# Stored data for newform 11.14.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "11.14.a.a", "space_label": "11.14.a", "level": 11, "weight": 14, "hecke_orbit": 1, "hecke_orbit_code": 234881035, "dim": 5, "is_polredabs": true, "trace_hash": 255063393573404633, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-195385344, 54095104, -755648, -17232, 64, 1]]], "qexp_display": "q+(-13-\\beta _{1})q^{2}+(96-2\\beta _{1}-\\beta _{3}+\\cdots)q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2156, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 11.795402184710397, "hecke_ring_index": 4608, "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": 1182023988677998153161, "field_disc_factorization": [[3, 1], [79, 1], [40163, 1], [124180041087631, 1]], "field_poly": [900864, 251749, 1520, -1179, -1, 1], "hecke_ring_index_factorization": [[2, 9], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.637", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58.294", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1183.834", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "13.2.3.c1", "atkin_lehner_eigenvals": [[11, 1]], "trace_display": [-64, 480, -454, -313920], "traces": [0, 5, -64, 480, -2400, -454, 79548, -313920, -255168, 1321749, -3535724, -8857805, -29768880, -36339498, -64558312, -162945300, -128942592, -309078454, -302859828, -147232948, -62530256, -859909128, 113379904, 677905444, 755940096, 1540265631, 1643160872, 5029885620, 6948937120, 2368825878, 7601916540, -83363076, 10024391680, -850349280, 7463914000, 591040520, -15037063632, -32935650382, -25107474384, -54599307000, -27853580928, -70273827286, -18264520200, -54501240436, 4251746400, -118334367738, -9391823524, -45017434472, 236995825920, 77867671053, 252640243516, -14973171168, 370262207008, 242684257518, 386371416420, 804288694, 508508098560, -78232137120, 338805253176, -384712501184, 607819216080, -795317095690, 567054167132, -1777323941640, -502608203776, -1104664950268, -140924134428, -1005952134296, 9188915584, -2334490276524, -50031562280, -1427050574148, 714622284864, -4111049036406, 2579474987436, -584109490620, 1028633987648, 556128429120, 4554998846160, -3666957194024, 1569918525184, 4090930814781, 4301648616232, 2718055516116, 8581863439392, 1506197091796, 6558172582872, 3556682104680, 452045677248, 7963494884214, -4671771563808, -604892444560, 6414213002576, 361484424660, -9832269652768, -5225122758984, -12178790559744, -13542719272730, -8557591646352, -2341558980189, -24304652266576, -19751413283306, -26664912710520, -20574558704, -8613096652416, 45044456145720, -47972999111568, 16501852669452, -37863082685520, -29381774498658, 6263750745164, 78623583032916, -80105883860480, 47214851928534, 76058590082112, 31687767233684, 57764398037088, 33127825134654, -8090393697676, 70249898548736, 739190592000, 15692141883605, 59755925707080, 11589346788360, -67607258453936, 159283038786696, 30169251100080, 37123948326016, -75291913125888, 81007330047912, -201401089542848, -65730477599340, 52737386821680, -116144554872320, -186903470859164, -84904429585860, 39116672330880, -4586234882162, 272816246806620, -393003753240324, -51436119824480, -393941780221056, -295192010090892, 64377637416378, 258647652225792, -597817070665884, 181302910672568, 752321881085040, -156268780439728, 427150082803030, -70834670517120, -348100100397632, 9497250292992, -522021543799158, 114368987765032, 529594824148292, -142685865186240, -275989181251982, 1262446058629528, 531263044178928, 763779647313920, -398202289084232, 651992117547744, -712150602119604, -30942307672928, 288667538613300, 233788646719992, -749394881317848, 262315252339200, 362969435378739, 611757033981176, 1492025686379820, -1137023774069344, -34159048786146, -759176139259296, -1295624899545320, 