# Stored data for newform 11.18.a.b, downloaded from the LMFDB on 25 April 2024.
{"label": "11.18.a.b", "space_label": "11.18.a", "level": 11, "weight": 18, "hecke_orbit": 2, "hecke_orbit_code": 4503599929360395, "dim": 8, "is_polredabs": true, "trace_hash": 1673373686771458761, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [52037343057540808704, 690666923807719424, -2743273869476864, -33707985430080, 112166877920, 193036540, -687186, -256, 1]]], "qexp_display": "q+(2^{5}-\\beta _{1})q^{2}+(382-9\\beta _{1}+\\beta _{2})q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3564, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 20.154429607901562, "hecke_ring_index": 5474304, "level_radical": 11, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [11, 1, [2], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [11], "conrey_indexes": [1], "field_disc": 277025175500626449217278640764690231484369578849873404629813237440, "field_disc_factorization": [[2, 6], [3, 2], [5, 1], [34429433, 1], [293086127, 1], [17858068672709, 1], [165905030584633, 1], [3217418648851241669, 1]], "field_poly": [70348376081176985600, -427120471274668032, -5237791784459264, 17831801296448, 132277346400, -57426812, -715858, 0, 1], "hecke_ring_index_factorization": [[2, 11], [3, 5], [11, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.179", "prec": 17}, {"__RealLiteral__": 0, "data": "7.226", "prec": 17}, {"__RealLiteral__": 0, "data": "3.806", "prec": 17}, {"__RealLiteral__": 0, "data": "151.330", "prec": 24}, {"__RealLiteral__": 0, "data": "146.215", "prec": 24}, {"__RealLiteral__": 0, "data": "4793.604", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "17.2.3.c1", "atkin_lehner_eigenvals": [[11, -1]], "trace_display": [256, 3058, 1795234, -896364], "traces": [0, 8, 256, 3058, 391332, 1795234, 13170682, -896364, -101682420, 413432462, -717567014, 1714871048, -3285295504, 1804014468, 17794023508, 8875276234, 53793011976, -27416338904, 28258692878, 58429836440, 650385049400, 562668763708, 54875873536, 1231860549578, 3528111117084, 3225446670918, 3698352129748, 5544189136510, 553346903392, 4016405848668, 28329117219490, 21044142033258, -7034951233624, 655509458098, 10491977089288, -37564178328188, 18688387613044, -38179864040434, -32101053490680, -133370005047128, -229151934325836, -84601913468108, -374381853665348, -79795156805452, 83885489619492, 85333967988848, -63876340102558, -333992064138544, -921917930639032, 16663435022976, -203190218406730, 445337187172876, 383080290241336, 351380494472328, 2142853805961238, 384824351373154, 4437023751861816, 3266305594995600, 4039861017699420, 1023638486071814, -3214396297711936, 3794216197393316, 425349364206562, -2372860203801592, 6201620853304640, -2999195217446768, 2823252655526842, 5095474549488046, -16863568290550648, 2954340406561046, -1215862479252572, -1512701018213922, -47801016625093920, 1243757422569468, -32612646811059594, -12043436835518416, -57190847748178480, -192143584008684, -39902196048908264, 11583193006100356, 11760711968111960, 34892948392364408, -36998674460297948, 28335131925089508, 99838504514799680, -13434364728244100, -50273004015301116, 149533775100988560, -21796529768572020, 188410727637478542, 27756107460171104, 136202135129762480, 55575922205377216, 150258196291800646, 9488865070270352, 95643103186605600, 143914463501217272, 209457880210246906, -306362245050391368, 88622919923395022, -117767659127271556, 492833448664691720, -852712540112533748, 54979016864860048, -308743387361496192, 365470795959618652, -907303840455954696, 86091439174794996, -811070622426064960, -50370209346498888, -153816862163551334, -641170410058959618, -1232527565965023344, 327349438892361018, -1418015300108808960, 467393150039160554, -856254022474269576, -183054101273756836, 666404288196533630, 1296583886202498904, 771752338730913468, 367597838908577288, -1719616471612096188, 959970668913508816, 1558558487149244896, 746208048662510994, 1418606906816412488, 3563875422898038976, -145572852257300880, 238269429251322084, -1088033913072340928, 2462966369289980268, -704232267991771024, 2703993656682569920, 1635616188383174630, 4351076875771045150, 9005463018099995784, -703738186281246454, 1548014046819593006, -1052474524659659196, -6073045061682442240, -1158467836063231024, -988809976020078618, 386706522668290308, -1211161028820938528, -4330893999771999864, -8400262984451692532, -9533975996837063574, -7250448222839413768, -4917544294279195456, 1993698759606128624, -4588874304315244100, 