-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_275.141', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [0.30901699437494745, 0.9510565162951535], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 1.2770946309817734, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '275.141', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 275, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_275.236', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^1', 'a^3', 0, 'a^0', 'a^1', 'a^2', 'a^2', 0, 0, 'a^4', 'a^2', 'a^0', 0, 'a^1', 'a^0', 'a^1', 'a^2', 0, 'a^2', 0, 'a^1', 'a^3', 0, 'a^1', 'a^3', 'a^4', 'a^3', 0, 'a^1', 'a^0', 0, 'a^4', 0, 'a^0', 'a^0', 'a^1', 'a^3', 0, 'a^3', 'a^1', 'a^0', 0, 0, 'a^0', 'a^1', 'a^2', 'a^2', 0, 'a^1', 'a^0', 'a^0', 'a^2', 0, 'a^3', 'a^3', 'a^2', 'a^0', 0, 'a^3', 'a^0', 'a^3', 'a^4', 0, 0, 'a^3', 'a^3', 'a^2', 0, 'a^4', 'a^4', 'a^2', 'a^4', 0, 'a^0', 0, 'a^2', 'a^0', 0, 'a^4', 'a^2', 'a^0', 'a^0', 0, 'a^4', 'a^4', 0, 'a^1', 0, 'a^3', 'a^4', 'a^2', 'a^0', 0, 'a^1', 'a^0', 'a^1', 0, 0], 'euler_factors': [[1, 'a^4'], [1, 'a^1'], [0], [1, 'a^1'], [0], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^1'], [1, 'a^3'], [1, 'a^1'], [1, 'a^0'], [1, 'a^3'], [1, 'a^0'], [1, 'a^1'], [1, 'a^0'], [1, 'a^0'], [1, 'a^3'], [1, 'a^3'], [1, 'a^4'], [1, 'a^2'], [1, 'a^0'], [1, 'a^0'], [1, 'a^1'], [1, 'a^0'], [1, 'a^3']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-275-275.141-r0-0-0', 'leading_term': '1.12190421562698597017740332268+0.516277285390330422305335543133*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/275/141', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2349944552311203, 1.7261571443462655, 2.3077656450464348, 2.531616629939636, 2.131688241568975, 1.1791330630810344, 0.05547165242519472, -0.7298429577514833, -0.8201090939302953, -0.2434034034384316, 0.5651139284449476, 1.0089682058876486, 0.72535829213637, -0.12672601403696493, -0.9210379855260116, -0.9916577879577119, -0.18465174707145032, 0.8688395866427527, 1.0371188305711823, -0.5603962599400296, -3.8053651031618756, -7.40243789359926, -9.513101197346016, -8.875382316151995, -5.671751109816974, -1.4989727892714217, 1.6113574096334942, 2.475847158233791, 1.4367488826676276, -0.05619728542412258, -0.6263897995408861, 0.012272690704076047, 0.9930397591732008, 1.1949724279582536, 0.3031426932458833, -0.9054483971891016, -1.305888386323926, -0.5248415333788897, 0.6322488461876727, 0.8741925220556143, -0.3489328221671698, -2.222196055449555, -3.194372308907504, -2.3610213388505614, -0.3415323352135854, 1.2257423923848065, 1.1860243291918784, -0.009926297113360823, -0.6843686429027527, 0.43761343353419213, 2.8414110233448095, 4.4707978989586135, 3.534758514053916, 0.27815357019274467, -2.98040093944047, -3.719062866237018, -1.3790163597926215, 2.141007028165915, 4.140923767812904, 3.425368329001027, 1.1652137632480306, -0.3986056331090826, -0.08436502947535252, 1.3134497169152355, 2.083739622583653, 1.4207206175546725, 0.1145928092459294, -0.5026086359191553, -0.09742317475123663, 0.37453539049574797, -0.06455549663256463, -1.072936324997177, -1.2172125293093887, 0.31822011678196127, 2.4140051816471386, 2.7656271515602113, 0.21928027579730752, -3.671270327697774, -5.708108705511583, -3.968936011477524, 0.23119114976887914, 3.3958946568403663, 3.0235998572098954, -0.16691653020771804, -3.1201936395187335, -3.469922606952876, -1.6231375814443516, 0.0894127937053732, 0.07418292799632534, -0.9850619376641716, -1.2515043176217366, -0.0721941651806336, 1.20407900017253, 0.8428735108842514, -1.133829223555013, -2.8019020223316513, -2.411173785720191, -0.3299898636427674, 1.3753076012775, 