/* 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 - 9*x^19 + 3*x^17 + 66*x^15 - 75*x^14 - 90*x^13 + 198*x^12 - 21*x^11 + 63*x^9 - 177*x^8 + 54*x^7 + 45*x^6 - 51*x^5 + 18*x^4 - 8*x^3 - 3*x^2 + 3, 21, 44, [9, 6], 2523828389200110188894232441, [3, 73], [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, 1/29*a^18 + 6/29*a^17 - 2/29*a^16 - 7/29*a^15 - 9/29*a^14 - 6/29*a^13 - 5/29*a^12 - 5/29*a^11 - 5/29*a^10 - 2/29*a^9 + 4/29*a^7 - 10/29*a^6 - 5/29*a^5 - 14/29*a^4 - 2/29*a^3 - 1/29*a^2 + 11/29, 1/29*a^19 - 9/29*a^17 + 5/29*a^16 + 4/29*a^15 - 10/29*a^14 + 2/29*a^13 - 4/29*a^12 - 4/29*a^11 - 1/29*a^10 + 12/29*a^9 + 4/29*a^8 - 5/29*a^7 - 3/29*a^6 - 13/29*a^5 - 5/29*a^4 + 11/29*a^3 + 6/29*a^2 + 11/29*a - 8/29, 1/554583883475930137031*a^20 + 1543879837230387866/554583883475930137031*a^19 - 9338021171565003108/554583883475930137031*a^18 - 38778221679230729329/554583883475930137031*a^17 - 99023689472789185765/554583883475930137031*a^16 + 74981095580659074871/554583883475930137031*a^15 + 21178924124033884797/554583883475930137031*a^14 + 129051592554330205204/554583883475930137031*a^13 - 208274738567600147827/554583883475930137031*a^12 + 248192584477477154597/554583883475930137031*a^11 + 169803346736758291664/554583883475930137031*a^10 - 75990319030138058373/554583883475930137031*a^9 + 245608091654983893030/554583883475930137031*a^8 + 206977738496375222384/554583883475930137031*a^7 - 217488545806445506167/554583883475930137031*a^6 + 216642111496161310247/554583883475930137031*a^5 + 106946772051958925848/554583883475930137031*a^4 - 214875708717009555993/554583883475930137031*a^3 + 172545894997721847072/554583883475930137031*a^2 + 34515952381658016192/554583883475930137031*a + 104690597026483562860/554583883475930137031], 0, 1, [], 1, [ (71796293939396877150)/(554583883475930137031)*a^(20) + (70233129724431961302)/(554583883475930137031)*a^(19) - (641808263161205679091)/(554583883475930137031)*a^(18) - (611144430145828074743)/(554583883475930137031)*a^(17) + (181985268726827278491)/(554583883475930137031)*a^(16) + (36554532867822203377)/(554583883475930137031)*a^(15) + (4698557199432691332849)/(554583883475930137031)*a^(14) - (810167797241305316553)/(554583883475930137031)*a^(13) - (11413614076571645500583)/(554583883475930137031)*a^(12) + (8940075364194870990212)/(554583883475930137031)*a^(11) + (10785805314091702023720)/(554583883475930137031)*a^(10) - (1988192309372043985932)/(554583883475930137031)*a^(9) + (6891900199132155532002)/(554583883475930137031)*a^(8) - (8375346761488411589247)/(554583883475930137031)*a^(7) - (5781578583955697897855)/(554583883475930137031)*a^(6) + (6490047723693580232893)/(554583883475930137031)*a^(5) - (2653370624818377907242)/(554583883475930137031)*a^(4) - (1142966001253727936582)/(554583883475930137031)*a^(3) - (84279530677444425198)/(554583883475930137031)*a^(2) - (364496880961661282496)/(554583883475930137031)*a - (97640917754121373826)/(554583883475930137031) , (22078462180699433487)/(554583883475930137031)*a^(20) + (23537888594343647847)/(554583883475930137031)*a^(19) - (216227345045331267341)/(554583883475930137031)*a^(18) - (211947782774454718681)/(554583883475930137031)*a^(17) + (215232283435441625235)/(554583883475930137031)*a^(16) + (65453797974853962111)/(554583883475930137031)*a^(15) + (1469039464489016025549)/(554583883475930137031)*a^(14) - (51709843206177510903)/(554583883475930137031)*a^(13) - (4821138640019025942205)/