# Stored data for newform 7.17.d.a, downloaded from the LMFDB on 07 May 2024.
{"label": "7.17.d.a", "space_label": "7.17.d", "level": 7, "weight": 17, "hecke_orbit": 1, "hecke_orbit_code": 206443642887, "dim": 20, "is_polredabs": true, "trace_hash": 2245235899409676854, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(9-\\beta _{1}+9\\beta _{2}-\\beta _{3})q^{2}+(438+\\beta _{1}+\\cdots)q^{3}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "d", "char_is_real": false, "Nk2": 2023, "analytic_conductor": 11.3627180699639, "hecke_ring_index": 46263319486686714584787977212658712576, "level_radical": 7, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.166", "prec": 17}, "analytic_rank_proved": true, "char_values": [7, 6, [3], [1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [7], "conrey_indexes": [3, 5], "field_disc": 1791390698938359489800594903668668352577949690984923458249230790927116787683450702175668245334420207092881858642268001142745393423475522715649403179237376000000, "field_disc_factorization": [[2, 40], [3, 10], [5, 6], [11, 2], [677, 2], [1297, 2], [8389, 2], [4550540889094989223, 2], [3603996928579837123981686623507272368647, 2]], "field_poly": [261490399505792227817024003348104130194641159225, -34923314543744821707168835219945993579648950, 44558299163904360256389313185385225104835245, 69498817213798305204024309903431721187110, 5465648386210730671112398026225318665199, 6884264619587692201297746565224842172, 292280160701254761307491650568975646, 50328102663961537370536178622316, 10848813785145958185022965942709, -772894989756975230685011586, 217775891572550635786539387, -78217760507911051825254, 3092605513604061172669, -921982218074544860, 25413927970368382, -5885709493452, 149610140535, -17792382, 470221, -2, 1], "hecke_ring_index_factorization": [[2, 38], [3, 16], [7, 22]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "18.247", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1430.693", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "199528.354", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "16.2.3.c6", "trace_display": [92, 6558, 241890, -1847944], "traces": [0, 20, 92, 6558, -285924, 241890, 0, -1847944, 23873872, 146092512, -567579804, 487037030, -2240722092, 0, 598121216, -2098975212, -13522996616, 16479299850, -21631627512, -29753076894, 0, 30310552398, 143879888720, -199076938822, 613456300512, 212723266388, -1359419612544, 0, 2531834927748, 438309600272, -2296351012392, 1037434908306, -3523947158064, 411779151054, 0, -7248579242478, -2493315404256, 5318067734218, -9079217417208, 13250117821332, 15010293809208, 0, 16256122433712, -621187489400, 25172272315980, -85040191344096, -15614039192704, 106960600327866, 0, -52978127838580, 35872835226128, 4235281588962, 126484190926632, 29048763888218, -635343594055560, 0, 230352840277168, 366396034764636, -279762037805080, -99092116656282, -173605217618196, -904353032308434, 0, 1188663557133192, 2502182430870944, -500211967540404, -951679982792988, -33326890567694, -964537664673492, 0, -569178593140080, 3111156268483352, 936737429904432, -1146801010325370, -2161044304782140, -4935640048894356, 0, 1321278185203718, 13747974994685232, 126874036566250, -18764997660746184, -2081051947014102, -11916006908925168, 0, 17065299612720828, 27928718307758508, -7493915124549152, -4167264363403248, -10398917942882000, -34000447101257730, 0, 6895892767523928, 113018032389709752, -15597881218045122, -7183919979926376, -19569222088313322, -137281944028491360, 0, 65453414234371436, 142672614742345392, -29373998845668600, -83625533774251806, -29167349642351496, -96618905127793050, 0, 66055768762488624, 231368680832994776, 3862674048208886, -153802829024138196, -26400513228178946, -216138834676575120, 0, 75532205315012824, 263868482258435024, -2912096561280588, -149693473817696166, -68763905898493152, -195421414725315072, 0, 57535482340868910, 800562167976963744, 1528641144762252, -295571864148139020, -69746203850580684, -291803133306706308, 0, 229153256162482680, 349342761108163240, -158331716104627744, -75726774830867484, -117340521444657168, -416446610934293634, 0, 414321770614221750, -168902989225090112, -292623723238352418, 14744673665124024, 43288468790561390, -521841585125579220, 0, 80129901365507448, 351342562868357580, 190456968101021120, 584561276503401204, -122222415750205344, 417027925248517320, 0, -1126576869380748534, -1070154182952665352, -65312456943905002, 1320439493999258064, 228107332416260854, 2331691771694091504, 0, -1123210451618754856, -3408734647867002228, 1422876537958247736, -46172108081526162, 1811769001259013376, 4469210331725613150, 0, -796328179694080306, -8459872015274954712, 882611286510767290, -45700651331202168, 478052304454347282, 6028670929719388608, 0, -3818159038637178984, -4278804549256528348, 397259765245767876, 4887823061759372712, 36595587530341080, 1028332119293950182, 0, -4362644391683059636, -11039744063789437040, 1079751187072176210, 9214993370044860852, 1920840384401188478, 8893491730704412272, 0, 2871357491951085144, -12877063892437397028, -3119842669067391008, 1367928968221948866, 3177682841635020108, 5789966747873928366, 0, 1573286022888020532, -9466943968381556928, 860601242431776854, 3925321592515114224, -963240937186833938, 4994616554377990848, 0, -6992672700931782060, 