1.2452339025151273, -0.04813543757084391, -0.7085905206043747, -0.11504589265513866, 0.3946714382081038, -0.7189258409132524, -2.9904529649925857, -4.115945170904494, -2.604708876510113, 0.07768114695833195, 0.6283745348478124, -2.558039233343137, -7.246878763450861, -9.206675718209516, -6.350679215940735, -0.8586833458011726, 2.9778383472089063, 2.8836407825136448, 0.3804849001098933, -1.3801599372527678, -1.0270333886153087, 0.13124981293726848, 0.2816407755971203, -0.600155465424798, -1.0663505642208653, -0.4010626689806712, 0.32420766053342054, -0.2515069303145579, -1.7409670761221308, -2.251593161799904, -0.8113849699227798, 1.1011442716408675, 1.1309653032277849, -0.9457508781455781, -2.53951800225733, -1.091946178755967, 2.703407211098968, 5.252242919680107, 3.898953470313188, -0.0501273938697009, -2.6856581698317865, -1.7672465131981085, 0.9847364361677605, 2.151343288562321, 0.6513117950591379, -1.2290767962585296, -0.8749668975612355, 1.3815045237310382, 2.72952031222273, 1.3936169987670912, -1.201474134850606, -2.2224186963425345, -0.8446260175106811, 0.9432638826552574, 0.9835610192734356, -0.4328811252824101, -1.2312568456114266, -0.4247498506996449, 0.6659610285369684, 0.3789922128219121, -0.9084936360045753, -1.3063942185427004, -0.17070153061894686, 0.7955779312041429, -0.05460460951563531, -1.4229642157269542, 0.09834431990649242, 5.778894239911872, 12.155824039260178, 13.817021702176202, 8.961829021030255, 1.4747373250278966, -2.9955361677836896, -2.575348198338881, -0.2099344343549266, 0.4542280149933595, -0.8959866489974342, -1.825757728110286, -0.8728215637473071, 0.6652947220378438, 0.862429481531654, -0.09781097107776267, -0.38807070457662113, 0.6350850123316282, 1.3858288592971975, 0.3771344897792354, -1.3322052481135813, -1.2055951263696987, 1.3433249786961987, 3.7972349501559304, 3.5091176508590403, 1.0946143087176294, -0.297970706919253, 0.937512105681483, 2.775757048005326, 2.3467773417741324, 0.015760762926479415, -0.7723119830683918, 2.018475449081463, 5.948536045124922, 6.672206782141016, 3.1520436231657216, -1.0343462918148616, -2.000448797941599, -0.07666460456679391, 1.0342061019601194, -0.845120080853237, -3.752706294405552, -4.3565443133210735, -2.1973924745518567, 0.07310836985786627, 0.34706441483985045, -0.5135725219827167, -0.46967110557838454, 0.6353853712994596, 1.1464006876618855, 0.39884745059596516, -0.1460090470877925, 0.7311250775954766, 1.708645401339675, 0.5269544710030436, -2.3304251683419324, -3.3081717357808547, -0.13410987842434097, 4.533054709614368, 5.477709198886816, 1.0703992925253492, -4.396895205364326, -5.422116689703749, -1.4803832309573968, 2.7867757915518863, 3.2995306931739616, 0.8771451393244045, -0.8069544442908902, -0.23374972548662795, 0.6964069433150568, 0.13886213985336146, -0.9206116471020774, -0.4731420123546215, 1.1024270236036, 1.2612753696149983, -1.028356730120656, -3.4906204419744915, -3.4048168913053427, -1.2259742066992536, 0.13235038142279135, -0.6502947758297338, -1.6576306958947804, -0.7872420473991191, 1.0038649632524155, 1.0899710659887054, -0.7374559553010275, -1.6019633380841594, 0.32094259830792893, 2.646445562193048, 1.5666862677031748, -2.7056662157925997, -5.399320057953649, -2.940858737951669, 2.246004696520762, 4.356137427183953, 1.1254639637873731, -3.6809883620227857, -5.117856353875489, -2.7398341658028675, -0.11483517037519719, 0.28932448063894683, -0.35430674156225206, -0.009693211786445898, 0.9367889523255108, 0.6742946592254584, -0.7942946778562139, -1.444992724470163, -0.3832093754619911, 0.6819120745443386, 0.17298955514217232, -0.5448349732117832, 1.0293051875568502, 4.325248876686155, 