/* Data is in the following format
   Note, if the class group has not been computed, it, the class number, the fundamental units, regulator and whether grh was assumed are all 0.
[polynomial,
degree,
t-number of Galois group,
signature [r,s],
discriminant,
list of ramifying primes,
integral basis as polynomials in a,
1 if it is a cm field otherwise 0,
class number,
class group structure,
1 if grh was assumed and 0 if not,
fundamental units,
regulator,
list of subfields each as a pair [polynomial, number of subfields isomorphic to one defined by this polynomial]
]
*/

[x^32 + 5*x^30 - 2*x^28 + 29*x^26 + 210*x^24 - 901*x^22 - 4431*x^20 + 4007*x^18 + 45913*x^16 + 21602*x^14 - 46434*x^12 + 2224*x^10 + 76721*x^8 + 36772*x^6 + 12160*x^4 + 2112*x^2 + 256, 32, 12882, [0, 16], 119193990224161520045746372986484162560000000000000000, [2, 3, 5, 89, 181], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15, a^16, a^17, a^18, a^19, 1/5*a^20 - 2/5*a^18 - 2/5*a^16 - 1/5*a^14 - 1/5*a^12 - 2/5*a^10 + 2/5*a^8 - 2/5*a^6 + 2/5*a^4 + 2/5*a^2 - 1/5, 1/5*a^21 - 2/5*a^19 - 2/5*a^17 - 1/5*a^15 - 1/5*a^13 - 2/5*a^11 + 2/5*a^9 - 2/5*a^7 + 2/5*a^5 + 2/5*a^3 - 1/5*a, 1/25*a^22 - 11/25*a^18 - 1/5*a^16 - 8/25*a^14 + 1/25*a^12 - 12/25*a^10 - 3/25*a^8 + 3/25*a^6 - 9/25*a^4 - 2/25*a^2 + 3/25, 1/50*a^23 + 7/25*a^19 - 1/10*a^17 + 17/50*a^15 - 12/25*a^13 + 13/50*a^11 + 11/25*a^9 + 3/50*a^7 - 9/50*a^5 + 23/50*a^3 + 3/50*a, 1/900*a^24 + 4/225*a^22 + 17/450*a^20 - 7/300*a^18 - 53/900*a^16 + 82/225*a^14 - 91/900*a^12 - 1/90*a^10 + 59/180*a^8 + 199/900*a^6 + 73/300*a^4 + 61/900*a^2 + 82/225, 1/1800*a^25 + 2/225*a^23 - 73/900*a^21 - 187/600*a^19 - 593/1800*a^17 - 49/225*a^15 + 89/1800*a^13 - 11/36*a^11 - 13/360*a^9 + 559/1800*a^7 - 47/600*a^5 + 601/1800*a^3 + 127/450*a, 1/1800*a^26 + 1/60*a^22 - 1/72*a^20 + 31/1800*a^18 - 11/75*a^16 - 139/360*a^14 + 43/300*a^12 - 49/1800*a^10 + 101/600*a^8 - 589/1800*a^6 + 769/1800*a^4 + 23/50*a^2 + 46/225, 1/1800*a^27 - 1/300*a^23 - 1/72*a^21 - 473/1800*a^19 - 7/150*a^17 + 493/1800*a^15 - 113/300*a^13 - 517/1800*a^11 - 163/600*a^9 - 697/1800*a^7 - 707/1800*a^5 + 13/90*a, 1/28717200*a^28 - 497/3190800*a^26 + 7417/14358600*a^24 - 312359/28717200*a^22 + 100573/1196550*a^20 + 153791/1063600*a^18 - 338381/1914480*a^16 - 12104791/28717200*a^14 - 261041/1914480*a^12 + 15077/3589650*a^10 + 564977/3589650*a^8 - 2109397/4786200*a^6 + 1428053/9572400*a^4 - 268106/1794825*a^2 - 10771/1794825, 1/57434400*a^29 + 3827/19144800*a^27 + 7417/28717200*a^25 + 166261/57434400*a^23 + 37313/1063600*a^21 + 1548977/19144800*a^19 + 6476543/19144800*a^17 + 5524379/57434400*a^15 - 9505561/19144800*a^13 - 66113/5743440*a^11 + 4676939/28717200*a^9 - 918887/2393100*a^7 - 810961/3828960*a^5 - 2474623/7179300*a^3 + 356171/3589650*a, 1/34504059406356713546178163200*a^30 + 1265341976857816501/121066875110023556302379520*a^28 - 1731106031936318815373411/17252029703178356773089081600*a^26 - 3404678782815345434410639/6900811881271342709235632640*a^24 - 29971938255193341307355321/1916892189242039641454342400*a^22 + 366182921814451896795706219/3833784378484079282908684800*a^20 - 5447637834455976888301734281/11501353135452237848726054400*a^18 - 2438387762084464973739586669/34504059406356713546178163200*a^16 + 307214732430874447557468271/11501353135452237848726054400*a^14 - 51638571341929502417331859/908001563325176672267846400*a^12 + 652179271843198026683871251/17252029703178356773089081600*a^10 - 142486803139640396422432219/287533828386305946218151360*a^8 - 114115227388136915237952491/244709641179834847845235200*a^6 - 14604127569119327522538307/1078251856448647298318067600*a^4 + 10764564984122256965275337/134781482056080912289758450*a^2 + 15922920576759299261489611/179708642741441216386344600, 1/69008118812713427092356326400*a^31 + 1265341976857816501/242133750220047112604759040*a^29 + 7853354914273879391898301/34504059406356713546178163200*a^27 - 3404678782815345434410639/13801623762542685418471265280*a^25 + 658754966280217572294573/1277928126161359760969561600*a^23 - 1361462877417261849479287423/23002706270904475697452108800*a^21 + 10852335414732166862865023927/23002706270904475697452108800*a^19 - 1128056751419899110195437941/2760324752508537083694253056*a^17 + 9668038256562834696659506991/23002706270904475697452108800*a^15 + 52021726413276231012259081/363200625330070668907138560*a^13 + 7083352566750241023763190003/34504059406356713546178163200*a^11 - 1045494033579006369814853087/2875338283863059462181513600*a^9 - 96305803502271156866993707/489419282359669695690470400*a^7 + 14748284078649404487231311/2156503712897294596636135200*a^5 + 4712863476871777925665211/67390741028040456144879225*a^3 - 30367853329751526906570391/119805761827627477590896400*a], 1, 168, [2, 2, 42], 1, [ (229538629707331)/(10476001317241561600)*a^(30) + (780836543602403)/(10476001317241561600)*a^(28) - (203871257104773)/(1047600131724156160)*a^(26) + (8275762342159647)/(10476001317241561600)*a^(24) + (3526956228361193)/(1047600131724156160)*a^(22) - (274884006257088183)/(10476001317241561600)*a^(20) - (644507433495587761)/(10476001317241561600)*a^(18) + (2238833240531205657)/(10476001317241561600)*a^(16) + (333051878861968159)/(419040052689662464)*a^(14) - (4639974179385949867)/(5238000658620780800)*a^(12) - (4582871017832765927)/(5238000658620780800)*a^(10) + (737330880690306697)/(1309500164655195200)*a^(8) + (75550036620976637)/(222893645047692800)*a^(6) + (10886251915333929)/(81843760290949700)*a^(4) + (499432533738121)/(20460940072737425)*a^(2) - (100628461885261997)/(163687520581899400) , (101519717266549589329344049)/(69008118812713427092356326400)*a^(31) + (9814756809491871509067481)/(1210668751100235563023795200)*a^(29) + (18259287081873723642833149)/(34504059406356713546178163200)*a^(27) + (548699673241276062906837857)/(13801623762542685418471265280)*a^(25) + (254118574121350280829841403)/(766756875696815856581736960)*a^(23) - (27049248516575068805183189263)/(23002706270904475697452108800)*a^(21) - (55627107382565054493165108979)/(7667568756968158565817369600)*a^(19) + (39027232426174851649098459943)/(13801623762542685418471265280)*a^(17) + (1651657932490947478613200167839)/(23002706270904475697452108800)*a^(15) + (118060818167691810266604766733)/(1816003126650353344535692800)*a^(13) - (2248599575579577228628362750877)/(34504059406356713546178163200)*a^(11) - (105309918353601354814717931159)/(2875338283863059462181513600)*a^(9) + (63268428325154320660849747781)/(489419282359669695690470400)*a^(7) + (7388526630409816921471024519)/(67390741028040456144879225)*a^(5) + (12114834843541589171118251011)/(539125928224323649159033800)*a^(3) + (1424031690588536696250051451)/(359417285482882432772689200)*a - 1 , (3726393528091076920007701)/(4313007425794589193272270400)*a^(30) + (303210695715729386809633)/(75666796943764722688987200)*a^(28) - (7044010656496288532130161)/(2156503712897294596636135200)*a^(26) + (111461154876649835574209473)/(4313007425794589193272270400)*a^(24) + (123959873660360981964786847)/(718834570965764865545378400)*a^(22) - (1212864341942261202684141067)/(1437669141931529731090756800)*a^(20) - (5089143477126854950534665409)/(1437669141931529731090756800)*a^(18) + (20834322984935803396102487267)/(4313007425794589193272270400)*a^(16) + (6112292163147132681280979247)/(159741015770169970121195200)*a^(14) + (488443048766568991035827351)/(113500195415647084033480800)*a^(12) - (97990313445037888483533450817)/(2156503712897294596636135200)*a^(10) + (130817284586715077023264973)/(7188345709657648655453784)*a^(8) + (1945143527348241782849123201)/(30588705147479355980654400)*a^(6) + (8066913471925383469492485247)/(1078251856448647298318067600)*a^(4) + (276881845916891634086944987)/(134781482056080912289758450)*a^(2) - (3832271038216559339231759)/(22463580342680152048293075) , (9570162089569181502574723)/(8626014851589178386544540800)*a^(30) + (823865173541316548963459)/(151333593887529445377974400)*a^(28) - (11957025630865769425673453)/(4313007425794589193272270400)*a^(26) + (277879202747852742479551279)/(8626014851589178386544540800)*a^(24) + (330897242287878054524591131)/(1437669141931529731090756800)*a^(22) - (2939878847896994282441827741)/(2875338283863059462181513600)*a^(20) - (13888825087186130324760391907)/(2875338283863059462181513600)*a^(18) + (42617680569080244800575949441)/(8626014851589178386544540800)*a^(16) + (48565114979542330988335185143)/(958446094621019820727171200)*a^(14) + (4310269140734126991953330723)/(227000390831294168066961600)*a^(12) - (238729883306655425464052163991)/(4313007425794589193272270400)*a^(10) + (106883059268596099789115951)/(14376691419315297310907568)*a^(8) + (5319643037463399676655890223)/(61177410294958711961308800)*a^(6) + (33684478942800905955919481003)/(1078251856448647298318067600)*a^(4) + (851700072602779945390507313)/(134781482056080912289758450)*a^(2) + (8789182609137442977032231)/(14975720228453434698862050) , (154974467343118756649483)/(95844609462101982072717120)*a^(30) + (1778262410944514033723777)/(227000390831294168066961600)*a^(28) - (3168894877447944035495849)/(718834570965764865545378400)*a^(26) + (206195706664839975620987683)/(4313007425794589193272270400)*a^(24) + (716269199067601948924538251)/(2156503712897294596636135200)*a^(22) - (86684800978206703639874513)/(57506765677261189243630272)*a^(20) - (9949791554614754022065229571)/(1437669141931529731090756800)*a^(18) + (3603689580377130664484425193)/(479223047310509910363585600)*a^(16) + (314241355400519628817419553231)/(4313007425794589193272270400)*a^(14) + (897651201217338508326572443)/(37833398471882361344493600)*a^(12) - (165335923258897913952155046119)/(2156503712897294596636135200)*a^(10) + (1151395788919819913652382826)/(67390741028040456144879225)*a^(8) + (3628074491455623467932707067)/(30588705147479355980654400)*a^(6) + (1702392718890292679250269523)/(39935253942542492530298800)*a^(4) + (1221727099880702561108326418)/(67390741028040456144879225)*a^(2) + (210847185024671344748890831)/(67390741028040456144879225) , (6179686227066180662617903)/(17252029703178356773089081600)*a^(30) + (1791111979447285794512933)/(908001563325176672267846400)*a^(28) + (1157628053713183150751611)/(8626014851589178386544540800)*a^(26) + (167875644259177606078233563)/(17252029703178356773089081600)*a^(24) + (695193490297771630873869241)/(8626014851589178386544540800)*a^(22) - (548527586514544518290037947)/(1916892189242039641454342400)*a^(20) - (2027974285604619693284335019)/(1150135313545223784872605440)*a^(18) + (11760606484722704360795103437)/(17252029703178356773089081600)*a^(16) + (60170306027338163486082117047)/(3450405940635671354617816320)*a^(14) + (1438887392614954515647074303)/(90800156332517667226784640)*a^(12) - (44435843384135333550130962961)/(2875338283863059462181513600)*a^(10) - (19347358779704590351732909031)/(2156503712897294596636135200)*a^(8) + (1281199243525191375000091273)/(40784940196639141307539200)*a^(6) + (28743555536362149586258348291)/(1078251856448647298318067600)*a^(4) + (736457022356595740280282221)/(134781482056080912289758450)*a^(2) - a + (259725004231023562915924207)/(269562964112161824579516900) , (89137940855158273657487543)/(13801623762542685418471265280)*a^(31) - (768228010794252609707969)/(638964063080679880484780800)*a^(30) + (22579911934161567574883053)/(726401250660141337814277120)*a^(29) - (590461207441293990410177)/(100889062591686296918649600)*a^(28) - (656784704230514085172037129)/(34504059406356713546178163200)*a^(27) + (200556877985389738385871)/(63896406308067988048478080)*a^(26) + (13070033716394472387326146223)/(69008118812713427092356326400)*a^(25) - (68012191031244393031735807)/(1916892189242039641454342400)*a^(24) + (1824318085030057969069732069)/(1380162376254268541847126528)*a^(23) - (237425638387168050941754661)/(958446094621019820727171200)*a^(22) - (139745578379442579286585232941)/(23002706270904475697452108800)*a^(21) + (712384712392315539694340189)/(638964063080679880484780800)*a^(20) - (211193095316798981428903626457)/(7667568756968158565817369600)*a^(19) + (3304571358984622565105532619)/(638964063080679880484780800)*a^(18) + (2161263229092481425125761335113)/(69008118812713427092356326400)*a^(17) - (698521711680146389882384551)/(127792812616135976096956160)*a^(16) + (20148180469251752763481083670423)/(69008118812713427092356326400)*a^(15) - (104090194097308801917805208023)/(1916892189242039641454342400)*a^(14) + (30284613859045254285236850619)/(363200625330070668907138560)*a^(13) - (12741957684081456927801629)/(672593750611241979457664)*a^(12) - (3787340584540334028441788857757)/(11501353135452237848726054400)*a^(11) + (10827524524204845084115724779)/(191689218924203964145434240)*a^(10) + (25011053343526995923678786617)/(345040594063567135461781632)*a^(9) - (2662469220649500709539231709)/(239611523655254955181792800)*a^(8) + (48793669890178245796830227651)/(97883856471933939138094080)*a^(7) - (241375448564735814676175027)/(2718996013109276087169280)*a^(6) + (37753179942345334810840201327)/(269562964112161824579516900)*a^(5) - (1273530201196807003964367797)/(39935253942542492530298800)*a^(4) + (3034815642662773499992909279)/(107825185644864729831806760)*a^(3) - (40887140483900191171041269)/(2995144045690686939772410)*a^(2) + (2563486666169617297342880059)/(1078251856448647298318067600)*a - (8137672281483476470060979)/(5990288091381373879544820) , (2704787283033152277742757)/(17252029703178356773089081600)*a^(31) + (22430385825422169567907699)/(34504059406356713546178163200)*a^(30) + (1237372992041447375651231)/(908001563325176672267846400)*a^(29) + (5827974734880764127025697)/(1816003126650353344535692800)*a^(28) + (20172002883936195373531829)/(8626014851589178386544540800)*a^(27) - (27194287061993186428179353)/(17252029703178356773089081600)*a^(26) + (12741631759521348992723731)/(5750676567726118924363027200)*a^(25) + (128549126805707360054367811)/(6900811881271342709235632640)*a^(24) + (434460785578363150840210399)/(8626014851589178386544540800)*a^(23) + (2340521693548252015841348749)/(17252029703178356773089081600)*a^(22) - 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