1852943784824486240, 2831631216380981352, 4521637232786575866, 5735410555760531248, -1215507111366053550, 0, 2057089051633925792, 2458134229998513528, -1045943645538467172, -25857494739964068672, -5369422228230859272, -6897394458758856528, 0, -11000085658326117612, 8263605915410948296, 16843560948250867620, 3114854573425661484, -7855754549410265464, -5340218092781100540, 0, -4341906275851765782, 40583056597177139704, -15910856608347067482, -18025738055556206724, -782688329564083740, -40810631846094762048, 0, 69592132811592767040, 84704004449201333568, -13612458549957122728, -39918976847997809430, -16227235769304638988, -44465115085364504526, 0, 8688284556656822838, 112944853500759059488, -2376990557315343010, -22955620442402838960, -22643756222946861378, -140501666253615503004, 0, 37150417811898747720, 61806913331572274192, -50222654187992220168, 46284957802224827958, 10851955012879562928, -68786977400740417392, 0, 20915795541274322094, 158212520703980623440, -8946063157259050956, -88685418661863249360, -72973722972542450184, -47808497273510371596, 0, 20805406263952832928, 58719583484703451220, -7165701917235247664, -23965178345774014590, -14714014413858731040, 4331156588380301874, 0, -5815057862787799430, 69559445108772546480, 21169842432283977696, -202501345629007069296, 31637980636490318234, 7571499562072484568, 0, 143145639970351201428, -35780948560277052228, 86069936143737663060, 40901827589700181782, 83223212472615571200, 53824876616880261534, 0, -148342293034646902212, -116439795435803450344, -6411121498004189788, 133478325899272679724, -58067914536049586654, 50618998462226061168, 0, -179382404359694486160, -157354195675571163712, 98441625860702201844, 284229298192139793282, 170922043099551269928, 307576179132649167798, 0, -183073708029250516296, -621617936431197560256, -142492286694423840028, -176606267606850499224, -137987683785255283644, 256765562481290367204, 0, 262844824956407685936, -79977838046800912188, -16254827059177697368, 476417444086017825138, 153118521371650662932, 91566465896793290004, 0, -295185130178504828192, -1018067080606940878352, -48770281369389125430, 359271898149716787864, 34076102322173854770, 277396211858499107784, 0, 31610839379304258948, -572592970423351822908, 207281696937450575136, 478164583658697700470, 458704526461912193904, 750226892550960885870, 0, -815197896510768523368, -961235464231682487816, 235852797904358050298, -171014468336050098096, -228079674663165043984, 880187928581364021456, 0, 441331644835551966356, -302764019420005954116, 156164448743653310964, 465078893996264171400, 269628406493238760960, 1213943522174238551106, 0, -1135343558797617065778, -806430331453548362328, 19575137430037935922, -771490384117143214608, -459803390508698380800, -455257415382622749288, 0, 280559421781717491504, -303697840010978509616, 90620691299852844908, 882162768543894326592, 469058838387156285156, 426644194797954892554, 0, -265996376027314665544, 969924171515527756544, -320013810045731308986, -1876945862984559749628, -976433220883353833470, -2284999109492031212112, 0, 1800084538864475299184, 1155773678373359660664, 159650619777700225536, 1662361905664943477322, 1960502158021931482572, -1009074664928776385748, 0, -728725807962228916098, 1955313911131155624176, -680370956228250065050, -2151363852749706746832, -1126177272104958662992, -2404812055512743848944, 0, 2434687494866071526088, 3260228875186130748084, 943930724956324704, 1687069062912566845182, -1473193234882514228312, -1271472395348340329760, 0, -2002519456088888590882, 4190599002345188174952, -1382434523385772805990, -3122553726060501879840, -2301593538165949959174, -2866899305965900419888, 0, 5802311102960648233692, 3005597069166256648816, -59419595370977825508, 559359170998689189252, 2725002967104120773384, 190042284605604139770, 0, -1051021462040747820924, 1947972534840143280568, -418220127562028815536, -6861325359706518351672, -2078720624927455678186, -6325354508006541206808, 0, 1354007764481403516016, 4405787553005892250164, 1358015794365738303560, 4155258192223863860106, 1498724047947368512224, -906600864015567980646, 0, -3960946689237677291544, 2688159662904230009824, 19445856118316721038, -10060869990046744980252, -2883403814447361742068, 855764635272043202748, 0, 5633884533087077930936, 2667863691743820064972, 762175738828385862768, 2287857804567663968058, 2959271503352859271584, 5136814059582677513634, 0, -7280726858852509055994, -2426461210791638833968, -1139504127987956781624, 3167412486450742406016, -5389739275849620909168, -4127654534266138886124, 0, 7594588626361791116076, 76002770928019987504, -843344273241366988208, 10857162179482904864808, 3517898641211954681416, 4745965718881148224116, 0, -4208615813977211504154, -6017526986615763321048, -2320595788127507028684, -6626632220902688148912, -1990840423746649027402, -4762922457104318880504, 0, 4952590069491224180832, -8869737371830045620192, 839973428099741694492, 10953515718053221874910, 10804004133839053144992, 7572200826184318174170, 0, -10803232378096727658432, -7878968924272444456416, 2084484052272595913822, -2572331094847416476364, -6375972338338386283134, 1125240211712528612064, 0, -2276283647437417918720, -9280111442175009367024, 6345687884708888259696, 14238115397055330287220, 5397521172041817182304, 15958450351228345873806, 