5.542588007593326, 2.6447907410973244, -1.175348189378143, -0.9597194241063217, 3.6163724323342574, 7.457790295828862, 6.261956196127167, 1.6991451489062803, -1.1364445914016108, -0.3212507129779616, 1.1126182737159107, 0.07964046176211607, -2.2360229497150206, -2.534302298651565, -0.4616722052274286, 0.8833718360978747, -0.4580176346499527, -2.477308577076756, -2.208890755368031, -0.04028459520722856, 0.9759975957594522, -0.36267436059149766, -1.782320731054519, -1.0478688488126666, 0.7694499235342318, 1.095533544297726, -0.20841648314945954, -0.8597029215868194, 0.019838406326951517, 0.45588099107368374, -0.8721440856707217, -1.6361924480324397, 1.2137862836950275, 6.103568257920356, 7.261048777130953, 1.697924828836839, -6.175164766709949, -9.03461850910266, -5.021591116070153, 0.5941626536287649, 2.261758735023671, 0.31378597779337075, -1.0393546544231769, 0.01261054655932145, 1.2067890773420151, 0.4562789826527743, -1.0103363261645646, -0.9946458252840362, 0.13161441708986943, 0.335505730294696, -0.5029382255441305, -0.385927344018106, 1.1584495227731615, 1.59958338185396, -0.958845825478573, -4.304131696820272, -4.543259408520727, -1.4683881557026786, 1.0099182423074886, 0.367152959018182, -0.987771020812805, 0.512566134508929, 3.892233495487334, 4.5573370275755, 0.8688738823943603, -3.100245391351888, -2.8626449354460117, 0.5008649434203214, 2.1252056875532457, 0.2381819320924015, -1.7198150579314124, -0.4775551086220434, 2.2676359022155386, 2.508924247619974, -0.15890672392746066, -2.0746701110111165, -0.8528338950855594, 1.4995179517596284, 1.913954555111555, 0.5838257927227691, -0.05969396773557796, 0.5518966781099187, 0.6492946277780255, -0.34049177679954373, -0.4892985954698258, 1.2518086140668672, 2.626034100706426, 1.2693428865655945, -0.9870873465134545, -0.060875845008922645, 3.9708712304242626, 5.535060637305987, 0.5331307761188947, -7.416410294915148, -10.576518767110805, -6.365473794844357, -0.1137620597054699, 2.03287814128781, 0.17402006111450682, -1.249588299311697, -0.2852852724789296, 0.7799479676728798, 0.053766873075309266, -0.9743423931743949, -0.43345362358262657, 0.4719328921275334, -0.554373117589586, -2.7535791234607196, -3.0090961219113916, -0.6452155186960868, 1.2438905840584435, 0.312521389521498, -1.5466348325999921, -1.2342880774867218, 0.6709202513818691, 0.8798850483263795, -1.2244046085610651, -2.367716378394813, -0.5549544273737557, 1.4047234977755771, -0.04387208365680815, -3.4416800838296506, -4.00590842419944, -0.867198774092198, 0.9727126245049368, -2.4857685558912808, -8.169116844720829, -9.615940127917266, -5.421105589722654, -0.6707521773419908, 0.1685763963311392, -1.4858464160701708, -1.7072615303794403, -0.024848130235775354, 0.817472613100255, -0.20922300246050196, -1.0483319172621437, -0.37556110734377823, 0.2140750056377875, -0.7643937946053542, -1.8444523809861058, -1.024314684980554, 0.5856044614523372, 0.4467509377971311, -0.6753726129602918, 0.8792316915348257, 5.5633414644317085, 8.175073817155045, 4.16391858142574, -3.5319815668370356, -7.397890725898103, -4.710580424205276, -0.4953325451527232, -0.17983880069116845, -2.623241367171957, -2.9993354181712544, -0.31838369359389906, 1.7015302133575387, 0.8195349498862448, -0.5691694641712631, 0.2088643038784972, 1.7356944504560894, 1.103800530271873, -1.0470780730388085, -1.4035515834012438, 0.634794703795546, 1.825833548102665, 0.13181443377528113, -2.088142086896013, -1.7918107378160875, 0.12664091693325738, 0.6109192464072437, -0.5415926191771242, -0.7220514779062539, 0.6585009650422515, 0.9915294972285125, -0.6263311268131525, -0.6973593770821129, 3.536298692991335, 