-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1728.1253', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.4617486132350339, 0.8870108331782217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.42261826174069944, 0.9063077870366499], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 185.69939004511204, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1728.1253', 'coeff_info': ['x^144 - 1', '0.999048221581858 + 0.0436193873653360*I', '\\\\zeta_{144}'], 'conductor': 1728, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_1728.1517', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^169', 0, 'a^170', 0, 0, 0, 'a^173', 0, 'a^175', 0, 0, 0, 'a^228', 0, 'a^231', 0, 0, 0, 'a^262', 0, 'a^50', 0, 0, 0, 'a^131', 0, 'a^136', 0, 0, 0, 'a^51', 0, 'a^57', 0, 0, 0, 'a^166', 0, 'a^173', 0, 0, 0, 'a^116', 0, 'a^52', 0, 0, 0, 'a^189', 0, 'a^54', 0, 0, 0, 'a^169', 0, 'a^179', 0, 0, 0, 'a^56', 0, 'a^211', 0, 0, 0, 'a^210', 0, 'a^150', 0, 0, 0, 'a^199', 0, 'a^68', 0, 0, 0, 'a^239', 0, 'a^109', 0, 0, 0, 'a^42', 0, 'a^57', 0, 0, 0, 'a^112', 0, 'a^200', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^169'], [1, 'a^170'], [1, 'a^173'], [1, 'a^175'], [1, 'a^228'], [1, 'a^231'], [1, 'a^262'], [1, 'a^131'], [1, 'a^136'], [1, 'a^57'], [1, 'a^166'], [1, 'a^173'], [1, 'a^116'], [1, 'a^189'], [1, 'a^169'], [1, 'a^179'], [1, 'a^211'], [1, 'a^210'], [1, 'a^150'], [1, 'a^68'], [1, 'a^239'], [1, 'a^42'], [1, 'a^200'], [1, 'a^17']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-12e3-1728.1253-r1-0-0', 'leading_term': '0.00318333621426206256772106506653+1.75095867738773504733461372266*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/1728/1253', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7509615711228101, 3.3789377009284762, 3.9481884363552164, 2.9777915719248274, 0.9071750484118766, -0.993698577785874, -1.5352610398335973, -0.7134049962115371, 0.13414147106507343, -0.4519794378837614, -2.47958751540027, -4.254819808348229, -3.988193465605823, -1.7655723274226596, 0.29997013493364455, 0.1700535000998561, -1.8902717978808339, -3.5091184852696533, -2.8109599318034553, -0.5420373661474744, 0.8393440268183029, 0.1585363751215078, -0.997405654252383, -0.273646397035628, 2.3202555020742164, 4.128852503581553, 3.0213797774078053, 0.15000137705638053, -1.3232942089642123, -0.1119251743870624, 1.6327767390299055, 1.196947509441457, -1.072074512052446, -2.2201892135563264, -0.6922169862502269, 1.510874731886037, 1.5603158114593418, -0.2481798786038863, -0.8564993896776906, 1.2019978973545655, 3.489885706781843, 2.8323147725013795, -0.2525877263597465, -2.083664103295624, -0.7258774991054162, 1.5313211538488065, 1.5873015648921074, -0.10685847494031199, -0.5544822164334874, 0.960951048712121, 1.5252595777976607, -1.0182839447903744, -4.356661203424363, -4.460309451023788, -1.1500291568858343, 1.5849834792247823, 1.0919996182476812, -0.5919853940093802, -0.30084730796593295, 1.373020988772609, 1.3431783823257604, -0.6448054777954799, -1.1513812084215325, 1.6575869724336982, 4.659641194409932, 3.910787325013481, 0.3513201443351513, -1.5481921779394023, -0.23296037658739185, 1.1279821823244887, -0.01283291290489807, -1.6537806130882966, -0.8803545852554444, 0.9696792578564188, 0.2041029639478557, -3.0556952451403054, -4.449344932268407, -1.8424458059352928, 1.3129874269557433, 1.137381149892572, -0.9887981217558882, -1.054190358119666, 1.056319249472198, 1.6885103450870156, -0.20845456058208148, -1.1400659093360657, 1.0728990252772423, 3.3056329511704567, 1.882967697236819, -1.457575379572332, -2.225528217608553, -0.2960064505195933, 0.11121724331592167, -2.440352948779784, -4.1298581140054065, -2.1591795384164203, 0.6279375847526525, 0.423919667413752, -1.4675882957944517, -1.3321611322929823, 0.22754683711115697, -0.7718033375530435, -4.443034936662276, -5.918251875537986, -2.8332204760605437, 0.7713500827572608, 0.7016654352632082, -1.205120541274153, -0.9189807566841206, 