', '9.52959782366720566773375829024', '10.35988965493714589834121427476', '11.21439482556973011312805900516', '12.11971694694043093625825331473', '12.37732076936191093058883684409', '13.38343077647096708347628151730', '14.09571107343558561363945628339', '14.964998076515176505616279428739', '15.84714360746877992193956133204', '16.493552356580290894970153138626', '17.61489544342606196108661099284', '17.975792872497148180874326337562', '18.69478658858033488634593076876', '19.21848478895536605226692742475', '20.43081518602962842274451078572', '20.830476111384170603591804860122', '21.97636133062140367597645985100', '22.52495048608806274869069832680', '23.19431671103150534276612306199', '24.09565722264995557664354432778', '24.57282601192773234448436555875', '25.211568630792233512672606497867', '25.91079085372159932028942279266', '26.97519892055247283300764100239', '27.71914883762946426582825260032', '28.28894551700785986032556887941', '29.02576723524564445369318012514', '29.68366491949699514154696674457', '30.256204859350256275344211973647', '31.24941077460802731916906038070', '31.52110407359442963684894200290', '32.36087193713535844875094698760', '33.568455938532041982985430582554', '34.16502285473220821276576238848', '34.38672736344260809908437151020', '35.32442052822581936950387986939', '35.955914428380730438647414603857', '36.58769658773857250655468183317', '37.48319954489680361071096114190', '37.75617849932398878076671426775', '39.13630536901149641441891462529', '39.3860847873165285367244681667', '40.30688855319513088239688051796', '40.8297770681536589968221593271', '41.44174566788426861055767996427', '42.20465130529717831351817020345', '42.53283771435146826223537129730', '43.67297490787752333011211329868', '44.479909028215852719805038724028', '44.74009275328405073938266059077', '45.67901371980393615559019236187', '46.50477490161995338197723497369', '46.948550744303496268037047438546', '47.46694003271914017170160016978', '48.07732037240144439630792696489', '48.87878071814996185988083217857', '49.83794060835131427800309814239', '50.30103961644466256502553421236', '51.04671429342301729656044560063', '51.795937907786581028293677018038', '52.32258157280569721619952201354', '52.8031709871516227090684978194', '53.80207065923807915277102835584', '54.15028741515570486019900116456', '54.671106771135121576044061664247', '55.88730169348467660714841051901', '56.40799489692648214687701810046', '57.10619577912688265031441224105', '57.628876579721534870152609082687', '58.128077135738424867389654332090', '58.99112536272167776128706680260', '59.54550777784165798117443249625', '60.13857050593854215808758812230', '60.82523023426082512805502820565', '61.60367994837782216299626853861', '62.46907380383975626685335969710', '63.03593300776060566042250227578', '63.49584985583906241717850990311', '64.05445775252587052949072168962', '64.8380096579059792571571371709', '65.354628715397817464510817672', '66.09987577360025527216254164798', '66.78022015522812003603394601099', '67.57559998278452365019606558236', '68.09969490272077733972626006755', '68.92617204025854758876884375553', '69.42194274116369793172266520866', '69.98389882517176391345087310937', '70.56975358509780114639154248860', '71.20437241801026406252096996565', '71.83510387720439792894216049665', '72.75294123415345253703329446430', '73.437840834691724802093329587081', '74.16031195176049773096573554035', '74.1872094967880181885205622852', '75.39378118207021761708425092738', '76.06837881361268911312358193795', '76.27653214665927347698883231356', '76.69011436440803081206362301186', '77.875074488796767084468875244378', '78.44041405847770874087144546432', '79.15502008821099039212264410110', '79.73452515993101280654790428710', '80.520324544980696358988453953344', '80.75523906847381298287679899990', '81.63889448778159611562935418507', '82.13069237900918693746310718614', '82.78419206306688290664996676053', '83.42217518107159980560804732039', '84.06154506221752543957188274041', '84.97739339329267065353942982288', '85.49346256619434353970334163513', '86.32045344500193797123201448990', '86.53640538029843034192885648293', '87.018729664786655983663170082909', '88.058566296177920344187012901371', '88.445275587439296660391138020571', '89.21853724074191609701232525877', '89.65415922645536306550670642785', '90.62268785676974216429161555918', '91.362056979322791419861512398863', '91.67295326444852842712260092940', '92.335000048253212032101298145575', '93.02627532470898848328990712001', '93.42979350593580204859139377184', '94.13107300184139586102369960911', '94.74065789232790955811280914371', '95.66726308162076564788034649967', '96.28293060967935668523585189789', '96.58233134393964620273672313325', '97.62412447974584602733556507508', '97.932899919282223934129491976555', '98.67406828016732574822674194752', '99.15961939939466128273485152152', '99.69138197505194934936948412096', '100.3382896639657718331644997969', '101.16593632861289006492403868211', '102.101780779463295583799695488705', '102.280275357388545016180303041453', '103.0371952028812643647459046158', '103.52350981794660193855253735914', '104.33731972288121990057353411589', '104.84011975994026502064232222829', '105.34492268651329087501936493012', '105.92543018713931513182141549333', '106.59411664387101497518723235534', '107.65774990159496610428948607808', '108.03023013169095363332254944358', '108.55907972955377469138033173948', '109.24354767766154302550946763642', '109.792650364243501169326768441522', '110.40239663796403004833072635555', '110.85515779473355454694244239293', '111.65673171005936017034106542266', '112.3208377886692201674282963914', '112.75401560085812594807736297412', '113.72345930861593815133039472001', '114.23991484445530092940695613034', '114.80220987238800883566441860043', '115.51634519972574368991144161933', '115.76494641820014443327142014026', '116.35376666015659786811032858496', '117.21237473823012158463338443638', '117.95277982179507858292350429667', '118.32167206867234548539219782498', '119.02192466458101137295227019643', '119.89760357200958823830082105997', '120.37778226979675280908394263554', '120.92638115