277368208435973280, -27656810105006205172, 3814306967662574548, -10763913310663267238, -5032299575024447776, 9449840051281972546, 2061900324793471700, -16853833664652545100, -551004318816283576, -3978947974070825572, 29771220121264153136, -18133321054023998112, 7625704206451970600, 1902494282086134154, 48971580750484518804, 1019426055591578616, -15730057587729740280, 12952423230690516576, 36481432468927007068, 5973040711958388840, 45924605365950738416, -10856670181444437672, -3327759251920738128, -6416099378369924576, 11531009852794958856, 23366784923309598050, 28598964675034695750, 3584407987691063646, 90648871758065954296, 32642922476199455238, 59362648485628914352, -74713007416679179704, 40574964427592809404, -80223012521674859718, 7671832131378476926, -5876935728578206424, -69655415029821159488, -92313767635156920620, 71233335797532533520, -1017776157835742554, -102118431632116872704, 46842727524211409628, -211746441533681936350, -95968404390210992168, 47329735069383484164, -112696781599577604704, 6057501783850749518, 95884595021565083504, -289233045686738083224, -152162639430661108918, 74041363106205544232, 13522660108003338720, 175100378232482675936, 115395672269783451160, -150970685606581516240, -65298284250726846596, 100330390736215334848, 12524954356291423640, -239688252844898667140, 74757588509111586224, -103440185853604316904, 305910965328335718786, 266831874403972850676, 165117168014920134156, -312202361533921065132, 322507445748583226492, -157595941762254723320, -284881243322046912248, 139415811408513721400, 275946405912389494216, -571750760294639641338, 372145443795340630098, 577587636227138121200, 492099673536306867478, 682017188782064397666, -56356141414333164444, 174873797431268276160, 282753661771600796630, -208762994301947901550, 120613046562100290748, 914943915564653848560, -535412206313005182972, -701622475051212973156, 763129013520792886448, -679720521582340835312, 435104531224853252540, -675005124124415944616, -225798191709218620308, -2109567352550086564216, -39230406041970915948, 11763130845074473216, 949515475246946434168, -426545984881526546824, -303230965674403320822, 1030675535537307051040, 41144078031157287760, -112396344442395927780, -633890272974879460476, 242196746198321434266, -921524757110635020674, -2269450418514010045664, 264060248955585102218, -249010394757712457776, -2066122772402086470212, -118636895819237103328, 1138665946403453681656, 48609426392960877876, 1349614495337172606412, -820227188151110365360, -573496559156303399220, 135517446190872300012, -1373707659875384919052, 756281951101786223004, 1831591731117725254212, -3079636346827383056640, -1031556663228353645370, 4645593704175073501872, -157352276250100339016, 3713699310223943407846, -488472595313240903768, -229685166020659482064, -800720946544896099344, -294548035125688770766, 691403139103157722758, 2559617934868214638240, -1964880281018171043744, 1973902082278207897540, 3789781380284750572844, 5385954388453706541432, 3347232751926765747432, -2911644265389705318448, 251885594234098328688, -1613860372396254542016, -472732237374281606160, 792774624076748091988, -1539195038233114263488, -5573953068281680802672, 1828515837820628254776, 6353397761317651621992, -4925806103536386165046, 9645756238396786231336, -3812235016249607125812, 1336125195533433842034, -6375785526013419389842, -4251265408923537756996, 1188446179354639845310, 3339935154244652446880, -7099007268682507570408, -4132088862117536401808, 3921560286505587323176, 847247541269258557772, 547695531276161238836, -8066522755382347956160, -662447153659931334192, -5417671221391653446932, -6042448165237871380664, 118614823015924224352, 582847288027681099712, -5882623617416759519774, -5273007514014837972168, 10603677831015723706800, 4218544977070845199918, 5848418571493966468250, -12776091075434351402536, 862404606803997436416, -6294763433188607135654, -3733996857184917798204, 860952263362327820508, 7246186980396632058496, -2912257859198295713916, -3727976399661132228868, 9378595278500238258000, 1664352488908254227332, 7828041294644583945796, -1573822898475385825472, 2672087502683936989300, -12321645632375424181200, 2904016639402781383136, 6072597866887707790690, -787351957534756790766, -7592678321646420242544, 5583320668667185418328, 6194280231749711946696, 5792778523124991487910, 28603549394313677055728, 3842301769829742364336, 8474325154284496627368, 3183497717048387565930, -20777460601482676138768, 4510998737854249664298, 17629976305844531264520, -11171800931956407861960, 2789806480905918011208, 