8.415202982682418, 7.4119740843337665, 0.18991316698275376, -5.895300032321877, -4.87521092163632, 0.4861977944513057, 3.1033839935435923, 1.0144145917651772, -1.3367290978184516, -0.4983582352356931, 1.529102264897951, 1.458568665752713, -0.16266676792291723, -0.6552283210794911, 0.15664321029023584, 0.2853412647298349, -0.3699269565869851, 0.2233428665964334, 2.1703875707663314, 2.7074367361873333, 0.738769246152348, -0.62358316381954, 1.428924459918604, 4.481097994060724, 3.9091466513113873, -0.1003900455048544, -2.4959750351705208, -0.9256732841524684, 0.5869975949525249, -2.139719171091756, -6.646570080539927, -7.029671884685632, -2.5099811421482507, 1.5039447640783405, 1.236550363606172, -0.7362744684981716, -0.5210432887159004, 0.8523847101732651, -0.2600047489923293, -3.515642239433438, -4.590526310381441, -1.784718783666701, 1.3299780590214394, 1.270280324347045, -0.5781207723692996, -0.8936096623013323, 0.31054893893775304, 0.5294978075791787, -0.475707049262643, -0.4260171110508437, 1.0623491949226829, 1.498391191927194, 0.03468471418247336, -0.508643404463291, 1.5646847627393137, 2.9869941360536396, 0.18156280650398943, -3.9211506378594105, -2.4642852996283304, 5.472738145323629, 12.103663584353836, 10.3979597477341, 2.967623990039053, -1.925360801515112, -1.0542576299691742, 1.3603851130480464, 1.23008482343204, -0.22382702225302017, -0.31233090102389, 0.20597906006149297, -0.8164917714691493, -2.4719693916669074, -2.1559674440730587, -0.27610681740627213, 0.1834142893765643, -1.1985900352139536, -1.3249354105845355, 1.1451298456879888, 3.088862817018258, 1.7630072954831766, -0.5287631365278913, 0.06544448133673911, 2.645858998261531, 2.8741937465967045, 0.07723212803043174, -1.4842891838747407, 0.39810637754790046, 1.9434563793573885, -0.6630726959421006, -4.695296484965951, -4.5944181730916664, -0.6360106796541087, 1.0995247572234794, -2.2149147214723537, -5.903797999796396, -4.7727595536291325, -0.4932542012003761, 1.5128405244532122, 0.07961624855986543, -1.1329435630716462, -0.17053801692805487, 0.6584456389221773, -0.4797787742694428, -1.6928865683101293, -0.8929992585743188, 0.5531134719561726, 0.44868254868337876, -0.3118467907638657, 0.261481205808951, 1.0132718207099336, -0.5580129543678805, -2.8405909023831755, -1.148206606182908, 4.589862609169337, 7.707572741189081, 3.4484368378673387, -3.6231640793376365, -5.163670124894344, -0.1949267164734076, 4.216916465348384, 3.242711465479185, 0.06810332777291576, -0.37571044888353267, 1.1858744943128778, 0.9192069123473253, -1.2224726893285696, -1.841723850296948, -0.18471178351409295, 0.826800382857591, 0.004532640721016597, -0.054597818986974196, 2.0567905235707795, 3.3707017003947053, 1.116929716865099, -2.3945016090869835, -2.984556835411969, -0.8610931286012307, 0.272708223025888, -0.5379289508864786, -0.5323175022408093, 1.1775201788446343, 1.6650983284390943, -0.2937294411634374, -1.031034812711537, 2.1934784555071043, 5.417004605791272, 2.8799989803397823, -3.7769712165363893, -6.699465750534686, -2.719165505768599, 2.1839207029999574, 1.6312853113459156, -2.421452756155467, -3.603761599639953, -0.6938628801435492, 1.7372526259572543, 1.061137138875227, -0.23456214137968395, 0.2377397758077164, 1.0212094673245082, 0.29693489890844527, -0.6218178784522853, -0.09441599489597681, 0.4369927508198361, -0.7724536999996942, -1.7476169156853816, 0.4123988889965149, 3.937523805261008, 4.180772683840999, 1.0290613835281903, -0.3776695426641145, 2.128544266780123, 3.6059430572717925, -0.524372177898404, -6.660725592086617, -7.582434377614103, -2.826902654344002, 1.0167004818313536, 0.18544234946440852, -1.7071174781858673, -0.631629001280088, 