/* 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^16 - 3*x^15 + 7*x^14 - 19*x^13 + 46*x^12 - 78*x^11 + 55*x^10 - 132*x^9 + 199*x^8 + 79*x^7 + 40*x^6 + 59*x^5 + 26*x^4 + 728*x^3 + 1273*x^2 + 659*x + 541, 16, 252, [0, 8], 2294177990240478515625, [3, 5, 29], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, 1/5*a^11 + 2/5*a^10 + 2/5*a^9 + 1/5*a^8 + 1/5*a^7 - 1/5*a^6 - 1/5*a^5 + 2/5*a^4 + 1/5*a^3 + 1/5*a^2 - 2/5*a + 2/5, 1/5*a^12 - 2/5*a^10 + 2/5*a^9 - 1/5*a^8 + 2/5*a^7 + 1/5*a^6 - 1/5*a^5 + 2/5*a^4 - 1/5*a^3 + 1/5*a^2 + 1/5*a + 1/5, 1/5*a^13 + 1/5*a^10 - 2/5*a^9 - 1/5*a^8 - 2/5*a^7 + 2/5*a^6 - 2/5*a^4 - 2/5*a^3 - 2/5*a^2 + 2/5*a - 1/5, 1/25*a^14 + 1/25*a^13 + 2/25*a^12 - 12/25*a^10 + 9/25*a^9 - 6/25*a^8 - 12/25*a^7 + 2/5*a^6 - 8/25*a^5 + 8/25*a^4 - 7/25*a^3 + 1/25*a^2 + 1/5*a - 11/25, 1/9770663281683072267775*a^15 + 90597681442201911296/9770663281683072267775*a^14 - 667384462946525359598/9770663281683072267775*a^13 + 189784150939862712007/1954132656336614453555*a^12 - 878919778291520712932/9770663281683072267775*a^11 + 2087436912086800354894/9770663281683072267775*a^10 - 1894788141106569146361/9770663281683072267775*a^9 + 2787986767801684757498/9770663281683072267775*a^8 - 11516975402988302369/1954132656336614453555*a^7 + 3994947058833607149267/9770663281683072267775*a^6 + 1956786331371084593773/9770663281683072267775*a^5 - 1711576079360032404632/9770663281683072267775*a^4 - 1644202407677464601789/9770663281683072267775*a^3 - 919899251075158275047/1954132656336614453555*a^2 + 106947854799349048464/315182686505905557025*a - 549652896820257125439/1954132656336614453555], 0, 4, [2, 2], 0, [ (196956895747)/(142623634607275)*a^(15) - (851232556477)/(142623634607275)*a^(14) + (418423802757)/(28524726921455)*a^(13) - (5186504291033)/(142623634607275)*a^(12) + (13208446275606)/(142623634607275)*a^(11) - (25677709131639)/(142623634607275)*a^(10) + (26946821453642)/(142623634607275)*a^(9) - (6378246767381)/(28524726921455)*a^(8) + (67588934868528)/(142623634607275)*a^(7) - (39404385511816)/(142623634607275)*a^(6) - (31792439440367)/(142623634607275)*a^(5) + (24593112320769)/(142623634607275)*a^(4) - (1009140356722)/(28524726921455)*a^(3) + (134495773280741)/(142623634607275)*a^(2) + (31116610182768)/(142623634607275)*a - (35546078503196)/(142623634607275) , (21156380952787669738)/(9770663281683072267775)*a^(15) - (62359968253001784662)/(9770663281683072267775)*a^(14) + (143346267518245637451)/(9770663281683072267775)*a^(13) - (15581422992065194168)/(390826531267322890711)*a^(12) + (948368577316555585584)/(9770663281683072267775)*a^(11) - (1615516971194984514403)/(9770663281683072267775)*a^(10) + (1097078100518539439552)/(9770663281683072267775)*a^(9) - (2762564243514058995866)/(9770663281683072267775)*a^(8) + (876953692289514416729)/(1954132656336614453555)*a^(7) + (1394775008079383962381)/(9770663281683072267775)*a^(6) + (782771832772442435439)/(9770663281683072267775)*a^(5) + (2984688391602893564364)/(9770663281683072267775)*a^(4) + (1138183674353901826328)/(9770663281683072267775)*a^(3) + (3022523773069376662401)/(1954132656336614453555)*a^(2) + (591196935031713335642)/(315182686505905557025)*a + (1899730188297776649626)/(1954132656336614453555) , (2535354322283547772)/(9770663281683072267775)*a^(15) - (1703271362274709642)/(9770663281683072267775)*a^(14) - (3026352596315994548)/(1954132656336614453555)*a^(13) + (48195239444577239502)/(9770663281683072267775)*a^(12) - (132890199824681731419)/(9770663281683072267775)*a^(11) + (430275220673758905076)/(9770663281683072267775)*a^(10) - (1187726876362045468793)/(9770663281683072267775)*a^(9) + (308082097416394707111)/(1954132656336614453555)*a^(8) - (1670417503352837802442)/(9770663281683072267775)*a^(7) + (3359060316881458359454)/(9770663281683072267775)*a^(6) - (2246021805133577331287)/(9770663281683072267775)*a^(5) - (1532840381658874360826)/(9770663281683072267775)*a^(4) + (123948728713171730598)/(390826531267322890711)*a^(3) - (1754239585206532428539)/(9770663281683072267775)*a^(2) + (433906503119175983023)/(315182686505905557025)*a - (4878240757578001425556)/(9770663281683072267775) , (4738347055014243502)/(1954132656336614453555)*a^(15) - (64063239615276494304)/(9770663281683072267775)*a^(14) + (128214504536665664711)/(9770663281683072267775)*a^(13) - (341340335357052614698)/(9770663281683072267775)*a^(12) + (163095675498374770833)/(1954132656336614453555)*a^(11) - (1185241750521225609327)/(9770663281683072267775)*a^(10) - (90648775843506029241)/(9770663281683072267775)*a^(9) - (1222153756432085460311)/(9770663281683072267775)*a^(8) + (2714350958094734281203)/(9770663281683072267775)*a^(7) + (950767064992168464367)/(1954132656336614453555)*a^(6) - (1463249972361134895848)/(9770663281683072267775)*a^(5) + (1451848009944019203538)/(9770663281683072267775)*a^(4) + (4236901892183195091278)/(9770663281683072267775)*a^(3) + (13358379280140350883466)/(9770663281683072267775)*a^(2) + (205020687630177863733)/(63036537301181111405)*a + (14391073465593954090349)/(9770663281683072267775) , (7191123749120873053)/(9770663281683072267775)*a^(15) - (19694619556002051282)/(9770663281683072267775)*a^(14) + (31679321138787114691)/(9770663281683072267775)*a^(13) - (15731064961163786859)/(1954132656336614453555)*a^(12) + (208975944033900844724)/(9770663281683072267775)*a^(11) - (263565068429719584838)/(9770663281683072267775)*a^(10) - (250597961385972605878)/(9770663281683072267775)*a^(9) - (30169853507564654436)/(9770663281683072267775)*a^(8) + (207503201213491623349)/(1954132656336614453555)*a^(7) + (1070075384299394801681)/(9770663281683072267775)*a^(6) - (1644788673407075792206)/(9770663281683072267775)*a^(5) - (327856241281587717346)/(9770663281683072267775)*a^(4) + (1091583526344123741468)/(9770663281683072267775)*a^(3) + (155157054979063341641)/(390826531267322890711)*a^(2) + (344374005565433570927)/(315182686505905557025)*a + (908070255454608388592)/(1954132656336614453555) , (28127142708410555576)/(9770663281683072267775)*a^(15) - (120939559009849136283)/(9770663281683072267775)*a^(14) + (302359110088632448203)/(9770663281683072267775)*a^(13) - (770045518351978136353)/(9770663281683072267775)*a^(12) + (1940167292175707114258)/(9770663281683072267775)*a^(11) - (3776189297965438915388)/(9770663281683072267775)*a^(10) + (4136265671573048269588)/(9770663281683072267775)*a^(9) - (5219613840806957668688)/(9770663281683072267775)*a^(8) + (10101841203532811317698)/(9770663281683072267775)*a^(7) - (5164156502175606420208)/(9770663281683072267775)*a^(6) - (469770142298596936576)/(1954132656336614453555)*a^(5) + (628582838086181772321)/(9770663281683072267775)*a^(4) + (3526085133428629932224)/(9770663281683072267775)*a^(3) + (16403680352603443341311)/(9770663281683072267775)*a^(2) + (197312837991808124419)/(315182686505905557025)*a - (35702283532188396993756)/(9770663281683072267775) , (622765056597504562)/(9770663281683072267775)*a^(15) - (11045926945715127199)/(9770663281683072267775)*a^(14) + (29436995089388861018)/(9770663281683072267775)*a^(13) - (65560087388373284112)/(9770663281683072267775)*a^(12) + (151491655360940173361)/(9770663281683072267775)*a^(11) - (67828949563317658523)/(1954132656336614453555)*a^(10) + (427121746203373341349)/(9770663281683072267775)*a^(9) + (156381621655093658312)/(9770663281683072267775)*a^(8) - (13670533574512804458)/(9770663281683072267775)*a^(7) + (203541151103559843209)/(9770663281683072267775)*a^(6) - (2143801653827085653481)/(9770663281683072267775)*a^(5) + (3143661655324210181698)/(9770663281683072267775)*a^(4) - (3654731683551349151551)/(9770663281683072267775)*a^(3) + (143139441468912625679)/(9770663281683072267775)*a^(2) - (67461811389158073717)/(315182686505905557025)*a - (5228411048260888220714)/(9770663281683072267775) ], 2578.17931228, [[x^2 - x - 1, 1], [x^4 - x^3 - 4*x^2 + 4*x + 1, 1], [x^8 - x^7 + 17*x^6 + 2*x^5 + 100*x^4 + 58*x^3 + 332*x^2 + 91*x + 241, 1], [x^8 - x^7 + 2*x^6 + 2*x^5 - 5*x^4 + 13*x^3 - 13*x^2 + x + 1, 1], [x^8 - x^7 + x^6 + 4*x^5 - 9*x^4 - 10*x^3 - 20*x^2 - 20*x - 5, 1]]]