29763170505205589295590, -3956107239659659250904, 2789181286131084930736, 7428494460937252735200, 9145761288315609841760, -1005205811474006453920, -12509444544955697569784, -1508004274329210214744, 8627309869366064364678, -27347849347601385652870, -11574333311626595953218, 20482184011452728044104, 6206633082540073871752, -28698194506026967591530, 981684276670076667208, -34696014104699029213080, -3878309006601068209432, -6874864945354801330418, 140514273922803668338, -12372238292289650796096, 18148984426438560497632, 4907009217128908338312, -15728627281100013357894, -19724095859189543704952, 35189069943978981208004, -41823681299674634202606, -12547633825152607685880, -18728089551260896235488, 3031193281253739368448, 2249048468337412766728, -2139209681818219839786, -8804751745743742825824, 12520561048731987250440, -19107957147744111329900, -17681349337703543794998, -25854299668015494817440, 18058966343732120596832, -44692244927867889213778, -5425113441076615230022, 33233524133178540976656, -8052215232114830437628, 18299673453552781581148, -18513167144002825014336, 12276296796011513148072, 23724851957899149568962, 7251527124880901042632, -36343953544660275920644, -4021363830277965836100, 61570047722877575954556, 5647386773778099948688, 8802355589474559858692, 4006021856426372843764, 12228405131937336500496, 22832562823688102701200, -11930777838332942736960, -21299602688854681723888, 73529981788798357890032, 17320653397465477895522, 4468038790003159674296, 124198700237036639881816, 100533376523027290343234, 8883480446516010654048, -8184192932439570994354, -39680221970248340523960, 31695379511701963273472, 9650020505499573501544, -101805250080898219425910, -2526862149015626024544, 47372406238898718072020, 104877274578352802800204, -96042220001055084198324, 40272066550259480533472, 68961027252272447037940, -6881145905183308729080, -43785353288152947967840, 167987464080285129996992, -13164501261050515196976, -104711923576027549498608, -86074462280278690896512, -93013874371286251954536, -14156092373414695628404, 34695793723531836429258, -84217802924615884525808, 79853654889371719781232, -28589045040866710343768, -74195660754633883319556, -40730273299425663252252, -98993664202856640021160, -111056729489704399258302, 27227831037052793107612, -185540064380853245120832, 45113467663939272370168, -21446136110770872615120, 170975072614800903980536, -61708556658623220238464, -49120752221071694349516, -76465623183996541990866, 101330518474867874678152, -8891236121137179796922, -132143955423597499069056, 37206542844866620181634, -176608842098372221736630, -16415753106543323041060, -62550677476517553842688, 119612961962086772353334, 101331229675260698282374, -18135171501482460067148, -124214016798634775900184, 242763805522721117061716, 56706955829774272232676, -241893616994924226766064, -178708622656643589905280, -96217968593403676895764, 262287553782655196606430, -167788113844185449082764, 78507307246926497044384, 73308178803075702136068, -80252075218409745755588, -31207512424020370930722, 230633488195797105852384, 171273558943669607914198, 56887019312295607304580, -134435005873650835853514, -79403389550423718103592, 270600347964835501891044, 128712156516650840650736, 33102000736069062294938, 306061018761660915570420, -17104800522036225419212, 61992751959135230835596, 213072477673197300864920, 333292169839387907546816, -208970035153064252931516, 184445729429767936114620, -334361098625601325675384, 343974876199919666716280, 204170982364033908315616, 56301566458314867238612, -8124138795927261374044, 17981599686971420908452, -79796882569979740347298, 217941384438227809525048, 65129582808236265680986, -609120932239614705873120, 170610479525201767701448, -299239183504987135098558, 54996796104680717315560, -396773851705861126648288, 528644836286108605137720, 36075730639797147593520, 18292093889379277759088, -95622696392447993147192, 44256409698175217421972, -350997261719223673472844, 21747203877760021336096, -313910760911306738201520, -196974169578481779493320, -368634581329566596912138, -10012745557842804378572, 310773511240227135973200, 475533625425711887432036, -13692460786759758117598, -328794659814634934483946, 536743783057289464532352, 118397636596688079788262, -1327373595781797254286116, -90217002133575301482640, -596744967047770010422304, 266598307362738865173840, 305696150603982552664840, -160825326543395962012384, -309752422979187034070400, -71594165131618520809264, -299154442532633691549396, 372790058117443076019924, 