-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_927.610', 'a10': [-0.092268359463302, -0.9957341762950345], 'a2': [-0.7790805745256705, -0.6269238058941065], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.21393308320649743, 0.9768483177596007], 'a5': [0.6961339459629267, 0.717911923064442], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5523649729605058, -0.8336023852211195], 'a8': [0.44573835577653825, -0.8951632913550623], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 99.6199852846174, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [103, [1]]], 'bad_primes': [3, 103], 'central_character': '927.610', 'coeff_info': ['x^102 - 1', '0.998103328737044 + 0.0615609061339428*I', '\\\\zeta_{102}'], 'conductor': 927, 'conductor_radical': 309, 'conjugate': 'dirichlet_L_927.193', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^62', 0, 'a^22', 'a^13', 0, 'a^86', 'a^84', 0, 'a^75', 'a^11', 0, 'a^52', 'a^46', 0, 'a^44', 'a^60', 0, 'a^54', 'a^35', 0, 'a^73', 'a^40', 0, 'a^26', 'a^12', 0, 'a^6', 'a^98', 0, 'a^61', 'a^4', 0, 'a^20', 'a^99', 0, 'a^87', 'a^14', 0, 'a^97', 'a^4', 0, 'a^83', 'a^33', 0, 'a^0', 'a^17', 0, 'a^70', 'a^88', 0, 'a^74', 'a^3', 0, 'a^24', 'a^68', 0, 'a^58', 'a^16', 0, 'a^26', 'a^21', 0, 'a^66', 'a^65', 0, 'a^67', 'a^82', 0, 'a^59', 'a^21', 0, 'a^21', 'a^47', 0, 'a^76', 'a^97', 0, 'a^98', 'a^57', 0, 'a^66', 'a^86', 0, 'a^73', 'a^43', 0, 'a^95', 'a^63', 0, 'a^36', 'a^62', 0, 'a^79', 'a^67', 0, 'a^8', 'a^30', 0, 'a^48'], 'euler_factors': [[1, 'a^62'], [0], [1, 'a^13'], [1, 'a^86'], [1, 'a^11'], [1, 'a^52'], [1, 'a^60'], [1, 'a^54'], [1, 'a^40'], [1, 'a^98'], [1, 'a^61'], [1, 'a^87'], [1, 'a^4'], [1, 'a^83'], [1, 'a^17'], [1, 'a^3'], [1, 'a^16'], [1, 'a^26'], [1, 'a^67'], [1, 'a^21'], [1, 'a^21'], [1, 'a^98'], [1, 'a^86'], [1, 'a^63'], [1, 'a^8'], [1, 'a^11']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-927-927.610-r1-0-0', 'leading_term': '1.55522047725965173338791468477+0.0261596030638580529901307765313*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/927/610', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.5554404706449538, 1.3273168500276253, 0.42066280374656123, -0.6904492168976238, -1.3546765365846067, -1.1590994622179203, -0.3352010317226204, 0.284181263218782, -0.09780233342512205, -1.4500471844631893, -2.7253733559062323, -2.652651216207702, -0.9834878307200696, 0.9555835530867525, 1.1545496128393726, -1.282003167469095, -5.015810734277203, -7.274787226516428, -6.126693848374571, -2.2461694641862175, 1.5695157504007569, 2.8440931333674433, 1.5712851743404714, -0.018903367298796544, 0.15847553727351607, 1.9466074440260315, 3.2880310485905135, 2.5737202099309284, 0.40781298423733636, -1.1360194164979993, -0.860578086407389, 0.32669793079392256, 0.6896187545476753, -0.15792611463988127, -0.8668865908188551, -0.250025451660591, 0.9624510138603073, 0.8940446420858508, -0.9535883972825925, -2.644128338345769, -1.89435030088388, 0.9782826065242575, 2.998761378634667, 1.8663380551357118, -1.138049427314562, -2.3990261309049714, -0.24282543891068248, 2.8017245195179434, 2.723746051684394, -1.243663294174989, -5.495966177635061, -5.987241739688793, -2.625826563064566, 0.9809135379215608, 1.8560355428912299, 0.6570593660134917, -0.02677221623650526, 0.6249121032411773, 0.925284270747922, -0.4545948805643524, -2.289096082037456, -2.418049040771165, -0.8464302003296166, 0.17219309985308334, -0.690914003638251, -1.9018257891450487, -1.2573734666847054, 0.8011309481038364, 1.6107654739985056, 0.11595585566871995, -1.34951174476017, -0.27739289587162763, 2.008735551081009, 1.5047556286531765, -3.0176069593870807, -7.484813861257933, -6.917426569741341, -1.5658816719125916, 3.1604336840586713, 3.0793650837664837, -0.16296291325267187, -1.9099551098223375, -0.5619556569907975, 1.1384006170642407, 0.6175728591894505, -1.030274558701525, -1.238695767695417, -0.06146998851691179, 