/* 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 - 6*x^26 + 31*x^25 - 80*x^24 + 117*x^23 - 51*x^22 - 243*x^21 + 807*x^20 - 1350*x^19 + 966*x^18 + 1935*x^17 - 9345*x^16 + 23103*x^15 - 43548*x^14 + 68751*x^13 - 94575*x^12 + 115269*x^11 - 125268*x^10 + 121785*x^9 - 105567*x^8 + 81027*x^7 - 54357*x^6 + 31122*x^5 - 14664*x^4 + 5393*x^3 - 1350*x^2 + 179*x - 1, 27, 8, [1, 13], -1543319746516623033280478216838436483146079, [1759], [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, 1/9*a^21 + 1/9*a^13 - 2/9*a^5, 1/27*a^22 + 1/27*a^21 - 1/27*a^20 - 1/27*a^18 - 1/27*a^17 + 1/27*a^16 + 1/27*a^14 + 1/27*a^13 - 1/27*a^12 - 1/27*a^10 - 1/27*a^9 + 1/27*a^8 - 2/27*a^6 - 2/27*a^5 + 2/27*a^4 + 2/27*a^2 + 2/27*a - 2/27, 1/27*a^23 + 1/27*a^21 + 1/27*a^20 - 1/27*a^19 - 1/27*a^17 - 1/27*a^16 + 1/27*a^15 + 1/27*a^13 + 1/27*a^12 - 1/27*a^11 - 1/27*a^9 - 1/27*a^8 - 2/27*a^7 - 2/27*a^5 - 2/27*a^4 + 2/27*a^3 + 2/27*a + 2/27, 1/27*a^24 - 1/9*a^8 + 2/27, 1/202797*a^25 + 254/22533*a^24 + 220/67599*a^23 + 442/28971*a^22 - 1472/28971*a^21 + 7313/202797*a^20 + 3403/67599*a^19 + 10271/202797*a^18 + 9236/202797*a^17 + 235/202797*a^16 + 3856/67599*a^15 + 11230/202797*a^14 + 766/5481*a^13 - 30865/202797*a^12 + 6691/67599*a^11 - 8143/202797*a^10 + 19178/202797*a^9 + 31636/202797*a^8 + 32230/67599*a^7 - 2675/28971*a^6 - 20306/202797*a^5 - 72379/202797*a^4 - 20714/67599*a^3 + 5501/28971*a^2 + 14401/28971*a + 17494/202797, 1/3401596152173459846238129*a^26 + 4307896242397707175/3401596152173459846238129*a^25 - 58800317973104262888547/3401596152173459846238129*a^24 + 696690136732004143805/1133865384057819948746043*a^23 - 609424976164941145585/161980769151117135535149*a^22 - 46066059511880976971/1725822502371111033099*a^21 + 10230492152795716098671/377955128019273316248681*a^20 - 44249908117598173524424/1133865384057819948746043*a^19 + 4564622200880778041351/161980769151117135535149*a^18 - 20032557056116754684054/377955128019273316248681*a^17 + 9722229141917537957788/377955128019273316248681*a^16 + 984162272193725786324/7509042278528608932093*a^15 + 448355665696345932485/7509042278528608932093*a^14 - 113341777598021175587/3669467262323041905327*a^13 - 3831422452649316745766/53993589717039045178383*a^12 - 2925478470162800351686/1133865384057819948746043*a^11 + 135067254605921093428537/1133865384057819948746043*a^10 - 152996910428730473766967/1133865384057819948746043*a^9 + 86822969295656201363557/1133865384057819948746043*a^8 - 205318045204383381101590/1133865384057819948746043*a^7 - 347912314047464599446505/1133865384057819948746043*a^6 - 178338945657990561998836/377955128019273316248681*a^5 + 37701538126997227113758/125985042673091105416227*a^4 + 227420428785178017308372/1133865384057819948746043*a^3 + 91694467203047109886865/485942307453351406605447*a^2 + 222647107579038322344767/3401596152173459846238129*a + 897274803829459144634932/3401596152173459846238129], 0, 1, [], 1, [ (168235528459239655870)/(3401596152173459846238129)*a^(26) + (6003518059181154848638)/(3401596152173459846238129)*a^(25) + (35770571241101585529407)/(3401596152173459846238129)*a^(24) - (11573572597209815433754)/(1133865384057819948746043)*a^(23) + (38728037111100148516862)/(161980769151117135535149)*a^(22) - (485771018790289262147)/(5177467507113333099297)*a^(21) - (31738690370555665435441)/(377955128019273316248681)*a^(20) + (121052675712922241646980)/(161980769151117135535149)*a^(19) - (1818232403041172335619011)/(1133865384057819948746043)*a^(18) + (250506781614804558886033)/(125985