25760289765486320381616, 182669508775841555786754, -556178656327530780373140, 24293890412143648702408, -219272846321893113815472, -20313729003006084431728, -253682616313217709702604, -463411396614725960973188, -197621295985618514443192, 208366599775091497756782, -420032318906793334729356, -131109851874378227033540, 51267343429268117226880, -75232658958082034080904, 603740400019301991308670, 549516706928629670107404, -100294234281932419053564, -605361136842040313194950, 890438137659231702291400, 3571955285141344649856, -84514582643754760952608, 825484007072504449216572, -478476326606548434877768, 494950251284640857802406, 1089610139944144741212464, 472663443982880398924324, 5757417536028936256432, 41439385913915252616856, 788948821396557250846792, 784950140761101212386044, -43555627847812245669130, 232542489717787226884080, -680566865964675029052540, 294877404009133586931480, 749470281853823336714608, -123425172910062317148930, 404898140780632867477744, -458479226121900471123104, 778136521458206352507836, 577603399264177495444960, -1104613344797364927796720, 95461981110065252911756, -479082723716455822539048, -386135577122620662799712, 1161777795584710431318784, 134487994877705247025086, 1170849707968458929105776, -258891441330923862876844, -209074979234772909701580, 132794594244905499491604, -1097936527343564499279840, -2706448480284399151664, 82116662349288004905016, -426379482192636307253014, 131119813542373533626944, -360164886544417434994616, 1467559039012830370489664, -556221803112577928765974, 305197902653178042493952, -28224174844812005429768, -747333989537224713606192, 32413202007212203571496, -900205721670179441219278, 75321529600314915544968, 149195930571094725057888, -2522530159103095133653768, -932033308764754464701604, -62321374988275267176704, -870618550160291849620368, 367395290512939310779120, 175485746718670469289302, -1137639722101445826030020, -1676701659995328589716664, -1509754383079705557691732, 459339743992442107054678, 1091098682669689883343160, -1619245106419537691702120, -2531575942436329936511520, 931196854773053320264136, 434387555153605852119040, 1885141694808045915213552, -1923453580211175972280592, 280403323161706975964712, -443655067874406119949092, -701323110571934712585312, 82490517341900104880674, 4266320964211965523323380, -2314891138837379816358884, 1508844308447866477100160, 1540749002316451394495232, -1575297131451767224527216, 971945764199097095280320, -3298823988812509531467224, -908751608184536924206292, -41782676527022099463880, -817209343765425965069792, 951115446419520544387896, -1709621662174871907775584, -607595453641622877708064, 674149145315405764342450, 2958031901364500261059424, 1115512988067970584518354, 1432697140126336064428632, -278110000935257650509540, 3015285119646265642390688, -2696250119823677160951492, 224671093401469605012134, 700161612347296015923600, 3843592180713533437250712, -344716682364323451534780, 2080157507165041032294872, 3603002367527176849668378, -13395869857193344903080, 1991000673815433676623576, 1337367081471222557248882, 1057605561193226426096768, -1324515341170525823183328, -2114663521774088572115964, 865980087149568865549020, 4587566932109942637904884, -3529706444844491050091280, -560922699095098718368002, 3347491248851833464536772, 3017832148847067132658918, 4628004852924743369187520, -3760583517348522123527004, -3016196901925657720673520, -28771235775313683320794, 823311829671993222268620, 219426000422888134680134, 817293413950337319526052, -185529095033432488721084, -7156186571980014615225584, 1675552871589070875814198, 2916694098633176351692516, 1883691077101810980851892, 574211765330836175606240, -3392653828890477287928076, -5744802469966269317628256, 1740555474241073727203428, -689034393468073461303616, -2469089638560730074018054, -6846728863181989009182278, 4250510453767821024494416, 4254836528863256508933768, 776512194613159690819200, 1028014401125046542946408, -3757464424155176873826240, 5941058594988748525386912, -2782597708044888657045794, -9481010301259902926332018, 813323938345306334639396, -6076106759284756474060528, -2818717781917135567158632, -23265362025587270817040, 5377627016768159323627160, -5971394724705259227274308, -2195735529129398153918304, -292135237902613661768814, 604095636800123727053892, 3373438409157937482260568, -3433813270113608316059580, 91177413745380083177122, 1139132298823223032194968, -3175123839876632103813360, -1711646102885632825231234, -352654913067158488172680, 1844913296005776197145270, 