0.06685636746051311, -1.6732495459697163, -2.9858072910499773, -1.822930188497644, 0.48560459612248075, 1.133277693066181, -0.09940235607504191, -0.8272872202028829, -0.052868539998306936, 0.22328330027293963, -1.4105226281776935, -2.5908043571397164, -0.09148321602317823, 4.718934364565457, 6.297147818378022, 1.851872994565294, -4.443138105599768, -6.272355193613228, -2.930835455958837, 0.42016977421514967, 0.060434713675615565, -1.758918378462415, -0.9961153242827808, 1.9461388187980169, 3.0235793124772385, 0.6980353691186414, -1.9311942975347813, -1.847051754599773, -0.22965503013704353, -0.002236188330271974, -1.180186894942836, -1.343235363801701, 0.019745292680264346, 0.6547239652420955, -0.4727246740207055, -1.1707974489701276, 0.33697886028058344, 1.9970926827510442, 0.7948346320241028, -2.2055384648434324, -2.9939964245537136, -0.8681037953281914, -0.041571419124227585, -3.3198950365486284, -7.135184293421523, -6.0958001720513195, -0.9587080280802245, 1.9013709754465054, -0.7719034535168383, -4.759647259441047, -4.608426674264672, -1.1102974753957207, 0.6869067187208473, -0.8237361110976757, -2.143720279766514, -0.7098202387533195, 1.355179301554828, 1.1771468260410287, -0.31432531778970974, -0.48937441319269415, 0.38918773733962814, 0.052608875904658126, -1.2016867074376498, -0.545620375973601, 2.3634263917788645, 3.9781611673422295, 2.0845254037074037, -0.6318372075178212, -0.7885596993852539, 0.4381225337366733, -0.1036392562926304, -1.224709965129895, 1.5575545761237164, 8.135999069731222, 11.791847732152522, 7.785706644528178, 0.46153938748871526, -2.1691242466480336, 1.0862699839361278, 4.0749741977705956, 2.666274616661653, -0.33246034211564374, -0.9268921905756742, -0.006060241598938968, -0.4950168086949647, -1.680938969196587, -0.6563789630434127, 2.0687456049586883, 2.8493723169579823, 0.7586797866081717, -0.9673902801052109, -0.28092952349770245, 0.730876719432465, 0.10249034657509176, -0.38161464147922514, 1.2250655247778566, 2.7516300745008513, 1.2551565053266371, -1.2259318329354054, -0.14880095503742188, 3.7274030597088874, 4.382270221907665, -0.199551274093764, -3.9564637899533923, -1.2824762466900501, 4.44283065363743, 5.645017061277864, 1.3979362481350703, -2.138443350507001, -1.4316859215264244, 0.20931260617300665, -0.5505780459178912, -1.5534861750651372, 0.3054877957021589, 3.156645910326311, 3.136987470753929, 0.7606957695656384, -0.3016780926324334, 0.5407683202391432, 0.492525964418451, -1.0612410356729651, -1.4818688460197593, -0.0670893061541155, 0.40700622923148333, -0.9423884039100211, -0.7749751535792782, 2.5087664630277864, 4.658482670360728, 1.7172345785072605, -2.9447643881821133, -3.1589320912974186, 0.3507585152084671, 1.0718463117445374, -2.651976815437343, -4.802726800911818, -1.5701110334731718, 2.191845063440468, 0.5618472500827218, -4.1828896679473875, -5.4065720499274965, -2.222462079168376, 0.3193684070844962, -0.1557749190052606, -0.7490948692644073, 0.39797540518561236, 1.0774536889506687, 0.0012774258225798408, -0.3709335808196851, 1.3409456246810318, 2.2257557838204494, 0.04115664309397037, -2.422567716448048, -1.860331418041519, -0.044229641607764096, -0.3074381818851639, -1.2191441208350522, 0.6574179123166546, 3.5215376757187373, 2.424808253558711, -1.6454213569135823, -1.8816519507465526, 3.412858138897393, 6.9336406414112055, 3.1552678929447326, -2.995381143931078, -3.640067503166853, 0.45065600910928005, 2.330061334567407, 0.09093955985061133, -1.655253279942941, -0.6170203772823847, 0.11535708076120466, -1.1998018740843768, -1.7355288664828685, 0.12447409333288752, 1.4373018770179533, 0.16043543695350906, -0.937109074774907, 0.621524636763953, 2.3591982476624764, 1.384546424132427, -0.2730591675392089, 0.4541841204298374, 1.8627207833142994, 0.9111428118796846, -0.49611554348400083, 0.9346403035624681, 2.1273703598493694, -2.885918974834657, -11.919160440883527, -15.194440913521586, -8.95764483092636, -1.023414340535263, 