0.874534436329105, 0.5914189883868535, -1.2748624280621463, -0.6061547721793277, 2.922844751287837, 4.509119803158377, 1.918482709076824, -0.632102247627617, 0.749159520353779, 3.397406219709013, 2.762630236561932, -0.14664958154773328, -1.0753256542442842, 0.0015830711789159351, -0.45049623812824247, -2.2199869543544004, -1.0049510981719816, 3.6935666215900245, 6.369319321987347, 3.7120255124417976, -0.2428474399889172, -0.6915153593606999, 0.8312090421545757, 0.4869880228749786, -0.6081279172429412, 1.0491755619287861, 4.021605665929391, 3.68385740382341, 0.4342850057945266, -0.4496569012793961, 2.3286922957040344, 3.878768576780692, 1.558568555083491, -0.677542946865079, 0.5080554705503193, 2.0562078124872265, 0.35796313880580466, -2.0412292012473388, -1.0512859778845074, 1.5001588070162226, 1.2472405357437335, -0.6085247483546217, 0.565516311258751, 4.053861550363984, 4.409195091291744, 0.8061032594443808, -1.4694084521616069, -0.09801399928706621, 0.8002774151943605, -1.3199381826577, -2.7881853315814853, -0.7844355730668497, 1.2054921739709308, -0.20882785210267743, -1.9637183212100915, -0.29653879833085683, 1.8287753776586952, -0.32233817840125856, -4.460981022228591, -4.67905824932454, -1.2555847565209945, 0.435491783808606, -0.6151389897458694, -0.492260956435122, 1.1802990767613832, 0.3815833341295637, -2.80744580719087, -2.9752406929913864, 1.1373348346961767, 3.6284632927624525, 1.12065775458858, -1.8016241770838897, -0.8857713953786256, 0.9536112297325444, 0.04756437905819255, -1.2186488697980844, 0.08008376553580883, 0.8585317367652032, -2.2263781001708836, -5.356890170797989, -3.318758093141094, 1.226825078202811, 1.9986845818082752, -0.5259720142701197, -1.1004848571101808, 0.3931071798891844, -0.3181892539982353, -2.7374244114613386, -2.123080007622386, 1.2009142695321793, 1.9507517597768849, -0.2606369879838791, -0.06677580619269582, 3.422501687353428, 4.48332347952882, 1.0482189601122314, -1.6415276051972705, -0.6309979398771713, 0.03703619752899093, -2.095153319399745, -2.976026933987556, -0.24862160108691778, 1.6008241898867444, -0.465335032635284, -2.136624871096219, 0.09171570709853001, 2.1116074652523, -0.05431865901442508, -2.5628720342533002, -0.8492612997122654, 1.9000745996036044, 0.9038456648036051, -1.3578715346124077, -0.33695789081693706, 1.841319756247194, 1.049770693421961, -0.36790255200429767, 1.5568930615278358, 3.614309088538499, 0.6185044490386571, -4.412457498392521, -4.667718770230809, -0.9511913905036125, 0.6771450521475706, -0.26103642278909384, 0.22624099728342234, 1.3027065577649055, -0.8363536335111832, -3.817396478407285, -2.0137497842633962, 2.772895305757077, 3.6654737224530116, 0.6351762995557477, -0.12026825854397308, 2.148289307395291, 2.1620524556382827, -0.6533961725142969, -1.3834460374905162, 0.3551658719234536, 0.05158764605519377, -1.7937874145171886, -0.002506122316723785, 4.47258836970553, 4.803183432672455, 0.3642170832314634, -2.0472095057475284, -0.25034331616232636, 0.668965569658436, -0.9850042876519534, -1.0281916598432415, 0.8543992027861531, -0.24249807192891754, -4.123479168976388, -4.574830696359059, -0.8038838337979224, 0.8715666785363416, -1.2711456483221508, -1.8216693020159211, 0.5684622583096658, 0.5751037979100648, -2.839432556932634, -3.9073818888873797, -1.0439825704867722, 0.4826315363129047, -0.7774084300018637, -0.058535755018250674, 3.1175578790448495, 3.2384209021785177, -0.07851237700789018, -0.5426724685920127, 2.872914957428655, 3.7586412403293044, 0.3498167837526124, -1.5478018935432971, 0.07404371956661958, 0.48902259320521885, -1.3114043269091407, -0.6932832369486013, 2.24526289129766, 1.9547996696430658, -1.2487583014015895, -0.8530788152038462, 3.391520535708738, 4.514996371019902, 1.1515156210600628, -0.5399726908003271, 1.1446994382728115, 1.4241090017776488, -0.2949707383252687, 0.3443657515556884, 2.384267316964163, 0.5806670302486998, -3.307558566284283, -2.429299059416029, 2.278231427575877, 