0, -11379025583778059480028, -26666033980144473978768, -3578657885174065614038, -17870401905310192689228, -3917051075747258842374, 17441455221065643728940, 0, 9802280383575036029064, -9282725543415884381096, 5531962088883082503232, 22660699669870894320294, 12404689580482624218884, 10677930984478815707886, 0, -18034104348263046654086, -31097921308014967767072, -4608756335367517880466, 8994567203099506327872, -3913412004144299654780, 26474716524245149157580, 0, 572919571559721062124, 3415493660169166788672, 11753139788995403495384, 5481748573544508510174, 8661456509087575033344, 5750546989489523114796, 0, -23419250024208300136476, -27155690603618178827856, 3887568940321335777564, -19335266048712330935568, -6169675091419157886998, 7685610760773974793336, 0, 24328565467326926401428, 1590002580988654144016, -954620118465512449608, 15089997982206811258824, 14996370343103658428472, -5824195833926683149192, 0, 2606800830492615639680, 1305804778377637085856, -5354133833332174701782, -30123562049351800775676, -13645464455607240685212, -44232099552628166937240, 0, 8996484197703163598640, 13297993098092842391100, 907286333723540714636, 26639759041695199936374, -1166386527688994538504, 17153968357156520571666, 0, -7874725163765422492950, 40425124176256856515456, -11899443664523018679246, 4905194734461792170532, -11368666367216778570270, -44427749135902451489352, 0, 21597869458198106154088, 16042281232339666051596, -27139730743818936917184, -150658810009612701042, -12374234330645378569248, -3965128411696683478998, 0, -5416890171028707070812, 65735165514336548698784, -4642484995495624702386, -9397569594171081573720, -10283822639984825973540, -43784733304836072534540, 0, 23985475729904281296312, 8240086296653278743312, 10866096201170478348000, -20948323214322453461226, 19196938565007294047264, -37277248742565583131018, 0, 4098059868845131847042, 113681028435691063376232, 15785197795222761731470, -86822964049236032147664, -10388064840623148574224, -38547664352269628309712, 0, 30689391204304747101936, 81786858473277498284560, 31241175190632425738460, -18540438895990428964416, -12749799815540195751328, -8558435184256095141840, 0, 4309723234646392727710, -11858658732548186957096, -20113090553047035631734, -19956531084981715131264, 9036486970450911889670, -26929804550826702368952, 0, 2043981736536518212392, 50831045370650196172404, -36536798197117504265992, -23235491158923310652442, -41447410029532293526908, -33053363911164447276024, 0, 25640881475849448750774, 7543020886639476178432, 7526150159830125720674, 25442885986291158731532, -18845106248373687301442, -10225040625988307853048, 0, -20115165499551815097048, 54886017023586259245320, -21443786380705820428992, -29273032993040988201114, 2826061379543542635896, -59088366012088082186862, 0, 30712339607125109008656, 57276425360556357476976, -16781365368388023125158, 3166185038696442478680, 20415966731444822140512, 28586140093055056264704, 0, 12279155532508532207148, -23286697230016588316268, 21371074824095590620744, -32914116890753115745800, -29155542659267012146744, 24046370922647181908490, 0, 39960012553617150173256, -44420758922034577736664, 13892679536555913601974, 156511051710256261035864, 66609312478518498644330, 16238938698026480512800, 0, -90265402882537429798664, -122801971018855477272240, -12348754483840890283764, -55660108019620872373956, -1340744481145397517912, -71546696391836937651774, 0, 50454017919374597860248, -37494293735575198447224, 36556984498603872410436, 87898850081884403752176, 47293595848884586337854, 213369301133810082136512, 0, -52512860283012817088408, -122227452751480252603744, -99293195945255461449660, 64239266169757833745422, -23648223066975066210588, 67149837277912590029082, 0, 16626479061070213188630, -266317497033128303846496, 26962573014126592658678, 129837892008662214368676, 81907555108178935189602, 156841215281273698953876, 0, -270224654996298266646480, -306519054384225596804312, 148337142863028423370976, -54232913403950422602540, -52998551072900037481612, 255560000513619749021364, 0, 77542146862201823311776, -217975251495959187917104, 103596361076916686908368, 100495512630317722797984, 27896700673164961616402, 178740429209015429933676, 0, -361626334268466436473360, -159402066376414307042376, -22042194983201234337072, -254640305184126696389514, 32702697579648577723416, -3469200263979212758074, 0, 102377728861073289447054, -7391321624070973734792, 107949721085186283501794, 500440511479785663401208, 212985280628917753122378, 383174816909068802944368, 0, -124867200470526640122444, -281490846903299950939864, -85516547566357752915420, -155194742433535182898962, -182118206365635380666624, -104597338476167884313820, 0, 37508664890312182129038, -113453086143380488440048, -35819795512012027349104, 89118215832377883655224, 186918203304289376417736, -66948567623411953813224, 0, 154113676510844305738224, 36435207201098716216624, 19971708962835937226152, -76392858446371626327324, -54712682549690000327508, 56730707339183487923010, 0, 326595189253165821638328, -26164299166828925204688, -127407937486843681299306, 346025749608784496262612, 37076620982334976472966, -113629062870152141572512, 0, -556146503576224445045560, 341194235228248648757268, -186899084763991109947408, -296233734599204962094892, -429971749468296510722004, -344789909921853915088362, 