/* 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^21 - 2*x^19 - x^18 - 8*x^17 + 16*x^15 + 16*x^14 + 21*x^13 - 27*x^12 - 29*x^11 - 63*x^10 - 3*x^9 + 86*x^8 + 60*x^7 + 11*x^6 - 69*x^5 - 49*x^4 + 30*x^3 + 16*x^2 - 6*x - 1, 21, 38, [5, 8], 12329728569841547876503864001, [7, 12503], [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, 1/3*a^18 - 1/3*a^17 - 1/3*a^14 + 1/3*a^13 - 1/3*a^12 + 1/3*a^11 - 1/3*a^9 + 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^5 - 1/3*a^4 + 1/3*a^2 - 1/3*a - 1/3, 1/3*a^19 - 1/3*a^17 - 1/3*a^15 + 1/3*a^11 - 1/3*a^10 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^4 + 1/3*a^3 + 1/3*a - 1/3, 1/13458429203169*a^20 + 252438425646/4486143067723*a^19 - 1849290991741/13458429203169*a^18 - 389171437909/4486143067723*a^17 - 4599705812698/13458429203169*a^16 - 2152989302937/4486143067723*a^15 - 861306887090/4486143067723*a^14 + 91273587584/4486143067723*a^13 - 1284864523994/13458429203169*a^12 - 3977374637917/13458429203169*a^11 + 1738759474967/4486143067723*a^10 - 925523404990/13458429203169*a^9 + 4646323794359/13458429203169*a^8 + 3045195796811/13458429203169*a^7 - 1063726261439/4486143067723*a^6 - 6618751463020/13458429203169*a^5 + 777365339824/13458429203169*a^4 + 928487349540/4486143067723*a^3 - 4721462855510/13458429203169*a^2 - 2487512109382/13458429203169*a - 797789331107/4486143067723], 0, 1, [], 1, [ (3564166044841)/(13458429203169)*a^(20) - (2309032631638)/(13458429203169)*a^(19) - (3987848183800)/(13458429203169)*a^(18) - (545264596148)/(13458429203169)*a^(17) - (31050476181073)/(13458429203169)*a^(16) + (17493247846723)/(13458429203169)*a^(15) + (10286979463062)/(4486143067723)*a^(14) + (10869306945797)/(4486143067723)*a^(13) + (76838172867361)/(13458429203169)*a^(12) - (111196936537442)/(13458429203169)*a^(11) + (21152682824314)/(13458429203169)*a^(10) - (261338132378656)/(13458429203169)*a^(9) + (36611170796129)/(4486143067723)*a^(8) + (34149907412314)/(4486143067723)*a^(7) + (87011197526440)/(13458429203169)*a^(6) + (81223183070339)/(13458429203169)*a^(5) - (171191436652336)/(13458429203169)*a^(4) + (22451679876764)/(13458429203169)*a^(3) + (38311179490987)/(13458429203169)*a^(2) - (49893604651988)/(13458429203169)*a + (8666462474098)/(13458429203169) , (1826018220280)/(4486143067723)*a^(20) - (770731019127)/(4486143067723)*a^(19) - (8324471970958)/(13458429203169)*a^(18) - (2517833812082)/(13458429203169)*a^(17) - (15401634941294)/(4486143067723)*a^(16) + (6039381210413)/(4486143067723)*a^(15) + (67068987593755)/(13458429203169)*a^(14) + (65236308984644)/(13458429203169)*a^(13) + (116484903284224)/(13458429203169)*a^(12) - (171450814083097)/(13458429203169)*a^(11) - (18898009269108)/(4486143067723)*a^(10) - (388957232169590)/(13458429203169)*a^(9) + (94337692385840)/(13458429203169)*a^(8) + (314407223880899)/(13458429203169)*a^(7) + (222024146244782)/(13458429203169)*a^(6) + (134114788449452)/(13458429203169)*a^(5) - (320270207626802)/(13458429203169)*a^(4) - (34397316925830)/(4486143067723)*a^(3) + (62979474490337)/(13458429203169)*a^(2) - (33767219714960)/(13458429203169)*a + (15471543853474)/(13458429203169) , a , (582609588499)/(4486143067723)*a^(20) - (1999872065328)/(4486143067723)*a^(19) - (3323363601949)/(13458429203169)*a^(18) + (5614713461581)/(13458429203169)*a^(17) - (3140474514692)/(4486143067723)*a^(16) + (17745378006814)/(4486143067723)*a^(15) + (31411689939718)/(13458429203169)*a^(14) - (25627217459518)/(13458429203169)*a^(13) - (42682184916467)/(13458429203169)*a^(12) - (208301041924396)/(13458429203169)*a^(11) + (15031750781188)/(4486143067723)*a^(10) - (82899929326400)/(13458429203169)*a^(9) + (404334287610206)/(13458429203169)*a^(8) + (187253988176543)/(13458429203169)*a^(7) - (94518429331858)/(13458429203169)*a^(6) - (217871773811593)/(13458429203169)*a^(5) - (303517436224754)/(13458429203169)*a^(4) + (42245021096252)/(4486143067723)*a^(3) + (144273182387969)/(13458429203169)*a^(2) - (30549614963513)/(13458429203169)*a - (2640833854937)/(13458429203169) , (290961355540)/(4486143067723)*a^(20) - (1202303038205)/(13458429203169)*a^(19) - (128440827954)/(4486143067723)*a^(18) + (105338668676)/(13458429203169)*a^(17) - (2682711581826)/(4486143067723)*a^(16) + (9757982582144)/(13458429203169)*a^(15) + (911368750814)/(4486143067723)*a^(14) + (2256987145664)/(4486143067723)*a^(13) + (6350496896915)/(4486143067723)*a^(12) - (37100175100931)/(13458429203169)*a^(11) + (29339830985153)/(13458429203169)*a^(10) - (28276736771872)/(4486143067723)*a^(9) + (59939779410893)/(13458429203169)*a^(8) - (24623602467280)/(13458429203169)*a^(7) + (13576581510143)/(13458429203169)*a^(6) + (8252851365268)/(4486143067723)*a^(5) - (28252407717445)/(13458429203169)*a^(4) + (58798908408976)/(13458429203169)*a^(3) - (1328074547717)/(4486143067723)*a^(2) - (33848244137243)/(13458429203169)*a + (181302859088)/(13458429203169) , (2671160955401)/(13458429203169)*a^(20) - (6560820062125)/(13458429203169)*a^(19) - (8029160271859)/(13458429203169)*a^(18) + (1462306372807)/(4486143067723)*a^(17) - (13730515424072)/(13458429203169)*a^(16) + (61307958323089)/(13458429203169)*a^(15) + (73255420670354)/(13458429203169)*a^(14) - (3860948361401)/(13458429203169)*a^(13) - (46928740462301)/(13458429203169)*a^(12) - (290877649295006)/(13458429203169)*a^(11) - (65468924963345)/(13458429203169)*a^(10) - (44256758833487)/(4486143067723)*a^(9) + (146396790745668)/(4486143067723)*a^(8) + (155642095499703)/(4486143067723)*a^(7) + (21296725074905)/(13458429203169)*a^(6) - (260216192477419)/(13458429203169)*a^(5) - (510363110698030)/(13458429203169)*a^(4) - (24929834167321)/(13458429203169)*a^(3) + (76698136506534)/(4486143067723)*a^(2) + (21576621093476)/(13458429203169)*a - (2892994404910)/(4486143067723) , (1251972987460)/(13458429203169)*a^(20) + (322604719084)/(13458429203169)*a^(19) - (342542445014)/(4486143067723)*a^(18) - (2925732133310)/(13458429203169)*a^(17) - (12932332549834)/(13458429203169)*a^(16) - (3086639132962)/(13458429203169)*a^(15) + (8448372800390)/(13458429203169)*a^(14) + (34053676243975)/(13458429203169)*a^(13) + (17764944875648)/(4486143067723)*a^(12) - (9027379180406)/(13458429203169)*a^(11) - (22687105712356)/(13458429203169)*a^(10) - (150566276010296)/(13458429203169)*a^(9) - (46871964562954)/(13458429203169)*a^(8) - (4209411168676)/(13458429203169)*a^(7) + (53622461568884)/(4486143067723)*a^(6) + (46312915680499)/(4486143067723)*a^(5) - (5958709048666)/(13458429203169)*a^(4) - (78910485458099)/(13458429203169)*a^(3) - (83104914797413)/(13458429203169)*a^(2) - (1553732833474)/(13458429203169)*a + (14144517134938)/(13458429203169) , (3900543319695)/(4486143067723)*a^(20) - (6601682650577)/(13458429203169)*a^(19) - (20969876801432)/(13458429203169)*a^(18) - (2242547724554)/(13458429203169)*a^(17) - (30566342473729)/(4486143067723)*a^(16) + (55549795105781)/(13458429203169)*a^(15) + (170548350440585)/(13458429203169)*a^(14) + (114677024944708)/(13458429203169)*a^(13) + (180660565273139)/(13458429203169)*a^(12) - (453762577566166)/(13458429203169)*a^(11) - (159814037310658)/(13458429203169)*a^(10) - (712018158241141)/(13458429203169)*a^(9) + (124594764823121)/(4486143067723)*a^(8) + (299496532998711)/(4486143067723)*a^(7) + (125409734340977)/(4486143067723)*a^(6) - (24496798437962)/(13458429203169)*a^(5) - (885520338088334)/(13458429203169)*a^(4) - (212135846257601)/(13458429203169)*a^(3) + (389404984438834)/(13458429203169)*a^(2) + (8684216946853)/(4486143067723)*a - (50079172231877)/(13458429203169) , (2332210300812)/(4486143067723)*a^(20) + (4479982927660)/(13458429203169)*a^(19) - (4383599715000)/(4486143067723)*a^(18) - (15874203173359)/(13458429203169)*a^(17) - (20805941196773)/(4486143067723)*a^(16) - (37184375076136)/(13458429203169)*a^(15) + (35067412726374)/(4486143067723)*a^(14) + (61071132798381)/(4486143067723)*a^(13) + (78306805104015)/(4486143067723)*a^(12) - (76372453776734)/(13458429203169)*a^(11) - (304231208950462)/(13458429203169)*a^(10) - (198017339407949)/(4486143067723)*a^(9) - (341788128655351)/(13458429203169)*a^(8) + (523337025434729)/(13458429203169)*a^(7) + (793786567840256)/(13458429203169)*a^(6) + (143327618038786)/(4486143067723)*a^(5) - (355836075616825)/(13458429203169)*a^(4) - (634796265899252)/(13458429203169)*a^(3) - (24841249556758)/(4486143067723)*a^(2) + (175563478014247)/(13458429203169)*a + (41170433224634)/(13458429203169) , (1029672745922)/(13458429203169)*a^(20) - (881286839531)/(13458429203169)*a^(19) + (20409846106)/(4486143067723)*a^(18) + (570489936458)/(4486143067723)*a^(17) - (8954487578711)/(13458429203169)*a^(16) + (4701909290162)/(13458429203169)*a^(15) - (3661704585737)/(13458429203169)*a^(14) - (8586328041757)/(13458429203169)*a^(13) + (5416749201747)/(4486143067723)*a^(12) - (14507269064240)/(13458429203169)*a^(11) + (67260230165387)/(13458429203169)*a^(10) - (36365530410418)/(13458429203169)*a^(9) + (59108984168891)/(13458429203169)*a^(8) - (57598844803042)/(13458429203169)*a^(7) - (92563193769647)/(13458429203169)*a^(6) - (10493524840243)/(4486143067723)*a^(5) + (2242098417344)/(13458429203169)*a^(4) + (126406257614323)/(13458429203169)*a^(3) + (61311313456468)/(13458429203169)*a^(2) - (14279703647701)/(4486143067723)*a - (5404614126418)/(4486143067723) , (1444055020823)/(4486143067723)*a^(20) - (2514203448341)/(13458429203169)*a^(19) - (6038472299768)/(13458429203169)*a^(18) - (1510712478698)/(13458429203169)*a^(17) - (12022029862669)/(4486143067723)*a^(16) + (19952098188410)/(13458429203169)*a^(15) + (48359111840402)/(13458429203169)*a^(14) + (47415367531240)/(13458429203169)*a^(13) + (82546564289774)/(13458429203169)*a^(12) - (146449316387095)/(13458429203169)*a^(11) - (19511086129432)/(13458429203169)*a^(10) - (310077936403249)/(13458429203169)*a^(9) + (46915638172632)/(4486143067723)*a^(8) + (66583564386904)/(4486143067723)*a^(7) + (59038915395009)/(4486143067723)*a^(6) + (33764788813318)/(13458429203169)*a^(5) - (245611242604337)/(13458429203169)*a^(4) - (60111272284862)/(13458429203169)*a^(3) + (84412937474035)/(13458429203169)*a^(2) - (3680493628548)/(4486143067723)*a + (4998453728989)/(13458429203169) , (4481378219306)/(13458429203169)*a^(20) - (55549947001)/(13458429203169)*a^(19) - (6987497659901)/(13458429203169)*a^(18) - (3131073907202)/(13458429203169)*a^(17) - (38346723821984)/(13458429203169)*a^(16) - (2806573862195)/(13458429203169)*a^(15) + (17822982899752)/(4486143067723)*a^(14) + (19203384898669)/(4486143067723)*a^(13) + (109734266502065)/(13458429203169)*a^(12) - (27500217686923)/(4486143067723)*a^(11) - (59452632894365)/(13458429203169)*a^(10) - (272887511765849)/(13458429203169)*a^(9) - (30456159481372)/(13458429203169)*a^(8) + (242931785232770)/(13458429203169)*a^(7) + (157996192691956)/(13458429203169)*a^(6) + (81067925178175)/(13458429203169)*a^(5) - (68251786866617)/(4486143067723)*a^(4) - (128682311152198)/(13458429203169)*a^(3) + (131324145780194)/(13458429203169)*a^(2) + (14938807678971)/(4486143067723)*a - (18674610073115)/(13458429203169) ], 564369.598704, []]