-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_417.59', 'a10': [0.06824241336467098, 0.9976687691905392], 'a2': [-0.5766803221148672, -0.816969893010442], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.33487961217098616, 0.9422609221188205], 'a5': [-0.8544194045464886, -0.5195839500354336], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7757112907044198, -0.6310879443260528], 'a8': [0.9629172873477992, -0.2697967711570243], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.9365398586159983, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [139, [1]]], 'bad_primes': [3, 139], 'central_character': '417.59', 'coeff_info': ['x^46 - 1', '0.990685946036331 + 0.136166649096247*I', '\\\\zeta_{46}'], 'conductor': 417, 'conductor_radical': 417, 'conjugate': 'dirichlet_L_417.311', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^30', 0, 'a^14', 'a^27', 0, 'a^28', 'a^44', 0, 'a^11', 'a^3', 0, 'a^34', 'a^12', 0, 'a^28', 'a^36', 0, 'a^13', 'a^41', 0, 'a^33', 'a^28', 0, 'a^8', 'a^18', 0, 'a^42', 'a^37', 0, 'a^24', 'a^12', 0, 'a^20', 'a^9', 0, 'a^8', 'a^43', 0, 'a^25', 'a^17', 0, 'a^23', 'a^17', 0, 'a^12', 'a^19', 0, 'a^10', 'a^38', 0, 'a^2', 'a^30', 0, 'a^30', 'a^26', 0, 'a^21', 'a^32', 0, 'a^29', 'a^8', 0, 'a^42', 'a^15', 0, 'a^20', 'a^4', 0, 'a^39', 'a^27', 0, 'a^21', 'a^38', 0, 'a^27', 'a^31', 0, 'a^6', 'a^9', 0, 'a^1', 'a^3', 0, 'a^17', 'a^7', 0, 'a^1', 'a^15', 0, 'a^16', 'a^42', 0, 'a^3', 'a^40', 0, 'a^23', 'a^40', 0, 'a^22'], 'euler_factors': [[1, 'a^30'], [0], [1, 'a^27'], [1, 'a^28'], [1, 'a^3'], [1, 'a^34'], [1, 'a^36'], [1, 'a^13'], [1, 'a^28'], [1, 'a^37'], [1, 'a^24'], [1, 'a^8'], [1, 'a^17'], [1, 'a^23'], [1, 'a^19'], [1, 'a^30'], [1, 'a^32'], [1, 'a^29'], [1, 'a^20'], [1, 'a^27'], [1, 'a^21'], [1, 'a^6'], [1, 'a^3'], [1, 'a^15'], [1, 'a^23'], [1, 'a^20']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-417-417.59-r0-0-0', 'leading_term': '-0.0866734715856032644154874855013-0.229105822236245644563075243277*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/417/59', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.24495258410403928, 0.17868470334090236, 0.6116748955071155, 0.8092976411464363, 0.4595859342046922, -0.4665679846459955, -1.5915635498193703, -2.292988601423789, -2.0928675324502444, -1.039345237775855, 0.22069102855046807, 0.8209945249796349, 0.32165430035257747, -0.8360665337253793, -1.4866843094379527, -0.529585456740454, 2.1485172457735877, 5.339287957282802, 7.154417507564395, 6.304963846739403, 3.1032776882503526, -0.6356556972672562, -2.8246260212817895, -2.580847102714787, -0.7932656321835411, 0.6925341054233712, 0.6110177395189761, -0.7529469753091496, -1.975244484854506, -1.8856272766542417, -0.6559580435719281, 0.42390571913524366, 0.25390302267635656, -0.9642247794061194, -1.922111238843436, -1.537013251250798, -0.08452168982403878, 1.0589219791497775, 0.8590244685448092, -0.22970766229194295, -0.6937228240438755, 0.3532827719961418, 1.9652855529303166, 2.064797794692711, -0.4258915202509014, -4.121182300867397, -6.046266931989361, -4.267608034084315, 0.18488700542074732, 4.072737888134581, 4.794555621785343, 2.6267929964005488, 0.2010482752289838, -0.20286324596642336, 1.205201856417792, 2.260429946761233, 1.342398035403162, -0.8824509992507974, -2.282519612895966, -1.629924986116026, 0.14045172365576344, 1.1093454985494988, 0.5408628674356648, -0.47869421397943424, -0.5983958145181327, -0.003415429364918435, -0.20414233353190553, -1.9954438876500245, -4.0923850241298325, -4.305776242239786, -2.0961696553277838, 0.5226302388636429, 1.0667083524982495, -0.5234871481147465, -1.5776258097684386, 0.3758371108065809, 4.5836868879359365, 7.473830350985189, 6.308808578057979, 2.165858369067826, -1.096319095646124, -0.8176885721377649, 1.8818036533936717, 3.6524657943187195, 