0, 376199950095205539093504, 140400721934375965887392, 154362631261593065224704, 316723642804090891783440, 67244281057605626253972, 475156569659111350711344, 0, 86731873031092800068712, 145694271151794481635272, -99845904538552599884520, -225289791584339297884062, -79777088717997984493072, -732344202594987933654738, 0, 37351583766382379076198, 391737117888812396002680, -52775273038249951561070, -218995143442092719041776, 252004734972324824357688, -738424457723774742184392, 0, -578186437714997617044, 328478869086439855764792, 216647716041340697537052, -729902338462715897151360, -163135412524882412664904, 61867815456871136663214, 0, 506741117246820412774650, 758111424097225352108624, -58768403810326365802650, 64812389440245248075904, 229313014670045516504048, -381366360576710949866328, 0, -559072649343811430670528, 188451806234690896393068, -157487298103980121405740, -598857803040091444083852, -262090067857322712120876, -307881293136483366305322, 0, 926434025190309176363340, 1173810440300893943606976, 268438890263286882769054, 267669542264945951272464, -103915682114797465046354, 458547513205927764110940, 0, 48247184402403150356696, 49003108723877076683528, -352684438134523902512136, -284902656953799220456002, -367234312718411705713868, -769547883062804768649216, 0, -178384653610874847323446, 1193334628083194998126224, -110768079998775638390090, -841044373528982892654792, 62375507683320251420028, -275213732462868525102000, 0, 27075379814956127453148, 497302446091410580771456, 498187484242254439182328, -225267664118148100785330, -249174035123354676074976, 146592822428507697561618, 0, 234155632002244925686210, -150352084426004636103960, -44120934941692730929632, 778009497081513998693160, 298778416819122648194052, -1298421677054404211094240, 0, -432688202174426210411532, 460978844853132057656052, -736486653762952417136484, -636741235863853319981622, -141200285812600158764784, -934882892401191732722028, 0, 419968915474850721083916, -146321907304806615554920, 444871325266221047322996, 1101931424621374997991096, 58050099811092260135468, 788680274270145688511544, 0, 614396891176087112293480, -867939481181410719364764, -839749539778080889066812, 660968735548947529059894, 159344039307004384710384, 210704993937709164940842, 0, -33808592274848669301184, 132119235806636685763872, -178449351331262672765580, -924962806012552730671116, -219732581883817199103030, 18684589706505517337676, 0, -65425048853119466015232, -362000218257081180021684, 1042908675925280994376224, 463673448980357862913056, -299247065542257707523244, 1516626888888096182487498, 0, -10283405935055183360094, -1791523242677169820524048, -577712866944896256691386, 1005385414131427359695160, 571067728096147966188530, 483037932320287168588668, 0, -669447993991353820006512, -389767755640721430200268, 8732079300883204867048, -1065549359869296041992134, 192180050327196333348840, 118397877834648217080012, 0, -1075978928603891813644080, -1708660380913915008810384, 1278153143338944690753566, 1402229610033797977924680, -50580303458791813898054, 4564703687063338721863392, 0, -983662412968283638552368, -925046683761862996687432, 264003738233663858151168, 1673134761491275097717778, 1212255160977166525212000, -25933446083694353313594, 0, -1575040427583701947490874, -2482184319994663117604064, -1056195680498974857810108, -2346423227879409514994508, -95333639361271578707778, -523411787688753146456448, 0, -196514807998254213348720, -1115917329025041711846996, 2259012305772825995343352, 2612400490284930599647608, 251751842589233126937240, 2830541201556382251511530, 0, 568143729218703311023140, -3306206634931536494034704, -547449479087101901204898, 583754237692560975701400, -202759289006310766180634, -977546285004964554226872, 0, -516985481969943078643656, -1475439016443880685026896, -310684626761464699566704, -1513473082618174115931858, 980368754044818147643872, 358446158385510487182546, 0, -55061700016391191701396, -403772691284923558478320, 1324117050489789266127026, 632135305184219254506816, -390294366779110366668198, 2851176758274777796895808, 0, 1259299224716687609980644, -1763298159872117804182988, -1400285942096408120867112, 1871768174733802320454332, 895287655971924640969544, 915552779546946046935744, 0, -2323894039312343085166740, 595108179597359610059976, -890922388425451015849802, -3797111646501798708095160, -1298885149374022328372352, -2717489591528357322857112, 0, 2772676952597686956192504, 915415280740573229805592, 1556185717755521360726904, 4784064154296778758029130, 1192215640527586039403912, 1417613152190095121614386, 0, -1286599658173414498840640, 698351664746340524587656, -1066764520444984245349758, 3457875468188652807484944, -964569736211702132515134, -4528807572703457410399800, 0, -1046526534771935066934784, 666519053992983844087176, -2353849379398042971349336, -1836066949424957865785136, -323645808656434284639264, -941202492280125628288038, 0, -54571493610120621233652, 2938354371371167302366304, 2465879911845957665364096, -1742163726618877773707532, -1149649613121256337880422, 2813202818483600420921484, 0, 4823028531389784256793112, 1922374321831626056274536, -1474513559537104472812632, 1288169172537989853481272, 3359649153830684416645684, -2594987470551181037563314, 0, -3505021229163555563345646, 