042673091105416227)*a^(17) + (40661677917588585326374)/(377955128019273316248681)*a^(16) - (48999022337107245412438)/(7509042278528608932093)*a^(15) + (503304722506019801387)/(28992441229840188927)*a^(14) - (118538926212989163564832)/(3669467262323041905327)*a^(13) + (18985987666491370556990173)/(377955128019273316248681)*a^(12) - (9153815552325234681360271)/(161980769151117135535149)*a^(11) + (64926106240360744627716397)/(1133865384057819948746043)*a^(10) - (48692129693064092503626628)/(1133865384057819948746043)*a^(9) + (16890293345919004756240264)/(1133865384057819948746043)*a^(8) + (19236687137166666302928143)/(1133865384057819948746043)*a^(7) - (40292945876697479313723202)/(1133865384057819948746043)*a^(6) + (6689502104272325747748761)/(125985042673091105416227)*a^(5) - (5713786686209990018302022)/(125985042673091105416227)*a^(4) + (41123596788033375775734242)/(1133865384057819948746043)*a^(3) - (8741819792961552064847731)/(485942307453351406605447)*a^(2) + (24020577576933223010213987)/(3401596152173459846238129)*a - (97145417049102992418770)/(91935031139823239087517) , (1481313539268797855030023)/(3401596152173459846238129)*a^(26) - (8477715186757989198701762)/(3401596152173459846238129)*a^(25) + (43420819422980207304385928)/(3401596152173459846238129)*a^(24) - (35231860761933009328116997)/(1133865384057819948746043)*a^(23) + (6667212939321247950534170)/(161980769151117135535149)*a^(22) - (42791218585702937789254)/(5177467507113333099297)*a^(21) - (41952782775153116283256274)/(377955128019273316248681)*a^(20) + (362998947052771444472942030)/(1133865384057819948746043)*a^(19) - (19095054007220288881323884)/(39098806346821377542967)*a^(18) + (13959598691867706210202382)/(53993589717039045178383)*a^(17) + (359200909200602199952803119)/(377955128019273316248681)*a^(16) - (28647334480890788745758971)/(7509042278528608932093)*a^(15) + (66866364970589026974131603)/(7509042278528608932093)*a^(14) - (19768830556276436122932098)/(1223155754107680635109)*a^(13) + (3115319262225754619203818220)/(125985042673091105416227)*a^(12) - (37486369550880670802480407399)/(1133865384057819948746043)*a^(11) + (44399174052052436535765158716)/(1133865384057819948746043)*a^(10) - (46793679178422630112177661320)/(1133865384057819948746043)*a^(9) + (44009277889222931507528180827)/(1133865384057819948746043)*a^(8) - (36717119117795550280100334427)/(1133865384057819948746043)*a^(7) + (26922259742894135698827129686)/(1133865384057819948746043)*a^(6) - (5685359052801492744719653301)/(377955128019273316248681)*a^(5) + (3007695936561362592367786589)/(377955128019273316248681)*a^(4) - (3781502756819236807125973462)/(1133865384057819948746043)*a^(3) + (494771304369399242570605397)/(485942307453351406605447)*a^(2) - (535198549596004617223732372)/(3401596152173459846238129)*a - (4202885862701103944752409)/(3401596152173459846238129) , (196374933640601381337314)/(3401596152173459846238129)*a^(26) - (1042814696043875262902239)/(3401596152173459846238129)*a^(25) + (5150294670556701074209924)/(3401596152173459846238129)*a^(24) - (3633122279167185184185476)/(1133865384057819948746043)*a^(23) + (435848477788285927671280)/(161980769151117135535149)*a^(22) + (17269456462973594610491)/(5177467507113333099297)*a^(21) - (706105228183845731715941)/(41995014224363701805409)*a^(20) + (1035763745631561616704238)/(30645010379941079695839)*a^(19) - (5772824278184118625710335)/(161980769151117135535149)*a^(18) - (1887515799530385703577252)/(125985042673091105416227)*a^(17) + (20509618164366029350165799)/(125985042673091105416227)*a^(16) - (3309316849940887925402111)/(7509042278528608932093)*a^(15) + (6444543445797803238421282)/(7509042278528608932093)*a^(14) - (4974222849149222733676655)/(3669467262323041905327)*a^(13) + (98002118951093227676463265)/(53993589717039045178383)*a^(12) - (2403767398924123508357195039)/(1133865384057819948746043)*a^(11) + (2455541352682175985645566906)/(1133865384057819948746043)*a^(10) - (2156465030652288278435971376)/(1133865384057819948746043)*a^(9) + (1606244329899307360259531327)/(1133865384057819948746043)*a^(8) - (970757460004591606237066670)/(1133865384057819948746043)*a^(7) + (412441708065301465259659750)/(1133865384057819948746043)*a^(6) - (4742974641675564538485112)/(125985042673091105416227)*a^(5) - (38761227236500480159552135)/(377955128019273316248681)*a^(4) + (116059338441490744080387448)/(1133865384057819948746043)*a^(3) - (21116315277741602288330282)/(485942307453351406605447)*a^(2) + (24055284696324889949088076)/(3401596152173459846238129)*a + (3846269554678613516990744)/(3401596152173459846238129) , (335026838960060935222106)/(3401596152173459846238129)*a^(26) - (279897514076841988002772)/(485942307453351406605447)*a^(25) + (1421701470364059277572412)/(485942307453351406605447)*a^(24) - (8153817117430094941111712)/(1133865384057819948746043)*a^(23) + (1490193373275226790830180)/(161980769151117135535149)*a^(22) - (2631121121600675258405)/(5177467507113333099297)*a^(21) - (10588817169304829329210564)/(377955128019273316248681)*a^(20) + (85313294123478774651927505)/(1133865384057819948746043)*a^(19) - (123670644628134069111818885)/(1133865384057819948746043)*a^(18) + (17269661327996006632690954)/(377955128019273316248681)*a^(17) + (92371827188900706503021320)/(377955128019273316248681)*a^(16) - (966857652587008175039642)/(1072720325504086990299)*a^(15) + (15239667126459534093264319)/(7509042278528608932093)*a^(14) - (4390057961050432455146371)/(1223155754107680635109)*a^(13) + (674931992973743600116376134)/(125985042673091105416227)*a^(12) - (7915933720387818675931206842)/(1133865384057819948746043)*a^(11) + (9129863880488458963370288441)/(1133865384057819948746043)*a^(10) - (9338769708019008546713485220)/(1133865384057819948746043)*a^(9) + (8471775192859403505010731329)/(1133865384057819948746043)*a^(8) - (6775781339613015916448159063)/(1133865384057819948746043)*a^(7) + (4714680185025869563534202317)/(1133865384057819948746043)*a^(6) - (927741186832515932012594896)/(377955128019273316248681)*a^(5) + (63256633363023425896209079)/(53993589717039045178383)*a^(4) - (470539461894266794516907897)/(1133865384057819948746043)*a^(3) + (46120217173485072575433295)/(485942307453351406605447)*a^(2) - (30389865434788034814869036)/(3401596152173459846238129)*a - (3775736374631235440885290)/(3401596152173459846238129) , (342455309147076639914899)/(3401596152173459846238129)*a^(26) - (1999224494559244640878928)/(3401596152173459846238129)*a^(25) + (10289987098095155041010450)/(3401596152173459846238129)*a^(24) - (8560135150867749299173972)/(1133865384057819948746043)*a^(23) + (58596364223553212466838)/(5585543763831625363281)*a^(22) - (16300291597023113312209)/(5177467507113333099297)*a^(21) - (152551409244019141699403)/(5999287746337671686487)*a^(20) + (87771988563253141018795520)/(1133865384057819948746043)*a^(19) - (139038973306992315465033016)/(1133865384057819948746043)*a^(18) + (28169958186670325138640560)/(377955128019273316248681)*a^(17) + (26696892884316903