2.6674179312425443, 0.3081321913049234, -0.876946291381185, -0.23203762945735834, 0.5868320447825366, 0.053351761303843476, -1.2043371657495472, -1.3523169818830076, 0.07830551482343197, 1.440185321636171, 1.085316308103501, -0.4081785721442597, -0.9108027071379242, 0.4185060366490208, 1.8322751529886538, 1.1340830860596716, -1.3296254609396505, -2.8047546710350586, -1.5695127006476235, 0.5438907908303556, 0.025022018754050197, -3.9294674855513074, -7.842243746386885, -7.467361771086383, -2.5463755710406013, 2.7457016558152882, 4.241372632402442, 1.9615613427212502, -0.632920661893995, -0.9835833195026268, 0.04773937165324801, 0.17875457679459222, -0.8834554138616659, -1.1854168016164197, 0.49852971803864143, 2.704498488983053, 3.0620752036800245, 1.3927797023853545, -0.10351570599682398, 0.1790617300684917, 1.2000622908064122, 0.9459724754511221, -0.5595183968301296, -1.2541108262085212, -0.225994170403708, 0.424229987575639, -1.8760317532407487, -6.213901217003176, -8.321753645709984, -5.370555159142128, 0.3022294093207865, 3.470892356169267, 1.8704368242204843, -1.4552163318956834, -2.1223110448932427, 0.35051014200894526, 2.4789947183148913, 1.6112377100132198, -0.8084584467389742, -1.5083205559764115, 0.20740957167781787, 1.8295931798529383, 1.285895895827057, -0.3680422470544938, -0.7590605012065094, 0.3492212758827349, 0.9261760329839172, -0.1273194238473114, -1.2613070776279824, -0.6148484221345458, 1.0505493245589563, 1.3155164515268583, -0.2149720705935148, -0.9632055729012549, 0.9959229483843459, 3.6426398875534463, 3.107760909738594, -1.0910297163538845, -4.753687780244595, -3.923118550554097, 0.10907377274912614, 2.3783777406800635, 0.5361008201855837, -2.3098534116357943, -1.8444103693355718, 1.8234455227291229, 4.493699850132516, 3.4020653979575255, 0.438400433278782, -0.8605163885203877, 0.06937769367158728, 0.8526522173233154, 0.13506110993880205, -0.6032752292819564, 0.22845471341719745, 1.5669635379480704, 1.2626434381360214, -0.40371404111306747, -0.791199806351292, 1.2282313340111348, 3.306728139437441, 2.7568122633329306, 0.39503930887519356, -0.6760566001721225, 0.20957400591532765, 0.106636202270588, -2.9396311726017625, -5.970987877256465, -4.129658809946084, 2.7224430000161126, 8.780930621143948, 8.728328968975468, 3.7606364925571345, -0.45645657080223145, -0.8712035161421754, 0.1906972519015064, -0.525702789756917, -2.4693297627387034, -2.7227362138698905, -0.7551295553343536, 0.7956584789250871, 0.17738852977218525, -0.9619364321561591, -0.33798389252302224, 1.3424273282807686, 1.514428848997762, -0.15949861294610768, -1.155852237082189, 0.031302488667287236, 1.5331878820578544, 1.0841796271755273, -0.22857625304169282, 0.42403205219555223, 2.6990201606180113, 2.613246612555606, -1.8234403240330186, -6.720625962034957, -6.498439305077897, -1.1684154408878582, 3.291505193562278, 2.352809206926413, -1.7022184378429503, -3.432877943911074, -1.4321221832786608, 0.7812079600467017, 0.538425493584598, -0.40101947375146, 0.7213243875568205, 3.0262589919624836, 3.2655782299776837, 0.791210721460282, -1.4613727320026377, -1.27894087398979, -0.026002464662734093, 0.07385287395347244, -0.4705511094204412, 0.2502165709262675, 1.6983844904726115, 1.2231362205779541, -1.4627859486336028, -2.915434124870738, -0.7065825625288799, 2.5002160125530564, 2.236269776849255, -1.295343913413175, -3.1691983996360276, -0.7489053798717089, 2.2603928846247747, 0.920597387082362, -3.7575053709310984, -5.923479165527317, -2.8143529921124553, 1.7141606808074032, 2.7461311818042726, 0.6671943466880893, -0.4375495922379258, 0.902501348380702, 2.0587518223470056, 1.0461824801149717, -0.4617136572753344, -0.27060619081132126, 0.6351877108046478, -0.06619456728943887, -1.8672288128134675, -2.005480242579179, -0.012625201729110122, 