1.5278608219920284, 1.1155447489898729, -0.684739059838114], 'positive_zeros': ['1.8918832796454049232607512255', '2.90544383540964401755056898758', '4.02086099955503291320702784374', '5.05169686641220846920301297971', '5.8623072248554413343017251737', '7.94031459313919406028927150582', '9.048046107702529750562746031', '9.6837155574902493206271065773', '10.69919959722557268601445204639', '11.6957056862519874076495452538', '12.43595586662515841567043992905', '13.80255153060498426013122543976', '14.68501199519011569476519256624', '15.23792629686533818232105260827', '16.58572680665735670445000484787', '17.62092850711693332233680836966', '18.9426862825543296195670279175', '19.39757085519289275366213812671', '20.65763018479266801136525768489', '21.29626501598227729395687790391', '21.85225943611461085927880522560', '22.765272269212752452856944931611', '23.768324973381979589944268633007', '24.98329485499676894767839980942', '25.92316322649982102051681849871', '27.16001943508222177410287207299', '27.526586259742761985787222739532', '28.45186036598082906366884454492', '29.21319078255298430661134685970', '30.35871731699145047979711383773', '31.23808484159854841886608010740', '31.91627143419942037025998626565', '32.362832119629253796197034110503', '33.73891905706739631418203275030', '34.16082128247847280482568549157', '35.67695826556812702561936090324', '36.60968170171028354999261158292', '37.45588053770654431938680011622', '37.93174247686117104036700076544', '38.882713969198792319095444326234', '39.30689866266505737426444696713', '40.43104239753150926288168035728', '41.12694802012284980285485335176', '41.97430676024817914935933613855', '43.121043952218447527245369761037', '43.94871960137056831852929537197', '44.77787827809401335109904669290', '45.44646848218621553602902423054', '46.413780720451043926070101674931', '47.31609689161870916999368335539', '48.03659643562093855498867987541', '48.85116692632198495373250103618', '49.473265468690511249315902133929', '50.34957867663629516276867553457', '50.92682409605334428650537032607', '51.554235661081443680714754046471', '53.198039449453281604159071430503', '54.099133801932395065846230150764', '54.510088078160684548515172660064', '55.4744137656700854202493044412', '56.21824400569451193091426378321', '56.71279995998181934144163663271', '57.56432652664107269754764534616', '58.29630823880075342099173142593', '59.55059138037921278602041455923', '59.83318753403006214010733575347', '60.93975253100959379511258479765', '61.380870041664674491805711477', '62.71904497004026960131159490801', '63.44858293235384606714681038102', '63.9669140522490872550777674342', '65.296676173542086062972189249153', '65.75381805149626353722117218397', '66.39562081882998339723399505945', '67.33307150596953009770659781544', '67.60535644193995004523469912606', '68.5002672759658580176754399568', '69.383747351832272251443480528939', '70.3676171875226459506377333937', '71.34232110830697655909847025177', '72.303069957545545665382312872381', '72.871848820456270262850661773964', '73.47312267448277068987741320875', '74.1596506304376650719182588783', '74.886357620126063146283564892077', '76.17064578301468061267827179223', '76.38601018306706508900940734217', '77.316698669814991874155485309288', '78.01121195799668598488932945426', '78.71405841161385107297560439930', '79.5023597419822877797974057790', '80.487256052797393376323134716673', '81.3186495975895254655029018576', '82.523831763405217835806061218466', '82.94314100962346075695985976008', '83.4407102946253640449898447393', '84.21500873729977144615875598712', '85.082861457126830771703287388166', '85.67436868846490000978570