/* 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^22 - 2*x^21 + x^20 - x^19 - 7*x^17 + 5*x^16 + 45*x^15 + 31*x^14 - 38*x^13 - 205*x^12 - 278*x^11 - 123*x^10 + 249*x^9 + 532*x^8 + 371*x^7 + 205*x^6 + 153*x^5 + 236*x^4 + 94*x^3 + 34*x^2 + 5*x + 25, 22, 52, [2, 10], 31524414620673611592542191616, [2, 11, 19, 547], [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, a^20, 1/1566600432296449248673012375*a^21 + 650975624423235334486530188/1566600432296449248673012375*a^20 + 539789351381108511797508471/1566600432296449248673012375*a^19 - 395864321856137327061736386/1566600432296449248673012375*a^18 - 114008859891265356629977943/313320086459289849734602475*a^17 - 132494403951115435316436732/1566600432296449248673012375*a^16 + 1865470605290737245825082/62664017291857969946920495*a^15 - 45254148489137336961030766/313320086459289849734602475*a^14 - 455876548303563091653333419/1566600432296449248673012375*a^13 - 511817988088865703725604898/1566600432296449248673012375*a^12 - 17156441912661997059184673/62664017291857969946920495*a^11 + 437033676120101220170443097/1566600432296449248673012375*a^10 + 781245610000102508713914057/1566600432296449248673012375*a^9 - 721844774901829305696513671/1566600432296449248673012375*a^8 - 248138526229904830234174458/1566600432296449248673012375*a^7 - 721117628843832794985138649/1566600432296449248673012375*a^6 - 111216791727665069954211371/313320086459289849734602475*a^5 - 450359046119162935571807547/1566600432296449248673012375*a^4 - 531206321846254884830676569/1566600432296449248673012375*a^3 - 149940144248907651758610141/1566600432296449248673012375*a^2 - 778555872930536758192447131/1566600432296449248673012375*a - 8749422640071527091633927/313320086459289849734602475], 0, 1, [], 1, [ (13661365753166911486120437)/(1566600432296449248673012375)*a^(21) - (117203479853914005990588094)/(1566600432296449248673012375)*a^(20) + (219918021199951938180369577)/(1566600432296449248673012375)*a^(19) - (186711162598147678877678057)/(1566600432296449248673012375)*a^(18) + (38188710559689959074805784)/(313320086459289849734602475)*a^(17) - (161224531585489464410456134)/(1566600432296449248673012375)*a^(16) + (27130744795135311382846774)/(62664017291857969946920495)*a^(15) + (12849690795488456331613158)/(313320086459289849734602475)*a^(14) - (3407060469658515052605007853)/(1566600432296449248673012375)*a^(13) - (2250254595943661297523773301)/(1566600432296449248673012375)*a^(12) - (1427120956476363752570601)/(62664017291857969946920495)*a^(11) + (13539447045985958074210513764)/(1566600432296449248673012375)*a^(10) + (20159278701507735631612257159)/(1566600432296449248673012375)*a^(9) + (12397831789913849037661032648)/(1566600432296449248673012375)*a^(8) - (13182838329567599002222797271)/(1566600432296449248673012375)*a^(7) - (39681695193521016726273632738)/(1566600432296449248673012375)*a^(6) - (5520664371527697801948828927)/(313320086459289849734602475)*a^(5) - (18686598295060245634233745539)/(1566600432296449248673012375)*a^(4) - (5491374871060261466174641403)/(1566600432296449248673012375)*a^(3) - (10527475586269564068187476742)/(1566600432296449248673012375)*a^(2) - (2365890161950967805396057122)/(1566600432296449248673012375)*a - (487158969649444194471240174)/(313320086459289849734602475) , (117433364634165871534108291)/(1566600432296449248673012375)*a^(21) - (262484320366189287561102042)/(1566600432296449248673012375)*a^(20) + (131218606135978224346491936)/(1566600432296449248673012375)*a^(19) + (11211958166348625195712049)/(1566600432296449248673012375)*a^(18) - (45570248519622196106291863)/(313320086459289849734602475)*a^(17) - (560207780088595243846820512)/(1566600432296449248673012375)*a^(16) + (25993061510850042186840227)/(62664017291857969946920495)*a^(15) + (1077942672440628082014874944)/(313320086459289849734602475)*a^(14) + (1856991040901647655326718071)/(1566600432296449248673012375)*a^(13) - (6530566132643167327281572193)/(1566600432296449248673012375)*a^(12) - (853971336140159737720961593)/(62664017291857969946920495)*a^(11) - (26303822425796754724305769398)/(1566600432296449248673012375)*a^(10) - (2113298298681532798150007788)/(1566600432296449248673012375)*a^(9) + (33103909170858319450671586364)/(1566600432296449248673012375)*a^(8) + (52422631567632105567769235472)/(1566600432296449248673012375)*a^(7) + (24710168639775699151008463766)/(1566600432296449248673012375)*a^(6) + (2117682292527718445686345864)/(313320086459289849734602475)*a^(5) + (16968511710595477579012485448)/(1566600432296449248673012375)*a^(4) + (12668864618871365598584908671)/(1566600432296449248673012375)*a^(3) + (818019539609965587451483844)/(1566600432296449248673012375)*a^(2) - (1731482474838363082482885871)/(1566600432296449248673012375)*a + (258893428598611457217573693)/(313320086459289849734602475) , (55394844882047590518099471)/(1566600432296449248673012375)*a^(21) - (133214082741834861023814952)/(1566600432296449248673012375)*a^(20) + (60852484828739054830060841)/(1566600432296449248673012375)*a^(19) - (6594431112196876309798681)/(1566600432296449248673012375)*a^(18) - (3460498096616220621928178)/(313320086459289849734602475)*a^(17) - (293069696521186751320995147)/(1566600432296449248673012375)*a^(16) + (14185943174105541778136402)/(62664017291857969946920495)*a^(15) + (539006416211425037511093514)/(313320086459289849734602475)*a^(14) + (627991029333222797989295151)/(1566600432296449248673012375)*a^(13) - (4679651113372901261511126833)/(1566600432296449248673012375)*a^(12) - (488475493225649622469756093)/(62664017291857969946920495)*a^(11) - (9954674677435196242023342188)/(1566600432296449248673012375)*a^(10) + (8485287108939404576620063097)/(1566600432296449248673012375)*a^(9) + (30297637457254759020965186459)/(1566600432296449248673012375)*a^(8) + (31927471926615896645084296157)/(1566600432296449248673012375)*a^(7) - (1058759832065876984947718304)/(1566600432296449248673012375)*a^(6) - (4958200943429565491804506991)/(313320086459289849734602475)*a^(5) - (19247332234871978473151035637)/(1566600432296449248673012375)*a^(4) - (496782762953140566485999499)/(1566600432296449248673012375)*a^(3) - (2335823225769901171546279536)/(1566600432296449248673012375)*a^(2) - (6629098954283329176483607326)/(1566600432296449248673012375)*a - (718827415964348811305302817)/(313320086459289849734602475) , (3815830925287737027293077)/(1566600432296449248673012375)*a^(21) + (83085403912323976888100351)/(1566600432296449248673012375)*a^(20) - (203693972409666770781011233)/(1566600432296449248673012375)*a^(19) + (167607662735724879372362903)/(1566600432296449248673012375)*a^(18) - (35096414122226387212022086)/(313320086459289849734602475)*a^(17) - (12059617304414234529821489)/(1566600432296449248673012375)*a^(16) - (20425831543638526269616296)/(62664017291857969946920495)*a^(15) + (128107003193296223297707018)/(313320086459289849734602475)*a^(14) + (3992573060056169491107057737)/(1566600432296449248673012375)*a^(13) + (1693136837903906810211553354)/(1566600432296449248673012375)*a^(12) - (146958320340791084114311191)/(62664017291857969946920495)*a^(11) - (18176547424251804610618917781)/(1566600432296449248673012375)*a^(10) - (23010530307384555261652322486)/(1566600432296449248673012375)*a^(9) - (8143819796703883632374284167)/(1566600432296449248673012375)*a^(8) + (21960954700057625002244988359)/(1566600432296449248673012375)*a^(7) + (45846538646665896303692335902)/(1566600432296449248673012375)*a^(6) + (6479466915874241499740334883)/(313320086459289849734602475)*a^(5) + (21752510812637587251972922506)/(1566600432296449248673012375)*a^(4) + (10916432374034440474621284312)/(1566600432296449248673012375)*a^(3) + (13305864164288253143466651768)/(1566600432296449248673012375)*a^(2) + (5081204750434192647618058538)/(1566600432296449248673012375)*a + (575556066370196532468835346)/(313320086459289849734602475) , (93935014977962104692479351)/(1566600432296449248673012375)*a^(21) - (185433147448572690973932137)/(1566600432296449248673012375)*a^(20) + (86508650715755796653541071)/(1566600432296449248673012375)*a^(19) - (132841901596860250092553986)/(1566600432296449248673012375)*a^(18) + (16625771233583645738264582)/(313320086459289849734602475)*a^(17) - (679435636482140452402919557)/(1566600432296449248673012375)*a^(16) + (18941644563101938645228172)/(62664017291857969946920495)*a^(15) + (850959304221577550462216284)/(313320086459289849734602475)*a^(14) + (3356373375780190019144012681)/(1566600432296449248673012375)*a^(13) - (3821486889824000154225794198)/(1566600432296449248673012375)*a^(12) - (868561249658373500769471663)/(62664017291857969946920495)*a^(11