/* 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^27 - 513*x^25 + 116964*x^23 - 15617943*x^21 + 1354686795*x^19 - 644328*x^18 - 80025043581*x^17 + 220360176*x^16 + 3282297025608*x^15 - 31401325080*x^14 - 93545465229828*x^13 + 2413017380592*x^12 + 1824136571981646*x^11 - 108068706973656*x^10 - 23533855837754592*x^9 + 2843038291153104*x^8 + 189417763194150150*x^7 - 42013788080373648*x^6 - 861008849860765383*x^5 + 311011158517051680*x^4 + 1862509228623929799*x^3 - 886381801773597288*x^2 - 1419315119960781051*x + 851940306004555639, 27, 1, [27, 0], 3463254175600113063839837232871102966170246194081956872095753304432278349849, [3, 19], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/19*a^9, 1/19*a^10, 1/19*a^11, 1/19*a^12, 1/19*a^13, 1/25631*a^14 + 21/1349*a^13 - 14/1349*a^12 - 4/1349*a^11 - 28/1349*a^10 + 25/1349*a^9 - 14/71*a^8 + 11/71*a^7 - 11/71*a^6 + 592/1349*a^5 + 12/71*a^4 - 5/71*a^3 + 34/71*a^2 + 12/71*a + 15/71, 1/25631*a^15 - 15/1349*a^13 - 27/1349*a^12 + 6/1349*a^11 - 21/1349*a^10 - 17/1349*a^9 - 12/71*a^8 + 2/71*a^7 + 345/1349*a^6 + 5/71*a^5 + 35/71*a^4 - 30/71*a^3 + 7/71*a^2 - 16/71*a - 21/71, 1/25631*a^16 - 6/1349*a^13 - 8/1349*a^12 - 25/1349*a^11 + 26/1349*a^10 + 10/1349*a^9 - 12/71*a^8 + 554/1349*a^7 - 6/71*a^6 - 31/71*a^5 - 18/71*a^4 + 2/71*a^3 + 18/71*a^2 - 9/71*a + 15/71, 1/25631*a^17 - 28/1349*a^13 + 12/1349*a^12 - 4/1349*a^11 + 13/1349*a^10 - 5/1349*a^9 - 92/1349*a^8 - 30/71*a^7 - 7/71*a^6 - 16/71*a^5 + 21/71*a^4 + 16/71*a^3 + 33/71*a^2 + 34/71*a + 6/71, 1/5752309428455797*a^18 - 18/302753127813463*a^16 + 135/15934375148077*a^14 - 546/838651323583*a^12 + 24453/838651323583*a^10 + 95774828/17809007518439*a^9 - 643302/838651323583*a^8 - 861973452/937316185181*a^7 + 9506574/838651323583*a^6 + 2585920356/49332430799*a^5 - 70373340/838651323583*a^4 - 5259221161/49332430799*a^3 + 200564019/838651323583*a^2 + 15177831378/49332430799*a - 130163161159/838651323583, 1/615497108844770279*a^19 + 35435971401/32394584676040541*a^17 - 70871940273/32394584676040541*a^15 - 767779391119/1704978140844239*a^13 - 30/1349*a^12 - 22371909491255/1704978140844239*a^11 + 13426160004815/1905563804472973*a^10 + 32057729920984/1704978140844239*a^9 + 37313215930755/100292831814367*a^8 + 21438772215069/89735691623381*a^7 + 9581408798475/100292831814367*a^6 + 7465107605596/89735691623381*a^5 - 354060351599/5278570095493*a^4 + 29530176746519/89735691623381*a^3 - 2115844214545/5278570095493*a^2 + 36593315219398/89735691623381*a + 783/7597, 1/615497108844770279*a^20 + 48/615497108844770279*a^18 - 590599528105/32394584676040541*a^16 + 70872746082/32394584676040541*a^14 - 460671209700/1704978140844239*a^12 + 2125559236999/1905563804472973*a^11 + 1559191635804/89735691623381*a^10 - 43029561648939/1905563804472973*a^9 - 34782673514/292298669783*a^8 + 991069579450/5278570095493*a^7 - 2264264980296/89735691623381*a^6 - 21745208333469/100292831814367*a^5 + 21517825584171/89735691623381*a^4 - 2619569715372/5278570095493*a^3 - 35109930917613/89735691623381*a^2 - 1216477654210/5278570095493*a - 186743791396/838651323583, 1/11694445068050635301*a^21 - 519727581001/32394584676040541*a^17 + 23623982830/1704978140844239*a^15 - 9792140264396/1704978140844239*a^13 - 625057783376789/36205712284986487*a^12 - 23742093131106/1704978140844239*a^11 - 21834644650342/1905563804472973*a^10 + 42771007000023/1704978140844239*a^9 - 31339717982114/100292831814367*a^8 + 