0.7801898780456604, -1.2437069632071158, -1.0825062323372396, 0.6221028013733414, -0.4555356897285433, -3.217300910399442, -2.795169191555262, 0.6311028646544197, 2.064800791707114, 0.20827433189639258, -1.081566910820849, -0.1436633320107409, 0.21326655008358741, -1.1510502720704463, -1.5441033706750857, -0.16751029643044116, -0.05500725242776516, -2.010767272023875, -2.4923798096352883, -0.44021312092496695, -0.21498866303162276, -3.812204533420519, -6.088519144682843, -2.9653358261500773, 1.10198202305554, 0.4444884206101189, -1.7052115434577622, 1.485002329034053, 8.101364942103316, 9.583416068934355, 4.282047328957742, -0.26083770888886953, 0.4240417753158876, 1.9884586517273453, 0.40738630387376507, -1.293107871639771, 0.3192726616402425, 2.546643709124369, 1.780328860899046, -0.16361088041648988, -0.1270111816177418, 0.5782781987091962, -0.33334457731154793, -0.9951885155163753, 0.7718166712581143, 2.3050866834387995, 0.5979271338182214, -1.5276384669113083, -0.01083988573221667, 2.8498212282132167, 2.296563515770022, -0.1697181867607895, 0.19393470509359803, 1.7349980863610939, -1.143030274708771, -6.47070063267428, -5.595112372117222, 2.740734664055163, 8.848649235872337, 6.225396166605024, 0.4833891446647527, -0.7390565380960958, 1.1468927124739228, 0.9262733168314088, -0.8040126125652477, -0.52788523722019, 0.665573116296261, -0.19498078394467228, -1.3922383445116633, 0.31305119175175156, 2.9142657111973302, 2.3256388766995135, -0.2391532314368293, -0.6952073887938465, 0.49282604293919824, 0.08942250601289266, -1.0141542161676669, 0.09327235790387567, 1.430058933719009, -0.7599510780529967, -3.631084343121638, -1.3307979504689131, 3.774016227636851, 3.222831283219758, -3.4355220150940275, -6.848400583299416, -2.6557762921405668, 1.9830082694575095, 0.8524514026383964, -1.856290113526324, -0.419671518071253, 2.4600418868171574, 1.7133997949585613, -0.8331696928217075, -0.8140270725067105, 0.4113327389281141, -0.6732846491425799, -2.3122845059727917, -0.9265103623148803, 1.681439516959535, 1.5613407948979172, -0.2242384358559748, -0.3321171269203298, 0.3126467371666277, -0.5997318988760063, -0.8874430728181963, 1.9198314917177937, 4.078430790679462, 1.2506997708717567, -2.766022412359538, -1.7474721021783348, 1.5023895509261493, -0.6119480305834955, -6.733214386853208, -8.002328865696988, -2.898086717630085, 0.676654878244519, -0.6078044112435068, -0.7237927556100181, 3.546815210550393, 6.412704257916225, 3.625220754741925, -0.1767967775599833, -0.008346045430254577, 1.6627353739239243, 1.0593491560937045, -0.19423016815395766, 0.17080995744777985, 0.22229791133268734, -1.1669471937548208, -0.8051964155652349, 2.4499290829225333, 4.138140647444836, 1.7738722753000526, -0.5414179894011101, 0.19252598321075795, 0.648846553083683, -1.2459107273325762, -1.2591343231806469, 2.4695994109661474, 3.7402234085658286, -1.2132672824399764, -5.3359680734674475, -1.7272457770941885, 4.079169052951085, 2.8914700620021927, -3.0200517597857885, -4.531534892064342, -0.909455811665968, 0.8733034436395009, -0.8846295085516191, -1.4388571460671864, 0.1919275564603933, 0.23413791051900884, -1.3709787608754578, -0.9377650915788078, 1.0705453293300051, 0.7920035043751024, -1.1653031395156097, -0.9167049111954435, 0.7651296492166655, 0.012579738528294616, -2.0573867225397384, -1.304527986749164, 1.049563100152014, 0.7407271864431595, -0.8872930076623011, 0.024135593034597107, 0.5136914624016815, -4.5906100672941355, -10.56103593270296, -7.497907269478264, 3.077752741313701, 8.872928968781398, 5.165726149547041, 0.15595505141747773, -0.050381445447863285, 0.6158091627717722, -1.3079106144219168, -2.190182598963731, 0.06655559562470717, 1.1033465451580817, -1.2461081348935432, -2.470168773423399, -0.01847709352595354, 2.0382859727459777, 0.9477680141102462, -0.28204661060565206, 0.20611531177568754, -0.11122168121103362, -1.573019524490101, -0.876149111675835, 