(554583883475930137031)*a^(12) + (3581020008515657505799)/(554583883475930137031)*a^(11) + (5246806118229980266086)/(554583883475930137031)*a^(10) - (3730267505683674096026)/(554583883475930137031)*a^(9) + (2152816650894275591352)/(554583883475930137031)*a^(8) - (2876260379020830271776)/(554583883475930137031)*a^(7) - (4153615355658469109116)/(554583883475930137031)*a^(6) + (3919161178920690672242)/(554583883475930137031)*a^(5) - (2119288966353492364128)/(554583883475930137031)*a^(4) - (1174616332487334980697)/(554583883475930137031)*a^(3) + (1389931351105124864184)/(554583883475930137031)*a^(2) - (328317689589945028497)/(554583883475930137031)*a + (396285738970291381717)/(554583883475930137031) , (51864130959178127441)/(554583883475930137031)*a^(20) - (31397281516280400942)/(554583883475930137031)*a^(19) - (399265554508073697395)/(554583883475930137031)*a^(18) + (247854821320663935929)/(554583883475930137031)*a^(17) - (411720303618332823582)/(554583883475930137031)*a^(16) + (188784580705905160747)/(554583883475930137031)*a^(15) + (3294692856086219517910)/(554583883475930137031)*a^(14) - (5828953521314888762680)/(554583883475930137031)*a^(13) + (2010127765722942874267)/(554583883475930137031)*a^(12) + (5882316569799937089054)/(554583883475930137031)*a^(11) - (8286060210462461744636)/(554583883475930137031)*a^(10) + (424102645201758614262)/(19123582188825177139)*a^(9) - (4466317051159380566480)/(554583883475930137031)*a^(8) - (3982829401849076456733)/(554583883475930137031)*a^(7) + (7191057379706818866173)/(554583883475930137031)*a^(6) - (8029219185948372383624)/(554583883475930137031)*a^(5) + (2640076687309242695206)/(554583883475930137031)*a^(4) + (618947860325316613860)/(554583883475930137031)*a^(3) - (1579932829318269242532)/(554583883475930137031)*a^(2) + (380798485750878378926)/(554583883475930137031)*a - (129909402325543604983)/(554583883475930137031) , (65769470842469183671)/(554583883475930137031)*a^(20) + (23138045068537474728)/(554583883475930137031)*a^(19) - (550591910175990292386)/(554583883475930137031)*a^(18) - (225515638628869323245)/(554583883475930137031)*a^(17) - (167129363779833949028)/(554583883475930137031)*a^(16) + (198816286661351949518)/(554583883475930137031)*a^(15) + (4403083681961035321349)/(554583883475930137031)*a^(14) - (3248085330605680359518)/(554583883475930137031)*a^(13) - (4953184018278227829042)/(554583883475930137031)*a^(12) + (6827473299658120545613)/(554583883475930137031)*a^(11) + (1229544029741963291965)/(554583883475930137031)*a^(10) + (7055795887325572823069)/(554583883475930137031)*a^(9) + (1514125622157453941235)/(554583883475930137031)*a^(8) - (8012410803931878786882)/(554583883475930137031)*a^(7) - (1455445781129815419137)/(554583883475930137031)*a^(6) - (1915642100089822949640)/(554583883475930137031)*a^(5) - (332281853369775351198)/(554583883475930137031)*a^(4) + (118687978141634605088)/(554583883475930137031)*a^(3) - (496673273633032454657)/(554583883475930137031)*a^(2) - (498999260820283321406)/(554583883475930137031)*a + (111846434293974088300)/(554583883475930137031) , (46894481187233500445)/(554583883475930137031)*a^(20) - (61579773188715510403)/(554583883475930137031)*a^(19) - (448943299505460200405)/(554583883475930137031)*a^(18) + (524049305553998812090)/(554583883475930137031)*a^(17) + (373684647394712301808)/(554583883475930137031)*a^(16) + (68977420176932958625)/(554583883475930137031)*a^(15) + (3104642197725662874674)/(554583883475930137031)*a^(14) - (7526985998053332149296)/(554583883475930137031)*a^(13) - (1479705799504013936476)/(554583883475930137031)*a^(12) + (14921054719226570767206)/(554583883475930137031)*a^(11) - (9103277357636998495595)/(554583883475930137031)*a^(10) - (1729593238617991698209)/(554583883475930137031)*a^(9) + (255374456935189615538)/(554583883475930137031)*a^(8) - (13312115292764163914819)/(554583883475930137031)*a^(7) + (9031348359350866535828)/(554583883475930137031)*a^(6) + (3808227336328221488055)/(554583883475930137031)*a^(5) - (3971942481483640085070)/(554583883475930137031)*a^(4) + (3010013618350298379823)/(554583883475930137031)*a^(3) - (315883553023430841095)/(554583883475930137031)*a^(2) - (1049605230016313247170)/(554583883475930137031)*a + (671031968558591979098)/(554583883475930137031) , (48813705243084413924)/(554583883475930137031)*a^(20) - (48770557084029338746)/(554583883475930137031)*a^(19) - (403472835749259201129)/(554583883475930137031)*a^(18) + (390657662326873102247)/(554583883475930137031)*a^(17) - (143309758204016256220)/(554583883475930137031)*a^(16) + (256911069459147016891)/(554583883475930137031)*a^(15) + (3070079147172998606839)/(554583883475930137031)*a^(14) - (6779048726267028503622)/(554583883475930137031)*a^(13) + (1429856106941650743933)/(554583883475930137031)*a^(12) + (8369083081614126589955)/(554583883475930137031)*a^(11) - (8266852110857673453700)/(554583883475930137031)*a^(10) + (8132038852617834424342)/(554583883475930137031)*a^(9) - (5595329558089337297553)/(554583883475930137031)*a^(8) - (6271034282594922403747)/(554583883475930137031)*a^(7) + (7987323996148224338024)/(554583883475930137031)*a^(6) - (3441144976771400801226)/(554583883475930137031)*a^(5) + (1994537620250513995086)/(554583883475930137031)*a^(4) + (168409669227348572671)/(554583883475930137031)*a^(3) - (1468527437767690899870)/(554583883475930137031)*a^(2) + (279720579736190474156)/(554583883475930137031)*a + (2306215064780893436)/(554583883475930137031) , (6777619643944088220)/(554583883475930137031)*a^(20) - (21278190953772725712)/(554583883475930137031)*a^(19) - (24060264608252086368)/(554583883475930137031)*a^(18) + (182091574751453896177)/(554583883475930137031)*a^(17) - (288118070608411192617)/(554583883475930137031)*a^(16) + (13268726006771938036)/(554583883475930137031)*a^(15) + (357794253783935512650)/(554583883475930137031)*a^(14) - (1876984004198510193247)/(554583883475930137031)*a^(13) + (3375563276070149246548)/(554583883475930137031)*a^(12) - (118933470184248752600)/(554583883475930137031)*a^(11) - (5508827386407108882212)/(554583883475930137031)*a^(10) + (217514243358781695031)/(19123582188825177139)*a^(9) - (2838914416085723236969)/(554583883475930137031)*a^(8) + (1647964644627572847291)/(554583883475930137031)*a^(7) + (4609999134709452983616)/(554583883475930137031)*a^(6) - (5908940507131067657463)/(554583883475930137031)*a^(5) + (1982260638465329303122)/(554583883475930137031)*a^(4) + (506893721455160225933)/(554583883475930137031)*a^(3) - (172821695848188055430)/(554583883475930137031)*a^(2) + (467130461616025308905)/(554583883475930137031)*a - (175359671420261222614)/(554583883475930137031) , (46919495690798495470)/(554583883475930137031)*a^(20) + (38285446474441497875)/(554583883475930137031)*a^(19) - (451151410781937370831)/(554583883475930137031)*a^(18) - (339097303396734666842)/(554583883475930137031)*a^(17) + (383886545968155217241)/(554583883475930137031)*a^(16) + (92699820658394308699)/(554583883475930137031)*a^(15) + (3146018550328793846968)/(554583883475930137031)*a^(14) - (1199696231120626282062)/(554583883475930137031)*a^(13) - (8924295261832525581467)/(554583883475930137031)*a^(12) + (8297270226428520223913)/(554583883475930137031)*a^(11) + (7698936837100104620460)/(554583883475930137031)*a^(10) - (4099115136283574356848)/(554583883475930137031)*a^(9) + (3139351903891326865720)/(554583883475930137031)*a^(8) - (9433317642086483665674)/(554583883475930137031)*a^(7) - (968108215940243827985)/(554583883475930137031)*a^(6) + (6423633068349795106961)/(554583883475930137031)*a^(5) - (1143188254006974637594)/(554583883475930137031)*a^(4) + (21328322842671642073)/(554583883475930137031)*a^(3) - (1318778390304714519813)/(554583883475930137031)*a^(2) + (1225455757985182443851)/(554583883475930137031)*a + (9620455108229742121)/(554583883475930137031) , (45459362496235900638)/(554583883475930137031)*a^(20) - (74413203666927662012)/(554583883475930137031)*a^(19) - (362531807913526345466)/(554583883475930137031)*a^(18) + (627907393940565504825)/(554583883475930137031)*a^(17) - (225550304395760955507)/(554583883475930137031)*a^(16) + (128663377180057901285)/(554583883475930137031)*a^(15) + (2661299764468715366824)/(554583883475930137031)*a^(14) - (8255949313594707213955)/(554583883475930137031)*a^(13) + (4414167703854755889593)/(554583883475930137031)*a^(12) + (331445259055589990107)/(19123582188825177139)*a^(11) - (13037440135481225880488)/(554583883475930137031)*a^(10) + (8736398245379788561186)/(554583883475930137031)*a^(9) - (7237554998663627110243)/(554583883475930137031)*a^(8) - (3070735240776891710906)/(554583883475930137031)*a^(7) + (12835677328462268325498)/(554583883475930137031)*a^(6) - (5426254851164599816968)/(554583883475930137031)*a^(5) + (1789788640033837402634)/(554583883475930137031)*a^(4) - (1845423209884301945600)/(554583883475930137031)*a^(3) - (1023001704391494214776)/(554583883475930137031)*a^(2) + (485626834772012110116)/(554583883475930137031)*a + (436831339538820260482)/(554583883475930137031) , (1528123048493631233)/(19123582188825177139)*a^(20) - (789682531770544415)/(19123582188825177139)*a^(19) - (11356670720224765291)/(19123582188825177139)*a^(18) + (6572197218590617363)/(19123582188825177139)*a^(17) - (15376301751947653973)/(19123582188825177139)*a^(16) + (1057806788439875005)/(19123582188825177139)*a^(15) + (94413469856651089851)/(19123582188825177139)*a^(14) - (157065810167624282703)/(19123582188825177139)*a^(13) + (78118019891872638187)/(19123582188825177139)*a^(12) + (164151359055697281701)/(19123582188825177139)*a^(11) - (262857808101670971195)/(19123582188825177139)*a^(10) + (333662862177114580781)/(19123582188825177139)*a^(9) - (50627394740085966780)/(19123582188825177139)*a^(8) - (3097741619500592258)/(19123582188825177139)*a^(7) + (137678614781413964354)/(19123582188825177139)*a^(6) - (272244596776504678670)/(19123582188825177139)*a^(5) + (22765181977186275212)/(19123582188825177139)*a^(4) - (43823713870400287286)/(19123582188825177139)*a^(3) + (8196582386278573142)/(19123582188825177139)*a^(2) + (7769074160367144029)/(19123582188825177139)*a - (16875420609193269080)/(19123582188825177139) , (206950319143616071753)/(554583883475930137031)*a^(20) - (383216626307264172)/(554583883475930137031)*a^(19) - (1841676339479771985141)/(554583883475930137031)*a^(18) - (49241518862296814877)/(554583883475930137031)*a^(17) + (473596276106622032229)/(554583883475930137031)*a^(16) + (438450464950186093473)/(554583883475930137031)*a^(15) + (13385159209588016084164)/(554583883475930137031)*a^(14) - (15428746791670409534264)/(554583883475930137031)*a^(13) - (17333351864576874101142)/(554583883475930137031)*a^(12) + (36152601936691762744079)/(554583883475930137031)*a^(11) + (182362871752574534869)/(554583883475930137031)*a^(10) + (3693933619697030774794)/(554583883475930137031)*a^(9) + (2936650480842800165250)/(554583883475930137031)*a^(8) - (28767656186437257426998)/(554583883475930137031)*a^(7) + (6727222423102852065063)/(554583883475930137031)*a^(6) + (7947405688719630950927)/(554583883475930137031)*a^(5) - (3938240653980063666010)/(554583883475930137031)*a^(4) - (1926906862037543333803)/(554583883475930137031)*a^(3) - (92487959924407200726)/(554583883475930137031)*a^(2) + (41866774777108638396)/(554583883475930137031)*a + (44885766255240511069)/(554583883475930137031) , (42683580106725290720)/(554583883475930137031)*a^(20) - (80255180808858742979)/(554583883475930137031)*a^(19) - (366829166190250218062)/(554583883475930137031)*a^(18) + (728323485510418544978)/(554583883475930137031)*a^(17) - (25924727215236035925)/(554583883475930137031)*a^(16) - (300298160332871530982)/(554583883475930137031)*a^(15) + (2838572995489089101542)/(554583883475930137031)*a^(14) - (8437519450277553361721)/(554583883475930137031)*a^(13) + (3441179464660537945588)/(554583883475930137031)*a^(12) + (14799185473312582670160)/(554583883475930137031)*a^(11) - (18682902925322160731710)/(554583883475930137031)*a^(10) + (140982820642494026818)/(19123582188825177139)*a^(9) + (2922569781285869055112)/(554583883475930137031)*a^(8) - (11183894986174215842872)/(554583883475930137031)*a^(7) + (17805105279491018182847)/(554583883475930137031)*a^(6) - (6996740357522592865172)/(554583883475930137031)*a^(5) - (6382699296860136066749)/(554583883475930137031)*a^(4) + (5163037974669732075498)/(554583883475930137031)*a^(3) - (1853571643697489459252)/(554583883475930137031)*a^(2) + (1130315816093023884063)/(554583883475930137031)*a - (551615143093245181316)/(554583883475930137031) , (38899654480965865207)/(554583883475930137031)*a^(20) + (112474403453133616245)/(554583883475930137031)*a^(19) - (365140404998641317723)/(554583883475930137031)*a^(18) - (988332631681771642613)/(554583883475930137031)*a^(17) + (230448701174190149735)/(554583883475930137031)*a^(16) + (127796869460308502743)/(554583883475930137031)*a^(15) + (2697497461041533167125)/(554583883475930137031)*a^(14) + (4536574213111583725695)/(554583883475930137031)*a^(13) - (12826714560810907019457)/(554583883475930137031)*a^(12) + (212915515599714701746)/(554583883475930137031)*a^(11) + (19593620629425291936272)/(554583883475930137031)*a^(10) - (5533158174428400896406)/(554583883475930137031)*a^(9) + (7743740449567178127100)/(554583883475930137031)*a^(8) - (2894509437223309954286)/(554583883475930137031)*a^(7) - (16779833855857365818618)/(554583883475930137031)*a^(6) + (8295719387410576644576)/(554583883475930137031)*a^(5) - (1044559177392390154429)/(554583883475930137031)*a^(4) - (2283193344329987763539)/(554583883475930137031)*a^(3) + (2410279855826683168604)/(554583883475930137031)*a^(2) - (766533468554695773365)/(554583883475930137031)*a - 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