1.26853586732715, 0.17104759545114917, -0.9583368395269392, 0.5248199536051841, 2.9823033883999073, 2.706106625745116, -0.006594177476551563, -0.6178145175384304, 2.821579551402628, 5.9122809655301145, 3.6270332501131994, -2.242480181335959, -4.941547319041665, -1.6997028502902074, 2.8190368406426365, 3.1832780940680805, 0.14853532541394068, -1.5881716021294543, -0.45734938463629415, 0.7152414185728196, 0.001354430403855334, -0.8348656968574877, -0.04512581273343626, 0.694002667675964, -0.9443309334029033, -3.6522857638740795, -4.019939936619178, -1.663459459804278, 0.2892579806329006, 0.1073152823584097, -0.2786873055494958, 0.7466548232284735, 1.2078194812341592, -1.0262905090010939, -3.543412278193495, -2.0005398701126773, 2.835107864842205, 4.740207784293166, 0.3128127323241895, -5.731496264829399, -6.4568993536236405, -1.7710064631877493, 2.133187927287489, 1.6301324083926054, -0.2762122310494573, 0.22417987349343185, 1.8148942370426036, 0.8845690925532453, -2.19496334381242, -3.522817184151317, -1.7328220277287425, 0.20825584039789358, -0.053935681788354686, -0.926651164704771, -0.2530236039213337, 0.7858049294866679, -0.07368713786662942, -1.856190014174163, -1.6967178147041406, 0.17210149720273082, 0.47602661124825435, -1.5463358900735515, -2.397242141818567, -0.06791320460106563, 1.7639164435534034, -1.2385696676926994, -6.798395616133168, -8.185355184726397, -3.529481090685918, 1.4507980584022413, 1.583707945034148, -0.828037703163023, -0.36246047045415264, 3.0330438870836165, 4.356892039180744, 1.5202479994881286, -1.6685788729345552, -1.5671094535294054, 0.238044603708239, 0.3540617614165835, -0.9236853690460445, -0.9041311171815665, 0.47614346202722707, 0.7777610242640378, -0.25326635103150824, -0.041187868340562775, 2.0135863077561145, 2.7741508891058397, 0.3450391170557124, -2.3175024672424853, -1.7090241455829327, 0.6449039778433507, 0.7258252391439044, -1.168845546294922, -0.8400828363025101, 2.1865592503735365, 2.4028639563309238, -3.650156579788913, -10.91917035941585, -11.63286235851007, -5.586723647214537, 0.010890134858200114, 0.5069139188715335, -1.2224191375369446, -0.9199554770948629, 0.5869375501451167, 0.18541496893370038, -1.5638881821812156, -1.5604634638657342, 0.21117394358085162, 0.5978331884580983, -1.2092880636713195, -2.2064980550907576, -0.6916125718278143, 0.9000497237996954, 0.3086623873039113, -0.6617461618215965, 0.44884595513458214, 2.0231910852239756, 0.9464548856247395, -1.6007429781610718, -1.581463424461328, 0.7600875236314146, 0.26899920012962386, -4.807074026287904, -8.530087988217666, -5.025591757744753, 2.6685209637489127, 6.312554779548119, 3.528183461395698, -0.07303092449909376, 0.04851833693882115, 1.5590529244862683, 0.6408454162607948, -1.471909010562024, -1.2774469022725135, 0.6251666863698376, 0.6470685983175872, -1.5169430130598633, -2.3998953362392053, -0.6933014872132632, 0.705894155846612, -0.2047268802386623, -1.3503518758785402, -0.6216770649752625, 0.4295185563484485, -0.006916275294736839, 0.13063483515898708, 3.358574337830966, 6.99664416636658, 5.961406251901334, 0.9177368364075937, -1.6229117433534623, 1.2983829612347348, 4.61792026526129, 3.1597798549249, -0.3411086096425608, 0.15998101230195122, 4.1868876589995185, 5.390220233020635, 1.461371339743793, -2.505858854887238, -2.0252801207242603, 0.5765658566846039, 0.9336469044108491, -0.4876714771029549, -0.4081323665150982, 1.0896807143562497, 1.1450210921404436, -0.3454934659247514, -0.5432897712025315, 1.0051788862083981, 1.4522713573216508, 0.020076409980290075, -0.14576969317429642, 2.4901901073869057, 4.544613080835595, 3.016451131951714, 0.3782511311751532, 0.23033834333450745, 0.6161516082392121, -2.9063826509458575, -8.701344339438464, -9.790548866633316, -4.19776634882782, 1.3216327996072377, 