1.4130886771610083, 0.7011314761629706, -2.267193972127399, -1.527019477686163, 2.6621715401991843, 3.1864376558022727, -0.6721757610780968, -1.0481807359323732, 3.9711472674387545, 5.900398191713192, 0.8061247200191575, -3.4900114269432954, -1.274673480535777, 1.635664762009079, -0.5590112687559001, -3.4634078762631817, -1.6573610415074154, 1.5274443546608398, 1.2568826599939602, -0.21076603244272551, 0.4916392296606651, 1.0007090916109789, -0.9758080201079887, -2.328166854480047, -0.8284949294995487, 0.4648840218917565, -0.10588648319198031, 0.5847119405143795, 3.02765285325853, 2.7850261133333833, -0.5350892323243683, -1.253353854592942, 1.7191899576780205, 2.273378613997044, -1.092389362082854, -1.9613827937271238, 1.2675821812468007, 1.4281484749427045, -3.312001025987027, -4.012742452388077, 3.5456077776857136, 10.09803956174236, 7.561581751199204, 1.3268775699426905, -0.3703297313358004, 0.9495636407731907, 0.43092338088519533, -0.5140933684093286, 0.6831391330161903, 1.2773143280988537, -0.7939835155651116, -2.0288039535258005, -0.4645547275645121, 0.11994177687698011, -1.9329950531043125, -2.403778502202312, 0.3607315124035244, 1.9520694098996982, 0.5137583454192981, -0.3073240818311718, 0.22200624658378848, -1.2523481061741932, -2.7632226980848493, 1.8284531308847238, 9.770706157873365, 10.385263968862171, 2.4118904751185024, -2.981815123718466, -0.4699301631952081, 1.987792465627237, -1.1885559668008672, -4.0360663075355845, -1.6482547876313902, 1.0565530557231506, -0.19704927159784236, -1.4363014356675743, 0.4765452218444862, 1.792377248160841, 0.31254136591507536, -0.12545115110515603, 1.9673782508211726, 2.49548106889811, 0.30419207436286344, -0.5243085256119597, 0.8596499336437473, 0.8001721630087523, -0.660255037267747, -0.09841986327295431, 1.018073585913337, -1.1844355817673344, -3.6398942529850586, -0.9665573537512666, 2.774006091875295, -0.2605476677839855, -6.681837127249226, -6.504626224471258, -0.6769523579916369, 0.8161918983529648, -3.1916171612219166, -4.309596302855628, -0.8526999691051578, 0.32563868403873025, -1.8550168798438944, -1.1203407039401232, 3.048374443235271, 4.1846642232127245, 1.092596387319369, -0.7828915748047687, 0.05960476577910932, 0.20685105730948805, -0.4016690911865122, 0.60271196780029, 1.3027160303913812, -0.8505504616134772, -2.4597500940700687, -0.17782157882055155, 1.9875783964531093, 0.07438549379340847, -1.850148574496638, 0.17120942229071573, 1.9823980132754506, 0.37889851042470685, 0.627758541334824, 5.325191552113627, 6.389603954947424, -1.082709082366119, -7.833719052809034, -4.844027031943316, 1.8453497319554268, 2.4434249217130586, -0.754153719156439, -0.6850320196883968, 1.0283122654728702, -0.39953114605272877, -2.568971073908233, -1.5261687357921592, 0.17112996586820037, -0.41573841728940497, -0.4975743277697095, 1.5781071520341339, 2.0322612690028143, -0.33783566101511886, -1.114376132770778, 0.731914554372791, 0.7181265699154433, -1.5980905405532762, -1.6614184147081787, 0.15149679816291478, -0.7429313284155774, -2.501195270229214, 0.2305792275250829, 3.8917212606907494, 0.8662074318066498, -4.796821638601035, -2.3168258262900734, 6.422852783169106, 8.938257387467829, 2.9074240275857357, -1.5887645356778417, -0.22610406386118478, 1.1145791949312793, -0.14493425317922976, -0.32558459974484594, 0.2785561490119328, -2.1849015753113625, -5.501754037675061, -4.308381785344498, -0.4156056782478202], 