3.3137524849171927, 0.018551357591318148, -1.409458011529841, -0.1171919106799591, -0.5882469266224271, -2.075378897273565, -0.29195438138704605, 2.3838178413403033, 0.5381470700858909, -3.036972070250315, -1.7615973286379414, 2.2926614851945444, 2.368293310897635, -0.3936674491854617, -0.28221047204421634, 1.4443140343798408, 0.2088513585430662, -1.5554773909437798, 0.6412924974920012, 3.4329289130271583, 1.8590569023661836, -0.5328043749127042, 1.317371433471246, 3.7894537402322515, 1.998835677985365, -0.21798474984400423, 1.8426152040792316, 4.044497134983483, 1.6118490382835793, -1.508219048491333, -0.8518733398553686, 0.15046254557524813, -1.4163976498792175, -1.127025490891892, 3.0893742794799746, 5.038272492695641, 1.585892932075564, -1.1416059914206875, 0.4503728121597686, 1.129198025045545, -1.7327943875025031, -2.6949570421654587, 0.4235652529680921, 2.1086329802538124, 0.34276546374453054, -0.2972202529855273, 0.36798253644779866, -2.764320274606683, -8.022653757970367, -7.703651933560724, -2.135436901978775, 0.5558716261164682, -1.1425766921100795, -1.4341080445607286, 0.2621107405662228, -0.3452740573397248, -1.8086600502076928, -0.017842125765531153, 1.5723319423434536, -2.1738003604397127, -6.69604883515084, -4.979227706912023, -0.2859539747046966, 0.5626615433465292, -0.49105296226848755, 1.1475459140163924, 2.5264006114358972, 0.2050116281921272, -1.5084996505767962, 0.5425307860964474, 1.2195527457426987, -2.319910678997825, -4.092188148692898, -1.1504412375274498, 0.24770479957090258, -2.8496274754838526, -4.327825384119637, -1.4135444261908883, 0.5034054406442418, -0.3510055615015044, 0.7027066545551159, 3.2442924661107, 1.5398487676382446, -2.9696991005121456, -3.217555702389035, -0.0489136040774149, -0.035644662893253874, -2.1085102688111657, -0.6381563436017953, 2.0172926171706065, 0.16922938193421017, -3.127508772027251, -2.0230655931848296, 0.6365948940908487, 0.009365753840966601, -0.8144181165436137, 1.216007098452502, 1.1807929053117838, -3.4681058880207734, -5.885641651074227, -2.3055845471809273, 0.7066154156482487, -0.9116384681095239, -1.8579873804827547, 0.5317806928725018, 1.3781182217857197, -0.31479630120967866, 0.3432557520309083, 2.452843583596417, 0.36749669822003905, -3.452927068430328, -1.710552344124149, 3.320836731063468, 3.6473770403171843, 0.2752057521662523, -0.41921464166023725, 0.42292973812551127, -1.3134379407183756, -2.5204165459261754, 0.05859952918989622, 1.5021160501306376, -1.2934048792740622, -2.106449626520874, 2.327598394401342, 5.015154155362847, 2.0509317896174775, -0.3595413427082899, 1.1785080664117655, 1.7455227885378808, 0.06022502620005022, 0.9186310551878992, 3.3617987327240924, 1.6712603031756532, -1.8946854945854663, -0.6564571108837071, 2.7593260980597205, 1.4043375351682383, -2.1338356934853007, -1.5202791435982677, 0.6174120443610223, -0.5373477706483163, -1.40852116285982, 1.4402687517908248, 2.870214984111552, -0.15043046183409647, -1.6860602162979434, 0.9339953799280256, 1.8179862746798197, -0.4512673021599164, 0.3349925035019927, 4.182114939521167, 3.912844011337549, -0.20968608147988557, -0.9660188355176582, 1.4320730998804891, 1.1578582468289262, -0.46669830837371057, 0.8904480426367143, 1.794158635268819, -1.4578648541134929, -3.2083338718700922, 0.8106714033486672, 3.975507805251068, 1.2522950346513169, -1.5653996008564879, -0.30332708149427084, 0.18790083744029656, -2.004323929930104, -1.7659433593568847, 0.8786120365075761, 0.26358837722776746, -2.0777587334270082, -0.1409274210962727, 2.978852592959291, 0.49517337339025397, -3.8111879839654215, -2.5316428979723757, 1.2529432778299523, 1.2328928088704443, -0.15885782528876644, 0.5229805513148352, -0.21842981757226304, -2.9028169595547197, -1.0481416908064447, 5.227350870171619, 6.935691170089062, 2.493350391126744, -0.05847297429854431, 1.0473037701493109, 0.17301632086829977, -2.014275515375351, -0.6395180195537654, 