29069475968525/89735691623381*a^7 - 52212248154/5278570095493*a^6 + 522432980681/5278570095493*a^5 - 1966817315052/5278570095493*a^4 - 20578997718262/1704978140844239*a^3 - 106867199239/5278570095493*a^2 + 25639668529675/89735691623381*a + 145/7597, 1/11694445068050635301*a^22 - 2/615497108844770279*a^18 - 354359742996/32394584676040541*a^16 + 1243384378/89735691623381*a^14 - 7762466434840/36205712284986487*a^13 - 5965084701527/1704978140844239*a^12 + 21955183324945/1905563804472973*a^11 - 125270033034/13425024731057*a^10 - 4443289501512/1905563804472973*a^9 + 5514058154485/89735691623381*a^8 - 29851775593581/100292831814367*a^7 + 33283616111462/89735691623381*a^6 + 1939595177417/5278570095493*a^5 + 51109638976/13425024731057*a^4 - 2397482499007/5278570095493*a^3 - 18738686832048/89735691623381*a^2 - 2395938728101/5278570095493*a - 167274203267/838651323583, 1/15775806396800307021049*a^23 + 21/830305599831595106371*a^22 - 23/830305599831595106371*a^21 + 35/43700294727978689809*a^20 + 1/2570605572234040577*a^19 + 7/344096808881721967*a^18 - 7547861909724/2300015511998878411*a^17 - 24320889131276/2300015511998878411*a^16 + 15095723367297/2300015511998878411*a^15 + 5991382553840387/830305599831595106371*a^14 + 667443206741717404/43700294727978689809*a^13 - 150484527872455043/43700294727978689809*a^12 - 14149362186453952/2300015511998878411*a^11 - 32601265896732028/2300015511998878411*a^10 + 29636454631141615/2300015511998878411*a^9 + 25298852033454122/121053447999940969*a^8 - 38072486489356772/121053447999940969*a^7 - 1127930850661315/121053447999940969*a^6 - 752004377163124921/2300015511998878411*a^5 - 42012522564274411/121053447999940969*a^4 + 11319242776374593/121053447999940969*a^3 - 133492776549786/374778476780003*a^2 - 2313992564953175/6371234105260051*a + 979565643527114/6371234105260051, 1/15775806396800307021049*a^24 - 24/830305599831595106371*a^22 - 27/830305599831595106371*a^21 - 32/43700294727978689809*a^20 - 1/43700294727978689809*a^19 + 10/142346236898953387*a^18 - 20127631760871/2300015511998878411*a^17 - 11741117974952/2300015511998878411*a^16 + 1450029416817506/830305599831595106371*a^15 - 20127748271826/2300015511998878411*a^14 + 742398449686952794/43700294727978689809*a^13 - 549592377507979722/43700294727978689809*a^12 - 13592341835687070/2300015511998878411*a^11 + 14945533628200828/2300015511998878411*a^10 + 28742032087581550/2300015511998878411*a^9 + 27194095827707697/121053447999940969*a^8 - 57957946118632005/121053447999940969*a^7 - 588202809440983616/2300015511998878411*a^6 + 31933552646015127/121053447999940969*a^5 + 7573686413460265/121053447999940969*a^4 + 45342156624010343/121053447999940969*a^3 - 199387281934886/6371234105260051*a^2 - 3080412214445355/6371234105260051*a - 912560619220086/6371234105260051, 1/299740321539205833399931*a^25 + 28/830305599831595106371*a^22 - 16/830305599831595106371*a^21 - 27/43700294727978689809*a^20 + 24/43700294727978689809*a^19 + 1323/43700294727978689809*a^18 - 19288980450167/2300015511998878411*a^17 + 219129523627051033/15775806396800307021049*a^16 - 39416610380297/2300015511998878411*a^15 - 8747900768940210/830305599831595106371*a^14 - 855851181369132676/43700294727978689809*a^13 + 45859120541697813/2300015511998878411*a^12 - 24634168517602762/2300015511998878411*a^11 + 7490117468921213/2300015511998878411*a^10 - 16881156705687759/2300015511998878411*a^9 + 1424510048844176/6371234105260051*a^8 + 16989314292268292882/43700294727978689809*a^7 + 31909549017268932/121053447999940969*a^6 + 175424434335400775/2300015511998878411*a^5 - 16730829004265818/121053447999940969*a^4 - 14083028844542663/121053447999940969*a^3 + 1435714354368838/6371234105260051*a^2 - 915407203602058/6371234105260051*a + 868208090098496/6371234105260051, 1/299740321539205833399931*a^26 + 30/830305599831595106371*a^22 + 8/830305599831595106371*a^21 + 6/43700294727978689809*a^20 + 18/43700294727978689809*a^19 - 165/43700294727978689809*a^18 + 370239988180551/927988611576488648297*a^17 - 44448522234155/2300015511998878411*a^16 - 15408525994595557/830305599831595106371*a^15 + 16773495889574/2300015511998878411*a^14 - 8091967522657492/615497108844770279*a^13 + 642234154897013633/43700294727978689809*a^12 - 5974495481780709/2300015511998878411*a^11 + 38244909446717838/2300015511998878411*a^10 + 28150893891331437/2300015511998878411*a^9 + 562745099224064973/2570605572234040577*a^8 + 53519347133091388/121053447999940969*a^7 - 981503597404758627/2300015511998878411*a^6 + 46652573821762958/121053447999940969*a^5 + 48364533802352549/121053447999940969*a^4 - 49938013858344491/121053447999940969*a^3 + 34617893852923/89735691623381*a^2 - 1429647918001797/6371234105260051*a - 1974414079203513/6371234105260051], 0, 9, [9], 1, [ (29360)/(5752309428455797)*a^(18) - (528480)/(302753127813463)*a^(16) + (3963600)/(15934375148077)*a^(14) - (16030560)/(838651323583)*a^(12) + (717940080)/(838651323583)*a^(10) + (394537)/(17809007518439)*a^(9) - (18887346720)/(838651323583)*a^(8) - (3550833)/(937316185181)*a^(7) + (279113012640)/(838651323583)*a^(6) + (10652499)/(49332430799)*a^(5) - (2066161262400)/(838651323583)*a^(4) - (224886090)/(49332430799)*a^(3) + (5888559597840)/(838651323583)*a^(2) + (1281850713)/(49332430799)*a - (4049586678424)/(838651323583) , (9787)/(5752309428455797)*a^(18) - (176166)/(302753127813463)*a^(16) + (1321245)/(15934375148077)*a^(14) - (5343702)/(838651323583)*a^(12) + (239321511)/(838651323583)*a^(10) + (32056455)/(17809007518439)*a^(9) - (6295996674)/(838651323583)*a^(8) - (288508095)/(937316185181)*a^(7) + (93040839738)/(838651323583)*a^(6) + (865524285)/(49332430799)*a^(5) - (688743878580)/(838651323583)*a^(4) - (18272179350)/(49332430799)*a^(3) + (1962920053953)/(838651323583)*a^(2) + (104151422295)/(49332430799)*a - (1672800387722)/(838651323583) , (264632338)/(15775806396800307021049)*a^(24) - (6351176112)/(830305599831595106371)*a^(22) - (611358263)/(830305599831595106371)*a^(21) + (66687349176)/(43700294727978689809)*a^(20) + (12838523523)/(43700294727978689809)*a^(19) - (7644961111915)/(43700294727978689809)*a^(18) - (115546711707)/(2300015511998878411)*a^(17) + (29275701278058)/(2300015511998878411)*a^(16) + (3989313450138675)/(830305599831595106371)*a^(15) - (74172666544461)/(121053447999940969)*a^(14) - (12287608016181345)/(43700294727978689809)*a^(13) + (50738041676417095)/(2570605572234040577)*a^(12) + (23795949674394351)/(2300015511998878411)*a^(11) - (968009365433130891)/(2300015511998878411)*a^(10) - (32006297680506384)/(135295030117581083)*a^(9) + (695429623326887766)/(121053447999940969)*a^(8) + (387139936540837482)/(121053447999940969)*a^(7) - (108303301711282888522)/(2300015511998878411)*a^(6) - (146717898727197663)/(6371234105260051)*a^(5) + (25004188455476758233)/(121053447999940969)*a^(4) + (8750219074012088398)/(121053447999940969)*a^(3) - (2491493691622841541)/(6371234105260051)*a^(2) - (555654459154236375)/(6371234105260051)*a + (1208764884657480332)/(6371234105260051) , (36388029)/(15775806396800307021049)*a^(24) - (873312696)/(830305599831595106371)*a^(22) + (214796359)/(830305599831595106371)*a^(21) + (9169783308)/(43700294727978689809)*a^(20) - (4510723539)/(43700294727978689809)*a^(19) - (1048507087045)/(43700294727978689809)*a^(18) + (40596511851)/(2300015511998878411)*a^(17) + (3976814582964)/(2300015511998878411)*a^(16) - (1399131185360413)/(830305599831595106371)*a^(15) - (9833689314963)/(121053447999940969)*a^(14) + (4279879293245655)/(43700294727978689809)*a^(13) + (108485404211763392)/(43700294727978689809)*a^(12) - (8136832847955363)/(2300015511998878411)*a^(11) - (109418717096279817)/(2300015511998878411)*a^(10) + (10482034598154970)/(135295030117581083)*a^(9) + (63462491297324091)/(121053447999940969)*a^(8) - (114890485318107750)/(121053447999940969)*a^(7) - (6288712977804514813)/(2300015511998878411)*a^(6) + (34067269445857947)/(6371234105260051)*a^(5) + (450139230503439972)/(121053447999940969)*a^(4) - (828944250876468764)/(121053447999940969)*a^(3) - (891728900646462)/(6371234105260051)*a^(2) - (37512531182942661)/(6371234105260051)*a + (45189260258547602)/(6371234105260051) , (48239083)/(15775806396800307021049)*a^(24) - (1157737992)/(830305599831595106371)*a^(22) + (101857593)/(830305599831595106371)*a^(21) + (12156248916)/(43700294727978689809)*a^(20) - (2139009453)/(43700294727978689809)*a^(19) - (73241229411)/(2300015511998878411)*a^(18) + (19251085077)/(2300015511998878411)*a^(17) + (278982847080)/(121053447999940969)*a^(16) - (663415002523262)/(830305599831595106371)*a^(15) - (697441789989)/(6371234105260051)*a^(14) + (2028633485260350)/(43700294727978689809)*a^(13) + (149760760379648597)/(43700294727978689809)*a^(12) - (3853079781344091)/(2300015511998878411)*a^(11) - (158856986143919625)/(2300015511998878411)*a^(10) + (260717793394236)/(7120791058820057)*a^(9) + (333680793362181)/(394310905537267)*a^(8) - (2853199361908053)/(6371234105260051)*a^(7) - (12942877419758844069)/(2300015511998878411)*a^(6) + (16460579324167992)/(6371234105260051)*a^(5) + (1957928947427515257)/(121053447999940969)*a^(4) - (617739273362444473)/(121053447999940969)*a^(3) - (108973667016973854)/(6371234105260051)*a^(2) + (22284447147790500)/(6371234105260051)*a + (25942512795280852)/(6371234105260051) , (166868832)/(15775806396800307021049)*a^(24) - (4004851968)/(830305599831595106371)*a^(22) + (26256548)/(830305599831595106371)*a^(21) + (42050945664)/(43700294727978689809)*a^(20) - (551387508)/(43700294727978689809)*a^(19) - (253722801389)/(2300015511998878411)*a^(18) + (4962487572)/(2300015511998878411)*a^(17) + (971654570730)/(121053447999940969)*a^(16) - (177127105983827)/(830305599831595106371)*a^(15) - (2462063265531)/(6371234105260051)*a^(14) + (614644454376525)/(43700294727978689809)*a^(13) + (544105127079474353)/(43700294727978689809)*a^(12) - (1543491484109226)/(2300015511998878411)*a^(11) - (610712733823694655)/(2300015511998878411)*a^(10) + (165963395839888)/(7120791058820057)*a^(9) + (438259392445808088)/(121053447999940969)*a^(8) - (3464448483879009)/(6371234105260051)*a^(7) - (67749274142860077455)/(2300015511998878411)*a^(6) + (46881300720452409)/(6371234105260051)*a^(5) + (15134212052724269217)/(121053447999940969)*a^(4) - (5472100214021236605)/(121053447999940969)*a^(3) - (78058781203389606)/(374778476780003)*a^(2) + (338289515730891225)/(6371234105260051)*a + (633880911385640010)/(6371234105260051) , (3933243)/(15775806396800307021049)*a^(24) - (94397832)/(830305599831595106371)*a^(22) - (198636437)/(830305599831595106371)*a^(21) + (991177236)/(43700294727978689809)*a^(20) + (4171365177)/(43700294727978689809)*a^(19) - (112774225596)/(43700294727978689809)*a^(18) - (37542286593)/(2300015511998878411)*a^(17) + (419768640846)/(2300015511998878411)*a^(16) + (1294065013830747)/(830305599831595106371)*a^(15) - (987250637556)/(121053447999940969)*a^(14) - (3960822582977985)/(43700294727978689809)*a^(13) + (9630914914861500)/(43700294727978689809)*a^(12) + (7542275242160529)/(2300015511998878411)*a^(11) - (6928769183884236)/(2300015511998878411)*a^(10) - (9753366820361737)/(135295030117581083)*a^(9) + (235436099718483)/(121053447999940969)*a^(8) + (107890097718123081)/(121053447999940969)*a^(7) + (3486760111287723)/(7491907205208073)*a^(6) - (32821186171525830)/(6371234105260051)*a^(5) - (523527094901581686)/(121053447999940969)*a^(4) + (933786243452777579)/(121053447999940969)*a^(3) + (31731659169404085)/(6371234105260051)*a^(2) - (18872259926983179)/(6371234105260051)*a - (8003520704907388)/(6371234105260051) , (147837599)/(15775806396800307021049)*a^(24) - (3548102376)/(830305599831595106371)*a^(22) + (7968471)/(830305599831595106371)*a^(21) + (37255074948)/(43700294727978689809)*a^(20) - (167337891)/(43700294727978689809)*a^(19) - (251198099492)/(2570605572234040577)*a^(18) + (1506041019)/(2300015511998878411)*a^(17) + (16345749191526)/(2300015511998878411)*a^(16) - (51598123367777)/(830305599831595106371)*a^(15) - (41367741781068)/(121053447999940969)*a^(14) + (154175729557395)/(43700294727978689809)*a^(13) + (479966060381885621)/(43700294727978689809)*a^(12) - (274268450337147)/(2300015511998878411)*a^(11) - (536468898153863040)/(2300015511998878411)*a^(10) + (295552250274381)/(135295030117581083)*a^(9) + (22538833535261565)/(7120791058820057)*a^(8) - (7094856997503)/(482284653386219)*a^(7) - (59431715815287472774)/(2300015511998878411)*a^(6) - (518815096086888)/(6371234105260051)*a^(5) + (13945709692106946141)/(121053447999940969)*a^(4) + (114282105416212118)/(121053447999940969)*a^(3) - (1544462477854501302)/(6371234105260051)*a^(2) - (38747339089469358)/(6371234105260051)*a + (1133692343926249164)/(6371234105260051) , (105200966)/(299740321539205833399931)*a^(26) - (1020087195)/(299740321539205833399931)*a^(25) - (2881181268)/(15775806396800307021049)*a^(24) + (25118147604)/(15775806396800307021049)*a^(23) + (34807522394)/(830305599831595106371)*a^(22) - (272795682702)/(830305599831595106371)*a^(21) - (244328980525)/(43700294727978689809)*a^(20) + (5599415878)/(142346236898953387)*a^(19) + (20985221266962)/(43700294727978689809)*a^(18) - (47716577420292482)/(15775806396800307021049)*a^(17) - (438747795058555310)/(15775806396800307021049)*a^(16) + (7628211809645538)/(48841505872446770963)*a^(15) + (48282876977558010)/(43700294727978689809)*a^(14) - (240533581132801832)/(43700294727978689809)*a^(13) - (1311502722350759062)/(43700294727978689809)*a^(12) + (303633671424827870)/(2300015511998878411)*a^(11) + (1252532920407015542)/(2300015511998878411)*a^(10) - (4861362007860777519)/(2300015511998878411)*a^(9) - 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