2331287717657789681644320, -1175592620723959692932138, -9844232222418075342750576, -2630669906200160288816016, -5193576825874615325031696, 0, 5265176352721299164793384, 4432469637946537528575400, 4035160255803839730070288, 1731637428348010003033176, -1461138899072189258697504, 3341769875039385667547430, 0, -216435414092461440269946, -1873276694828953514921208, -2153355319025410100280606, -3323934300047095614236064, -870909151160367201988614, -5509290671565918050263968, 0, 1034563158370571775740200, 7847223583881444429519036, -1340942145899239030596372, -2201967837475515353432658, -297685496703175082085600, -2186826563615120934033996, 0, -3275658934512358533604038, 2843314348685486018066992, 695751741645352783128074, -2697963629289284522091828, -2882220067307926724577156, 4182094983157601042849088, 0, 3063235678119965058660768, 603492266262089530776560, 449006087843780979061944, 6199201128880932507322518, 2731345847120803699304640, -1931025665703928765233672, 0, -5060490510155857311568222, 12103995439019353954084128, -2163978825215968052702320, -8263175172281328580069824, -1846555727010356222800056, -12421538918440096499115516, 0, 9788379584674139606030328, 2677207665089605333989112, 5058852414838482377746368, 3320594486911223225055342, 1839105086291597346545904, 3016119176598994748033694, 0, 1187593059175676799495360, -1050887460109031731416992, -4159306712767359166876968, 1104970422286958452191336, -1534864712135840001390610, -11684340087658148250555444, 0, -4324824503630240615812800, 6367797301778260121354880, -2537383375770302849955016, 1252607324610392429255898, 43631928670972459752144, -2357698286466646388842224, 0, 1544699558372567359260456, 8036798076697406861245968, 2585546516312655663602284, -4925237891912884592947224, -3330787413556553228173430, 11152745042949676300542912, 0, 9031660159064203113123944, -5674108565264973570674628, -6274939562291422506827952, 2365041329134633260696486, 118348739861130315311872, -4722953488230716350772634, 0], "weight_parity": -1, "has_non_self_twist": 1, "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], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "7.17.d.a", "char_is_minimal": true, "conrey_index": 3, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -1, 9, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [438, 1, 219, 2, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 10, 28595, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8103, -201, -8102, 202, 0, 0, -3, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-71449, -1886, -142897, -943, -52, 4, 0, 4, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-432974, -194, -680825, -878, 115, 21, -27, -13, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1200801, -1, -1, 34631, -300, -42, 601, 42, -1, 1, 2, -1, 1, 0, -2, 0, -1, 0, 0, 0], [14605406, -21134, 14605422, -21149, -1331, 57, 664, 0, 1, 14, -16, 0, 3, 0, 2, -2, 0, 0, -1, 0], [-37848956, -22179, -18924484, -44325, 3639, 297, -3633, -150, -7, -27, 4, 2, 1, -1, 1, 6, 1, 1, 2, 1], [-8, 71636, -48689418, 23, 99, 4, 106, 173, 12, -20, -50, 0, 9, 4, -4, 0, 2, 2, 0, 3], [-74750909, 279299, 74750832, -279332, -11, 769, -21303, -1538, 18, 42, 5, 9, 19, -4, -15, 45, 18, 6, 2, 6], [63890330, -960858, 127780847, -480401, 21739, 595, -26, 559, 49, -13, -181, 18, -206, -3, -17, -35, -18, 10, -3, 12], [67557631, 2061809, 75435369, 649317, -29890, 3070, 32909, -1833, 11, 951, 1448, -35, -405, 7, 436, -7, 7, 20, -7, 23], [-104497627, -309, -1493, 2400839, 47137, -5364, -93839, 5337, -316, 2364, 1424, -48, 740, -2, -1383, 347, -48, 33, 2, 39], [-1353271500, -4742130, -1353268458, -4745192, 66226, 43246, -33218, -124, -152, 2876, -3066, 24, 982, 0, 814, -198, 0, 58, 30, 66], [1098829900, 511180, 549414516, 1030952, 3730, -1876, -3432, 851, -580, -8311, 293, 24, 155, 23, 1031, 187, 12, 58, -46, 74], [-258, -11066710, 2161157803, 14509, -328129, 57, -327793, 4572, 655, -14165, -28944, 0, 2897, -113, -1487, 106, 15, 81, 0, 69], [-991065170, -3188216, 991053617, 3176116, 94, 59457, 354475, -118800, -273, 11498, 11885, -146, 1558, 124, -1511, 391, -292, 23, -62, 61], [1306825601, 37391782, 2613651160, 18695646, -154171, -106795, -136, -106783, 150, -212, 448, -334, -9808, 86, 104, -376, 334, 10, 86, -4], [-2094000048, -2533771, -7212418653, -20132654, -158010, -1933, 1414383, 258434, -299, 10321, 68962, 714, -5753, -210, 7366, 772, -168, -162, 203, -180], [7181570553, 4230, -35842, -60335240, 536250, -246856, -1078053, 247123, 4185, 79280, 35812, 1341, 2145, 57, -5289, -3905, 1341, -352, -57, -437], [-19913254111, -20323389, -19913228719, -20348684, 4878361, 690342, -2437638, 1813, 2001, 27846, -25119, -572, -953, 0, 1491, 2818, 0, -861, -412, -952], [40932655031, 87064854, 20466335126, 174324703, -1465949, -1614868, 1460295, 808928, 9681, -200635, -4915, -1278, -2480, -194, -3247, -4401, -639, -996, 388, -1290], [6342, 19074182, -21266751894, 62402, -2846954, -1454, -2854066, -496282, -13536, -68900, -124816, 0, -19444, 1416, 10214, -1816, -1116, -1742, 0, -1598], [-45311744356, 2113982, 45311735606, -2122560, 929, 1478593, 13335756, -2959547, 370, 15917, 16997, 555, -12665, -1754, 11224, -13501, 1110, -1351, 877, -2138], [29386417800, -437768034, 58772927295, -218885193, -14893227, -536355, 6675, -529623, -11763, 5592, -100071, 2058, 105849, -1092, 1221, 