1.3355204847944697, -1.0055375619760092, -3.3568175756485883, -1.0465072361280372, 0.8238544535875872, -1.582102162821353, -2.316947853676934, 1.5319595927231118, 3.1862901515894304, 0.1570882408933741, -1.0909228270253912, 0.770713459722634, -0.05124717251525675, -2.8850610340620384, -1.9832078862502702, 0.4170815793668404, -1.1231455759849243, -2.847632792519504, 0.3115232211765949, 3.1981819650943137, 0.825705867270605, -1.249296047436658, 1.0992482867415303, 2.11013933562582, -0.9787477817214443, -2.1285060536318605, 0.1778343238426877, 0.29895596999018526, -1.3573951141880207, 0.48946277245506425, 2.970218797428814, 0.325977678272783, -2.7991338400186248, 0.17316338055833305, 4.203583698583837, 2.586097673582806, -0.5300347724576316, -0.20642767289140043, 0.10590255892391304, -1.0229765536745647, 1.0947952148022564, 4.893995809683025, 3.0291872735073238, -2.4401071624093076, -2.962734288587482, -0.0206499170297639, -1.0197253468630179, -3.8444748807428604, -2.4811458645957107, 0.1530957846136912, -0.14736995188012866, 0.35621334870476173, 3.0979021564731615, 1.944529576883049, -3.1757726470476566, -3.8352064338353573, 0.5643440498925776, 1.76723465706926, -0.781282544942769, -0.653077488788468, 0.8587808287990535, -1.363454563444942, -3.7427867946218116, -1.5471998392851112, 0.6233882513228223, -0.6795009977368957, 0.09944948784804145, 4.464692157014341, 4.955587206979127, 0.49088723807222884, -1.0115271198587878, 1.2835995745047077, 0.7953669438919425, -1.5376825942288552, -0.2584887701765585, 1.4729989224814721, -1.2322523150756157, -3.5698596682323878, -1.1728769533069794, 0.5559756557452931, -1.2090896996525664, -0.4828235369066746, 3.319523048332699, 2.693991483227424, -1.992270293152965, -2.578318063044856, 0.5133791900378231, 0.4882740669181071, -1.2443811975702295, 0.0005252362192753574, 0.9167019346208144, -1.096263732889665, -0.19837661982957133, 4.842694723484368, 5.470115045143203, -0.0961383375478621, -2.9087057477020397, -0.6051641482115294, 0.19367723345860036, -0.9048824104183605, 0.7044432351645828, 2.245169838185851, -0.15975756819789394, -1.2793659272757207, 2.248885243397265, 3.483616537645773, -0.4287011793324001, -1.6746115903713785, 2.0411818716663013, 3.152454717236972, 0.4051106498656718, 0.1861166396979896, 1.8802354913298345, 0.5100273225402384, -1.0384149558198796, 0.6486472977824858, -0.11215045532709605, -5.83150153301548, -8.01884985475502, -3.106543788770666, 0.6926455583513105, -0.22219875080261514, -0.33527770705447174, 0.49618448671520987, -2.3951460842312255, -5.426072529767582, -2.93556427081039, 0.28449379139265013, -1.0582902620143155, -1.8335258067397973, 1.1603738703969524, 1.550610380394353, -2.1157771906363854, -2.4614011113037657, 0.7433049925414008, 0.18645269484749724, -2.941207390765963, -1.9652263260510676, 0.7319434904559121, 0.11782070235436445, 0.04251338668315301, 3.1750557743231815, 3.23471804312193, -1.1430031573507038, -1.9606269592334846], 'positive_zeros': ['1.38183577368485443850344162533', '2.41505414094283300064626673291', '2.68748507694422721920562471711', '4.30848382997090723010448155307', '4.723102296022672961777212582060', '6.01938470919951452528574487982', '6.59817536321283592759387435165', '7.22861907320794584299525758622', '8.45537368689551261158084054739', '9.07956845605108509437525794223', '9.860136610262701177763390667162', '10.712048897239022195748880956155', '11.52006249047516322885082595313', '12.04346496520492796678403438724', '13.09998966060965648353093108423', '13.83970226179036891511109708916', '14.666400603788330934654985972772', '15.13956293471927567076460888154', '15.84555000614519830994152349593', '16.97496188192180811888889062360', '17.68258401328581379357609023806', '18.184013654740384700090908879353', '18.966022710462632491942544607977', '19.53832293505712050729072670373', '20.65803195783730515211709505027', '21.28570779850618973374327227155', '21.87302150454332607092301971235', '22.63175151015038967831231934547', '23.149