228429667226112, 44692642354620, -1927939106340900, -380089208886312, 2209214065531968, -1256140036153998, 1281986127577760, -1425287636260200, -688726811071488, -2186260110833712, -1895029518995076, 547551335046694, 1190158698845312, -3613142727187704, -1183172050136544, 3352191897099412, -4722248048640, 1707333464145474, -1641037732426796, 1446836566893360, -2503275920467488, 299073583623542, 536534659751508, 3297337054763408, -2277703867123008, 23566589783052, 3994476731806160, 2820953150269680, 3937670833538784, -841565715222548, -212248461915488, 2128774921076088, -1375729374981632, 260832148591828, 1472452823360280, 466760474082284, -847786090633728, 3149630497217340, 1564536628358136, 3873336202602864, -3084252996911616, 1952670120107960, -2643072574605808, -1585246730318664, 110776162849616, -1026731745051988, -6764658626319660, 3269668744326876, -832445858521088, -2620735285193613, 350085328588212, 420538343982180, -6331207808522880, -3393390884057470, -5648389243740116, 1523381474708808, 2593520555632512, -10219968779594454, -5190675326843976, 8612964626195888, -3044778031085584, -2380275668737560, 1254819422576080, -671813076860808, -3519965719668480, -1323819019266846, -200859416110144, 3990255315385860, 4718602040239904, -10376108443285062, -3280996390825536, 11475463051668712, -1603985612975616, -10002792425036184, 10867138824521556, 3451867333157408, 13904883328357440, -1200950846278084, -408613131478304, 16464733693658040, 14552322903769088, -8058422143067302, -2302174356812280, 1519825153751416, 9455579616924928, -8007259804802658, 20846125397858568, 4396411341679024, -1339193992409856, -9401991373823412, 8976000503356032, 5892885769544100, -720781654943184, -13554059317488538, -6488406337769100, 16670661030571408, 3506213358936064, -6219039843686400, 9287974145480372, -2728674521519991, -16285272917621808, 12146082842250150, 2658086206583192, -40661927281104048, 2762048256791040, -41738660625925230, 19795721049507840, 1443474891572004, -1399912581660816, -17283794915532240, -2910959717561192, -2749333520010640, 14219191351157760, -15386631840400833, -26530980794519664, -10134473836846260, -5924134217189024, -16053563437290210, -20555129735069940, 28187646791732324, 10527285130005888, -8910749198852820, -28473888613769920, 35566044756893248, 8603197689544320, -55425760515878672, 10078101767584168, -18501094866573600, 13278937519846400, 10088707802412660, 31583876513875704, 62747982410141020, -12310465993244320, -39510975247882176, 55589838111621772, 48668331683019072, -22600595552532480, -12995131595536202, -47417872526195180, 104440733731261440, -5046568128072672, 57103015604834402, 31832214536692440, -4196519541255558, -2235598427865088, 91484141750172504, 23217067440682520, -40313083835187624, -56858629872100320, -53062135464301238, 31559078365557248, 60665603466131760, -8135523349574016, 45571214206821760, -13467258867518940, 1666726559398872, 67012592485004064, -7025727064521114, -121171473015370704, 18723506005200484, -96709733247235584, -12401838725592854, -20447891404242864, 35035941289873932, -47487253722542176, 147682774281636, -28501685804001168, -37030484803161120, -54881616678611712, -46313242349151900, -63253091529287856, 14915751885336116, 1474654616161920, -101959541795355394, 15850109673522880, 12083123400198480, -17758821349012480, -39807396492606162, -62756320740963996, -59429381924874852, -48015163939881456, 170133962032546800, -64571039244530556, -12439228106949640, 51186048266496384, -36317124342167455, 102781813018525340, 1506445620826080, -80969479884620160, 121750774660057724, 52604940817099440, 14507264274221004, -23970301754408704, -24965763073677486, 70380462255356148, -42801666455465952, 