892724165)/(125985042673091105416227)*a^(16) - (6838965276094069075041904)/(7509042278528608932093)*a^(15) + (16319429859035932787589380)/(7509042278528608932093)*a^(14) - (77714944822527330000158)/(19415170700121914843)*a^(13) + (2343074447247305426647365962)/(377955128019273316248681)*a^(12) - (9499219444134954065610846616)/(1133865384057819948746043)*a^(11) + (11374688705302021676199310099)/(1133865384057819948746043)*a^(10) - (1732507910336070496164893998)/(161980769151117135535149)*a^(9) + (1649580550897368356953324324)/(161980769151117135535149)*a^(8) - (9771944235204101569278134728)/(1133865384057819948746043)*a^(7) + (7287580179727162698239557739)/(1133865384057819948746043)*a^(6) - (1571014438012018472781666737)/(377955128019273316248681)*a^(5) + (29517529313337499727738594)/(13032935448940459180989)*a^(4) - (1122136098536480300572144744)/(1133865384057819948746043)*a^(3) + (156801438495467309395843250)/(485942307453351406605447)*a^(2) - (207722357834158352033164510)/(3401596152173459846238129)*a + (5081096273243357525804950)/(3401596152173459846238129) , (4976124757465342392398)/(46597207564019997893673)*a^(26) - (28997848210143185353942)/(46597207564019997893673)*a^(25) + (148829157832401792486652)/(46597207564019997893673)*a^(24) - (123433836768948682458371)/(15532402521339999297891)*a^(23) + (24171568853802096692539)/(2218914645905714185413)*a^(22) - (16097804466912538441579)/(5177467507113333099297)*a^(21) - (139384420103231305505828)/(5177467507113333099297)*a^(20) + (180245928933501824976409)/(2218914645905714185413)*a^(19) - (1987821605342204026929650)/(15532402521339999297891)*a^(18) + (131619915646380356422772)/(1725822502371111033099)*a^(17) + (1167123479454510657544883)/(5177467507113333099297)*a^(16) - (98602991608993442928008)/(102863592856556286741)*a^(15) + (33518388997084627409887)/(14694798979508040963)*a^(14) - (210855303095063708797451)/(50266674826343039799)*a^(13) + (33593270438553157554420218)/(5177467507113333099297)*a^(12) - (19443173867266519610717813)/(2218914645905714185413)*a^(11) + (162850040166747361027302650)/(15532402521339999297891)*a^(10) - (173506466710551079962025430)/(15532402521339999297891)*a^(9) + (165105869669367202699586564)/(15532402521339999297891)*a^(8) - (139630715340575308790550242)/(15532402521339999297891)*a^(7) + (104022985430080094808309235)/(15532402521339999297891)*a^(6) - (7468918224449850522284860)/(1725822502371111033099)*a^(5) + (4060463908904142843875257)/(1725822502371111033099)*a^(4) - (15921037795636004606331458)/(15532402521339999297891)*a^(3) + (2215101679547707710358696)/(6656743937717142556239)*a^(2) - (2870514736403203461030350)/(46597207564019997893673)*a + (73135303805967591746798)/(46597207564019997893673) , (217734896446252682812424)/(3401596152173459846238129)*a^(26) - (28977502415823054407332)/(91935031139823239087517)*a^(25) + (5543506968473329290293533)/(3401596152173459846238129)*a^(24) - (3757161116136202985800004)/(1133865384057819948746043)*a^(23) + (589914793498173973004632)/(161980769151117135535149)*a^(22) + (1511617285225546974746)/(1725822502371111033099)*a^(21) - (5407061658032761919929000)/(377955128019273316248681)*a^(20) + (39451713534478181956029649)/(1133865384057819948746043)*a^(19) - (52410777877095717170935016)/(1133865384057819948746043)*a^(18) + (512059076504817541073918)/(53993589717039045178383)*a^(17) + (49985150670662424081745960)/(377955128019273316248681)*a^(16) - 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