111360139369409845708028678', '24.2192009870304728785887811922', '24.849354714970188152305490914334', '25.47730560890098321609543236055', '26.22026071086997772013501034585', '26.760556717985586603469695111386', '27.66879758355464848819857729482', '28.491625962904928132873189629535', '28.77318386387616252873211214534', '29.905914013248758330507137203256', '30.382325634451896713790546426611', '31.1866019166367279975052073254', '31.45735264897158965968647707636', '32.72065044873869894523076792534', '33.23374147229380650626854971290', '33.900577023075512183898920483', '34.47183040242583221689319492824', '35.064030332788806177866726024379', '36.12637999595413525633056170162', '36.47425879112742958929254395492', '37.48187472877883395362848896065', '38.1243881561604972701847892883', '38.330555289864528787297068596338', '39.14100665744601972967862580304', '40.28470422540135763821942915247', '40.75932363480909325630275677729', '41.353744419083975671246226018987', '41.75045173325302523361646723965', '42.86347781491564973907757765325', '43.19914134525501264912303932288', '44.23013105297153561271527180096', '44.61419027486949571996407077203', '45.350099715811183943421985838753', '46.05421385267980880609615532141', '46.748864197037993373621698389692', '47.12421335076990573967879609904', '48.19339325391761546372681271', '48.76513512678425504343922603426', '49.217765297979453677655412932184', '50.08606682708986493479290431043', '50.59886853044409817753174674822', '51.28154642497615311593970429058', '51.85034891404505492036722871813', '52.9593964796390799620725606311', '53.2884614257322515905014094972', '53.84222326388203806606406675295', '54.41672401496493024706086219878', '55.23589672924433367036860093688', '56.029361640966159921539490408279', '56.68057691877532043467386872932', '57.19536467460476674844166093386', '57.79973526237661019010666094286', '58.25438416862332267032966422293', '59.2787023765758313386427973986', '59.93377936126585565613468659998', '60.53104592451242641243571314177', '60.89017993434838336581868125038', '61.759995877123369481769315809816', '62.460297826657286157828354746193', '62.82076918442098567240378686243', '63.8333285293286104408546563646', '64.5083732817473902442260950874', '64.698777853830044248667343257280', '65.64868636759741295253092539261', '66.20082688681724594810699874368', '66.86615766569126777040615529206', '67.49512008866150879169840650895', '68.203047147920758727818202167422', '68.85293549492477092326199515743', '69.415748546838503574125693835722', '70.16886177932840097889052932990', '70.43816312253318376411938787951', '71.28582216333635413702938572338', '72.28788304190957241780730118776', '72.72598476604198533789620630828', '73.0746827872292602241733343521', '73.67291530984621551499999750184', '74.50292581603661798644150999491', '75.39675476385523068022549860675', '75.64883598541568380733785439198', '76.48912062523332896668437908128', '77.118188148406753213024494423291', '77.50850040682034274224539654574', '78.12518985118529194853711232357', '79.08794706923233959943881437886', '79.72274222121879671970021672375', '80.14665331875959094632803971615', '80.78625843865626173115092799372', '81.226178589865246379487180081401', '82.26063539203829684185138838953', '82.65588472509142439820591713765', '83.36369772835911701445830624312', '83.81526893964172167419846543649', '84.811059912435866130331652682373', '85.14480326233987213960118638860', '85.63183423916162116478803247190', '86.55421213162031516909254368516', '86.93883604998593665967331587910', '87.84273342837563526984427246738', '88.42534397394691558595948211717', '88.84407094705756749960656118092', '89.45065347796244987387423471473', '90.184276419117015124307525603840', '90.697004993043476608965164090503', '91.68205087363035448303737746343', '92.00792916525138795953254136999', '92.74684919455428147833550881844', '93.07199553745751627952097452042', '93.79375099204032172283967136206', '94.535893943117070488964177