102986204724124462848', '121.32232053347932369215368695089', '122.12306673742824192550789149760', '122.69132263011038243535082642505', '123.06830059367075494490516442309', '123.96481928640876037670186533926', '124.87050529577168480970130633799', '125.28386404441495069805133395287', '125.604033641187082357023772135673', '126.42708806363945780167524929094', '127.09868911703947707003980747868', '127.64489515849357968225509424313', '128.01657036110879163457538980330', '128.73632948080527907434965728185', '129.21876509028790235588129489383', '130.37982022424340236519802258434', '130.67883707921817741647384361712', '131.40444657793176186167369060546', '131.78711953259334028616089195543', '132.474917129892128547872751150046', '133.016664079042717764642483777011', '133.75577617192828060643521383867', '134.22543823648987446169117018970', '134.59002681602968209051866075988', '135.76983992334919269281068566275', '136.033093038868998926308371504966', '136.82800385766004333062803204450', '137.54095597581259755861852028849', '137.9712704413183867857331029313', '138.37176223687589818403939526610', '138.96971800944450667073669869501', '139.80139749700594189064343979918', '140.29701622184937885018663591644', '140.763676751647799810120092504187', '141.87173443320942562496898193351', '142.05792647836024094902008407078', '142.7865802170238013271704149881', '143.51760577578600466502152701321', '144.17050487873227858574929533815', '144.31976176785082234702987413750', '145.07185125698541893508217762143', '145.498242401907749281687870865835', '146.56612446308037617886257699857', '146.94994624251072465771969293675', '147.64618665030135203852987862237', '148.15241193538014046547351857636', '148.96119646615414721306305648381', '149.43395465796345652551985706404', '149.863336661003488912651843111182', '150.61823163738511754448803189276', '151.00635621482216918279954315307', '151.63385351323052316371936156849', '152.34160842558251247094263065958', '153.058401948967343874283738224972', '153.733913306882534462106813651569', '154.407419081152952787484277506406', '154.67098497146302277606887262629', '155.17374343798353635187258304723', '156.08598340471664924877514260591', '156.60305687647885231963639374320', '156.97967609653612234208572965541', '157.63811462268020000489045484548', '158.211397891434631933859352403162', '159.234273575985460459787500707594', '159.77863758359432210502735132431', '160.10815463079217208351813091595', '160.6579268258003395625170839486', '161.30439110634970230071243494999', '161.9319643069820007463498427859', '162.59179847255228175671445318204', '162.795297445032501927604706646663', '163.7575503499600405738522886738', '164.41966405934450399628211664969', '164.86801875136994319393061024899', '165.665199249017444145128295731876', '166.188950066532102544579601627999', '166.6922678940165130756186780764', '167.361953539242087728356311823168', '167.66747959954542154810165661934', '168.21129321388776922207937052234', '169.19940012710869011798018377225', '169.660026583313949760848848128582', '170.26693713093995033092075897155', '170.87790915981918961946813107257', '171.56780896063446251029742648088', '172.04334353731960558670145514862', '172.75772968246108116344740409212', '173.06552770399088191359392353027', '173.73440422815532037979425732449', '174.254179800026534199872360866783', '174.784570160659282072368671441393', '175.88034058678398274585720018198', '176.23630246146533971986692093547', '176.72614970308018984962535502646', '177.38163859940364826958364473893', '178.02999258165535987055110927906', '178.591234449276080329092521666559', '178.9102673952075857070743516130', '179.84599685834584511363168912982', '180.03277235138968998048189888304', '180.811712483818701055726424362736', '181.47552578050925348785199741084', '182.36620425584355535694131320110', '182.81317455750870178120998195622', '183.11771972324273406104594024381', '183.84474745342599709464861346744', '184.47016058430181901387670601363', '184.77602619453862920825931416142', '185.68518156658438712375475873113', '186.125595971855663883081560180571', '186.64291679186379313753038764048', '187.31889760008575135192185910460', '188.19063537380976566487535937048', '188.797092294891526178158079452745', '189.07039466149777196299441361669', '189.615885975441577356334786943005', '190.16003087446310620477516931154', '190.93746446019329522456370586023', '191.48014519086126118744512258694', '191.760170640293656149794067115739', '192.744851460680121697909518468838', '193.42235765585829867180769207074', '193.7795504378305937264733320747', '194.497981004648135703584109121579', '194.9078441714210032500814083421', '195.89786424005263989780003408349', '196.13955129460169204843521896805', '196.31767396516663321067655926886', '197.18685447818132431659680420497', '197.95210091960942580330574890596', '198.6069652001947945271216579147', '199.196332230288596952816602194836', '199.65675990907061012751572428906'], 'prelabel': '1-1480-1480.1469-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.9531759332480523, 'root_number': '-0.989199975867338936801612104018+0.146572192942781834624957490229*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.476587966624', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.694400798013584162773546553537-0.164949452232119643561825715449*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0866112133605', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.44555319554', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.38681478199', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.1469', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/1469'], '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': '1-1480-1480.1469-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': '1-1480-1480.1469-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.47658796662402614, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0866112133605', 'prec': 50}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.1469', 'Lhash_array': ['dirichlet_L_1480.1469'], 'label': '1-1480-1480.1469-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/1469'}