/* 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 - 2*x^15 + 2*x^14 - x^13 - 12*x^12 - 18*x^11 + 113*x^10 - 178*x^9 + 279*x^8 - 90*x^7 - 190*x^6 - 289*x^5 + 578*x^4 - 457*x^3 + 606*x^2 - 396*x + 81, 16, 675, [0, 8], 39930996351612609453125, [5, 59], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/3*a^9 - 1/3*a^7 + 1/3*a^5 + 1/3*a^3 + 1/3*a, 1/3*a^10 - 1/3*a^8 + 1/3*a^6 + 1/3*a^4 + 1/3*a^2, 1/3*a^11 - 1/3*a^5 - 1/3*a^3 + 1/3*a, 1/3*a^12 - 1/3*a^6 - 1/3*a^4 + 1/3*a^2, 1/3*a^13 - 1/3*a^7 - 1/3*a^5 + 1/3*a^3, 1/45*a^14 - 2/15*a^13 + 2/45*a^12 - 1/15*a^9 + 4/9*a^8 - 7/15*a^7 - 4/15*a^6 - 2/5*a^5 + 1/9*a^4 + 1/15*a^3 + 11/45*a^2 - 2/5*a + 1/5, 1/23022704005324155*a^15 + 6118614445979/2558078222813795*a^14 + 89622963393031/4604540801064831*a^13 + 329872151979661/2558078222813795*a^12 + 21804027292676/1534846933688277*a^11 + 326999140210904/7674234668441385*a^10 - 3222883301852011/23022704005324155*a^9 - 231886256307139/2558078222813795*a^8 + 15331085009039/2558078222813795*a^7 + 2942887117739161/7674234668441385*a^6 + 39620328552929/23022704005324155*a^5 + 1090353183796337/2558078222813795*a^4 - 6363241788458443/23022704005324155*a^3 - 1041182199292164/2558078222813795*a^2 + 2460584559086276/7674234668441385*a - 982689252628238/2558078222813795], 0, 3, [3], 1, [ (98887491888224)/(4604540801064831)*a^(15) - (200946628810435)/(4604540801064831)*a^(14) + (142649503440988)/(4604540801064831)*a^(13) - (73180294933553)/(4604540801064831)*a^(12) - (137142006726441)/(511615644562759)*a^(11) - (194473064266500)/(511615644562759)*a^(10) + (11949201001062322)/(4604540801064831)*a^(9) - (15735367610566016)/(4604540801064831)*a^(8) + (8074718192339855)/(1534846933688277)*a^(7) - (1924008754969879)/(1534846933688277)*a^(6) - (28393857722546276)/(4604540801064831)*a^(5) - (37469308821907478)/(4604540801064831)*a^(4) + (56801899786571314)/(4604540801064831)*a^(3) - (23171092458716207)/(4604540801064831)*a^(2) + (20198836219127872)/(1534846933688277)*a - (2690546812943842)/(511615644562759) , (468558164821594)/(23022704005324155)*a^(15) - (563322582633001)/(23022704005324155)*a^(14) + (94228265999848)/(4604540801064831)*a^(13) + (26921332357261)/(23022704005324155)*a^(12) - (124146809239379)/(511615644562759)*a^(11) - (4298610760948079)/(7674234668441385)*a^(10) + (42992949277846661)/(23022704005324155)*a^(9) - (49711289821394279)/(23022704005324155)*a^(8) + (9479851693365226)/(2558078222813795)*a^(7) + (10434022082771594)/(7674234668441385)*a^(6) - (67188418289053399)/(23022704005324155)*a^(5) - (183922573942402733)/(23022704005324155)*a^(4) + (152913276235913063)/(23022704005324155)*a^(3) - (78911585924045324)/(23022704005324155)*a^(2) + (60477114948644929)/(7674234668441385)*a - (7799887488042772)/(2558078222813795) , (468558164821594)/(23022704005324155)*a^(15) - (563322582633001)/(23022704005324155)*a^(14) + (94228265999848)/(4604540801064831)*a^(13) + (26921332357261)/(23022704005324155)*a^(12) - (124146809239379)/(511615644562759)*a^(11) - (4298610760948079)/(7674234668441385)*a^(10) + (42992949277846661)/(23022704005324155)*a^(9) - (49711289821394279)/(23022704005324155)*a^(8) + (9479851693365226)/(2558078222813795)*a^(7) + (10434022082771594)/(7674234668441385)*a^(6) - (67188418289053399)/(23022704005324155)*a^(5) - (183922573942402733)/(23022704005324155)*a^(4) + (152913276235913063)/(23022704005324155)*a^(3) - (78911585924045324)/(23022704005324155)*a^(2) + (60477114948644929)/(7674234668441385)*a - (5241809265228977)/(2558078222813795) , (128651483568617)/(7674234668441385)*a^(15) - (88667344734167)/(2558078222813795)*a^(14) + (286752579406163)/(7674234668441385)*a^(13) - (117261744550898)/(7674234668441385)*a^(12) - (324959389205969)/(1534846933688277)*a^(11) - (2147181718354451)/(7674234668441385)*a^(10) + (14570024721285892)/(7674234668441385)*a^(9) - (24784377852056227)/(7674234668441385)*a^(8) + (7583966006870596)/(1534846933688277)*a^(7) - (3127448504095771)/(2558078222813795)*a^(6) - (29424833764404128)/(7674234668441385)*a^(5) - (8385990680820208)/(2558078222813795)*a^(4) + (5013038087204355)/(511615644562759)*a^(3) - (16415335774938041)/(1534846933688277)*a^(2) + (13799728566104356)/(1534846933688277)*a - (6337069639722497)/(2558078222813795) , (76655971139469)/(2558078222813795)*a^(15) - (365492614017637)/(7674234668441385)*a^(14) + (104680197756688)/(2558078222813795)*a^(13) - (7394582284675)/(511615644562759)*a^(12) - (556743466672729)/(1534846933688277)*a^(11) - (1751775638668117)/(2558078222813795)*a^(10) + (1589261734781376)/(511615644562759)*a^(9) - (31185555248811677)/(7674234668441385)*a^(8) + (17304435648089577)/(2558078222813795)*a^(7) - (649004848431596)/(7674234668441385)*a^(6) - (8559212907896942)/(1534846933688277)*a^(5) - (84990480095616229)/(7674234668441385)*a^(4) + (97930320448213757)/(7674234668441385)*a^(3) - (21627995055174237)/(2558078222813795)*a^(2) + (114321946509643588)/(7674234668441385)*a - (3052347110734763)/(511615644562759) , (13261901446916)/(4604540801064831)*a^(15) - (164454795484252)/(23022704005324155)*a^(14) + (62623814874737)/(23022704005324155)*a^(13) - (2027402526419)/(23022704005324155)*a^(12) - (59291839196833)/(1534846933688277)*a^(11) - (53504269939993)/(1534846933688277)*a^(10) + (9518644645094291)/(23022704005324155)*a^(9) - (2315899788678400)/(4604540801064831)*a^(8) + (4799778944894504)/(7674234668441385)*a^(7) - (812036991597727)/(7674234668441385)*a^(6) - (35764807191235954)/(23022704005324155)*a^(5) - (4471553500847530)/(4604540801064831)*a^(4) + (63099805149519269)/(23022704005324155)*a^(3) - (27447446923686587)/(23022704005324155)*a^(2) + (18612636843618347)/(7674234668441385)*a - (2683262681051672)/(2558078222813795) , (180940876472839)/(4604540801064831)*a^(15) - (380721073313413)/(7674234668441385)*a^(14) + (896658693966139)/(23022704005324155)*a^(13) - (103146255065786)/(7674234668441385)*a^(12) - (251571638319558)/(511615644562759)*a^(11) - (1653430037728366)/(1534846933688277)*a^(10) + (84652130684034262)/(23022704005324155)*a^(9) - (6350314228412458)/(1534846933688277)*a^(8) + (61055546858159228)/(7674234668441385)*a^(7) + (20584433408271716)/(7674234668441385)*a^(6) - (137367632455712993)/(23022704005324155)*a^(5) - (25574377665686143)/(1534846933688277)*a^(4) + (211946349905562988)/(23022704005324155)*a^(3) - (90747306852484313)/(7674234668441385)*a^(2) + (109532271440748044)/(7674234668441385)*a - (10385407687350119)/(2558078222813795) ], 98285.3111503, [[x^2 - x + 15, 1], [x^4 - 2*x^3 + x + 15, 1], [x^8 - 4*x^7 + 5*x^6 - x^5 + 11*x^4 - 25*x^3 + 14*x^2 - x + 1, 1]]]