0.8297115104081865, -2.4622344399268585, -1.8601942371951887, 2.455930647518131, 4.456324977253978, 1.9554609247101058, -0.8198419749751565, -0.6546847281357474, 0.35550273818435063, -0.20946737465994894, -0.7520537287851421, 0.5988686319365532, 1.797479468090681, 0.34855938454670254, -1.8002687858266913, -1.1424262513166559, 1.4238826536743059, 2.078888925932515, 0.5171363766086368, -0.008467967789698659, 1.0454040682546892, 0.5830449570544807, -1.584262320915797, -0.8991323296992165, 4.122957876755616, 7.2424606628301635, 2.6382971807264712, -5.681842301655815, -8.580988791972123, -4.296116224022479, 0.09197808516063852, -0.2930685173276005, -2.18171720097926, -1.3115278690728853, 0.5512483379946492, -0.13411568659703518, -1.8736371054931953, -0.8404410225338731, 2.1985619254404734, 3.069181349914981, 1.1424333636536055, -0.12692363696660044, 0.5596703225319859, 0.6985592541005458, -0.6532485555434453, -0.8955827300530937, 0.9421152132109719, 1.7788790741240907, -0.00952280946136604, -1.033214378149644, 1.365919033552366, 3.689168912844539, 1.6646090820243304, -1.813531677498315, -0.41440578166523073, 5.116657967330449, 7.090506754797951, 2.442924328619771, -2.5458279165448126, -1.9489193979167596, 1.3478238326311582, 1.4366213866633737, -1.0623827609162433, -1.212289027223464, 1.2833977365191838, 1.9168250108599072, -0.5841313831242672, -2.3128963700891996, -1.04811933838414, 0.5249967373891447, 0.1771158050954052, -0.32190900356074276, 0.46404531477756455, 0.343070494604695, -2.107367458683203, -3.829182932667197, -2.085084660249813, 0.32967379843176603, -0.5283483785465249, -2.7851319518753916, -1.8036208983576985, 1.4680667008337946, 1.7526093090607882, -1.093167514275904, -1.0087321232471926, 3.9222092823711945, 6.956216830739684, 2.685549392243044, -4.073088835150787, -5.087146322763732, -0.5086274927865327, 2.616170172493056, 1.3834312406698652, -0.36699197371790065, -0.008562062349819237, 0.25176993086303356, -0.9264589144433679, -0.8930910617115744, 1.7014254836784681, 3.578105070317794, 2.151234949766389, -0.04370768653790348, 0.06673378761616269, 0.8600662588300522, -0.3789355570628061, -1.9547797707998766, -0.9109698599412621, 0.9089430810121482, -0.2606741384256729, -2.8480572666710486, -2.125707578987768, 0.7687726795589096, -0.7055636339492103, -7.45993750682178, -11.464658001946377, -7.173786457996968, -0.03208613971670971, 1.6846514266622128, -1.3932210728071968, -2.5775888806096283, -0.2959604747649284, 0.9758882414717246, -0.38778021082610425, -0.8292343232724382, 1.152745739950425, 2.1809711205685227, 0.42327602856230984, -0.9954049188612429, 0.208833369873465, 1.3683941557285872, -0.0669405891530369, -1.8429984155583952, -1.1891344208116552, 0.17170599317424443, -0.3126218937550427, -0.9796895444372384, 0.27336607739136465, 0.3756038384566882, -4.398983721314828, -10.324546364108144, -9.916398361896952, -3.418261530049973, 0.9028155953664347, -0.7951686709175482, -2.749846396706757, 0.08407469725699417, 3.7777772682999844, 2.6956877863779187, -0.8133897208853317, -0.7307159123955246, 2.444712676515967, 3.1128868761707618, 0.23609332014374534, -1.6257985365262297, -0.5261610540418477, 0.4285937424280466, -0.42151064248327275, -0.6674003611210565, 0.6845942293353744, 0.9386028565814403, -0.7840730424160202, -1.1896450909327785, 1.1552974902501487, 2.597994619816452, 0.736578262532338, -1.019816073872649, 0.3578820312891761, 1.5480399748933475, -1.2386652388509032, -4.523508365105556, -2.7723626563097503, 1.412260474130084, 0.46265877704265745, -5.612334676507149, -8.398667957767522, -4.061251499525526, 1.0426303202971134, 0.8596387051818064, -1.664611545614051, -1.146838406661331, 1.1594824951909823, 0.8956261084818264, -1.260870225404033, -1.4920571816320432, 0.022851798738626874], 