/* 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 - 4*x^15 + 4*x^14 - 24*x^13 + 62*x^12 - 220*x^11 + 300*x^10 - 732*x^9 + 851*x^8 + 36*x^7 - 220*x^6 - 788*x^5 + 552*x^4 + 1192*x^3 + 1208*x^2 + 660*x + 121, 16, 799, [4, 6], 62019327754240000000000, [2, 5, 19], [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, 1/179*a^14 + 23/179*a^13 - 86/179*a^12 - 83/179*a^11 + 76/179*a^10 - 15/179*a^9 - 83/179*a^8 - 5/179*a^7 - 57/179*a^6 + 83/179*a^5 - 54/179*a^4 - 41/179*a^3 + 70/179*a^2 + 13/179*a - 60/179, 1/134649745112255363682967297*a^15 + 15419481657047592971909/134649745112255363682967297*a^14 - 56958795750569214576877381/134649745112255363682967297*a^13 + 45919246215476089422403567/134649745112255363682967297*a^12 + 9624619039235876863593589/134649745112255363682967297*a^11 + 3909282912498808090787417/12240885919295942152997027*a^10 + 46345286975823437262665821/134649745112255363682967297*a^9 + 65747504507688178632442859/134649745112255363682967297*a^8 + 41557460792313171014573004/134649745112255363682967297*a^7 + 8660125581071806411867146/134649745112255363682967297*a^6 + 539851088893449544159006/12240885919295942152997027*a^5 - 526000237792060958962848/2282199069699243452253683*a^4 + 29148887457046730528242925/134649745112255363682967297*a^3 - 39210499208188415076376645/134649745112255363682967297*a^2 - 27751160762151170760469055/134649745112255363682967297*a + 968907266702276821206350/12240885919295942152997027], 0, 1, [], 1, [ (2965742677561089655016)/(2282199069699243452253683)*a^(15) - (8329703192294106189496)/(2282199069699243452253683)*a^(14) - (4394126656505823286318)/(2282199069699243452253683)*a^(13) - (47593850872832950457181)/(2282199069699243452253683)*a^(12) + (85335102743474968145382)/(2282199069699243452253683)*a^(11) - (34000898106965250639870)/(207472642699931222932153)*a^(10) - (44431151424004736924732)/(2282199069699243452253683)*a^(9) - (553562038025578932586641)/(2282199069699243452253683)*a^(8) - (968499201325132929237758)/(2282199069699243452253683)*a^(7) + (5228157989397237960033066)/(2282199069699243452253683)*a^(6) - (291528157776845747058148)/(207472642699931222932153)*a^(5) - (1557701439268222835160700)/(2282199069699243452253683)*a^(4) - (1008584057123864221407646)/(2282199069699243452253683)*a^(3) + (6606026535332314781993550)/(2282199069699243452253683)*a^(2) + (6343589193846892966137134)/(2282199069699243452253683)*a + (386970572666729059235965)/(207472642699931222932153) , (3554108504057596383092646)/(134649745112255363682967297)*a^(15) - (15782058923496852766294948)/(134649745112255363682967297)*a^(14) + (21280615362610186161075237)/(134649745112255363682967297)*a^(13) - (95081848041727395494463589)/(134649745112255363682967297)*a^(12) + (262457071849916212479202659)/(134649745112255363682967297)*a^(11) - (81783901753649332689799702)/(12240885919295942152997027)*a^(10) + (1467832371640133794686685682)/(134649745112255363682967297)*a^(9) - (3268455088938252843242243043)/(134649745112255363682967297)*a^(8) + (4481658187606694249881191877)/(134649745112255363682967297)*a^(7) - (1895318103633704098172427667)/(134649745112255363682967297)*a^(6) + (6611378925472389439731418)/(12240885919295942152997027)*a^(5) - (46192982565634289432424431)/(2282199069699243452253683)*a^(4) + (2993599092145132434177141457)/(134649745112255363682967297)*a^(3) + (2858276309005127050479856256)/(134649745112255363682967297)*a^(2) + (3125361841117675970292781275)/(134649745112255363682967297)*a + (102395279148237306000460446)/(12240885919295942152997027) , (1274094906882002099414680)/(134649745112255363682967297)*a^(15) - (5911650545404477877453474)/(134649745112255363682967297)*a^(14) + (8553993727694800345274129)/(134649745112255363682967297)*a^(13) - (34603305431199820421024612)/(134649745112255363682967297)*a^(12) + (99365427962916973371419101)/(134649745112255363682967297)*a^(11) - (30531060629369799563704603)/(12240885919295942152997027)*a^(10) + (573714500054110189119250044)/(134649745112255363682967297)*a^(9) - (1222345281042225036521213568)/(134649745112255363682967297)*a^(8) + (1740390774546564557267653343)/(134649745112255363682967297)*a^(7) - (811264738152809111594127830)/(134649745112255363682967297)*a^(6) - (11603069492570681419914338)/(12240885919295942152997027)*a^(5) - (15413629583421226232441965)/(2282199069699243452253683)*a^(4) + (1392889538326808805413039075)/(134649745112255363682967297)*a^(3) + (805158088892075372447476001)/(134649745112255363682967297)*a^(2) + (762357844176374352353129583)/(134649745112255363682967297)*a + (13121982945485766860980641)/(12240885919295942152997027) , (3729087322033700672738590)/(134649745112255363682967297)*a^(15) - (16273511411842205031475212)/(134649745112255363682967297)*a^(14) + (21021361889876342587182475)/(134649745112255363682967297)*a^(13) - (97889885243224539571437268)/(134649745112255363682967297)*a^(12) + (267491842911781235599780197)/(134649745112255363682967297)*a^(11) - (83789954741960282477552032)/(12240885919295942152997027)*a^(10) + (1465210933706117515208126494)/(134649745112255363682967297)*a^(9) - (3301115249181762000264854862)/(134649745112255363682967297)*a^(8) + (4424516734728511407056164155)/(134649745112255363682967297)*a^(7) - (1586856782259267058530476773)/(134649745112255363682967297)*a^(6) - (10588782383361509636699314)/(12240885919295942152997027)*a^(5) - (47750684004902512267585131)/(2282199069699243452253683)*a^(4) + (2934092632774824445114090343)/(134649745112255363682967297)*a^(3) + (3248031874589733622617475706)/(134649745112255363682967297)*a^(2) + (3499633603554642655294872181)/(134649745112255363682967297)*a + (125226542935574320495382381)/(12240885919295942152997027) , (1559438910065710130452361)/(134649745112255363682967297)*a^(15) - (6887990872190350498695230)/(134649745112255363682967297)*a^(14) + (9313570891739870233127332)/(134649745112255363682967297)*a^(13) - (42193938970996204939006004)/(134649745112255363682967297)*a^(12) + (115364140669300668589504301)/(134649745112255363682967297)*a^(11) - (36029494609808161672402861)/(12240885919295942152997027)*a^(10) + (647492868871820015082039549)/(134649745112255363682967297)*a^(9) - (1460876044382610055674021412)/(134649745112255363682967297)*a^(8) + (2011753136182946599719378763)/(134649745112255363682967297)*a^(7) - (952379199896321088755740758)/(134649745112255363682967297)*a^(6) + (25702156683837626183291791)/(12240885919295942152997027)*a^(5) - (24006795447316659932322618)/(2282199069699243452253683)*a^(4) + (1378236602307732626934210038)/(134649745112255363682967297)*a^(3) + (1156178790721359186603473224)/(134649745112255363682967297)*a^(2) + (1567546242401226407658293961)/(134649745112255363682967297)*a + (50983706901197437914478483)/(12240885919295942152997027) , (321206137995477493688)/(207472642699931222932153)*a^(15) - (1477917942431834718762)/(207472642699931222932153)*a^(14) + (2143997580784836478473)/(207472642699931222932153)*a^(13) - (8958267569573871860510)/(207472642699931222932153)*a^(12) + (25313955444256542460450)/(207472642699931222932153)*a^(11) - (7720280617291996970492)/(18861149336357383902923)*a^(10) + (147032872904467154080461)/(207472642699931222932153)*a^(9) - (317486019993601838696034)/(207472642699931222932153)*a^(8) + (465581023000458066586590)/(207472642699931222932153)*a^(7) - (232213304225623953957828)/(207472642699931222932153)*a^(6) + (6440527195453849694148)/(18861149336357383902923)*a^(5) - (240515819557962337361498)/(207472642699931222932153)*a^(4) + (279169205789045083019498)/(207472642699931222932153)*a^(3) + (250997458123008787534346)/(207472642699931222932153)*a^(2) + (416498654712994902867158)/(207472642699931222932153)*a + (15895406658796294247907)/(18861149336357383902923) , (9907895993153557833462060)/(134649745112255363682967297)*a^(15) - (43371830727349928068426278)/(134649745112255363682967297)*a^(14) + (55938092765514522384451879)/(134649745112255363682967297)*a^(13) - (258578789461265103364768705)/(134649745112255363682967297)*a^(12) + (711065289657486151575999970)/(134649745112255363682967297)*a^(11) - (222303727261968261179876647)/(12240885919295942152997027)*a^(10) + (3889667925972326131965977335)/(134649745112255363682967297)*a^(9) - (8695264757094221854531833283)/(134649745112255363682967297)*a^(8) + (11667609544979106970610376629)/(134649745112255363682967297)*a^(7) - (3925549996186841620547751937)/(134649745112255363682967297)*a^(6) - (76098336776331167710812524)/(12240885919295942152997027)*a^(5) - (122966309253371779175256882)/(2282199069699243452253683)*a^(4) + (8175832949561680548368231457)/(134649745112255363682967297)*a^(3) + (8646097615680424008981664338)/(134649745112255363682967297)*a^(2) + (8666444488771806396678350224)/(134649745112255363682967297)*a + (319705950196859542440351208)/(12240885919295942152997027) , (6880935118319571097248183)/(134649745112255363682967297)*a^(15) - (30382767840034475011228789)/(134649745112255363682967297)*a^(14) + (39969481250294895477932482)/(134649745112255363682967297)*a^(13) - (181158197949684546198716401)/(134649745112255363682967297)*a^(12) + (501997452438513719430399632)/(134649745112255363682967297)*a^(11) - (156369124136140989326414254)/(12240885919295942152997027)*a^(10) + (2772170631018325890966174633)/(134649745112255363682967297)*a^(9) - (6164167963538980312751382548)/(134649745112255363682967297)*a^(8) + (8414658566445724648256889416)/(134649745112255363682967297)*a^(7) - (3223566512282299254446490242)/(134649745112255363682967297)*a^(6) - (11666362109953079546145453)/(12240885919295942152997027)*a^(5) - (96750285593039380615396360)/(2282199069699243452253683)*a^(4) + (6474156520248357821381160403)/(134649745112255363682967297)*a^(3) + (5749700972747406393506595921)/(134649745112255363682967297)*a^(2) + (5762169606167582627129712067)/(134649745112255363682967297)*a + (144841476281416724010450398)/(12240885919295942152997027) , (5778092678346894735270334)/(134649745112255363682967297)*a^(15) - (18114389288552134933319966)/(134649745112255363682967297)*a^(14) - (1951075674428492578154286)/(134649745112255363682967297)*a^(13) - (99693446921346005479807996)/(134649745112255363682967297)*a^(12) + (226662515479780720581750959)/(134649745112255363682967297)*a^(11) - (78130711518952665211928760)/(12240885919295942152997027)*a^(10) + (366045854475556225076533161)/(134649745112255363682967297)*a^(9) - (1773704775290697037297408830)/(134649745112255363682967297)*a^(8) + (244900709899758851942048651)/(134649745112255363682967297)*a^(7) + (39180697367729954573011324)/(752233212917627730072443)*a^(6) - (306471941051922238951219523)/(12240885919295942152997027)*a^(5) - (157590826116290203579083006)/(2282199069699243452253683)*a^(4) + (3104575620656845493173571650)/(134649745112255363682967297)*a^(3) + (14842577646863156389034074735)/(134649745112255363682967297)*a^(2) + (8223947605027176460794926795)/(134649745112255363682967297)*a + (120699569541362274234859397)/(12240885919295942152997027) ], 123599.450849, [[x^2 - 2, 1], [x^2 - x - 1, 1], [x^2 - 10, 1], [x^4 - x^2 - 1, 1], [x^4 - 2*x^2 - 4, 1], [x^4 - 6*x^2 + 4, 1], [x^8 - 4*x^6 + 7*x^4 - 6*x^2 + 1, 1]]]