208587171939170640, -5351249796227562, -13222778949754000, 134142440130905580, -6834531726405120, 119448819401623332, 59039364819609000, -121347481062353304, 196637384494543104, 5782570911578832, 83373670123165028, -71701312908750932, -43133789271932928, -1047064334651720, 113621874886471064, 81462030942368628, 39323860737724080, 91074334787347194, 88306757766842160, -169826237845620568, 102873352671840576, 32688102200777640, -126764047704105248, -66402232094300792, 26639075484969552, 61460542619070150, -268321472565803040, -336234953616681312, 208264413029851904, 76242490681658842, 312706874704175220, -407067809395716976, -71348844282809344, -182847157204109526, -81661449929005248, 58347513726386302, 30872515110312960, -374540839828932622, 20386913557215632, 159373877672035596, 142384240407417984, 124070849408129320, -298696579067078136, -123885048882024384, -176950136561960960, 13269020233976760, 44479422427193424, -295850055153487268, -472237308362340960, -203009333499922434, 376275883590583584, -209885755246983144, 205900419036538752, -47750666621045474, -34785129861827532, -25554637109942000, -347478751564778592, 96726002908227000, 365922567069949704, -168451684217918472, 355408857547534080, 381480574964889798, -185855477668025512, 300722872506800400, 93114838321349248, 380837337926886864, -518268472273818480, -461038267118689608, 49344317682388608, 670241930355357741, 163740954843578512, -89204458260468112, 231691440731603184, 484202804068157640, 355797328519003820, -233974279530826800, 492234605818920960, -136258763107656338, -128127556477667268, 124494371740613446, 212482941632959536, -126080483609402760, 54524189557035480, 514523601029329760, -268626915716276736, 1093387426004450954, -224786597380248420, -675552800631757176, 172216312451850256, -111777681016460394, 32356711670032200, 47966303117746164, -848962864927123968, 426407562208551300, 543466898409738408, 532903027703229480, 11744587707006816, -416055177612835320, -172183083409835072, -614745109607267604, 80717605304978688, 96552272008040596, -671540325151758504, -374076935310344764, -652544240951111744, 1323590551155221886, -423443268490667832, -86099127667061072, -739512864163430400, -133086639077158364, -780932337045984760, -608640731759308200, -7532228104130400, 352838132559851200, -1246931328408785136, -422269897044951932, -384113661012339840, 335575427806869888, 733233594702964068, -778838094785948956, 418086102760314240, 78783330324592236, -866671108168966368, 209636550844299018, 221613045507182848, 660359924772972840, 34636554947769480, 77171921707599724, -1039119779590361616, -761148986048784288, 1282424283931615972, -587647930272043216, -348359090307715584, 654851558115103340, 16638188274000964, -9378387828209520, 141493849310052864, 143426538132212346, -754517949224806200, 1135651533376152464, 446823230117249024, 801296522561405520, 1368954866256236752, 596711027769752416, 189214552644589152, 79751131230650792, 159908599670381640, 1386660518373279024, 1510469529880929024, 68183062462006878, -195938331824758248, -353764983695782460, -83099232425444256, -328551668618822400, 1243133900441058968, 1367557400028350552, -419852562362661120, -700217274439448655, -9363380323666392, -1348156208106221508, 448697936317438720, 755091244528969724, 247090337985682548, -1087209541135043328, 337281351272313600, 987550768313697420, 621712689873670672, -137947329198323733, 645905575154052720, 1076142829067552214, 127391401448662480, -1437402816774843900, -959283012621064192, -2238452831946633748, 1103634029356424160, -2330399187802303988, 380148821466715952, -698751694386835794, -447567602443448476, -729533562554924376, -628326512857704960, -1464216584198582160, -2031316004667690208, 1284865823004625260, -402225952803341024, -282161691669477490, 