'positive_zeros': ['0.182259467548113459064845996012', '1.42392182003894063025194018760', '3.06365207887040871781046236696', '3.84359429500773541476628387278', '4.76500770733229539946737615575', '6.50403004587815370063711035453', '7.63700959398804963656791162345', '8.28403725679356446574146157347', '9.5330275216370024745850562806', '10.08025700914217393279420560966', '11.26709898568614271545749313348', '12.122134944165621847893769770154', '12.74110481476646750151918115498', '13.71128001837321488564734203193', '14.98790042269610509525446462643', '16.29300701256154747420417072486', '16.62827225690313936862102861923', '17.69204383902831418115629657475', '18.72401707368279758297638836375', '19.52617004015489419680445683977', '20.31479915778149127868933610757', '20.545253034523400755037461737', '22.11082645988445682257117655161', '22.726961393463407146414552822621', '23.402767078808147081594052475225', '24.86095636328655606008934243039', '25.42038835247287067643946598362', '26.61059125858969215654592113871', '27.2534474460825558908749632676', '27.82637309601227173268264464354', '28.73619830941296445893431652339', '29.600640574277247879269331343398', '30.238872432864567626261080257745', '31.090812068479933869467401193806', '32.08743178156658381175311139048', '32.50310553543206946528825349729', '33.884886392660273529988584508458', '34.901488929368960935711532461042', '35.60857389179457430556212243498', '36.00601085280166097901459113526', '36.80701313445349284914771232718', '38.084311777143654661015093720938', '38.37688492617875560987708467472', '39.26448264413320694697079205667', '40.05286117130096757840931445696', '40.423085002579126170337126649506', '41.85720637296775085598846757557', '42.66561289651670151055457959812', '43.40115730969666611525879227212', '44.26476936298865968884166657801', '44.97058337270099820411945806790', '45.86020631686164125970306477711', '46.4771545990504339293929740826', '47.16097388996981694113553389233', '47.92602628268871793181172663762', '48.71105445636858763918885752617', '49.26016512941374447732280244124', '50.24226227220369952727321614851', '51.24147758728754999530235889707', '51.9263669719945936395423255424', '52.67133686150519830756641365372', '53.80757112789617101424527022868', '54.358499478136873412580471827138', '55.03772166061393828314650753301', '55.57469007923485549496750314384', '56.48518306370358919560975105066', '57.031516150724988313015399525761', '58.18646051660803838312699876183', '58.68976048393691276350460042061', '59.081742019665868706132404757412', '60.20137246580869851506123191115', '61.5095355326359111462044758381', '62.105894781408364299000348828189', '62.38698153370205438428649566493', '63.548379012044044317935124419448', '64.102196844444068926632503134804', '64.75093290998639257269640927384', '65.59818336175713855369493172528', '66.24473037762059042132459915123', '67.111024889105652488978731725998', '67.41980148691207305193441482860', '68.33383820305057838062756572897', '69.43665974894073838263078817590', '70.18179083475297635920334019181', '71.10579506697425330777673434476', '71.70030158800371297170117038456', '72.066665379310432880936552536555', '73.21082232116619955443359837884', '74.07202108262700749889890765340', '74.41319370318181100392275444842', '74.942837629356767472815812462248', '75.78066797733998474714978491891', '76.62349986223016100795366085328', '77.39371002449577924770591109334', '78.187242244471925927267514327634', '78.81886179341829324356980132347', '79.86657569069964799369685886680', '80.73189987201394104468598012116', '81.086209500073955067003100707481', '82.06450691639556135696837329815', '82.57977816177454501561953575564', '83.112287641847592648859163900452', '84.06429305549990260416522730966', '84.71824831156909482988521163403', '85.24589931354060593649851917766', '86.24916658665281