'positive_zeros': ['0.740411760487409706391576967578', '2.00347215626170982819592767898', '2.46636374098908687639813168091', '3.89375396343439441019045739290', '4.5595062245943541424614966305', '6.10452713299605142731882534261', '7.18111223008552868450909414641', '7.45458984489207022455741867205', '8.809963895421612329506242713948', '9.596920515691329100097588116919', '10.26674944919314528501161982433', '10.99929998370360117428801426193', '11.73743246067668969725906365945', '12.71416289406897201460463980475', '13.63119501262779728838870332074', '14.3976863946783714616394261568', '15.2321055823886703019926180742', '16.45835302378751672637653371612', '17.418966519166846069097410654042', '17.53984023201399127308657074676', '18.36329809265039314753873097406', '19.57045126536279922647630254785', '19.82264011423839062586981492655', '20.81699268771488860212452656027', '21.580139119864833647473670813626', '22.224345107590814641165448640578', '22.94109555433267970576414360321', '24.14523935764907742743378517568', '24.98422550383195967503964901153', '25.70644034548918803367473164947', '26.36290229985111618727786150592', '27.20625933733239483911063557015', '27.52000384793079110320305515212', '28.67558611849018419412115944443', '29.35323458643933481090963363075', '30.01707190990035682460317782501', '30.38269342671157379990618640584', '31.25646183022050752735688780781', '32.27351765382562695429627681427', '33.373581279090638627252180565130', '33.75995498796042363272840424912', '34.48722447561696123662611643856', '35.38064238921953419209564718098', '36.31703616283391544303062426009', '36.561629559356010717806655351110', '37.495710963091214970861564509287', '38.022659259347071401186145531618', '38.70146711121773286558643349373', '39.45946391781380511870016800666', '40.46471691207220387576209436910', '40.61403531128785466056880276148', '41.93722348249617492804009987141', '42.44397506420446998551518358865', '43.556108623591800473354134234309', '43.93988391669149376917689491242', '44.77875926293025378057671695278', '45.54969674685712688003179749559', '46.10312995263636561552055638599', '46.576064826200596113606091781916', '47.25791982372224468562348436657', '48.344315664123049627880909358454', '48.931594266850374452239358424564', '49.35321591737970132902887380993', '49.89304551539113142264901867491', '51.274929136058553171555347781737', '51.79619281117716083405332102691', '52.76782781149218884192122439417', '53.44130157831218567253879309786', '53.59039558307332121069715231993', '54.45377447814613067810377822515', '55.41039556826656945140791522837', '55.999771170698118418331453594568', '56.59228356720366697188188534787', '56.99257521698199455060944851566', '57.94781804465825506350726625711', '58.45142375961548828520286884409', '59.363830793942681944136974491109', '60.06888140242550297478403786569', '61.02853463555134980876669770232', '61.80184112306334431846604948601', '62.066627861207369403823397824774', '62.780859998726196618303251484320', '63.88132084652983155549766044775', '64.20688327040901739552251885811', '64.79950078927482842712057031686', '65.63952903495689318221588982364', '66.05320332725353026943378566433', '66.65846490521077116863348232733', '67.60413468452550275348812747878', '68.40438860715900536576233509905', '68.86492645240396882998061232824', '69.79019745238296846334436566216', '70.351523856208979230418107426985', '71.48644796055141790812374884522', '71.83358385298622030915798913097', '72.41516329915284890066256665665', '73.12531292940028455434814181399', '73.533387508486092435303713512414', '74.37913400434373903813658138327', '75.3265732275965139720256154600', '75.536404742829752741545367919937', '76.18230768791124312413261553030', '77.05696235360056326539348630859', '77.633925769398818643694772555951', '78.58320417124507358277012376510', '79.341284934237696555397609310965', '80.00990507034135060242073408349', '80.77419017498172228613412860373', '80.99077219739468477106389522623', '81.85796682273547835740884966662', '82.526601809720831887878851496320', '83.039947285847105865227362671874', '83.97901887690461456667128844910', '84.283877991679991076389535123084', '85.1516041915169692794357338079', '85.49260402464955951602284212734', '86.12454247287389867860822853246', '87.56997522883637966215996287756', '87.94118275929396123395568869201', '88.611789535768251760875685020278', '89.005400130591373502952681607622', '89.9422422180