2214038239598057751777008, -336254650299567892041288, 757399348377291756063662, 2330934710665021072871806, -6076271575086876562398984, -508643658056341207138552, -2645378223719444957454752, 746305103715837705004828, -2626111718321673133538880, -4256222477503038044611448, -2981830952722276143469920, 11615795680656663372864864, -8446386724114164489454368, -796751635383063395991112, -6776907505748638699739240, 5021119401203516605006720, 1329372506500647782507840, 1976371246493229420795728, -1545734149485106877519778, -2675560665627290195812888, 9612426268585629251130400, 4589909303416856887328038, 4253556698950833012824694, 3551515163316561192897880, -8879786903030855871802740, 3106493954466276454418966, 14580310381918888774333384, -642904130712440865546608, 6339316442437507559625840, 4249569516651809828746260, 5604973299725376549213400, 7921504031632584213165786, 3334312052453174058170608, 473627857845753002803776, -2456476170357324274469344, 4986409047317738987183776, 2349714173481362828432824, -3607645092792404551883196, 605189280019012316583802, 286917438341020777273826, 3835816624573560001837920, 1762878708627594844692440, -15944783428177308749169008, 5201463646577683644033432, -12437736366654521612477088, 7936182188731912316094788, 10416300111865446471423538, -4636080407954360217051582, 4239791137301356223352952, 1092260222592236663436526, 1502611771819372537293956, 15294345325373176916323924, 3104015870224195919964912, -4436646443399615480310240, -8258799906269990446705848, -1265473227445254682367192, 10482326250003875468821860, -2751924125746342864051012, 5375053706183925947464384, -6901738016903714181776496, -3614855628429519779104888, -5988733489011013067979000, -1800019382163660130086690, 1589416692985615346105814, -19420728323370667865601344, -15094664490657396188253014, -311153384123520413554296, -3111487076824127574045364, -630817073112273760311232, 1847875086624128467840456, 1832257002297269528332210, 633289103643510878749526, 3834145088906749644957120, 634702992585455296586988, 7569244924458673258732592, -6213388568067923950832440, -1632488772495893376234848, -35520586567570542782376976, 6032673689518947776860658, -10222096639735825976814280, 6622489813846334482007008, 11032205276974086803114572, -260630920502467050291932, -11808600810973512451096964, -456480324886116734353784, -9148687497866424732420312, -16011198026841286162768416, 8732994047983079287069432, -17626726714458591884234892, -8544789210148282436330988, 11490800636734580095242810, 680703417851593090345200, -871347274821300419605696, -324260897551896938541282, -13865132546991295810402468, 6132676144850073065657280, 17220570640895189052248232, -15294097842225254806136194, -3452669439031087202253636, -8159646073473452033045304, 12540858254540062284390872, -21187993917672627974238244, 9685279624565256347709812, 1264655970635497323036996, -10246572434417529211103520, 4677304828846560292829416, 20823076368241295645766880, -16393894729942534294416252, 563345613841379703840800, -1225820675302604826213814, 9672602835973034691973440, 20351020664134192018432928, -5224157693936537950733888, 22377657686222563059521520, 13494724530344011949868512, 266610449337435305245308, 1063849703004877964641312, 28229925847435424519644412, 8330682744833450830042216, -14151949154405521610817740, -14961422957693331128304840, -25099119972186637050680796, 42725656086112192094215226, 8534492274345173393001588, 28405977937492790159071680, 6239824406203758524517656, -6990810476866952994154314, -19861394288959532256820472, 57301722660948059300366192, 3251012840746151486991040, -10858298592164831681341200, 8430647192779706836249664, 13869782258518107646558832, 4537194293466334575481168, 14584465042065032200972082, 24467816634191586574508378, 14927051975739278834824704, -2581617643455908708652496, -22033799543473959626279212, -2930688150807829128936304, 121503102393942966660128, 928423969392298640225442, 12182937872893039898888604, -41058037436141164671106724, 21297804395329337651746176, -12270941845754665746754248, -2657803155754458900922316, 32273082901536212913196680, -12259366126740908761080880, 6015480362936632310292130, -20250196414337122430964640, -15878728634919197471975822, -73522454902059793740625656, 26089973349989765675168672, -20199338162686012266341408, -29161803442948148414744964, 25172866445935622387659472, -5168673978033029844367434, 25473844963724703261227008, -41187683659430996522604, -11154419139426472350272112, 30708726381035016036701608, -661393176516448727136340, -23227663989302516402836098, -30595721812771435596994848, 