/* 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 - x^21 + 3*x^20 + 3*x^18 + 5*x^17 + 7*x^16 + 4*x^15 + 12*x^14 - 17*x^13 - 35*x^11 - 28*x^10 - 29*x^9 - 20*x^8 - 6*x^7 - 11*x^6 - 26*x^5 - 22*x^4 - 11*x^3 - 4*x^2 + 9*x - 1, 22, 53, [4, 9], -969538443288973935184255159, [173, 7043, 28208540809], [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, 1/828204689715717011*a^21 - 289070269254590605/828204689715717011*a^20 - 166019745221986257/828204689715717011*a^19 - 152170991881510079/828204689715717011*a^18 + 30735041949926004/828204689715717011*a^17 + 245770178671964005/828204689715717011*a^16 + 251046993100387380/828204689715717011*a^15 - 103020705440085255/828204689715717011*a^14 + 166380821876545465/828204689715717011*a^13 - 406908123388535667/828204689715717011*a^12 + 83316211157219379/828204689715717011*a^11 - 330497846319408425/828204689715717011*a^10 + 276855857755791978/828204689715717011*a^9 - 325570347416634728/828204689715717011*a^8 - 398236988782989238/828204689715717011*a^7 + 245014594335145052/828204689715717011*a^6 - 93724578219585522/828204689715717011*a^5 - 9160698337253660/828204689715717011*a^4 - 187775435186994389/828204689715717011*a^3 - 111863643463248221/828204689715717011*a^2 + 122114417229796539/828204689715717011*a + 195002868157984756/828204689715717011], 0, 1, [], 1, [ (13870713499334607)/(828204689715717011)*a^(21) + (20134131853593770)/(828204689715717011)*a^(20) - (35808076760056195)/(828204689715717011)*a^(19) + (154066848952081573)/(828204689715717011)*a^(18) - (39724003380072404)/(828204689715717011)*a^(17) + (120477166232464893)/(828204689715717011)*a^(16) + (282845456105939877)/(828204689715717011)*a^(15) + (137454563207770912)/(828204689715717011)*a^(14) + (48586649091835020)/(828204689715717011)*a^(13) + (348986212161026240)/(828204689715717011)*a^(12) - (729676232784706550)/(828204689715717011)*a^(11) + (160044118624890924)/(828204689715717011)*a^(10) - (1128057382492232421)/(828204689715717011)*a^(9) - (850520745540917286)/(828204689715717011)*a^(8) - (524083967464944947)/(828204689715717011)*a^(7) - (681063782790953763)/(828204689715717011)*a^(6) - (1072196783971415916)/(828204689715717011)*a^(5) - (1246974589671091708)/(828204689715717011)*a^(4) - (691215225316981025)/(828204689715717011)*a^(3) - (884014298712724002)/(828204689715717011)*a^(2) - (175197446697823006)/(828204689715717011)*a - (662419994208176400)/(828204689715717011) , (203196563545654002)/(828204689715717011)*a^(21) - (135215036396694155)/(828204689715717011)*a^(20) + (491082032230843649)/(828204689715717011)*a^(19) + (244273774551240996)/(828204689715717011)*a^(18) + (528481369104500173)/(828204689715717011)*a^(17) + (1099749714113226379)/(828204689715717011)*a^(16) + (1772706829302336708)/(828204689715717011)*a^(15) + (1032435370799148857)/(828204689715717011)*a^(14) + (2287615429351702230)/(828204689715717011)*a^(13) - (2569353307818060525)/(828204689715717011)*a^(12) - (1543286825878526369)/(828204689715717011)*a^(11) - (6549832906858039409)/(828204689715717011)*a^(10) - (7283785088473782324)/(828204689715717011)*a^(9) - (7042184227942710502)/(828204689715717011)*a^(8) - (4346163912393984210)/(828204689715717011)*a^(7) - (1552257280464464506)/(828204689715717011)*a^(6) - (2755380027890060205)/(828204689715717011)*a^(5) - (5655410636813052526)/(828204689715717011)*a^(4) - (6194836316837302331)/(828204689715717011)*a^(3) - (2751234668436668975)/(828204689715717011)*a^(2) - (1239510493340885244)/(828204689715717011)*a + (1309837107217656354)/(828204689715717011) , (69808517640434076)/(828204689715717011)*a^(21) - (35771074722518717)/(828204689715717011)*a^(20) + (182594363645991584)/(828204689715717011)*a^(19) + (104898272031037160)/(828204689715717011)*a^(18) + (230223402055498699)/(828204689715717011)*a^(17) + (450608039842611234)/(828204689715717011)*a^(16) + (721835389046607621)/(828204689715717011)*a^(15) + (583982894081375334)/(828204689715717011)*a^(14) + (1015150972071870244)/(828204689715717011)*a^(13) - (584746949896037184)/(828204689715717011)*a^(12) - (423860487841632075)/(828204689715717011)*a^(11) - (2636740025189102104)/(828204689715717011)*a^(10) - (3064688857237703231)/(828204689715717011)*a^(9) - (3274494389350386395)/(828204689715717011)*a^(8) - (2860743216713444694)/(828204689715717011)*a^(7) - (1370008477782526731)/(828204689715717011)*a^(6) - (1802675193681161273)/(828204689715717011)*a^(5) - (2428376986152414121)/(828204689715717011)*a^(4) - (2804114018112539989)/(828204689715717011)*a^(3) - (2803097658777790814)/(828204689715717011)*a^(2) - (1263229186001132629)/(828204689715717011)*a + (801256405132690177)/(828204689715717011) , (257792796726988611)/(828204689715717011)*a^(21) - (148053768199168083)/(828204689715717011)*a^(20) + (682374438627634964)/(828204689715717011)*a^(19) + (311841747487928454)/(828204689715717011)*a^(18) + (814775116606227893)/(828204689715717011)*a^(17) + (1635400932211344735)/(828204689715717011)*a^(16) + (2378825970181138111)/(828204689715717011)*a^(15) + (1899115807671414493)/(828204689715717011)*a^(14) + (3625212870399553471)/(828204689715717011)*a^(13) - (2996294391589301269)/(828204689715717011)*a^(12) - (1736195845016846552)/(828204689715717011)*a^(11) - (9356493342097206086)/(828204689715717011)*a^(10) - (11122528600220101550)/(828204689715717011)*a^(9) - (10878540028966098401)/(828204689715717011)*a^(8) - (9068019222943911908)/(828204689715717011)*a^(7) - (3777569067773939616)/(828204689715717011)*a^(6) - (3890632796920376212)/(828204689715717011)*a^(5) - (7900092289165341019)/(828204689715717011)*a^(4) - (8834632030438262172)/(828204689715717011)*a^(3) - (5863647518673740445)/(828204689715717011)*a^(2) - (2764187727297183796)/(828204689715717011)*a + (2353982543841880649)/(828204689715717011) , (48549012270540116)/(828204689715717011)*a^(21) - (20914918413911875)/(828204689715717011)*a^(20) + (165986243356521771)/(828204689715717011)*a^(19) - (5501507638690217)/(828204689715717011)*a^(18) + (291196607998493222)/(828204689715717011)*a^(17) + (307620311428711624)/(828204689715717011)*a^(16) + (452127128768914816)/(828204689715717011)*a^(15) + (627119331578189085)/(828204689715717011)*a^(14) + (793047149963240999)/(828204689715717011)*a^(13) - (692756492911466989)/(828204689715717011)*a^(12) - (89589780361082173)/(828204689715717011)*a^(11) - (2635965651314377641)/(828204689715717011)*a^(10) - (2102869922456279410)/(828204689715717011)*a^(9) - (2846127731539550048)/(828204689715717011)*a^(8) - (2546656059624073100)/(828204689715717011)*a^(7) - (433393618221663467)/(828204689715717011)*a^(6) - (649733240845381864)/(828204689715717011)*a^(5) - (1283079212475783054)/(828204689715717011)*a^(4) - (2624013749343335581)/(828204689715717011)*a^(3) - (1499230916143591961)/(828204689715717011)*a^(2) - (213482339908388526)/(828204689715717011)*a + (1148416906099823071)/(828204689715717011) , (94991264414489067)/(828204689715717011)*a^(21) - (100899273990929471)/(828204689715717011)*a^(20) + (344787875236631588)/(828204689715717011)*a^(19) - (86716658543637316)/(828204689715717011)*a^(18) + (444331082379535997)/(828204689715717011)*a^(17) + (425428555414193855)/(828204689715717011)*a^(16) + (785754240525064634)/(828204689715717011)*a^(15) + (490331399098058520)/(828204689715717011)*a^(14) + (1489104787283812485)/(828204689715717011)*a^(13) - (1686931797576150095)/(828204689715717011)*a^(12) + (569004776184236059)/(828204689715717011)*a^(11) - (4350635012707057115)/(828204689715717011)*a^(10) - (2220447835939142217)/(828204689715717011)*a^(9) - (4344859774354005453)/(828204689715717011)*a^(8) - (2250051833814540351)/(828204689715717011)*a^(7) - (1692782351312190490)/(828204689715717011)*a^(6) - (941815889905204983)/(828204689715717011)*a^(5) - (3060802796410024711)/(828204689715717011)*a^(4) - (2669478679460576597)/(828204689715717011)*a^(3) - (2634013018421735213)/(828204689715717011)*a^(2) - (1382433877967359855)/(828204689715717011)*a + (517398317716614029)/(828204689715717011) , (54495020263930822)/(828204689715717011)*a^(21) - (129888548849243068)/(828204689715717011)*a^(20) + (266878190171970599)/(828204689715717011)*a^(19) - (299617220713104406)/(828204689715717011)*a^(18) + (248921652475773983)/(828204689715717011)*a^(17) - (6035386563630863)/(828204689715717011)*a^(16) - (60086157876013178)/(828204689715717011)*a^(15) - (251112555703701126)/(828204689715717011)*a^(14) + (308094698588445104)/(828204689715717011)*a^(13) - (2203572545944319526)/(828204689715717011)*a^(12) + (1312208542189215336)/(828204689715717011)*a^(11) - (2657305668118173426)/(828204689715717011)*a^(10) + (1484968410377243356)/(828204689715717011)*a^(9) + (593421349570982046)/(828204689715717011)*a^(8) + (1709350253434895268)/(828204689715717011)*a^(7) + (2499430993632873347)/(828204689715717011)*a^(6) + (966945875414846786)/(828204689715717011)*a^(5) - (206374247734775791)/(828204689715717011)*a^(4) + (117599644604450330)/(828204689715717011)*a^(3) + (679078027359516349)/(828204689715717011)*a^(2) + (1126639297266200830)/(828204689715717011)*a + (2073612512636733905)/(828204689715717011) , (236374769471393697)/(828204689715717011)*a^(21) - (188986689635075985)/(828204689715717011)*a^(20) + (681918859553749385)/(828204689715717011)*a^(19) + (112970356140033890)/(828204689715717011)*a^(18) + (765788642241144182)/(828204689715717011)*a^(17) + (1301850827517689379)/(828204689715717011)*a^(16) + (1929639506729403843)/(828204689715717011)*a^(15) + (1347852195355015252)/(828204689715717011)*a^(14) + (3071744558562341902)/(828204689715717011)*a^(13) - (3475836202398454296)/(828204689715717011)*a^(12) - (663788372730723114)/(828204689715717011)*a^(11) - (8835754281674166550)/(828204689715717011)*a^(10) - (8072933727073046963)/(828204689715717011)*a^(9) - (8600977435013933416)/(828204689715717011)*a^(8) - (6256338713775860445)/(828204689715717011)*a^(7) - (2218702415527703008)/(828204689715717011)*a^(6) - (2652425749480410612)/(828204689715717011)*a^(5) - (6342859729442664866)/(828204689715717011)*a^(4) - (5994530679089350366)/(828204689715717011)*a^(3) - (4246294454166017705)/(828204689715717011)*a^(2) - (1694115503756802085)/(828204689715717011)*a + (1624716876791619812)/(828204689715717011) , (384163729033804167)/(828204689715717011)*a^(21) - (306909615565957404)/(828204689715717011)*a^(20) + (1046766023136206428)/(828204689715717011)*a^(19) + (270068617972218572)/(828204689715717011)*a^(18) + (1097864374098103118)/(828204689715717011)*a^(17) + (2136917803514515413)/(828204689715717011)*a^(16) + (3084154541093712157)/(828204689715717011)*a^(15) + (2008179164472746371)/(828204689715717011)*a^(14) + (4798337812464932055)/(828204689715717011)*a^(13) - (5456084458116108592)/(828204689715717011)*a^(12) - (1349267604157473908)/(828204689715717011)*a^(11) - (12814824365876340234)/(828204689715717011)*a^(10) - (13305382659396640531)/(828204689715717011)*a^(9) - (12867677293104838442)/(828204689715717011)*a^(8) - (9550142177470709340)/(828204689715717011)*a^(7) - (4163609302893749573)/(828204689715717011)*a^(6) - (5496605755070920520)/(828204689715717011)*a^(5) - (10983650082628139257)/(828204689715717011)*a^(4) - (10241171637217791578)/(828204689715717011)*a^(3) - (5504649940324060727)/(828204689715717011)*a^(2) - (2584480321121127991)/(828204689715717011)*a + (2760500485586208841)/(828204689715717011) , (155003052502005017)/(828204689715717011)*a^(21) - (158045997836506405)/(828204689715717011)*a^(20) + (469990829897033769)/(828204689715717011)*a^(19) + (88281973666942)/(828204689715717011)*a^(18) + (533049701345011494)/(828204689715717011)*a^(17) + (664597171303353545)/(828204689715717011)*a^(16) + (1341947249035008915)/(828204689715717011)*a^(15) + (548223398601858684)/(828204689715717011)*a^(14) + (2036635424541806459)/(828204689715717011)*a^(13) - (2290425476451525434)/(828204689715717011)*a^(12) + (429004618450987490)/(828204689715717011)*a^(11) - (5466436435486314900)/(828204689715717011)*a^(10) - (3664486287402941582)/(828204689715717011)*a^(9) - (5809574324222456048)/(828204689715717011)*a^(8) - (2651295639979285544)/(828204689715717011)*a^(7) - (3256773275423217382)/(828204689715717011)*a^(6) - (2777712557378941017)/(828204689715717011)*a^(5) - (5076652200566671854)/(828204689715717011)*a^(4) - (4210432046751264373)/(828204689715717011)*a^(3) - (1993801412466479684)/(828204689715717011)*a^(2) - (2683583109279488762)/(828204689715717011)*a + (831861649704266400)/(828204689715717011) , (137677133492944517)/(828204689715717011)*a^(21) - (163286854343273996)/(828204689715717011)*a^(20) + (438584968981046998)/(828204689715717011)*a^(19) - (52003006867708695)/(828204689715717011)*a^(18) + (347155409889645986)/(828204689715717011)*a^(17) + (751515531492004904)/(828204689715717011)*a^(16) + (688291705037916971)/(828204689715717011)*a^(15) + (499079681667125445)/(828204689715717011)*a^(14) + (1574147645872196449)/(828204689715717011)*a^(13) - (2636607209938304962)/(828204689715717011)*a^(12) + (325834056304859456)/(828204689715717011)*a^(11) - (4487244305095126828)/(828204689715717011)*a^(10) - (3862156248088010248)/(828204689715717011)*a^(9) - (2442855544616947007)/(828204689715717011)*a^(8) - (3164031608032468822)/(828204689715717011)*a^(7) + (346088306078784671)/(828204689715717011)*a^(6) - (1769147873132581068)/(828204689715717011)*a^(5) - (2918151094101273365)/(828204689715717011)*a^(4) - (2268091855016807010)/(828204689715717011)*a^(3) - (1552072120818861515)/(828204689715717011)*a^(2) - (117190294192549079)/(828204689715717011)*a + (1311589940206339902)/(828204689715717011) , (29465155808170116)/(828204689715717011)*a^(21) - (7459067350072365)/(828204689715717011)*a^(20) + (128099082612086830)/(828204689715717011)*a^(19) + (45245296888272450)/(828204689715717011)*a^(18) + (182930459758085519)/(828204689715717011)*a^(17) + (412422756328640781)/(828204689715717011)*a^(16) + (337696694875302432)/(828204689715717011)*a^(15) + (743474902922667280)/(828204689715717011)*a^(14) + (1010030607508937590)/(828204689715717011)*a^(13) + (38020646121501554)/(828204689715717011)*a^(12) + (362783190153046431)/(828204689715717011)*a^(11) - (1519877606484066293)/(828204689715717011)*a^(10) - (2921737983577231836)/(828204689715717011)*a^(9) - (2506705251595848117)/(828204689715717011)*a^(8) - (4469180327337451708)/(828204689715717011)*a^(7) - (2502977131116287626)/(828204689715717011)*a^(6) - (1951396390639709078)/(828204689715717011)*a^(5) - (1475953675036098659)/(828204689715717011)*a^(4) - (2087927263452160286)/(828204689715717011)*a^(3) - (3166709955304765863)/(828204689715717011)*a^(2) - (2170322531258034955)/(828204689715717011)*a - (270909585967557405)/(828204689715717011) ], 42357.726741, [[x^11 - x^10 + x^9 - 3*x^5 + x^4 - 2*x^2 + x + 1, 1]]]