1219467210887191464, -1334501500343933192, 1199753440659980800, 26525886087553248, 343968202370534448, 1043219395904696156, 888899296311985920, -3312844535751885216, -1550441059770202720, -3076498445697593280, 2089781748851076096, -1298125051859812566, 992201398161909120, -878081376352977164, -655942085709299488, -2450345052102413460, 1278052233698828032, 619401535927966064, -2945282985182195712, -1504799224044935002, -981331147969931456, 3793277297734020264, 720879254169728064, 2278467845956312560, 1804475971575540300, -429929965932845598, -26037047246128512, 4066241867294506164, 2318780232675652728, -598850154434684764, -2400322549237363440, -4734768789711666320, 3096531508356780724, 1079463759770520096, 1527893800864454912, 3444385447068428962, -684480532844431620, -2634093490381589360, 2138339063561580608, -759158201129911200, -3311364602336505232, 4618198673562271616, 157251919020284160, -2955575796467262734, 2018607498030461520, 6313413416553030708, 3153550674482245344, -1424846483031334, -1726803480344440872, 2912860582891865128, 1180816842701844480, 1523399883623714304, -2137454150046908640, 1545889706901779536, 2241975871408755168, -4768519113511478546, 1340298232690737616, 2611120921928957280, -900853115593052160, -53138731721493678, 1108867437236189280, -755962878892119128, -6328160388477978992, 3095824589710658172, -4651188833918271024, 2545510039875456600, 3039268817141744640, -971912703410988039, -828561429282659972, 138593003068444320, 417523715951245872, 3429245367034687236, 96874051197880080, 249618090849664644, -5109279687185240064, -2156777785885646880, -160938111126029660, -495020060294568464, -6321331591640199648, -5652409947147157914, -600214173121727736, 3571169751189226872, -4038307961516802048, -2541045298236982626, -7398254137445366040, -327713960407245176, 1095362470755559328, -2288727804270434760, 4383355828538570592, 1629299699893093900, -2485501713955668672, 681541663310028224, -4571408859866224568, 9701010535342598040, -143550994079052416, 1440750521072246090, -6044329895093257800, -4566371410054433472, 2372630385023781376, -12679276897153986462, 316831951466378240, 6015270976411197524, -1076788818257900880, -6382643215823366502, -9986097036402733636, 4293951478708814160, -418949257385164032, 8598806395710467040, 6866259565724874864, -2850731618623008096, 6213717521220623808, 1909156881789929892, -747639403565950396, 1408952749357672090, -1043689937351884800, 7449156004203752554, 9570824505161416480, 6748909671994137720, -2194556312396162784, -5478632072084119818, 1009494298514253420, 1852907656066719432, -716791392400604928, 5468664369334369464, -1004571047378533052, 566362970935181764, -3265389806777773632, -11689678354801969072, 3386407163167379344, 10511487944445500100, 14360761218369061376, -2521051106672834364, 5193360510309291180, 2926260243246244264, -8079756744255302784, 3148637779375700040, 12666229529046797824, 2713389886837407872, 2072150219701624320, 4206645029376084052, -4276240322902206720, -1143835901370189000, 5382694478903339520, -6312162987751072034, -5334831171929853360, -3907475914569314792, 890401092089614336, 4370340870060468000, -8814768845790943764, -6388374550839612800, 9605066662669343280, 6913740633687279490, 5144780424661245348, -13423285658121706944, 7324710635701084800, -10377656306519450972, -2078809816345181808, 1956981343961728348, 4491834217067424432, -20267046337888670760, 3515733595980480208, 15531591883996047372, -19879537844605658112, 5636762796337291776, -5139202223971382528, -10262697264215572200, 853156409719322512, -16242108873094020054, 249655700511402108, -3885460349922252508, -12676453449885204480, -3925065063448812951, 14119952927482831264, 1671788045942991960, 4386871105495848000, -11192696735696017738, -2215731924910648324, -15263968836386375460, 