) - (27927237546793916116158552078)/(1566600432296449248673012375)*a^(10) - (9660696951619362187308894618)/(1566600432296449248673012375)*a^(9) + (33997186928401581064979935979)/(1566600432296449248673012375)*a^(8) + (64184298046550427424529395617)/(1566600432296449248673012375)*a^(7) + (39858514609218699559802958701)/(1566600432296449248673012375)*a^(6) + (908279077527303704216819979)/(313320086459289849734602475)*a^(5) - (14343760654445254518842892622)/(1566600432296449248673012375)*a^(4) + (6148490247767048491826528656)/(1566600432296449248673012375)*a^(3) + (4030189421031670199490603259)/(1566600432296449248673012375)*a^(2) + (798525781638363164370662894)/(1566600432296449248673012375)*a - (1140545430458523550789679552)/(313320086459289849734602475) , (214893381321907677400060207)/(1566600432296449248673012375)*a^(21) - (566564382450808024948003084)/(1566600432296449248673012375)*a^(20) + (580537012509784620931759372)/(1566600432296449248673012375)*a^(19) - (552676096812682828605915277)/(1566600432296449248673012375)*a^(18) + (38744199219870339700490224)/(313320086459289849734602475)*a^(17) - (1401758451065597052481579274)/(1566600432296449248673012375)*a^(16) + (71596450398539106332508259)/(62664017291857969946920495)*a^(15) + (1713272822945377247029480638)/(313320086459289849734602475)*a^(14) + (1004009714866533303179326142)/(1566600432296449248673012375)*a^(13) - (7897093120250149602524293511)/(1566600432296449248673012375)*a^(12) - (1503399820217525967518329606)/(62664017291857969946920495)*a^(11) - (38132996423945376994543744171)/(1566600432296449248673012375)*a^(10) - (5627722900466052536023923201)/(1566600432296449248673012375)*a^(9) + (50728926320348361995442562978)/(1566600432296449248673012375)*a^(8) + (84118638560503169211757371944)/(1566600432296449248673012375)*a^(7) + (38738882906041508451612347657)/(1566600432296449248673012375)*a^(6) + (6902723574213815405322444453)/(313320086459289849734602475)*a^(5) + (14401201322458486471781302771)/(1566600432296449248673012375)*a^(4) + (24835527468708004613299294217)/(1566600432296449248673012375)*a^(3) - (1812260015142357339671785562)/(1566600432296449248673012375)*a^(2) + (5804013951550539297308083633)/(1566600432296449248673012375)*a - (153010311664250208885608789)/(313320086459289849734602475) , (277137170473556829821082704)/(1566600432296449248673012375)*a^(21) - (415810806618347469082236148)/(1566600432296449248673012375)*a^(20) + (828564788364535315159209)/(1566600432296449248673012375)*a^(19) - (101764875651276695148120744)/(1566600432296449248673012375)*a^(18) - (58467285417884731134044697)/(313320086459289849734602475)*a^(17) - (1744994290797161161371564578)/(1566600432296449248673012375)*a^(16) + (12749306914031721566403533)/(62664017291857969946920495)*a^(15) + (2633049957855055011577782211)/(313320086459289849734602475)*a^(14) + (14680220519447421959938667774)/(1566600432296449248673012375)*a^(13) - (5624352771121935429535808817)/(1566600432296449248673012375)*a^(12) - (2425166771750790737694735337)/(62664017291857969946920495)*a^(11) - (107951314630657640836960725337)/(1566600432296449248673012375)*a^(10) - (76274756437682189587516193372)/(1566600432296449248673012375)*a^(9) + (47576786555620809025828235116)/(1566600432296449248673012375)*a^(8) + (186714470809496228687256931443)/(1566600432296449248673012375)*a^(7) + (193456218024308306332759504354)/(1566600432296449248673012375)*a^(6) + (24846829998380994948622913141)/(313320086459289849734602475)*a^(5) + (70390929459269139154881863787)/(1566600432296449248673012375)*a^(4) + (59870010536850486459026584674)/(1566600432296449248673012375)*a^(3) + (40263271536379501378902473486)/(1566600432296449248673012375)*a^(2) + (15718486915331991097703158401)/(1566600432296449248673012375)*a + (701083435825400250921063317)/(313320086459289849734602475) , (32178174392226073261830042)/(1566600432296449248673012375)*a^(21) - (107670777046280601297771229)/(1566600432296449248673012375)*a^(20) + (135011352007385466758524907)/(1566600432296449248673012375)*a^(19) - (64972077864191102617857962)/(1566600432296449248673012375)*a^(18) - (14206512531899875934496581)/(313320086459289849734602475)*a^(17) - (87691078098785423743647119)/(1566600432296449248673012375)*a^(16) + (13210199841039366314954179)/(62664017291857969946920495)*a^(15) + (234649783902541433420028453)/(313320086459289849734602475)*a^(14) - (1154571868124389391384038348)/(1566600432296449248673012375)*a^(13) - (1336412253899883694511845216)/(1566600432296449248673012375)*a^(12) - (115323017078043213996603096)/(62664017291857969946920495)*a^(11) - (1213260564269386937536552176)/(1566600432296449248673012375)*a^(10) + (2832299617053024915761267019)/(1566600432296449248673012375)*a^(9) + (2071340002094105869215388568)/(1566600432296449248673012375)*a^(8) - (59372647699936066603852986)/(1566600432296449248673012375)*a^(7) - (4221750417088770287409042758)/(1566600432296449248673012375)*a^(6) + (2095169543166249346262088393)/(313320086459289849734602475)*a^(5) + (15069493888054097274546547901)/(1566600432296449248673012375)*a^(4) + (4740929603470051417591086477)/(1566600432296449248673012375)*a^(3) - (553800686810855876182230047)/(1566600432296449248673012375)*a^(2) + (2095225282707155760221000498)/(1566600432296449248673012375)*a + (751366708261638407319260816)/(313320086459289849734602475) , (143547415586037218151962384)/(1566600432296449248673012375)*a^(21) - (354468961378990217931232183)/(1566600432296449248673012375)*a^(20) + (273327603322945301068823489)/(1566600432296449248673012375)*a^(19) - (267213080293625303165580849)/(1566600432296449248673012375)*a^(18) + (37121535504647804473999888)/(313320086459289849734602475)*a^(17) - (1007744292414045062493878963)/(1566600432296449248673012375)*a^(16) + (45857842871869821939258683)/(62664017291857969946920495)*a^(15) + (1252887651793450115767303931)/(313320086459289849734602475)*a^(14) + (1769042644121414704915986604)/(1566600432296449248673012375)*a^(13) - (8026082792895803844554920957)/(1566600432296449248673012375)*a^(12) - (1212087726741940235125468457)/(62664017291857969946920495)*a^(11) - (28038529411065675826439806252)/(1566600432296449248673012375)*a^(10) + (5844103679732339121403551263)/(1566600432296449248673012375)*a^(9) + (59737744208361896441945164336)/(1566600432296449248673012375)*a^(8) + (79360608758464081701608954378)/(1566600432296449248673012375)*a^(7) + (20122549427520226729833028534)/(1566600432296449248673012375)*a^(6) - (4339008847610047201993555264)/(313320086459289849734602475)*a^(5) - (34412070855177785760584138423)/(1566600432296449248673012375)*a^(4) + (751254109356255824701728254)/(1566600432296449248673012375)*a^(3) - (4854397400561469548627900894)/(1566600432296449248673012375)*a^(2) - (5320506853117634757793144179)/(1566600432296449248673012375)*a - (1835020237306400080336171893)/(313320086459289849734602475) , (109990812653467283825954348)/(1566600432296449248673012375)*a^(21) - (223703528845797940297809201)/(1566600432296449248673012375)*a^(20) + (16372788272000596879321783)/(1566600432296449248673012375)*a^(19) + (49805432672905857643459297)/(1566600432296449248673012375)*a^(18) - (1368811385993715786207964)/(313320086459289849734602475)*a^(17) - (733535847546520952599027861)/(1566600432296449248673012375)*a^(16) + (25582502921653444010667786)/(62664017291857969946920495)*a^(15) + (1121855737670297243587458657)/(313320086459289849734602475)*a^(14) + (2997456500425699573947050563)/(1566600432296449248673012375)*a^(13) - (9142484193703703246389755629)/(1566600432296449248673012375)*a^(12) - (1087159270892037575415423869)/(62664017291857969946920495)*a^(11) - (26684952140866411175973078369)/(1566600432296449248673012375)*a^(10) + (10089296935342517682138018961)/(1566600432296449248673012375)*a^(9) + (64106714608067081187372274242)/(1566600432296449248673012375)*a^(8) + (78884278863410187665794152241)/(1566600432296449248673012375)*a^(7) + (13878552282544251361810145898)/(1566600432296449248673012375)*a^(6) - (9497464763989525583129706608)/(313320086459289849734602475)*a^(5) - (43698048268168246867844126106)/(1566600432296449248673012375)*a^(4) - (4905665580271988542651282637)/(1566600432296449248673012375)*a^(3) - (3374048515339668870589603068)/(1566600432296449248673012375)*a^(2) - (11810152117368599081655029213)/(1566600432296449248673012375)*a - (1792449095398189768609737946)/(313320086459289849734602475) , (163213106967279941146536869)/(1566600432296449248673012375)*a^(21) - (294212955301365188977406128)/(1566600432296449248673012375)*a^(20) - 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