451706350506615687', '90.65389416557690829793866183910', '91.288751899194253187912270652984', '91.631447438160429290643483679686', '92.54394744525817077873806107049', '92.79833737707758191365108260818', '93.83142682166107263179202402355', '94.0236431819152354827450727121', '95.19833517078562536669492010021', '95.67418598167801248116384311497', '96.16618063713960787744076959627', '97.46282755398988191918734953183', '97.75012042924955132683848363274', '98.48766234398590655112181232079', '99.02585184624090982412579741178', '99.96116749624756518979912929634', '100.353315088070426270098567465706', '100.86189678568799608221366724110', '101.46056370923622561961084718212', '102.25318029474819271048369817317', '102.81358167448867858581654317628', '103.71883717423402838107592857185', '104.02944120163970872601469347383', '104.61498286857790168684579290410', '105.533500632547314106927738066517', '106.60273731353905504491216291145', '107.00163277560599607370300156224', '107.65329723214332887291372770618', '108.23747273282238165855229298226', '108.71401998364240436124833823300', '109.341146177722039096976020702168', '110.27713075040268534599921803945', '110.79764009883747557933947723346', '111.270387409606714411895507904096', '111.86053043426813098546130559755', '112.43173286707223318983299786676', '113.20253663131295610216620765695', '113.91336195718174122908039470496', '114.83030369231243390456636997647', '115.39112629130632125485141159177', '115.976853581565144681754692501858', '116.75540564698160163165627887894', '117.357978971264666632189246743438', '117.70067548710537539253731822197', '118.536588676443336315961891515627', '119.325591009213918678951916025383', '119.80361955213574485312576005669', '120.16474647520621686171085101007', '120.75808209004410961513098796239', '121.64361063182431741412300441575', '122.33172903494299623910425619247', '122.77497936217635541256394342581', '123.94710704747610090255922623201', '124.28346151508276124413596904360', '124.76189863105740399120747998456', '125.912755836205516805064128151400', '126.25143237712135591752434090651', '127.1048304118859312223426395928', '127.42909282121129784404030644636', '127.87565281369204996565823286458', '128.53164651479929286121690162336', '129.56795612452312431289121427040', '129.958193215850186361933737863803', '130.442844602226674420934890829749', '131.06253220591138346851148071645', '131.81518137728143537154360466623', '132.57969760281796825930178641221', '133.276948356203000142651655884278', '134.14639798005003737591974021639', '134.55753666762168335468781982721', '135.27320006304567614467019279733', '135.67444194028138262774034181464', '136.38779332106585246724678872618', '136.99595259811882724207074699071', '137.65237284360379052430876225125', '138.12681862632691494828381989188', '138.907383687697406480068713544358', '139.49407928121982848785426815652', '139.99591052100482741141362329613', '140.37265069022561609451708984090', '141.47372455662046435503970686041', '142.5196561117362862493287507443', '142.82412518598974191943736275841', '143.260631324291683824310960972721', '144.05450399295790186421047373696', '144.55057261307610846822996652475', '145.314313901212598012858032239348', '146.12034881358898946106612995868', '146.46950639933323743914631857128', '146.84704034534937474565627540177', '147.61192787034173038532039647925', '148.19816599419899945394965228505', '148.867830111373185234731149009949', '149.63211459274834484915082632659', '150.08296664326121198147901142842', '150.97702942680459056588750462177', '151.66020339147233542369257949625', '152.14180121040000905235996391635', '152.95153253395621028105936464776', '153.67065768866999633792075176716', '153.94023805771424532121231251512', '154.562845361652692717086392842408', '155.450394993649881708751247647982', '155.887482799377097693967365632360', '156.13480513196538372177715722070', '157.1354452181668495817470719846', '157.64737