697900', '86.11498643195179036149840054444', '87.38340387757089157925622359518', '87.89729050188149918832896633077', '89.19918744165899897098085967084', '89.74072580717022155200981024647', '90.32354651355929180923319779081', '91.31574639334742806580080603712', '91.80886835482328063336356080443', '92.81854076279783956798225448974', '93.377670688209709265714979005488', '94.23419565251898279500251046904', '94.954349180118836605401550978756', '95.61938662924312364197087385222', '96.08262989437426461539675335777', '96.78525452485887698598422175187', '97.87719529885046618220727214576', '99.02082573184901188004483797131', '99.73083489121466139026246466402', '100.3101393781614626925461485458', '101.025369653998099278948233937994', '101.83436967883590771344697741230', '102.322317229489243415815754082299', '102.90620379421006758570613501099', '103.66334417138408013671279998646', '104.83079937784427216012051384335', '105.37692763443723255944668200435', '105.88148993951780610879140299641', '106.931469089758962024343729308603', '107.76642602325125211479850641821', '108.4647992263280618139094211884', '109.11565766398991315964398333366', '109.983576207688044765455705345622', '110.73024936510965076109187429731', '111.75218981471031751555827559593', '111.93580462700812641707368639342', '112.71337304627575060540415770632', '113.242353574592903101482642718747', '114.21576193085506627476690281574', '114.69362290549799356047037764827', '115.64627857635269676127441338956', '116.8824772797953532946586207737', '117.523197217321635265320981689265', '118.18284980908782301363641428599', '118.76258159853847240392010095089', '119.488292541257433286477619545723', '119.904352377739285127354180804441', '121.01289987064084276929922696537', '121.60956084994691664796580514156', '122.38577384004427112992284973050', '122.963423812001396994378034601', '123.81546725524099540629199740909', '124.37063825863376165152254073624', '125.39482520630095738252526833886', '125.7713446874366810095124042766', '127.273244643834522719306656789881', '127.541825120175466492886330478174', '128.44199351906593614404612085945', '129.01523958610148442386217558388', '129.81000801482804248696075764329', '130.12291872811183023213378223153', '131.11770139702924648226825073238', '131.66948929308367988441636607556', '132.09634206061051293531015044507', '133.29307965074813285421485652030', '134.44645980336978989305804116706', '134.65331272951209886347168271766', '135.65783763999549683284099566849', '136.39605807491676220291786144724', '136.83533466109685792111381038142', '137.657825290113769185525585747468', '138.35286867903780136610209080115', '139.07814025832511481208054818262', '139.97623830736517457118593770033', '140.49037264663901075386881833461', '141.113708255590379514073847185856', '141.7669110399437898345987104631', '142.26769135731168171817666983512', '143.44479043648598851132704713142', '144.34543450825188682852657997381', '145.102870938980441236226416655216', '145.69506137737773400702751451948', '146.52806106741393040653832752886', '147.12888525019651578559590836673', '147.630546750859655445293807431641', '148.07658266465036949500719976538', '149.16713580457462656260522979432', '149.53208470184488424544471273199', '150.61739669311587901603563196634', '151.37163952327451147207774191463', '151.69221098635281306123553380367', '152.97337153688430572000317292302', '153.61549451417775635990511983142', '154.1658412854141084337121576262', '154.65635606905043018261419141233', '155.777264939155389956838441419684', '156.458093047737097797253537733998', '157.10694076049705933104856026002', '157.66999195491405012161666499828', '158.228182042390584346307