/* 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 - 4*x^26 + 14*x^25 - 10*x^24 + 37*x^22 - 3*x^21 - x^20 + 139*x^19 - 26*x^18 + 76*x^17 + 144*x^16 - 117*x^15 - 101*x^14 + 12*x^13 - 340*x^12 + x^11 + 205*x^10 + 307*x^9 + 774*x^8 + 909*x^7 + 892*x^6 + 864*x^5 + 521*x^4 + 327*x^3 + 86*x^2 + 71*x + 1, 27, 8, [1, 13], -14905779350658261917360296447434047234191, [1231], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/3*a^8 - 1/3, 1/3*a^9 - 1/3*a, 1/3*a^10 - 1/3*a^2, 1/3*a^11 - 1/3*a^3, 1/3*a^12 - 1/3*a^4, 1/3*a^13 - 1/3*a^5, 1/3*a^14 - 1/3*a^6, 1/3*a^15 - 1/3*a^7, 1/9*a^16 + 1/9*a^8 - 2/9, 1/9*a^17 + 1/9*a^9 - 2/9*a, 1/9*a^18 + 1/9*a^10 - 2/9*a^2, 1/9*a^19 + 1/9*a^11 - 2/9*a^3, 1/9*a^20 + 1/9*a^12 - 2/9*a^4, 1/27*a^21 - 1/27*a^19 + 1/27*a^18 + 1/27*a^17 + 1/27*a^16 - 1/9*a^15 - 2/27*a^13 - 1/9*a^12 + 2/27*a^11 + 1/27*a^10 + 4/27*a^9 + 4/27*a^8 - 2/9*a^7 + 1/3*a^6 - 8/27*a^5 + 4/9*a^4 - 10/27*a^3 + 7/27*a^2 + 13/27*a + 4/27, 1/27*a^22 - 1/27*a^20 + 1/27*a^19 + 1/27*a^18 + 1/27*a^17 - 2/27*a^14 - 1/9*a^13 + 2/27*a^12 + 1/27*a^11 + 4/27*a^10 + 4/27*a^9 - 1/9*a^8 + 1/3*a^7 - 8/27*a^6 + 4/9*a^5 - 10/27*a^4 + 7/27*a^3 + 13/27*a^2 + 4/27*a - 2/9, 1/81*a^23 + 1/81*a^22 + 1/81*a^21 + 1/27*a^20 + 4/81*a^18 + 2/81*a^16 - 8/81*a^15 - 5/81*a^14 + 4/81*a^13 + 1/9*a^12 - 1/9*a^11 + 10/81*a^10 - 1/27*a^9 + 5/81*a^8 - 38/81*a^7 - 5/81*a^6 + 4/81*a^5 + 11/27*a^4 - 4/9*a^3 - 23/81*a^2 + 4/27*a + 38/81, 1/135999*a^24 + 206/135999*a^23 + 1538/135999*a^22 - 1697/135999*a^21 - 2246/45333*a^20 + 3988/135999*a^19 - 3137/135999*a^18 - 742/135999*a^17 - 121/15111*a^16 + 128/135999*a^15 + 11759/135999*a^14 - 6080/135999*a^13 - 1181/15111*a^12 - 16958/135999*a^11 + 2437/135999*a^10 + 13640/135999*a^9 + 53/15111*a^8 - 51472/135999*a^7 - 157/1863*a^6 - 485/135999*a^5 - 14119/45333*a^4 + 29305/135999*a^3 + 5695/135999*a^2 - 52588/135999*a - 56035/135999, 1/21623841*a^25 + 58/21623841*a^24 + 93617/21623841*a^23 - 41273/21623841*a^22 + 205801/21623841*a^21 - 509888/21623841*a^20 + 70070/2402649*a^19 - 217667/7207947*a^18 + 647686/21623841*a^17 + 2937/88987*a^16 - 3541480/21623841*a^15 + 2405755/21623841*a^14 + 100081/21623841*a^13 - 84328/940167*a^12 + 16042/313389*a^11 + 835195/7207947*a^10 - 5197/407997*a^9 - 701096/7207947*a^8 - 2521333/21623841*a^7 + 9580327/21623841*a^6 - 7559657/21623841*a^5 - 9563372/21623841*a^4 - 2451215/7207947*a^3 + 2971090/7207947*a^2 - 1035866/7207947*a - 9106297/21623841, 1/717044643038151*a^26 + 15099116/717044643038151*a^25 - 445493129/239014881012717*a^24 - 525974495980/239014881012717*a^23 - 6273715611433/717044643038151*a^22 + 7554204232715/717044643038151*a^21 + 38591987442955/717044643038151*a^20 + 32820573286/611291255787*a^19 - 37328321562947/717044643038151*a^18 + 357275968862/8639092084797*a^17 - 376548944054/42179096649303*a^16 - 1200727106698/26557209001413*a^15 - 1565854272901/9822529356687*a^14 - 71411258304379/717044643038151*a^13 + 53009882666989/717044643038151*a^12 + 12441069640637/79671627004239*a^11 + 9892065981073/717044643038151*a^10 + 28139744111119/717044643038151*a^9 + 5385579118484/717044643038151*a^8 - 10536512001476/239014881012717*a^7 - 276749630863258/717044643038151*a^6 - 98538605571637/717044643038151*a^5 + 208887455610868/717044643038151*a^4 - 45066103184386/239014881012717*a^3 + 87820955548717/239014881012717*a^2 - 344841463323733/717044643038151*a + 42099399472001/717044643038151], 0, 1, [], 1, [ (409678074001)/(717044643038151)*a^(26) - (432331809635)/(31175854045137)*a^(25) + (15974627535236)/(239014881012717)*a^(24) - (18420093224269)/(79671627004239)*a^(23) + (251786574910409)/(717044643038151)*a^(22) - (224934277119883)/(717044643038151)*a^(21) - (159910226355986)/(717044643038151)*a^(20) + (7203133391330)/(14059698883101)*a^(19) - (400166684898851)/(717044643038151)*a^(18) - (11279923546894)/(8639092084797)*a^(17) + (97117569696331)/(42179096649303)*a^(16) - (775359303538325)/(239014881012717)*a^(15) + (359716734682451)/(717044643038151)*a^(14) + (1909398707883089)/(717044643038151)*a^(13) - (1828584649827953)/(717044643038151)*a^(12) + (102833200896734)/(79671627004239)*a^(11) + (163582751191214)/(31175854045137)*a^(10) - (4689428638063013)/(717044643038151)*a^(9) + (1989229487243237)/(717044643038151)*a^(8) - (535608052586218)/(239014881012717)*a^(7) - (6614018912417287)/(717044643038151)*a^(6) - (821807328323647)/(717044643038151)*a^(5) - (4182891949164512)/(717044643038151)*a^(4) - (1442110781708095)/(239014881012717)*a^(3) + (156379040572100)/(79671627004239)*a^(2) - (2090497752572314)/(717044643038151)*a + (946211382680999)/(717044643038151) , (3671227302868)/(239014881012717)*a^(26) - (16060633004918)/(239014881012717)*a^(25) + (6362790613421)/(26557209001413)*a^(24) - (19304302504823)/(79671627004239)*a^(23) + (6908525069242)/(79671627004239)*a^(22) + (127225734441353)/(239014881012717)*a^(21) - (798948181871)/(2950801000157)*a^(20) + (2204732282522)/(14059698883101)*a^(19) + (471399151823789)/(239014881012717)*a^(18) - (3490691469776)/(2879697361599)*a^(17) + (24392460593131)/(14059698883101)*a^(16) + (116426995692827)/(79671627004239)*a^(15) - (213542499668639)/(79671627004239)*a^(14) - (7578945204055)/(239014881012717)*a^(13) + (1718085047788)/(79671627004239)*a^(12) - (55025018331874)/(10391951348379)*a^(11) + (677530081652087)/(239014881012717)*a^(10) + (539588210357714)/(239014881012717)*a^(9) + (736397959808312)/(239014881012717)*a^(8) + (312797434459778)/(26557209001413)*a^(7) + (724176337794118)/(79671627004239)*a^(6) + (2251500384573125)/(239014881012717)*a^(5) + (811943262312827)/(79671627004239)*a^(4) + (925047236563564)/(239014881012717)*a^(3) + (728007802546519)/(239014881012717)*a^(2) + (161582083708288)/(239014881012717)*a + (137068124541119)/(239014881012717) , (34913949297793)/(717044643038151)*a^(26) - (42439859550863)/(239014881012717)*a^(25) + (441284105617303)/(717044643038151)*a^(24) - (192261621565921)/(717044643038151)*a^(23) - (22868792615911)/(239014881012717)*a^(22) + (392556666059993)/(239014881012717)*a^(21) + (357286816355936)/(717044643038151)*a^(20) + (1575686503147)/(14059698883101)*a^(19) + (4534697297723509)/(717044643038151)*a^(18) + (7267605190249)/(8639092084797)*a^(17) + (162266077902175)/(42179096649303)*a^(16) + (4808545029295175)/(717044643038151)*a^(15) - (97437443439637)/(26557209001413)*a^(14) - (1588900818755359)/(239014881012717)*a^(13) - (2330103379726171)/(717044643038151)*a^(12) - (47535922216186)/(2950801000157)*a^(11) - (2029281372973949)/(717044643038151)*a^(10) + (6683427134521001)/(717044643038151)*a^(9) + (15333215610980570)/(717044643038151)*a^(8) + (32357879523478100)/(717044643038151)*a^(7) + (13034126954771017)/(239014881012717)*a^(6) + (13248806445458141)/(239014881012717)*a^(5) + (36400346340691154)/(717044643038151)*a^(4) + (7171530186228940)/(239014881012717)*a^(3) + (4023878175776726)/(239014881012717)*a^(2) + (1811972979411344)/(717044643038151)*a + (823183542136870)/(717044643038151) , (5360115432233)/(717044643038151)*a^(26) - (6251824790168)/(239014881012717)*a^(25) + (1243886994190)/(13529144208267)*a^(24) - (27201566156543)/(717044643038151)*a^(23) + (4148528679559)/(239014881012717)*a^(22) + (44775603059597)/(239014881012717)*a^(21) + (60619161582145)/(717044643038151)*a^(20) + (1309123396429)/(4686566294367)*a^(19) + (454637627875004)/(717044643038151)*a^(18) + (1862464628642)/(8639092084797)*a^(17) + (49713693560156)/(42179096649303)*a^(16) + (340999150356193)/(717044643038151)*a^(15) - (6073284498952)/(8852403000471)*a^(14) + (23611795529615)/(239014881012717)*a^(13) - (1409960247523850)/(717044643038151)*a^(12) - (539342105955895)/(239014881012717)*a^(11) + (608182244995610)/(717044643038151)*a^(10) - (115500472185482)/(717044643038151)*a^(9) + (2473031858731843)/(717044643038151)*a^(8) + (6460705764735493)/(717044643038151)*a^(7) + (1786388257530491)/(239014881012717)*a^(6) + (2217192958429601)/(239014881012717)*a^(5) + (6327983942898796)/(717044643038151)*a^(4) + (1087723007944909)/(239014881012717)*a^(3) + (270067063185835)/(79671627004239)*a^(2) + (654870716996854)/(717044643038151)*a + (413606949187670)/(717044643038151) , (8849104875941)/(717044643038151)*a^(26) - (28584332957233)/(717044643038151)*a^(25) + (81030822904573)/(717044643038151)*a^(24) + (64549519391051)/(717044643038151)*a^(23) - (251384942201116)/(717044643038151)*a^(22) + (351555699890240)/(717044643038151)*a^(21) + (162035090434121)/(239014881012717)*a^(20) - (13887216198451)/(14059698883101)*a^(19) + (38047853387725)/(31175854045137)*a^(18) + (2013919780315)/(959899120533)*a^(17) - (1279298133634)/(577795844511)*a^(16) + (809872948684574)/(717044643038151)*a^(15) + (1180657168293053)/(717044643038151)*a^(14) - (4134345200601187)/(717044643038151)*a^(13) - (49020727706599)/(79671627004239)*a^(12) + (612104442516559)/(239014881012717)*a^(11) - (3234517791421279)/(717044643038151)*a^(10) + (44466874321318)/(10391951348379)*a^(9) + (7641699228290950)/(717044643038151)*a^(8) + (3752069498063840)/(717044643038151)*a^(7) + (5183337296815940)/(717044643038151)*a^(6) + (6258950661747128)/(717044643038151)*a^(5) + (667868289674779)/(239014881012717)*a^(4) - (368151959628149)/(239014881012717)*a^(3) - (216169207622705)/(79671627004239)*a^(2) - (700639394215289)/(717044643038151)*a - (28491500627923)/(26557209001413) , (996295636388)/(239014881012717)*a^(26) - (1137402128054)/(239014881012717)*a^(25) + (1094656092740)/(239014881012717)*a^(24) + (11576947424920)/(79671627004239)*a^(23) - (46025567134181)/(239014881012717)*a^(22) + (44438033338595)/(239014881012717)*a^(21) + (85514940787346)/(239014881012717)*a^(20) - (938951142197)/(14059698883101)*a^(19) + (25878110751910)/(79671627004239)*a^(18) + (1281110986453)/(959899120533)*a^(17) - (6576251487155)/(14059698883101)*a^(16) + (96647792733350)/(79671627004239)*a^(15) - (21506320620209)/(239014881012717)*a^(14) - (419693141541808)/(239014881012717)*a^(13) - (325384732162120)/(239014881012717)*a^(12) - (95000521419889)/(239014881012717)*a^(11) - (73530543340774)/(26557209001413)*a^(10) + (221473115473774)/(79671627004239)*a^(9) + (963523754098430)/(239014881012717)*a^(8) + (61437447985196)/(8852403000471)*a^(7) + (1930036642049575)/(239014881012717)*a^(6) + (1975306926963890)/(239014881012717)*a^(5) + (1384727733121874)/(239014881012717)*a^(4) + (32388434694337)/(10391951348379)*a^(3) + (22977728801653)/(239014881012717)*a^(2) - (233686061693377)/(239014881012717)*a - (59535538560955)/(79671627004239) , (11580232358185)/(717044643038151)*a^(26) - (51468033172363)/(717044643038151)*a^(25) + (62656768047559)/(239014881012717)*a^(24) - (2423018643860)/(8852403000471)*a^(23) + (67466167704143)/(717044643038151)*a^(22) + (7709085831797)/(9822529356687)*a^(21) - (376266244059470)/(717044643038151)*a^(20) + (196956346379)/(4686566294367)*a^(19) + (2183848584904546)/(717044643038151)*a^(18) - (12852726707005)/(8639092084797)*a^(17) + (59080829470627)/(42179096649303)*a^(16) + (920032365750580)/(239014881012717)*a^(15) - (2270323539528244)/(717044643038151)*a^(14) - (771952918499959)/(717044643038151)*a^(13) + (1442554361738782)/(717044643038151)*a^(12) - (2042363348162650)/(239014881012717)*a^(11) - (556329401875196)/(717044643038151)*a^(10) + (154613307247571)/(31175854045137)*a^(9) + (1772584309642613)/(717044643038151)*a^(8) + (2969505008125568)/(239014881012717)*a^(7) + (11977436032642637)/(717044643038151)*a^(6) + (11619856107000878)/(717044643038151)*a^(5) + (11814297901935223)/(717044643038151)*a^(4) + (2270245256038303)/(239014881012717)*a^(3) + (21545577702926)/(4509714736089)*a^(2) + (981801060615920)/(717044643038151)*a + (649409067897197)/(717044643038151) , (3473993142259)/(79671627004239)*a^(26) - (118718592005480)/(717044643038151)*a^(25) + (407142667725049)/(717044643038151)*a^(24) - (218531696141032)/(717044643038151)*a^(23) - (74536923822128)/(717044643038151)*a^(22) + (1007279191110460)/(717044643038151)*a^(21) + (244784938946185)/(717044643038151)*a^(20) - (1818055740997)/(14059698883101)*a^(19) + (1270247183085182)/(239014881012717)*a^(18) - (968865324610)/(8639092084797)*a^(17) + (12280955891558)/(4686566294367)*a^(16) + (3501743600604128)/(717044643038151)*a^(15) - (3092849498745152)/(717044643038151)*a^(14) - (4519884872124011)/(717044643038151)*a^(13) - (968627551598456)/(717044643038151)*a^(12) - (103472904813044)/(8852403000471)*a^(11) + (7346887250473)/(10391951348379)*a^(10) + (7410176455569988)/(717044643038151)*a^(9) + (4161235040900227)/(239014881012717)*a^(8) + (24441004428488426)/(717044643038151)*a^(7) + (27279617000429887)/(717044643038151)*a^(6) + (24673606339438492)/(717044643038151)*a^(5) + (20335455444912322)/(717044643038151)*a^(4) + (3353517493538360)/(239014881012717)*a^(3) + (1724098484711636)/(239014881012717)*a^(2) + (2613870458575)/(26557209001413)*a + (659182473179159)/(717044643038151) , (12773761978436)/(717044643038151)*a^(26) - (18407744452598)/(239014881012717)*a^(25) + (189962787577439)/(717044643038151)*a^(24) - (162559132947572)/(717044643038151)*a^(23) - (12664463004296)/(239014881012717)*a^(22) + (59889537271316)/(79671627004239)*a^(21) - (180391132715711)/(717044643038151)*a^(20) - (4218393746669)/(14059698883101)*a^(19) + (1833249643548260)/(717044643038151)*a^(18) - (10217183140927)/(8639092084797)*a^(17) + (23222249680712)/(42179096649303)*a^(16) + (1661751017878660)/(717044643038151)*a^(15