12129, -2058, -2175, -1092, -2244], [88858832399, 139620168, -75517970383, 156229287, -33384546, -1335570, 29392868, 4196543, 4873, -79599, -123291, -5516, 89280, 2842, -106179, -12445, 1841, -898, -2618, -1200], [21973277834, -13100, 35331, 297840033, 3036925, -944425, -6062570, 945231, -10175, -81409, -22595, -13126, -91758, -715, 181787, 1417, -13126, -338, 715, 130], [-229703618525, -173227537, -229703836016, -173008430, 113795543, 5734521, -56902858, -8529, -6796, -226984, 217842, 5889, -86816, 0, -96025, -9025, 0, 4323, 3409, 4206], [69137988487, -30410641, 34568951510, -61909392, 28231558, -3704933, -28196783, 1845526, -48068, 1127600, 24400, 16568, 11997, 326, -70107, 35896, 8284, 4627, -652, 7044], [-53442, 2356631644, 352910340452, -789982, -74906698, 7864, -74854002, -2177836, 97258, 835486, 1569666, 0, -85244, -10112, 41106, 13526, 15690, 12584, 0, 10224], [13832925217, -373390302, -13832664303, 373687644, -19472, 2819902, 160997660, -5617862, 22068, -320706, -359428, 4932, -38768, 14804, 48330, 87648, 9864, 9474, -7402, 16788], [-43484334257, -1434499288, -86969121219, -717224416, -54439068, 915498, -49601, 849561, 104569, -35868, 515297, 1011, -124056, 7857, -14511, -84691, -1011, 21590, 7857, 21979], [-303710616981, -1818977540, 118222769682, -3112852826, -199294972, 4307184, 162919366, -3894749, -35794, -255200, -2695502, 13132, -223017, -22554, 207584, 82154, -12586, 15012, 19292, 19445], [-124671073044, -88002, 1488358, 403619948, 145536098, 4581372, -290890996, -4606296, -124446, -3268064, -1610608, 60474, 407644, 5022, -741992, 182472, 60474, 22758, -5022, 20592], [531234354891, -2355755613, 531234063022, -2355497135, 338753643, -11097767, -169397925, -418, -41867, -303003, 267695, -32970, 492457, 0, 460966, -43366, 0, -3820, -18777, 4238], [-603315627752, 4933787425, -301657764638, 9863198286, 11547031, 27203985, -11618227, -13614714, -20207, 4237826, 5234, -112750, 11013, 7053, 544734, -164588, -56375, 8481, -14106, -4521], [233904, 7279769309, -1323459476061, -742993, -161486208, 9150, -161668929, 22712841, -292334, 605658, 1606924, 0, 1170541, 42940, -600354, -67310, -115140, -39588, 0, -15219], [502024717958, -7758616833, -502022518281, 7760519922, 143923, -33189594, 644176318, 66256884, -240446, -2063002, -1787673, -62207, 740177, -81176, -746809, -39869, -124414, -6812, 40588, -47580], [45726038626, -8377888034, 91450597227, -4189085697, -136363097, 442971, 88286, 690273, -371855, 30107, 1265415, -84568, -2042202, -32901, 40887, 135685, 84568, -91080, -32901, -82434], [1760466520719, 663577540, 1904554656072, -23575689935, -595684221, 11889769, 539281726, -84643895, 116998, 2708111, 7793809, 85911, -951911, 112868, 1849592, -202037, 64386, -50769, -84665, -77130], [-29507481536, 813546, -827536, 7928797534, 53308542, -1116322, -108024300, 1280680, 1061622, 3712748, 1274998, -81912, 100638, -19956, -650544, -1097948, -81912, -143104, 19956, -121850], [2513975681599, -15867586753, 2513978988604, -15870585038, 246842933, -139020423, -123291243, 117692, 493944, 3335916, -3104409, 98387, -258793, 0, 90435, 299039, 0, -25080, 71392, -92612], [-5658862560688, 26800413830, -2829430902783, 53631426278, 650704354, 69756168, -650780630, -34634265, 1029402, -30194059, -436949, 460788, -330031, -67609, -1484461, 609489, 230394, -162546, 135218, -99876], [-626796, 74267768283, 1576383842741, 10624361, -196714416, -256316, -196418246, -47557316, 42276, -10566965, -21964948, 0, -4050598, -92214, 2199431, 348626, 514788, 37336, 0, -109490], [3565983502924, -2965995800, -3565999270657, 2951299501, -602669, -76101109, 218165046, 152671049, 1270478, 16404540, 15443058, 278172, -3033457, 288668, 2812040, -2007161, 556344, -209474, -144334, -53197], [-3072795297874, -126665445382, -6145582910350, -63332345048, 479217264, 73976434, 577980, 73816846, 345894, 673104, -7418488, 511842, 7202452, 61266, 111264, 1044696, -511842, 156390, 61266, 53196], [45423153153, 13195023562, 5409891784115, -44440517597, 1103322003, -68834899, -1400280518, 23724211, -31871, -3881591, 19035471, -811832, 3150070, -343049, -8457239, -457191, -284200, -116382, 186151, -15372], [1797486895198, -2283104, -31238468, 17034829314, -764749228, 91146016, 1533499836, -91710288, -3416816, 57240004, 31111724, -488448, -2903720, 30628, 6992072, 1994552, -488448, 384668, -30628, 205064], [418287036918, -30122595900, 418284612295, -30121973992, -2605537034, 54722811, 1303226563, -110844, -2227821, -797150, 1481837, -83250, -3783950, 0, -4606175, 370425, 0, -101709, -184566, 212553], [8475954109334, 107169450934, 4237976275878, 214324904760, -2037849032, 33207728, 2037701754, -17554138, -3238750, 11725580, 1014708, -1143260, 1257136, 290230, 3505468, -2576296, -571630, 633516, -580460, 333390], [1555678, 120910478179, -2882296916936, 24484125, 2704738129, 1026336, 2704027699, 167708595, 1602536, -24040944, -46434305, 0, 6822605, -39603, -4233733, -1913621, -1424170, -43836, 0, 491250], [-21165703720275, -70906061829, 21165721471980, 70922432778, 1542351, 332093439, -8861579088, -665544897, -3916818, -22750824, -21219252, -469431, 4930296, -570198, -3645507, 10071693, -938862, 1117215, 285099, 664542], [-2823306813856, -153936813093, -5646585684530, -76968943079, 563456455, -123369185, -3243592, -124959206, 478485, -3363004, -28165235, -1364248, 