857017464', '159.069273853387459417081938963573', '159.486158617077904439422427046913', '160.32484587292855164202545479716', '161.05316179013847814257861556561', '162.330974203927439874795042462839', '162.93105393517234204570733104069', '163.68948178074304638766353927672', '164.19994291731784796290549455853', '164.50713783421911151615243103298', '165.68495155718880440029053179399', '165.995560593462933740100363114260', '166.75285751530914882240914389353', '167.71566653355626137214637001391', '168.11571761513743190068820238984', '169.07058894200309981421473313434', '169.64089047587864162934476931556', '170.262627809722140905096943801089', '171.30422100807492370481408696680', '171.711436993880908514419262738118', '172.85413588583161300146822946480', '173.44986180509085288732841311331', '174.09964337813172628690429345471', '174.596158270978423944790940570381', '175.482510309802421730873884026999', '176.08942202349442135518698423852', '176.48726857366425519986306450966', '177.117856222302856210082708295245', '177.88546108465041529188373462340', '178.89309689149237679248568551024', '179.697553173759449986312636222649', '180.63460956734477414020800371712', '181.01862387924690569291085764714', '181.70265902691989361562637441662', '182.5315161996203495503908224277', '183.12642344527122656458073060425', '183.45120627598728577678075455893', '184.46669185681767551179426389203', '185.46558034121203116274442549567', '185.77177902067273229914828273975', '186.36386887527848944880011119826', '187.14681117280467123160081751226', '187.63973792651062535305715173731', '188.576282170982462553019569357639', '189.52196168100227481903495221254', '190.12907371948549032556518813548', '191.00063100666175049087504360746', '191.782704434507947819155773578587', '192.11550623951051297151009885610', '192.8868447761852748431021748465', '193.467473887766135590382982563758', '193.911187297844333046090650391353', '194.65065066584871729100865780725', '195.745168514082912464139412996939', '196.0195282102079826170034479377', '196.8489866687845375534368534039', '197.99928784740199649765861948534', '198.46184309335124325805876323116', '199.14219433005695610868038129117', '199.86328914068557107538903826549'], 'prelabel': '1-275-275.141-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2770946309817734, 'root_angle': 0.1372828699303932, 'root_number': '0.650484841500904341653443553817+0.759519236739625546579803198654*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.13728286993', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(5)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13966685878682610468027432320+0.0654887585408806537732478085988*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.89188327965', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90544383541', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.02086099956', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2770946309817734, 'bad_primes': [5, 11], 'central_character': '275.141', 'conductor': 275, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/275/141'], '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': '1-275-275.141-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': '1-275-275.141-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2770946309817734, 'root_angle': 0.1372828699303932, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89188327965', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_275.141', 'Lhash_array': ['dirichlet_L_275.141'], 'factors': ['1-275-275.141-r0-0-0'], 'label': '1-275-275.141-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/275/141'}
Lfunction data - 1-275-275.141-r0-0-0