058420', '95.31426094824139556159394995393', '95.98268529937541379678104541105', '96.104909864243479014905063228312', '96.90209851420835415894867604097', '97.54103290887695159750238391536', '98.252453505167918741509220235410', '99.00730472403213711264275914579', '99.41986919811377835866657401118', '100.025489469534944895208336773428', '100.56883780700169680780520171773', '101.44435432491661213589064574473', '101.73589182497103719973244812417', '102.73155993558026818719741260485', '102.91302237912928344351059894045', '103.878948313953742643302335491410', '104.5412558675727673469595341220', '104.74602725495746798856478296702', '105.414103790234026180105763547780', '106.37354278977895217481951667243', '106.81560869930588153177638820713', '107.33386369177982086492599871135', '108.08785239745376993093172128584', '108.80969141272883493554361955788', '109.15796857989717088729124356740', '109.46443342704798737871176595456', '110.78731756434177267365224818485', '111.08027559964972938857687144455', '111.81227714100978859778533120543', '112.12656702582055418637376219710', '112.81440549035531614692956060025', '113.306037141624935436760324995749', '114.40372332470373229105994791163', '114.81315835201121560313892669876', '115.156900829679517833989634092', '115.9580472585956278082593622786', '116.498982006191026991629962483261', '117.00892949709382961014222235818', '117.93721800577796855306741673663', '118.170217450104553437253333146530', '119.21738220872749195456683387838', '119.57455236016004287019203932064', '119.90320929286810522830844978793', '120.7276648967973019809307155143', '121.56909669619442129111402188981', '121.8695792855471264593402740703', '122.55946055650717318468981656925', '123.13859799699065094019115245300', '123.957228737419397344149023759242', '124.376667507763307667399483651737', '124.84199285338802554230777756889', '125.41259652767575494053696021350', '126.42895113884046047444260245998', '126.75944250438962174503857163848', '127.43843351124752544296465568655', '128.05909449497674966162818181177', '128.38800539258779890900291189985', '129.08873628594366025822830260040', '129.78908079701777703049944612248', '130.65942939750259557343227575000', '131.047224368032042633886127404208', '131.38205374071975342487787679708', '132.181863307151679002833913508841', '132.69367572620618416976225661419', '133.297678232280421557100672256838', '134.2624415243524850958545333339', '134.50701213140980436620322951432', '135.33132249722392656948124135218', '135.47226634248769243131832809012', '136.37617494843619157986409394370', '136.92784596972921756051387560840', '137.60880190300512114372141971161', '138.30740392298012116920368344244', '138.67013493689377938520432171737', '139.24554894033296836442678719240', '139.98689053617452782418187148080', '140.53077170740097088449251702606', '141.18240987980157562126372776770', '141.52883250944723650406611458859', '142.48141160842462683890671785038', '142.9398399877721824901816048486', '143.616394160824584166986182449772', '143.93260590864675854021232653164', '144.57466096839785280710083519194', '145.264338492544858317184086882590', '146.03431677098200681616403224337', '146.614318036511479428094321444622', '146.91181868110626216445178830401', '147.69534988878536777880655756650', '148.15532889895490449865851249251', '148.76106091055473964168132681688', '149.405561315784902080094086473342', '150.18871900136713368850269261786', '150.86026605643316656453440320280', '151.082115835611006168290530148212', '151.53336673847282323680090895074', '152.24512649834770556596226761729', '153.386704546046454170772315909560', '153.48734142044527352469047151709', '154.08385977958806870195004782980', '154.75608261066825018668916991609', '155.2245331243265842583448707931', '156.03964470294418559763107288491', '156.398808877904893502810174817004', '157.078364735163124255811471069372', '157.82767368661897188091316522947', '158.30898979161931045858843100356', '158.744311927207