7139299, 120032, -939362, -5547822, 1364248, 620, 120032, 530007], [5430138684445, -136870148171, -12061478801227, -340892270707, 8638001650, 168246712, -7507433525, 487369648, -828729, -21863445, -55259476, 2844877, 16959037, 436870, -1007600, 4305646, 1109087, 1367054, 116914, 1001848], [18322298687355, 567504, 60944836, 6288397988, -1994039036, -70382892, 3985162432, 71645232, 4430604, -120866468, -65096284, 2536020, -8166536, 100464, 15347740, 3845412, 2536020, -361932, -100464, 538476], [-27990198255682, -87531813776, -27990179337542, -87543632064, -11753903141, 1198916587, 5871362830, -1902215, 6186716, 6927879, -15950903, -377169, 1260185, 0, 170750, -8033945, 0, 1445647, 280269, 456568], [-6533753476512, 180320707801, -3266882071947, 360546682066, -854362335, -1452188286, 859776165, 727529652, -818532, 106304968, 2891124, 1600248, -1317918, -563244, -23805138, 9850548, 800124, -957006, 1126488, 202332], [-5520159, 583936222380, 17474018516679, -197798757, 5215559442, -1139652, 5221222386, -794203821, 455547, 199235613, 390378483, 0, -24470202, 822828, 14350107, 7776057, 2124747, 1131804, 0, -3924], [-30127458236501, -99269908033, 30127467002492, 99275542065, -2329537, 361119691, -11080586249, -719207744, 6934639, 4255399, 4595083, -736642, -4874087, -69082, 1587976, -18422028, -1473284, -2241024, 34541, -1230478], [2641519794463, -256733063852, 5282884170882, -128365323782, 5443594522, -529981910, 3764611, -526408013, 6304551, 5203166, 160553560, 730477, -64695371, -1056539, 1708075, 5821147, -730477, 382016, -1056539, -1191299], [70544321995481, -45207803339, 22342267794446, -324672391135, 8516160656, -302348403, 1804444754, 862374462, 933559, 134010610, -135736071, -3837372, -96187594, 1044246, 63012637, -9657953, -3356640, -4007991, -2044630, -2541495], [125195233009376, 9121584, 133679376, 427387015364, -879677216, -1726622804, 1753513468, 1723803596, -1085688, -251017044, -123015768, -3128808, 70441092, -608148, -141028920, -19330848, -3128808, 153804, 608148, -2511600], [-50044102409288, -127408639380, -50044301996418, -127227359173, -7873087371, 534546027, 3954891180, 7486462, -13056627, -163309736, 192878632, 732768, 47087403, 0, 54991460, 27332730, 0, -4861314, 28613, -2625148], [-63418576377510, 56617218599, -31709264302235, 112960916470, -10798703532, 642313324, 10780414300, -321405368, 20802636, 244170240, -15330568, -1157160, -2965220, -458372, 108528144, -21579504, -578580, 165804, 916744, -2672652], [15675594, -88893389843, 3315768064197, 219389410, -1123182985, -3160090, -1145051027, 1282781074, -21361020, -232098748, -434787266, 0, 130992652, -1897422, -67982984, -18427046, -43536, -5210686, 0, -4185388], [-32158232441747, 38141344970, 32158536859003, -37824559738, 2127988, 193448475, 2654961767, -391209570, -6588212, -315528316, -318664288, 4270778, 30551232, 4172292, -26781456, -3493508, 8541556, 246090, -2086146, -1191450], [-153342540569927, -401204062236, -306685024292533, -200607283253, 3075520509, -68969852, 12630400, -63849698, -43489956, 5521142, -84820035, 5420964, 30052194, 2497274, 1298726, 23962074, -5420964, -4611984, 2497274, -1706718], [120393558532016, 433297533247, 297551097178798, 590223561176, -29838914846, -742196820, 6556052725, -2228813551, 8041875, -428466945, 185149347, -5475673, 138264764, -5995213, -62073352, -2466847, 5866063, 3465300, 5192537, -1324083], [155521579470208, -6418460, -170721402, -186995563418, -2173316722, 3340617280, 4335794034, -3333211668, 12572692, 351437502, 177008514, -8799432, -116746346, 779038, 224419472, 2636396, -8799432, -3284086, -779038, 837440], [93652908215032, -44645684140, 93653423374100, -45136399680, 37714888644, -4786221660, -18876624948, -6200112, 21273248, 477002688, -506069572, 3366768, -101449732, 0, -107854716, -26037052, 0, 4614972, -1649564, 1585140], [-76525881091060, -156748447838, -38262951271293, -312416240462, 26610922842, 1975760406, -26608638034, -985782012, -9801760, -1071703926, 4732294, 501984, 5211666, 5353866, -225063024, 2634910, 250992, -1398794, -10707732, 1256594], [-13964500, -902259534039, 215938313958973, 35889410, -23858648000, 9087472, -23830987990, -957027400, 41536616, -13299854, -62188222, 0, -330747328, -154850, 163847926, 15869338, -7504664, 7156388, 0, 8121930], [-164596095491434, 462245967612, 164594707976004, -463629710336, -4471286, -5098985022, 91262549112, 10198259772, 9724062, 1374972710, 1362823222, -2001036, -120906034, -12365188, 120027968, 50707548, -4002072, 5401104, 6182594, 5497680], [-402028133641814, 2007534025219, -804055954081775, 1003775299703, -32145470341, 5285467909, -31597229, 5263264969, 80382521, -20773481, -258673552, -12474289, 217379381, -114256, -4206724, -58987734, 12474289, 10709492, -114256, 7400980], [272617362733058, -46078821419, 412666219957912, 1040684586988, -33896138540, 4945733391, 24963432701, -5305290605, -26843867, 952605152, 986382711, 28743470, 7967514, 10533873, -212167861, 46986817, 2506378, 6733746, -474439, 15480476], [686889671216446, -43054782, -1201005005, -2401381710721, 46477508458, 824634876, -92871659711, -834430827, -54618677, 2263430630, 1139388563, 29991351, -32884188, 2886563, 99161411, 91615837, 29991351, 10168824, -2886563, 10541697], [13023404387369, 1883970912139, 13022919273089, 1884473146406, 