299244014051997581977700', '158.343100022351284120166412245437', '158.94841532527395643216893040164', '159.48454852672616208338221218481', '160.1906453338050603555543494812', '161.368332063453244362837333797208', '161.65708758182489668239512101875', '162.280528470936005053448415648', '162.68222255084535882753402142800', '163.33932456662216603849079075290', '164.150976865506090582387764527671', '164.40517772585004638279144135870', '165.27641860475293456030584218182', '166.03957028136626029445440619514', '166.40396322537609686841211747502', '166.67864458418193151871823647016', '167.42075420230241576661121819103', '168.530745613663352146744160333328', '169.09697843956728506862367562528', '169.604516173231201505658574025241', '170.4556483745262754860519838387', '170.9106530993317119903102053757', '171.50402468685089187229752343842', '172.24859078336947254509864788941', '172.52890177124168346485378263678', '173.48328752967806576257520973692', '173.885263868873033575389553895392', '174.5318826448949830581116288202', '175.01845520855426974876174174940', '175.510497887484500750636906160286', '176.31220658743786876576029538101', '176.86220584925205647008855844452', '177.8576482815894185134998015119', '178.20740611034810934782985533105', '179.15431832308026130403427654317', '179.43605747047629747121024131237', '180.09171438426842604862007973535', '181.05325958431611420434383912379', '181.54454858941362732417642683831', '181.95673763597586914545179915396', '182.37151266041108240643819586662', '183.03106470792947678141538101953', '183.766621149702549744816695087974', '184.38255331268762502820960425157', '184.98245590224858050859138106502', '185.699638805470784428435673576549', '185.84865952414759935731590132613', '186.83919857418898212218026062799', '187.70914589601085429898246788289', '188.35134105607265472104317335061', '188.8511663367239213257222870017', '189.32828052939248690717263574890', '190.24859648602883387010186483110', '190.5026461136179912356489933699', '191.03057530171068227474256878209', '191.832688153481231149039961818013', '192.38368632431103908593730464904', '192.91552531230872830765574339817', '193.7096082511742519892397780897', '193.945102459578457849924187325015', '194.67206034507783564397916663711', '195.35455534295726607069340203230', '196.02467533556830713954664298031', '197.022862866125291487642095317292', '197.52833131333936356043843582604', '198.09242857334928165222316074124', '198.53909287348948330019496387019', '198.83069112823203121655197167035'], 'prelabel': '1-927-927.610-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 99.6199852846174, 'root_angle': -0.01070726012658336, 'root_number': '0.999434300875935943454794248768-0.0336315065471225396541773395931*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00535363006329', 'prec': 57}, 'spectral_label': 'r1-0', 'st_group': 'mu(102)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.871727756896466741065472750696-0.122783254774012253789317040887*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.740411760487', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.00347215626', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.46636374099', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 99.6199852846174, 'bad_primes': [3, 103], 'central_character': '927.610', 'conductor': 927, 'conductor_radical': 309, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/927/610'], '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': '1-927-927.610-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-927-927.610-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 99.6199852846174, 'root_angle': -0.00535363006329168, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.740411760487', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_927.610', 'Lhash_array': ['dirichlet_L_927.610'], 'label': '1-927-927.610-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/927/610'}