563655936987378122', '159.59608081561351186349072179138', '159.86735541703270323940435572869', '160.60349475522801405409654054769', '161.32303770541058055609454979719', '161.76406882848962057358176344175', '162.41278386117947017173430403276', '163.099349906111149699056592829690', '163.487320377586677188428898890692', '164.017091928904304744806740996724', '164.71004732135290292469130995922', '165.30199853118970758964376223509', '166.16788919076912144225539245777', '166.6174004881038137997473682497', '166.90616513119648370222912193489', '167.40774813111006662373234019112', '168.28852989185154179982160346802', '169.06636900385590182228686746106', '169.24817200792221436681849383325', '170.27786588978475113064564127348', '170.57544257221485587260216755489', '170.88038420404544950759631681070', '171.68399870992886811741137910241', '172.45866981936739297913304570672', '173.02546577045136475766189394262', '173.536071512262414302365376704693', '173.93280360689581411482423021581', '174.8450229012021423213334170085', '175.18952106375960175510527230787', '175.61562627180987951440225101943', '176.60115903487086142185701243604', '177.0206971326974080649415389501', '177.59113210268821670140035489281', '178.15381693508466949545517471078', '178.64933524184486998209035645052', '179.49945198783190953632969222656', '179.81662566263723954595697155019', '180.35543886865475088213750443644', '181.11364704495626596185637591084', '181.81423657385257908977502896155', '182.25937351413502319238315763752', '182.812423714440883418085505577029', '183.28476813022314249675653506268', '183.76536463512926811650861567965', '184.6822835264011620876355970668', '185.39985601825834558824736899007', '185.67662138227517719496731972560', '186.16516940515012813463939870113', '186.85918785046998574479053426436', '187.328457043630784459830416135325', '188.09326360790416179661079423095', '188.595926771310427741602247096819', '189.43982487336397069945871364925', '189.65042337204104141072319010259', '190.37496987972348846129770092944', '190.840526479749453111314305054682', '191.240941876378486953214014009730', '192.39070253717304043762556622670', '192.76719153320992731613976619795', '193.20262804259118046220954450555', '193.54107703279486721354444187353', '194.626905826035748533611331821988', '194.85364075524636728470288990979', '195.5160114499786613330125441117', '196.07876116326429095298206805216', '196.79217672202034378838635899012', '197.20584976732375437970476982697', '198.0083888559164421411465443319', '198.46248947765509200805705485377', '198.74323473809751784986289274593', '199.6061112593044835472995434535'], 'prelabel': '1-12e3-1728.1253-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': 0.9988425925925926, 'root_number': '-0.999993389386194260707108841417+0.00363609459602795498439485246783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.499421296296', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(144)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02273425927880603574204923860+0.513668898328187953637653833988*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.38183577368', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.41505414094', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.68748507694', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 185.69939004511204, 'bad_primes': [2, 3], 'central_character': '1728.1253', 'conductor': 1728, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1728/1253'], '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': '1-12e3-1728.1253-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': '1-12e3-1728.1253-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': 0.4994212962962963, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38183577368', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1728.1253', 'Lhash_array': ['dirichlet_L_1728.1253'], 'label': '1-12e3-1728.1253-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1728/1253'}