138074806307, -9011278830, -69072365584, -19901725, -788045, -553868698, 491095359, -15627168, -41449115, 0, -62521283, -60779646, 0, 10947709, 5789880, 8954016], [-1251907573578700, -2202644466218, -625953907544306, -4404689149502, 67808622122, 16102952192, -67702114696, -8066259070, -125650692, -466386558, 84559474, 8821592, 14978216, -11134786, 176353226, 108744746, 4410796, 9855316, 22269572, 16257686], [-53441766, -4432319877798, 207260709396546, 1283589024, -68277817002, 3913794, -68232883890, 4320023013, 49002066, -1263672663, -2603956557, 0, 295471587, 8090541, -138810867, 26267409, 22181760, 10420002, 0, 7166898], [-397162936908432, -40595773750, 397165005960714, 42579721452, 17140409, -400135835, 141585875572, 810332281, -38522870, -2046957611, -1983010751, -20825833, 152883931, 12750374, -151995416, 4981155, -41651666, -2133135, -6375187, 1220402], [-436244325303274, 4245365239808, -872487240360086, 2122701205744, -122193709660, -4549497752, -40395666, -4562004416, 61422532, -23535206, -1400597130, -718128, 37999522, -13287482, -18052280, -62739052, 718128, 3572978, -13287482, 4168888], [1814880395991103, -157780056084, 1920644744200917, 6107184218842, -176947225896, -9136018087, 184968624715, 174777260, 3585414, -1614592504, -689074372, -35229432, 172492516, 939918, 209492780, -53225928, -45534426, -16130772, -25976076, -15189762], [1396367275371015, 54773286, 1602451460, -298775834346, 16922900356, 13575631011, -33862881812, -13598531223, -10049751, -3128611057, -1562774894, -559878, 53020560, -11985837, -103234983, -87394673, -559878, 4930658, 11985837, -13038896], [-749413711543598, -30585272362, -749412586483684, -31861732844, 48528775408, 10381528428, -24154373616, 35893404, -137809056, 1372102658, -1191965590, 13061908, 222318214, 0, 231197050, 157835176, 0, -29097648, -11508432, -6795756], [-279117493151478, -3307710038059, -139558538537351, -6617285991971, -61493013420, -24840839864, 61319836177, 12422777581, 172099320, 1598803290, -116575384, -66933504, -28256411, -988886, -115875594, -226635570, -33466752, -1571766, 1977772, -25695759], [172953393, -7523816998032, 1038383607499928, -3379184795, 1273181783, -36183172, 1108525165, -7568774500, -263326857, 3268654455, 6823006413, 0, 100608262, -9088026, -58168799, -52470813, -51121257, -40610712, 0, -38396942], [-1134025558181419, 3377615813966, 1134023018283937, -3380045928826, -19353886, 1591844294, -3784717150, -3186060796, 35995362, 2525565910, 2460838162, 32599748, 175301750, 21747308, -171798604, -106841680, 65199496, -8161244, -10873654, -8951980], [-2560783779672964, 9614970974474, -5121572456828835, 4807402052417, 308109286756, 1405760430, 165289405, 1506532755, -412119645, 88070420, 4687754587, 21159105, -1083867040, 28995395, 47953355, 282625455, -21159105, -48223590, 28995395, -33590775], [1180800466131755, 4025636951854, 1671038024623961, 4740048926648, 110036530422, 16619548463, -185919512135, 11377027179, 133782313, 2932931624, -3176850593, -4938514, -992817595, -36170134, 795807425, -76631261, 118122046, 11933635, 49222460, -35920780], [5651926300618496, 114947465, 2700167381, 5002862743561, -37068321647, -65249462287, 73715862819, 65360987847, 359779001, -4849697431, -2541474626, -104654535, 510677093, 6963254, -1208698382, -215834324, -104654535, -64769150, -6963254, -18012740], [-1559115656046703, 3236446790977, -1559119937954710, 3241013808995, -66286604535, 29406388995, 33085770057, 24885474, 357085879, -4488585569, 4423179189, 67217082, 161672459, 0, 278171074, -18315986, 0, 11102460, 8534813, -35987934], [-482390633361852, -8845972791493, -241195063018352, -17698790641198, -203628303027, -26828761545, 203431481881, 13518660666, 452669903, 6770493942, -267145184, 180466126, -70700185, 44124349, 531416642, 12542750, 90233063, -69519929, -88248698, -45304605], [-155026473, -4961605158384, 1955821662348947, -389975501, 179836238070, 18148611, 179932349568, 1598472843, 244696014, 475098218, 707434240, 0, -325026954, -17611854, 157627059, -40087176, 84902604, 23374623, 0, 20761617], [-4577033634215012, 4144521341854, 4577041548534750, -4136328244700, -94216666, 47944968024, -715072900528, -95911858752, 266915484, -7738038692, -7978744378, 69797982, -880226486, -92682776, 809051902, -366372426, 139595964, -32140764, 46341388, -39448332], [-2110577608826772, 3252190123964, -4221156451251417, 1626171824031, -235726523661, -41560252973, 129550426, -41529316577, 356540577, 188657889, 1540704005, 45621304, -192656940, -5475623, 68780481, 190320371, -45621304, 53631840, -5475623, -10312132], [5338480411994149, -2573121062771, 4128712437574501, 6167336921893, 645172732113, -49624091167, -130909317854, 48276896283, -263480924, -5704912787, -838015297, 14098525, -463455937, 56335496, -652671614, 145270461, -103493488, -44154467, 22080919, 73686256], [7133365373253121, -172944468, -949845605, -2148219803638, -274208356220, 62279383257, 548947734817, -62414483187, -541562219, 1188938606, 865721639, 43467798, 303752793, 51196010, -333331597, 131546431, 43467798, 74325993, -51196010, 13552056], [-2936064957066266, 4943329845968, -2936060515214222, 4938785649524, -1171776387424, 39887178430, 585845743322, -3882960, -118308000, 4351251984, -4478093964, -223020900, -162145740, 0, -160329420, -138922620, 0, -4098840, 25761720, 7981800]]}