11328311034737297684829088, 15188949591076138523547024, -38731858895655097136129520, -14944729672218380228965464, 22688314498152010842251876, -8553390094486596742692584, -15744863549106808696151986, 7576860038584040632913760, 3183858070932638884388896, -44017166545289307374902908, -19543763094074733417237072, -21131366122712322354361432, 27854759661326655198445380, 349720050327719331022858, 4491419257788780277786646, -18589383162548549723666496, 2482960291194698485861636, -48318498904875362817620256, 32730883996043142695021880, -4521685544163316268056680, -14558997520018169730447992, -38204194610460802141194720, -26846130307404905951376708, -51833101165662233747503456, 24710338987183701637093316, 7848807278761167257027680, -19547830200167846417913648, 2521013057247787428316760, 6208230074938436722705058, -40835104465923522602700114, -1132523004323937615269952, -22935300139046311082242576, 69969653201439417917873522, -31843215182918546840516834, -48689579488335404704830004, 43561511063050429477620660, 30407892252177426418228896, -35303594368956320921333334, 7479613372177983443107448, 33653934367465337549996896, 56465476487275925660512320, 16411136711428875927966428, 51273855596430826691941302, -5736393656611511502943200, -15020394983798247323360152, 16776386284019762645250350, -22727565753080257254939360, 54181327828964240665095116, 38052613524713898482733888, -7930994455792747059876188, 19422159920257156840628376, -47885688380719451862399180, 27757063873913495816823442, 12656875467380089891996388, 66490086008388372807893456, 36715054273968087028095312, 57252856473988641437857444, 14109080963555200258590736, -18437522085771652976845656, 50376461961616344102274560, 6073887172449562759720548, 29642391356182536104975052, -5833599110720036763350856, 9969203673170588686969208, 61577139867194970713937912, -95255228564666899535653580, 2370078654957034493834892, 41905258853337155833670268, -32124400332302904868919776, -40114425795643203392687388, -13776578236841610326531064, 21401270108505907343958080, 50764710949627468182795404, -35827967822052090295039610, -40817831712015779211184496, 15787882720190030546550720, 17112424650065975147005776, 139002637006942437413134654, -55775994598585592269403880, -25711508241133129489684824, -2356737670613375150208264, -62487161641661220361382418, -2879775390092274370852100, 18500578008115399912398480, 90307569191584041777301396, 94688748336995416512493604, -13317468895659046148609818, -135610259057864954864147840, 42312476004668018720600856, 123954740386437998995928402, -58968859511480711323263904, -95380747965285035121049448, -43422591108011206021035020, -10776464885228454103811196, -15384017201759135404740714, -89103573826030969428536000, -14362752705266188215177640, 86685312928383370304841240, 70458816319371329627212546, -59802810501326413110441840, -69744457640065062788114672, -14050631481936908215108476, -63041006287876569796396042, 2434457812645287360056064, 32053892702353569715401360, -15276766536071734749234760, -86229599305299165914055292, 1649870618345040047848192, 13671998939488994739902478, 25917064689851606132188272, 17403291138997500451435008, -121741964429322803108822840, 25696939501785389213536432, -23509386981177081126667708, -121479787366542968661277584, -4672279730874287175109620, -73908085883904696595587840, -243346249129328802580546858, -162719364090772124495772862, 249816431671643190722768816, 70369888057431540409637480, 86390922446060077467902354, -170570332329813754167622480, 27333172740192952117741952, 16708696793841769227317826, -129790412215380670817177624, 40387512744765673924631502, 109963330280264470301984760, 16557418534533944669123060, -43483570336144407555090008, 116946450889110764264117658, 16250030244791657469489504, -37094707376844491319180356, 44453101687727611948822392, -94215108302092394921696608, -155932211813794247780028320, -78830882685002743141802076, 5949768136078029921974624, -65613382159595691057484368, -37966769057072538079200328, -88231600984310640949211114, -34702090143284367188686476, 53975111798012867593197888, 283890042142847872534963200, -21923398816065673868965184, 249949514927887597788706880, -142551396240526060284122982, 11425793746646874194671164], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "11.18.