6505907317871140864, 1782105568985556056, 3614061568785612264, 769435396447049284, 2414968512797807472, -3471837096172214880, -5149617271293580560, 2041200832746821240, 6428187000382938624, -3269147363507552260, -7898643518299334080, -13269835671321409668, -16278724480906624, -2311140881246518320, -16418477400355486620, -3732434765780019996, -8465690320089192448, 22472396956937912460, 25141170335775738192, -16922363419729159352, 20867173744406686560, -1743364627772229794, 6087316369878294380, 4135691928769133964, 9139521766770496512, 2883551398178407338, -9170256328433610720, 24332965275774947360, 3390515290125694640, 11228583263467084812, 2218951520978744732, -17686139009080451432, 48452665138544640, 1581367082111769394, 88633964504319080, 15521913761981475984, -13115733074884409504, -1530416244610396866, 7755848675650087488, 20458392695461927672, 5301560502546279552, -2850114365506344600, 18674952957182185716, 1214913193089927960, -13270838131565597760, 2528107142188205028, 14883203385661437064, -8526996003478830480, 20579167032463606272, 27738381057003739768, -6850365139379057256, -7128813915435869268, -12337543376122980032, 80968890636949368, -7466786310587550472, -1851903333102658872, -1265996969595952704, 25482645867019361860, -21727693480913957440, -28922051866607627400, 9841048560767261312, -10124928394781486942, 9786428392118918400, 2472916438625582000, 11413548126969236480, 5117163246720075834, -14301855653080197568, 7282974141984449766, -21627839264606100240, 9750188789600168600, 9736625834675937584, 18209225679453803760, -20381639850757015680, 18334313840777513610, 5209565391794811924, -26478678565568933364, -11645667225907841280, 6745918174204156800, -4569697288217107596, -18854496820240568104, -36800369878877993472, 2438306462132016784, -22225733270423863776, 15987117616502903280, -1082227685687382592, -9473289114729372250, -306657872537436660, -11621433125140039996, -2126644526373777408, 1034785593312257820, -5871909473949371800, 17005210146334430692, 6463416931105241952, -2086495816514538030, -26630658965344400184, -25260945043414211520, -14010745591875280896, -6767713409728758822, -5711597004759055032, 9858266422896870192, -1822287855791678528, -22123529893047901860, -1292958719271836608, -17252395796026600588, -11908826155999618560, 23904486925078108259, 13762815897500392256, -9070521930028766160, -5068233620085605632, 27434461895079203526, -16192044439168896288, -985215436020256320, 6963423722150848512, 75881012610957707712, -8732114096858507464, -35940886466962072164, -3488170258020698640, -36367528287416723018, 24518446527136367712, -4138847626108678488, 7366567734430341888, 50523920276997601162, -8069458310902055760, 1507742384955968528, -13688374129106726304, 3798462243706270944, -10745343780269172744, 39516103415640213144, 3564177680762044416, 13290278958791519724, 25518495776853128708, 722830866401965920, -10150793781357176160, 6496238353602351464, 12727706996981692800, 23691703562312268648, 41158519521190879104, 20176952991531175890, -49040831149565196288, -32091020599306819320, 80131868275113773376, 9610745708381478758, 17890207317285051392, -9669095289465486696, -2781206432393492224, 20306280269501699878, 43659309832686029196, -8918685641846625876, -25527009366287867072, 19538537447908355100, -21212939994629507756, 3027912505341303856, 4035661140336468480, 32534275536630840864, 48086773661461015860, -7247333485164243141, -28951388406122579696, 5439162762923931168, 35967832530269604360, -58058733853993620156, -8106520977988091904, -2945584007111981760, 1958974345236041612, -26792976015262618896, 12108481668552422448, -36192529941139228068, -7620632924220578152, -44874361576240786800, 6963741102642027648, 