) - (235925290235653)/(79671627004239)*a^(14) - (174057930475997)/(79671627004239)*a^(13) + (1124635817988316)/(717044643038151)*a^(12) - (1161272769637394)/(239014881012717)*a^(11) + (943230560978504)/(717044643038151)*a^(10) + (3611986157080582)/(717044643038151)*a^(9) + (3666808614268711)/(717044643038151)*a^(8) + (6493624122636043)/(717044643038151)*a^(7) + (2413689320298275)/(239014881012717)*a^(6) + (24505383160772)/(3463983782793)*a^(5) + (3320261403782008)/(717044643038151)*a^(4) + (6504389521735)/(8852403000471)*a^(3) - (41551730698337)/(239014881012717)*a^(2) - (1239862673757527)/(717044643038151)*a + (553633620534470)/(717044643038151) , (33754202481797)/(717044643038151)*a^(26) - (135856146805507)/(717044643038151)*a^(25) + (470892133363393)/(717044643038151)*a^(24) - (327086088411295)/(717044643038151)*a^(23) - (69458806810711)/(717044643038151)*a^(22) + (1325643828720581)/(717044643038151)*a^(21) - (47932935559955)/(239014881012717)*a^(20) - (4270694984647)/(14059698883101)*a^(19) + (4783559881659188)/(717044643038151)*a^(18) - (4017895688042)/(2879697361599)*a^(17) + (113849577889949)/(42179096649303)*a^(16) + (5229383834168747)/(717044643038151)*a^(15) - (4495084329572509)/(717044643038151)*a^(14) - (3845020963728808)/(717044643038151)*a^(13) + (496613557167599)/(239014881012717)*a^(12) - (3807088466755661)/(239014881012717)*a^(11) + (56447382256382)/(717044643038151)*a^(10) + (2839671044429140)/(239014881012717)*a^(9) + (9319849634318041)/(717044643038151)*a^(8) + (24872099193469685)/(717044643038151)*a^(7) + (29488978646214233)/(717044643038151)*a^(6) + (26152482853754531)/(717044643038151)*a^(5) + (320800637989409)/(8852403000471)*a^(4) + (4894140381677557)/(239014881012717)*a^(3) + (2772743711056363)/(239014881012717)*a^(2) + (1620456661840582)/(717044643038151)*a + (179990203623193)/(79671627004239) , (137267459419)/(3366406774827)*a^(26) - 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(143825746713899)/(717044643038151)*a - (104332904770739)/(717044643038151) , (12145560773719)/(239014881012717)*a^(26) - (48977926472491)/(239014881012717)*a^(25) + (1091757573829)/(1503238245363)*a^(24) - (45152227765175)/(79671627004239)*a^(23) + (33892196896631)/(239014881012717)*a^(22) + (421786573875881)/(239014881012717)*a^(21) - (47402406423506)/(239014881012717)*a^(20) + (1396112590400)/(4686566294367)*a^(19) + (1642748453457253)/(239014881012717)*a^(18) - (4276793518204)/(2879697361599)*a^(17) + (70927341224851)/(14059698883101)*a^(16) + (529714639298069)/(79671627004239)*a^(15) - (1342561381429567)/(239014881012717)*a^(14) - (12155968404616)/(3274176452229)*a^(13) - (204078586735154)/(239014881012717)*a^(12) - (464647138696888)/(26557209001413)*a^(11) + (46089978139306)/(239014881012717)*a^(10) + (1996451622573910)/(239014881012717)*a^(9) + (3753904874480900)/(239014881012717)*a^(8) + (1088325074583446)/(26557209001413)*a^(7) + (11120673546939314)/(239014881012717)*a^(6) + (12202001612947967)/(239014881012717)*a^(5) + (11129654257973923)/(239014881012717)*a^(4) + (2496046548481811)/(79671627004239)*a^(3) + (1514499052985000)/(79671627004239)*a^(2) + (1499471116863515)/(239014881012717)*a + (1055397507754118)/(239014881012717) ], 5105816638.575763, [[x^3 - x^2 - 4*x + 9, 1], [x^9 - 4*x^8 + 4*x^7 + 3*x^6 + 21*x^5 - 24*x^4 + 25*x^3 + 17*x^2 + 7*x - 33, 1]]]