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [32, -1, 0, 0, 0, 0, 0, 0], [382, -9, 1, 0, 0, 0, 0, 0], [48917, 56, -2, 1, 0, 0, 0, 0], [224401, 543, 12, 3, 0, -1, 0, 0], [1646319, 2313, 64, 21, 7, -2, 1, 1], [-112121, -12398, 310, 13, -22, 7, -7, -3], [-12710791, -75410, 1940, -1, -61, 30, 26, -9], [51678030, -10007, 4223, 21, 206, -5, -75, 21], [-89699717, -632657, 15262, -911, 119, -118, 107, 63], [214358881, 0, 0, 0, 0, 0, 0, 0], [-410666559, -3740568, 16310, -3135, -1090, -508, 206, -730], [225533837, -2557630, -124462, 605, -2710, 759, -1003, 945], [2224326094, 51002, -288006, 21762, 4058, 2344, 1328, 1800], [1109395472, -19583481, 40864, -5322, 9518, -5920, -5821, -7633], [6724271904, 15335876, -564072, 59268, 7518, 9732, 12324, 10074], [-3427110049, -7881656, 279620, -63901, -50246, 5205, 9751, 6711], [3531724573, -49943678, 2389298, -144585, 35185, -33738, -28999, -27055], [7303052361, 24142448, 2711910, -238653, -61858, -16463, -21811, -1107], [81298219779, 240163704, -280702, 318155, 101622, 43444, 606, 15438], [70333450583, 274092390, 640456, 203829, -5338, 43187, 89579, 53663], [6859484192, -214358881, 0, 0, 0, 0, 0, 0], [153981798638, 72409639, 2461206, 84192, 117142, -129238, 52039, -218877], [441023286115, 1018596690, -36744012, 2054805, -138967, 334154, -57502, 225125], [403182805218, 213353773, -7640441, -1353893, 24474, -284915, -375873, 77007], [462302529406, -353941132, -34234070, -141806, -1406550, 217704, -46272, -222648], [693010738724, -1366632799, 50850661, -3841758, 2476832, -1075062, -92228, 110068], [69160565610, -4711398160, 28414892, -3012358, -2089468, 47096, 1091516, -864972], [502030204682, -2721162166, 84350534, -3749488, -1108296, 1230904, 1848888, 1431456], [3541149929527, 2057231433, -38058428, 12186621, 8132727, -398922, -2103039, 672909], [2630491348902, 187803023, 109129632, 3239928, -451022, 2465734, -2635787, -796455], [-879375542986, -9404986852, 21406968, -4948302, -10250362, -1456212, -717124, -2204538], [81885092542, -1929229929, 214358881, 0, 0, 0, 0, 0], [1311623674332, 14454489114, -501032898, 32689356, -2988112, 894012, 5112254, 4669014], [-4695598265137, 48504434, 284086536, -12898731, -6484590, -2495913, 6004395, -5654805], [2336205441152, 31124993552, -633588704, 15044796, 27835106, -11600196, -503222, 2733178], [-4772415258245, 21906787209, -248568904, -36640291, -15008616, 9823049, -18065772, -2735244], [-4012446396252, 33772995704, -732310850, -36350684, 39289176, -12557204, -2106018, 9650334], [-16671326824677, 24919205760, 309821122, -8108907, -11222186, 18006979, 26275903, 6657451], [-28643978713995, -72858333586, -69041284, -114448525, -50318321, 21750150, -15335498, -26909997], [-10575479950623, 24066361914, 984772466, 54479429, 40216414, -10453253, -10762031, 10697625], [-46798149012350, -129368044938, 1639248490, -140196546, -71111826, 6521616, 23847204, -6321324], [-9974530208542, 33431424734, 577002090, 234961566, -82331564, 9656258, -13802762, 5555814], [10485793381877, 12004097336, -428717762, 214358881, 0, 0, 0, 0], [10665741783656, -17120420936, 3877703564, 464541990, 309390516, -113105494, 15755098, -5147822], [-7984417544753, -153166209223, -370434616, 166035797, 167607303, 29475134, 4008813, 51985665], [-41748843831386, -14048971864, -798228422, -164582126, -165304816, -135096150, -41836384, -24112464], [-115239764810600, -443891636676, 256058552, -944111580, -404091590, 195707596, -6598892, -20085410], [2084204762905, 213573058524, -5185488810, 39836736, 101426836, 42204236, 88063342, -19044786], [-25398650153751, -217518880620, -583689394, -1303444309, 105665733, -126345770, -116522991, -32639127], [55671721803019, 603213509838, -17703989528, 100147401, -266700630, 432372387, -6370821, 75446451], [47886334057704, -115352772544, -5254110368, 631869568, 240118468, 140136696, 214490620, 5676852], [43924062461664, 641023647924, -6308726890, -728420698, -311870608, -243648242, -14472748, -38470452], [267850182566017, 110183516579, 25667412964, -157796853, 681537249, -572359046, -297349357, -115146949], [48102347255281, 116396872383, 2572306572, 643076643, 0, -214358881, 0, 0], [554629072589190, 908401239332, -3965577016, 5327155562, 88445458, 19033044, 173232868, 301524330], [408283481498679, 1065770656692, 19545167880, -306348687, 446605758, 319878423, -137009499, 108388437], [504982497298458, 320515697328, -97200880, 5892165374, -871683766, -179796908, 433256822, -1901514], [127951603384616, -440848686507, 12515354983, -3151823438, -118794140, 507943446, -39884018, -430984962], [-401824904055127, -3189738967704, 101363744534, -7666117191, -1906662618, 236834772, -102502794, -221478786], [474288412861938, 1279935832070, -45075933598, -4052330896, 