35798117227689971360, -36940260275451229560, -27785989889800222060, -7657638673026912480, -52208474475373320618, -4544209499937950240, 5598408230205628680, 65118351720218757120, -4815201148185977076, -49597783614346622664, 41703850085339211840, -47593857859945906288, -44037533834744375760, -4678326583857350280, -47608769957473149840, 13700214821155135488, -606216735529030272, 25111920814463225736, -23439687358280773344, -15203294576552730912, -33683003979449825542, 55816039317022923764, -37362506619486370608, -74744165337350277120, -13472353827258726294, -43174130877148709940, 7841695976862354348, 22373521255649009184, -12620893939468755120, -31605502643296157868, -2668320026139213556, 6661548351983346048, 57317760729878729146, 28335915549157498120, -76251006282420903036, -20511724563566893568, -95282161165484919618, 72444546719123549340, -8909965243965188272, 25795737762184344320, 84921578685771512040, -11618202779085303192, -5196508774008251400, 62533526721971734560, -56975263374540588772, -27352815621645344304, -46720939134121028580, -4968482465106877440, 72464743790581135298, 16515265152914899560, 47133178365769125788, 76785858047576553312, -6300879306049005480, -49108516509942301936, -29129255125718526776, 62870125065124208640, 38814776858714808873, 78290199184424107296, -18128473307508416796, 38279832993749659552, -78561605043522341956, 46396617278838515736, 47322428797488240648, -800826492031144128, -3519183332810610432, 7716862496141775980, 72181401510929433016, 22616974268250027840, 5837382028272838160, -15091538922343869860, 60764167376806016760, -6970900248486063616, 43234447136220913350, -7559796038337790320, -14107816960573038054, 72132301365607667952, -32861771721162033426, 13032633391810481392, -25427146202244757164, -12194066164317281280, 42443273417359933612, -53993412955948317072, 106700185551724996800, -9739067554108026752, 2545919000730822744, 8276328303351264288, 7130343058555512312, 5319001320809512960, -23173587804635878380, -30009471831134321784, -556993652276105280, 19965327912594718560, 13668215737838682694, -23640802846868264576, -16239963231645148620, -51511902853681244928], "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": "11.14.a.a", "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], [1, 0, 0, 0, 0], [-13, -1, 0, 0, 0], [96, -2, 0, -1, 0], [-477, 21, 1, 3, 0], [-81, 87, -7, 18, -1], [16029, 641, -6, 34, 12], [-62469, 1827, 51, 89, -37], [-50180, 4084, 52, -116, -24], [266310, 7647, -99, -816, 261], [-706301, 3147, -352, -772, -236], [-1771561, 0, 0, 0, 0], [-5960781, -27307, 129, 2611, -1248], [-7275597, -32771, 1901, 4871, 2013], [-12930584, -95676, -1058, 1378, 1912], [-32625660, -146710, 4740, 14335, -3810], [-25809328, -165008, -12240, -26928, 3552], [-61838523, -88969, 2443, 3455, -9141], [-60505434, 232914, -1800, -57972, -8100], [-29288843, 704109, -4999, -13219, 29093], [-12146969, 1545473, 15197, -96633, 28336], [-171969927, 749257, 36849, 269015, -75867], [23030293, 1771561, 0, 0, 0], [135502910, -89460, -32818, 229433, 78716], [151161276, -44556, 21300, -3636, -48216], [306513334, -7347923, -258837, 168138, -7381], [328288018, -2195586, 297746, -401874, -164472], [1003939110, -11964636, -220374, -628245, 259038], [1389870222, -1718942, -236742, -914962, 151504], [471949278, -9323492, 935936, -263730, -141728], [1523329485, 16445065, 242190, 985790, 128700], [-20180182, -14930296, -438742, 506365, -797404], [2011959040, 37260288, -841728, 1073920, 145536], [-170069856, 3543122, 0, 1771561, 0], [1504815016, 63346340, -366990, 2165510, 572880], [121590815, 2146535, 505815, -5774955, 1608555], [-3001563702, 49645110, -508482, 9254346, -945648], [-6594950987, -54085055, 1549503, -8232762, -742511], [-5015704094, 16467150, 865326, -8006694, -1763312], [-10942067385, -103633205, -1966305, 