/* 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^20 - 8*x^19 + 38*x^18 - 133*x^17 + 323*x^16 - 570*x^15 + 608*x^14 + 608*x^13 - 2280*x^12 + 5662*x^11 - 2527*x^10 + 4731*x^9 + 8265*x^8 - 6935*x^7 + 27265*x^6 - 20539*x^5 + 29469*x^4 - 20178*x^3 + 16226*x^2 - 6696*x + 729, 20, 10, [2, 9], -558854584859141340505879659895771, [7, 19], [1, a, a^2, a^3, a^4, a^5, a^6, 1/3*a^7 + 1/3*a^6 - 1/3*a^5 - 1/3*a^3 - 1/3*a^2 + 1/3*a, 1/3*a^8 + 1/3*a^6 + 1/3*a^5 - 1/3*a^4 - 1/3*a^2 - 1/3*a, 1/3*a^9 - 1/3*a, 1/3*a^10 - 1/3*a^2, 1/3*a^11 - 1/3*a^3, 1/9*a^12 - 1/9*a^10 - 1/9*a^8 + 1/9*a^7 - 1/3*a^6 + 1/9*a^5 + 1/3*a^4 + 2/9*a^3 - 2/9*a^2 + 2/9*a, 1/45*a^13 - 2/45*a^12 - 1/45*a^11 - 7/45*a^10 + 2/45*a^9 - 2/15*a^8 + 1/45*a^7 + 22/45*a^6 + 13/45*a^5 - 4/45*a^4 - 7/15*a^3 + 2/5*a^2 + 8/45*a - 2/5, 1/45*a^14 + 2/15*a^11 - 2/45*a^10 - 2/45*a^9 - 1/45*a^8 - 1/45*a^7 - 2/5*a^6 - 2/5*a^5 + 16/45*a^4 + 1/45*a^3 - 11/45*a^2 + 8/45*a + 1/5, 1/135*a^15 + 1/135*a^14 + 2/45*a^12 - 11/135*a^11 - 19/135*a^10 - 2/15*a^9 - 2/135*a^8 - 4/135*a^7 - 7/45*a^6 - 62/135*a^5 + 62/135*a^4 - 11/27*a^3 - 1/45*a^2 - 43/135*a + 2/5, 1/135*a^16 - 1/135*a^14 - 1/27*a^12 - 2/135*a^11 - 2/135*a^10 + 4/135*a^9 - 11/135*a^8 + 22/135*a^7 - 38/135*a^6 - 44/135*a^5 - 16/45*a^4 - 2/135*a^3 + 32/135*a^2 + 4/135*a + 2/5, 1/135*a^17 + 1/135*a^14 + 1/135*a^13 + 7/135*a^12 - 19/135*a^11 + 2/15*a^10 - 17/135*a^9 + 14/135*a^8 - 7/45*a^7 + 67/135*a^6 + 28/135*a^5 + 4/15*a^4 + 16/135*a^3 - 56/135*a^2 + 44/135*a - 2/5, 1/2025*a^18 + 7/2025*a^17 - 1/405*a^16 + 1/2025*a^15 - 17/2025*a^14 + 2/2025*a^13 + 34/2025*a^12 - 61/675*a^11 + 308/2025*a^10 - 134/2025*a^9 + 11/225*a^8 + 98/2025*a^7 + 2/225*a^6 - 919/2025*a^5 + 796/2025*a^4 + 37/225*a^3 + 776/2025*a^2 + 26/675*a + 8/25, 1/1486299344023045856654884219725*a^19 + 19799292315508951344617354/87429373177826226862052012925*a^18 + 73355763810520263497339284/114330718771003527434991093825*a^17 - 5337429646775956199944866824/1486299344023045856654884219725*a^16 - 4657498925220160484004727676/1486299344023045856654884219725*a^15 + 913188289314214809706021723/297259868804609171330976843945*a^14 - 3797741184436848776229886139/1486299344023045856654884219725*a^13 - 85936255733656706112123302/12703413196778169714999010425*a^12 - 40229454640718049499902381026/297259868804609171330976843945*a^11 + 67045699865285811184058958229/1486299344023045856654884219725*a^10 + 664646400220409725397642332/19817324586973944755398456263*a^9 + 62302299384296487929898445262/1486299344023045856654884219725*a^8 + 12912145933134306396767316257/495433114674348618884961406575*a^7 - 23694780683256160578769307242/114330718771003527434991093825*a^6 + 18001307206740566375813567396/87429373177826226862052012925*a^5 + 229983918148422167554682139298/495433114674348618884961406575*a^4 - 129816578006258372469643589131/1486299344023045856654884219725*a^3 + 3219072564131263512561634288/495433114674348618884961406575*a^2 - 68423867988464735805928786463/495433114674348618884961406575*a + 1769269393939747239258651038/18349374617568467366109681725], 0, 1, [], 1, [ (27442260685208561852801498)/(87429373177826226862052012925)*a^(19) - (23421780471644387579285153)/(9714374797536247429116890325)*a^(18) + (8346255530399864378217047)/(747259599810480571470530025)*a^(17) - (1108271515128159478356599449)/(29143124392608742287350670975)*a^(16) + (2553027336843091472692096012)/(29143124392608742287350670975)*a^(15) - (12454780172755223091519172708)/(87429373177826226862052012925)*a^(14) + (9983163615545578458869338141)/(87429373177826226862052012925)*a^(13) + (2049858029592431765764804678)/(6725336398294325143234770225)*a^(12) - (65520650914092734576158227887)/(87429373177826226862052012925)*a^(11) + (144842451103376000393482722589)/(87429373177826226862052012925)*a^(10) - (1832942370628834749706080881)/(87429373177826226862052012925)*a^(9) + (58271298930819601870642017442)/(87429373177826226862052012925)*a^(8) + (75590518355646426982536099388)/(17485874635565245372410402585)*a^(7) - (8638745001299889394300611617)/(6725336398294325143234770225)*a^(6) + (134626224617996994201852069677)/(17485874635565245372410402585)*a^(5) - (100163194327880279206261804424)/(87429373177826226862052012925)*a^(4) + (481479239996949959298479828134)/(87429373177826226862052012925)*a^(3) + (3506946482033793177515598356)/(87429373177826226862052012925)*a^(2) + (2246154744621141859027970726)/(1165724975704349691494026839)*a + (474039723444845230630660936)/(1079374977504027492124098925) , (22693900474729429223674213)/(114330718771003527434991093825)*a^(19) - (10275392632588489256914646)/(6725336398294325143234770225)*a^(18) + (835446942151196948788304429)/(114330718771003527434991093825)*a^(17) - (2961743086543265168303145397)/(114330718771003527434991093825)*a^(16) + (7316766902134706022774043961)/(114330718771003527434991093825)*a^(15) - (4556658741702655835140679426)/(38110239590334509144997031275)*a^(14) + (5411952032844290318016674162)/(38110239590334509144997031275)*a^(13) + (8552741610011654278665176734)/(114330718771003527434991093825)*a^(12) - (41774407208810950573075745227)/(114330718771003527434991093825)*a^(11) + (15769179428985949030666712351)/(12703413196778169714999010425)*a^(10) - (69891468455349915152123071001)/(114330718771003527434991093825)*a^(9) + (198965395213680495822731551202)/(114330718771003527434991093825)*a^(8) + (49746444145434886438265750074)/(22866143754200705486998218765)*a^(7) - (50392023929752966849047879121)/(114330718771003527434991093825)*a^(6) + (3319590350610535965750897667)/(448355759886288342882318015)*a^(5) - (418024512283878951054357148109)/(114330718771003527434991093825)*a^(4) + (862203493363707529497457276694)/(114330718771003527434991093825)*a^(3) - (545629668889760121821273271544)/(114330718771003527434991093825)*a^(2) + (6691394270113412444173239716)/(1524409583613380365799881251)*a - (3147076297968428874006256034)/(1411490355197574412777667825) , (91398170148163749160030981)/(1486299344023045856654884219725)*a^(19) - (16321189212020404011149983)/(29143124392608742287350670975)*a^(18) + (797816166910696430060571)/(282298071039514882555533565)*a^(17) - (5113611148437763036541745548)/(495433114674348618884961406575)*a^(16) + (1469860117764429055167318404)/(55048123852705402098329045175)*a^(15) - (72722377721405063581777013393)/(1486299344023045856654884219725)*a^(14) + (82349282438419478242915533479)/(1486299344023045856654884219725)*a^(13) + (4078338755174534739737604209)/(114330718771003527434991093825)*a^(12) - (338885422304999160871371205807)/(1486299344023045856654884219725)*a^(11) + (705676552053953770537698113801)/(1486299344023045856654884219725)*a^(10) - (566273823844995499783658559946)/(1486299344023045856654884219725)*a^(9) - (10092492752011934326314946897)/(1486299344023045856654884219725)*a^(8) + (705006569234588644399518945613)/(1486299344023045856654884219725)*a^(7) - (148956716543185411059757510063)/(114330718771003527434991093825)*a^(6) + (94745977287392242694589465583)/(87429373177826226862052012925)*a^(5) - (3958482070461201257387105402617)/(1486299344023045856654884219725)*a^(4) + (1795674106529938994152431496136)/(1486299344023045856654884219725)*a^(3) - (3054258235522648342524569620532)/(1486299344023045856654884219725)*a^(2) + (209240988601171703335542851566)/(495433114674348618884961406575)*a - (2915049284609617962776859989)/(3669874923513693473221936345) , (12749338852149163502627449)/(297259868804609171330976843945)*a^(19) - (9452223594863854936805747)/(87429373177826226862052012925)*a^(18) - (20904821672418822633123871)/(114330718771003527434991093825)*a^(17) + (789528889475085697268609371)/(297259868804609171330976843945)*a^(16) - (21788983890231574710180145069)/(1486299344023045856654884219725)*a^(15) + (62209325521810956876070897498)/(1486299344023045856654884219725)*a^(14) - (124872118442167316494843912543)/(1486299344023045856654884219725)*a^(13) + (4800652455236794241506095251)/(38110239590334509144997031275)*a^(12) + (141212140873044469574945567977