462097789439385', '86.647484060759024831116308788731', '87.69327795575321594046290907381', '88.5409351774854146256043037184', '89.39014434008426912829393985975', '90.08415982489898823662465612214', '90.62533624159954313339675824542', '91.26098313214863501150767879705', '91.75167511043061702272177105022', '93.04597876591911334917779008696', '93.48072857805647709534123026584', '93.87560130026367793343578350273', '94.580234877017579027239065397733', '95.44790909999032084684313445608', '96.26479352232657520678256561833', '97.29600392432691340072066945607', '98.05768404851782369566082420255', '98.393369242480802851460213302356', '99.15906395875559242451605132952', '100.25507420261329925649886329491', '100.60905959415220287776932818831', '101.30862231349282689327917640452', '101.86208832262041920529259317891', '102.7809742290334982104773974300', '103.21993885786988968054330325655', '104.06945744353710111511410265339', '104.607753932553850601614834618895', '105.819727261093894719467525389029', '106.44319248710899851497897436618', '106.91584846337438254561957414557', '107.93661087318914270545387906370', '108.69966141210880522061664967757', '109.15441401220030576492184841054', '109.89271981309895468603383386824', '110.546269713116790110052087148996', '110.94635417378282971143060278002', '111.9072240196693949802062319404', '112.71511899995943122513476748009', '113.2477972770674629378237056848', '113.847773180963610265909254593859', '114.53312890144363029012858670369', '115.93642147911608869840151368574', '116.33875054094339893279778207560', '117.04796474645019810259654870803', '117.53506115837167442887672310636', '118.39845524418676960747735815103', '118.877969464304946817894735462571', '119.79027884237157717524426239798', '120.38260182743653572676230417995', '120.86139205282283381857824030546', '121.67257311835870907638651545021', '122.394240496684408761855427919725', '122.83713283082804334900627191476', '123.95170278727196366425130151619', '124.988563829736901912490577200303', '125.303144788224542917737591889343', '126.02446001706161465548477865846', '126.765463331722283682114281333455', '127.29565205997284577545327318150', '128.23142985878390293486381577532', '128.7091388274943695009450748682', '129.51910829569491306764237741825', '129.99721753788679021734153605660', '130.28404942582827057397035843216', '131.624820188387928422004022672811', '132.09052005049793818158674451475', '133.08241319605205655076211360643', '133.420789076195425653733534785047', '134.46640830915096769833433852913', '135.23206406686232643512615964333', '135.82495067541449088738951301469', '136.34007666364361994836050359844', '137.1130254081731388005964314066', '137.62552771202231497792672985386', '138.44191300210302806058385372676', '138.77872975669686182539730011608', '140.11028526801728834135037961675', '140.2152722482577706583545290697', '140.72651372785591159734104951803', '142.082289539819585684285739243967', '142.575642875757463972437917230685', '143.26878074275269793818394849886', '144.24947572389307837940603978780', '144.8501636728665468634087940498', '145.24998755017428932864385031929', '145.83521085856517779664608691533', '146.60543351276367193469482215290', '147.32642422850832830814969989362', '148.26319471561249088891702327778', '148.44163030410168076298042916116', '149.14988132276162671994692589136', '149.759898078873211665603069519157', '150.72222966184844649156920391020', '151.86192464741625169257580449722', '152.14174560660952474880328432266', '153.002820567159332200312951284269', '153.41510297402795599728387792514', '154.15155583344564685531669971530', '155.22211791036474689483725262932', '155.43255914301393864362886210830', '156.11199807444570280435043958324', '156.73434583212604845169126363180', '157.49865788548361801595883503876', '157.98968