1146938608, -138199360, -335152040, 139932408], [53174879289143, -3009498968239, -24530139928, 212657357, 1377977807, 269596270, -294481747, -129582327], [-296601029344690, -1046601565772, -25009264852, -10388658126, -428843316, 922686446, 211684594, 132127666], [775220213730564, 874855758400, -69660188608, 4991236388, 1273595624, -582582336, -891384592, 229639536], [-374883476273867, 684493532380, -64622924756, -4238691785, -691676014, -1107677887, 2461170503, 1324775775], [352903098609039, 495812091753, 13718968384, 4501536501, 1500512167, -428717762, 214358881, 214358881], [636965190965464, -1044294468631, -124469192551, 20353292426, -2669496744, 100808986, -1996585608, -1538734656], [-2107962215839322, -7618199301008, 61291839828, -5449653330, -3016063920, 788986848, 415120344, -1900054320], [369276070036517, -1006948974075, 61541507558, 14290452909, 1121618844, -3804257547, -1362959814, -970164582], [-151954947143186, 7635146957114, -106112818574, 18303573442, 5221858602, 1091599896, 1690982976, 2968809024], [-189145306343204, 686640822773, 236504158420, -6137916506, 3135524890, 2061044964, -1019539127, 1353654237], [-5975152793630974, -1913480381532, 104203384080, -39720662178, -9334495778, 1661639932, 988936864, 334352038], [155508484946825, 5871075129654, -156654963202, 40316280581, -1544510274, 1157859355, 2398866969, -92726511], [-4076493203172883, 7786902729229, -346857363102, -40600435449, 4656071409, 1105950470, -3439036515, -404755911], [-1505597866652396, -1576421552640, 669481724630, -7736317008, 5559427348, -1254738404, 1477680034, -417353654], [-7148899385859888, 1493039503456, 161024501680, -50009840336, 1139074064, -4531811296, -2841764872, -5477401104], [-24034132096601, -2657621406638, 66451253110, 2786665453, -4715895382, 1500512167, -1500512167, -643076643], [-4987772149976596, 14831596890732, -9231597830, 27954626028, -11769012472, 3744922052, 6029063258, 1238545562], [1447824330627022, -1137329278290, 317794301856, 2759551998, -7470131752, 4426775326, 438274472, 7312629456], [1470438570698264, 21437253307588, -1380135708440, 60485879404, 9360725366, 3698825428, -1891006372, 6286598418], [4361351050506647, -19882671608792, 1046778012470, 25868494842, 18458488392, -15906106438, -570158756, -3940097732], [-4625039264647914, 1703737377952, 802803736386, -57109450374, 1937029266, -8557166360, -3208198896, -5837869416], [3542094220721960, -33683806833890, -827782795550, -39625219040, 8696961880, 1587840232, 3469510936, -7490390880], [12480118894080662, 47316610902480, -1212612858988, 182034178182, 15547122300, -3275552952, -2796611244, 5592502764], [-1678850934006157, -25984534448378, -1792253533932, -96432271851, -48048295402, -6322445053, -619924441, -3961457949], [-6284072557598570, -25925604891770, -207986238068, -3396697598, -9007229490, 8797301588, 12248854446, 3621285534], [18691747397136074, 5658740843904, -32166821136, -20003349714, -3897834884, 37570411402, -9946566890, 11177125294], [-2724670935384871, -16164803216210, 415856229140, -214358881, -13075891741, 6430766430, 5573330906, -1929229929], [23551590575101171, -15900364702547, -987598753241, 44372765797, 17757253206, -1297547581, -9220599927, 1479929913], [3468285701728608, -69868350017678, 4851707300492, -48389290800, 25205204648, -30854263832, -8263819596, -18312713196], [17025531356656666, -38586310116376, -1060542684110, -102979729250, 50110416192, 18315729430, 15664073340, -2666297388], [6946560119636473, -20990118591192, 1738669599670, 67549538089, -65991950666, 3983112436, -17759587946, -1848621714], [18781064669803293, -1368465846795, 4841824140676, -63444252291, 3495991384, -7606702487, 20019894220, 14992025116], [1186472935975488, 79241591418024, -1422399473388, -95961171120, 52242526744, -13796204424, 3630339172, 27117918492], [11955568824408525, -47676986549140, -826255866050, -96847799765, -48350757270, -57142496675, -3939211155, -24674124615], [17990147429422458, 158450114436708, -3369106986328, 386022407262, 44093389034, -6401507212, 16226339636, 5743970858], [26182806417263019, 152314479694663, -2256798479451, -75700729071, -57290470546, 27267675207, -20331121363, -9416673699], [-38295450458675332, -41316561159485, 691231676160, -113700066252, -55351452132, 25947886808, 2643081516, -5691317388], [11077644683084430, -2145089322167, 905237554463, 4501536501, 44157929486, -1071794405, -16076916075, 4501536501], [-14720720824906786, 217816349685728, -967018477516, 15921061970, 127820736266, -26214523156, -18997755262, -6768850494]]}