)/(1486299344023045856654884219725)*a^(11) - (402397521238323363803347638097)/(1486299344023045856654884219725)*a^(10) + (531569219632061342793904392607)/(495433114674348618884961406575)*a^(9) - (38157374672748595810736494691)/(1486299344023045856654884219725)*a^(8) + (614407880525017686982560210136)/(495433114674348618884961406575)*a^(7) + (257871520398985726723663822921)/(114330718771003527434991093825)*a^(6) - (24298271250516638556245665262)/(87429373177826226862052012925)*a^(5) + (745631216834409624143075557219)/(165144371558116206294987135525)*a^(4) - (2345348791397859311810638046177)/(1486299344023045856654884219725)*a^(3) + (217696360390261533198688912243)/(55048123852705402098329045175)*a^(2) - (691168008781451428573759747829)/(495433114674348618884961406575)*a + (21915742312274314654111960598)/(18349374617568467366109681725) , (99963551228690764324757629)/(495433114674348618884961406575)*a^(19) - (57399592898712515670458947)/(87429373177826226862052012925)*a^(18) + (55164100770100037544020533)/(114330718771003527434991093825)*a^(17) + (7631388202006845156587093557)/(1486299344023045856654884219725)*a^(16) - (57593167538731231903830661892)/(1486299344023045856654884219725)*a^(15) + (30959531101548192596186320139)/(297259868804609171330976843945)*a^(14) - (256014528695534499189755313163)/(1486299344023045856654884219725)*a^(13) + (21331054232980794269460717409)/(114330718771003527434991093825)*a^(12) + (16957465423172870586130599613)/(19817324586973944755398456263)*a^(11) - (1797987367506604328282093596327)/(1486299344023045856654884219725)*a^(10) + (987473152924880210855572915166)/(297259868804609171330976843945)*a^(9) + (1773397805959956915078277961573)/(495433114674348618884961406575)*a^(8) - (26423376228400774169519848708)/(1486299344023045856654884219725)*a^(7) + (445860583782335505361280771822)/(38110239590334509144997031275)*a^(6) + (265391200162675363791191789512)/(87429373177826226862052012925)*a^(5) + (12580940540927359602834847820998)/(1486299344023045856654884219725)*a^(4) + (5684335712305764231928680203686)/(495433114674348618884961406575)*a^(3) - (4917077646307379385782632534342)/(1486299344023045856654884219725)*a^(2) + (502691749370881746152683018346)/(55048123852705402098329045175)*a - (8464635020255119682105810894)/(18349374617568467366109681725) , (861394260203656914297596)/(38110239590334509144997031275)*a^(19) - (1629086920732695145629274)/(6725336398294325143234770225)*a^(18) + (130298076682008554063159302)/(114330718771003527434991093825)*a^(17) - (435945493756580082910170332)/(114330718771003527434991093825)*a^(16) + (199577852900204369602438217)/(22866143754200705486998218765)*a^(15) - (1208546316779165200129486226)/(114330718771003527434991093825)*a^(14) + (90220600420276500124881794)/(114330718771003527434991093825)*a^(13) + (225415119870803062167126196)/(4573228750840141097399643753)*a^(12) - (5299216655963995254461859208)/(38110239590334509144997031275)*a^(11) + (7753335231043511971070757281)/(114330718771003527434991093825)*a^(10) - (5769124218817504260672445907)/(114330718771003527434991093825)*a^(9) - (7162099138795929335779672348)/(12703413196778169714999010425)*a^(8) - (35988766441214632915695173398)/(114330718771003527434991093825)*a^(7) - (53480696175437398074839637823)/(38110239590334509144997031275)*a^(6) - (8068193861114017933817659553)/(6725336398294325143234770225)*a^(5) - (38116198227434414055975678427)/(22866143754200705486998218765)*a^(4) - (94705122195753483359531986748)/(38110239590334509144997031275)*a^(3) - (29371590083818365447340014446)/(22866143754200705486998218765)*a^(2) - (57908781843659847480474824536)/(38110239590334509144997031275)*a + (29844413801547239141535848)/(1411490355197574412777667825) , (922658497673013093644451601)/(1486299344023045856654884219725)*a^(19) - (81655035587041989045047533)/(17485874635565245372410402585)*a^(18) + (2384414933367274862685521342)/(114330718771003527434991093825)*a^(17) - (103280328590008120833260110744)/(1486299344023045856654884219725)*a^(16) + (230819037408073187933110500086)/(1486299344023045856654884219725)*a^(15) - (121063532727061058377577700473)/(495433114674348618884961406575)*a^(14) + (20070676912082840217410254613)/(99086622934869723776992281315)*a^(13) + (60702982368464939712340647913)/(114330718771003527434991093825)*a^(12) - (1677840498843243217719688275271)/(1486299344023045856654884219725)*a^(11) + (242136399839697529495413106379)/(99086622934869723776992281315)*a^(10) - (289962026330167791371866935368)/(1486299344023045856654884219725)*a^(9) + (587294645409731047045714975786)/(297259868804609171330976843945)*a^(8) + (6169697411196323021496808545542)/(1486299344023045856654884219725)*a^(7) - (21836431556913961986513830185)/(4573228750840141097399643753)*a^(6) + (298649752370531842751749909309)/(29143124392608742287350670975)*a^(5) - (12939096174586401274014477706019)/(1486299344023045856654884219725)*a^(4) + (3260244506763975225457186803964)/(297259868804609171330976843945)*a^(3) - (9109612845270426753040299235144)/(1486299344023045856654884219725)*a^(2) + (2366086868274350197166392290274)/(495433114674348618884961406575)*a - (11113798789073289380085334991)/(18349374617568467366109681725) , (345322366890042313257321119)/(1486299344023045856654884219725)*a^(19) - (177817804063634743546131617)/(87429373177826226862052012925)*a^(18) + (1080271734596297701782189122)/(114330718771003527434991093825)*a^(17) - (45947585275802990727586216936)/(1486299344023045856654884219725)*a^(16) + (19577961936615462587043093268)/(297259868804609171330976843945)*a^(15) - (109111417135658710978061063543)/(1486299344023045856654884219725)*a^(14) - (68867628539565539342982248773)/(1486299344023045856654884219725)*a^(13) + (274850053495306824487477868)/(508136527871126788599960417)*a^(12) - (1710012673906384794680545400072)/(1486299344023045856654884219725)*a^(11) + (1626456675656300952019788760898)/(1486299344023045856654884219725)*a^(10) + (491968261164674005933192423793)/(495433114674348618884961406575)*a^(9) - (5841096092770672221310696647806)/(1486299344023045856654884219725)*a^(8) + (2054012747042082187477635904487)/(495433114674348618884961406575)*a^(7) - (455907149164498832459164223954)/(114330718771003527434991093825)*a^(6) - (168902342775353856033127494344)/(87429373177826226862052012925)*a^(5) + (112928198433814692010284437752)/(33028874311623241258997427105)*a^(4) - (15975924519069541275920832256322)/(1486299344023045856654884219725)*a^(3) + (120297032665595135917698005648)/(19817324586973944755398456263)*a^(2) - (2231082149327199004584899937368)/(495433114674348618884961406575)*a + (27630003380581442731025634534)/(18349374617568467366109681725) , (7974150984616497571735454)/(1486299344023045856654884219725)*a^(19) - (10794394369431199532475124)/(87429373177826226862052012925)*a^(18) + (108107670245679921947144761)/(114330718771003527434991093825)*a^(17) - (7037439874025025636520776281)/(1486299344023045856654884219725)*a^(16) + (26015276554189464754892423206)/(1486299344023045856654884219725)*a^(15) - (942201981324733948438841815)/(19817324586973944755398456263)*a^(14) + (15939150902184809023944471826)/(165144371558116206294987135525)*a^(13) - (14511885997009216063575516202)/(114330718771003527434991093825)*a^(12) + (1736030833770993171464635103)/(297259868804609171330976843945)*a^(11) + (173963976991999194515550670532)/(495433114674348618884961406575)*a^(10) - (307241648669996311103567979104)/(297259868804609171330976843945)*a^(9) + (1741877070546721852296373106413)/(1486299344023045856654884219725)*a^(8) - (906637933825838823398220289901)/(1486299344023045856654884219725)*a^(7) - (183433921713703129856734345238)/(114330718771003527434991093825)*a^(6) + (26533465274427003992939606491)/(9714374797536247429116890325)*a^(5) - (4729969379861783250744754504024)/(1486299344023045856654884219725)*a^(4) + (6476781730173856048402237410196)/(1486299344023045856654884219725)*a^(3) - 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