3391835, -306525], [-5573264692, -17837916, 3179876, -1085924, 1461768], [-14072079313, -89770475, 399269, -1326337, 274261], [-3662605428, -38057536, -1798758, 7294198, 2069496], [-10927742698, -157351090, -10282262, -8246624, 1692394], [845034597, -37202781, -1771561, -5314683, 0], [-23650533972, 160297014, 13527486, 36020166, -3279402], [-1932549543, -301961443, 5512098, -23703462, -8184836], [-8967147870, 264323866, -1919422, 40791586, -522786], [47423533776, 73889264, -3179856, -10368176, 13608672], [15652094357, 221298076, -3944156, -84523256, 1228072], [50566155724, 221561672, -4477132, 10861968, -4651316], [-2902046541, 687195611, 6869763, 107156317, -4972257], [73991649852, -265409564, -12857996, 21705244, 2431152], [48810769800, 1203085818, -1456294, -72424754, 10828078], [77231161827, -207728937, 13236858, -7744806, -11683980], [143496441, -154125807, 12400927, -31888098, 1771561], [101793641752, 455216328, 1465288, -19667656, -17220720], [-15985689831, -1966680963, -20248335, -124675119, 10509345], [67296690660, -2180469420, 43720468, 94131812, 23466584], [-76887475122, 348366096, -27508498, 4587755, -32032506], [121288318935, -1833501935, -27027315, -213888745, 14051520], [-159388427858, -1361950092, 4607568, 151624834, 20078080], [113659035953, 1530560501, -55145806, 184466506, 39692572], [-355778856450, -320945034, 1265814, 562883970, -61813818], [-100550104320, 24657152, 39961856, 22087424, -61400064], [-219660502477, 5803904619, 115832311, -247579289, 31687343], [-28396351269, -1135570601, 10629366, -60233074, -21258732], [-200057378590, 5250930188, -77247086, -106571997, 100583582], [1491577978, -2567999498, -46207746, -410658150, 7828752], [-468047212293, -6363188867, -38702781, -313686514, -4984551], [-9683112400, 1337442540, 82603390, -166857150, -27578280], [-283557130888, 8450828306, 49132688, -432506863, -25461162], [142044440904, -3920180328, -48193128, 249672744, 9722736], [-823082363681, -3403815731, -46948715, 267401139, -212081995], [517759300609, 10185168649, 15142880, 596734404, 164907884], [-116336858880, 2055309860, 43564740, -66501860, 118441320], [206374032144, 4634593680, -113546512, 680196656, -19013648], [110667644109, -3236641947, -90349611, -157668929, 65547757], [913704669690, 14052548510, 14188290, 219343030, -44680080], [-740065878162, -32331398590, 54267806, 523973372, 3574274], [310660000016, -14735256912, 136947312, 667142032, -274492064], [814978996695, -18432162306, -130896810, -1130783706, 67381794], [863143040654, 14582740682, 116825186, 261231390, 3154568], [541648434916, -7229623268, 514585824, 1209528446, -82330688], [1716565056366, -5366419006, -157008294, -2784191474, 379939248], [298714724589, -16273158623, 109298953, -1707039937, 117804949], [1319505998442, 39680502842, -300754736, 28805880, -132740872], [714865324578, 18800080146, -200455062, 415269762, -162511206], [88896930980, -7235055124, -92121172, 205501076, 42517464], [1602581932971, 48593491439, -529909307, -805266180, -394621579], [-940413463362, -30938550546, 574270596, -381429204, -60030432], [-127944444930, -34678003410, -1194202170, 750739350, 674851010], [1285826695095, 17620836849, 111072429, 1579756727, 229574752], [80442295983, 49331649865, 742271199, 4091778842, -210518463], [-1969437394708, -17728879244, -66546732, -1884853028, -479073792], [-1038963937151, 33249697317, 1494876633, 1458186633, -15125411], [-2443990475520, -46098337280, 411035136, -2857969408, -389709696], [-2699048371177, 47722472983, -337551519, 406160822, 283632753], [-1701446523233, 51227510971, -1009695016, 1322592984, 888352592], [-471784409910, -13547126967, 175384539, 1445593776, -462377421], [-4857339516964, 14590078708, 1459360452, -1508221348, 174080176]]}