280327671698045258294605', '158.87870704173618292050264864584', '159.402741327594783931650592267021', '160.437555875227439551219166534620', '161.11071848832953520967743838288', '161.740007544606660140093659789555', '162.34808924283630384116414051254', '163.06329142214145075720316591397', '163.91887314372809093611966691968', '164.43623590648498531013040141137', '164.84951111103544774775605917292', '165.37504577216295654881088090837', '166.49298948792299424239534598634', '166.797762908905698806430215182536', '167.666528984799892900688697193725', '168.319697180632692680650232199171', '168.833754951142102014652473318197', '169.80147936611974667763418884456', '170.65739856426341941078796522401', '171.457495558177936815174577876549', '171.87811474117824713182208212142', '172.27643512031070317047257368037', '172.94439578233920466224197786487', '174.05162077676725759690744455448', '174.355023254508388883268068588416', '174.94028495473086651930294290703', '175.75210907560272396090666564678', '176.21866723969857257843470863382', '177.08697382431621657750308986663', '177.44960949998221916342842430485', '178.75190659007875640745507418227', '179.24805250165074947874758874589', '180.037116154213313954180938918496', '180.553538426026320488600417757864', '181.09288737551603552264427255578', '181.93386400982545899506988041149', '182.46537417613374074257698959292', '183.11583568455939524778159370760', '183.99541237748375150224348516448', '184.283638399320814829306526426843', '184.94794965765911100478945944463', '185.35762766197679072568510111985', '186.756108807853867847455928046583', '187.10716937659009934209765215159', '187.806669777622994893338432378507', '188.663313143463700640156457225905', '189.14268031656928787424494838106', '190.02348823773712319306717763293', '190.73149975714431772129220088500', '191.13249047811202412138626458689', '191.73222933727647509681286385389', '192.37143084774578559818347409149', '192.99420907571339935464349113328', '193.83895039678761340857493716032', '194.324920893411601731909173733231', '194.90222188113143590427203114920', '195.81436356692663859432361030761', '196.28008293663389641355035433272', '197.40997845140197653069351964079', '197.91011678955654789504728296989', '198.58105044559651486209232353443', '199.19099683788205421779816015934', '199.99427471984109550577505136214'], 'prelabel': '1-417-417.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9365398586159983, 'root_angle': 0.38487650186918576, 'root_number': '-0.749597691214626333048259316756+0.661893723588388252660760200678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.384876501869', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(46)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.433685614862964683790271143536-0.291775734236051425013122852260*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.182259467548', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.42392182004', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06365207887', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.9365398586159983, 'bad_primes': [3, 139], 'central_character': '417.59', 'conductor': 417, 'conductor_radical': 417, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/417/59'], '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': '1-417-417.59-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': '1-417-417.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9365398586159983, 'root_angle': 0.38487650186918576, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.182259467548', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_417.59', 'Lhash_array': ['dirichlet_L_417.59'], 'factors': ['1-417-417.59-r0-0-0'], 'label': '1-417-417.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/417/59'}
Lfunction data - 1-417-417.59-r0-0-0