/* 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 + 6*x^14 - 12*x^13 + 5*x^12 + 12*x^11 - 2*x^10 - 74*x^9 + 223*x^8 - 360*x^7 + 432*x^6 - 504*x^5 + 548*x^4 - 464*x^3 + 272*x^2 - 96*x + 16, 16, 1553, [0, 8], 157416167833600000000, [2, 5, 13, 29], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, 1/2*a^10 - 1/2*a^6 - 1/2*a^2, 1/2*a^11 - 1/2*a^7 - 1/2*a^3, 1/4*a^12 + 1/4*a^8 - 1/2*a^7 - 1/2*a^5 - 1/4*a^4 - 1/2*a^3 - 1/2*a^2, 1/8*a^13 + 1/8*a^9 - 1/4*a^8 - 1/2*a^7 - 1/4*a^6 - 1/8*a^5 + 1/4*a^4 + 1/4*a^3 - 1/2*a^2 - 1/2*a, 1/8*a^14 + 1/8*a^10 - 1/4*a^9 - 1/2*a^8 - 1/4*a^7 - 1/8*a^6 + 1/4*a^5 + 1/4*a^4 - 1/2*a^3 - 1/2*a^2, 1/349519026352*a^15 + 3198020747/174759513176*a^14 + 9126055723/174759513176*a^13 - 2005249531/43689878294*a^12 - 36875631911/349519026352*a^11 + 3794332693/87379756588*a^10 + 46568871031/174759513176*a^9 - 57494818107/174759513176*a^8 + 124205160155/349519026352*a^7 + 12158552293/43689878294*a^6 - 15880691359/43689878294*a^5 + 14269108655/87379756588*a^4 + 19345045631/43689878294*a^3 - 6637424582/21844939147*a^2 - 6290917317/43689878294*a + 1861989776/21844939147], 0, 1, [], 0, [ (13575659101)/(87379756588)*a^(15) - (22011766923)/(87379756588)*a^(14) + (38384192091)/(43689878294)*a^(13) - (67790770139)/(43689878294)*a^(12) + (32885156881)/(87379756588)*a^(11) + (159135469221)/(87379756588)*a^(10) + (3447434000)/(21844939147)*a^(9) - (241524572151)/(21844939147)*a^(8) + (2716698251445)/(87379756588)*a^(7) - (4076400711961)/(87379756588)*a^(6) + (2378484403553)/(43689878294)*a^(5) - (1371437386015)/(21844939147)*a^(4) + (1464263354823)/(21844939147)*a^(3) - (2371136667267)/(43689878294)*a^(2) + (603200970805)/(21844939147)*a - (141721104574)/(21844939147) , (27282837511)/(349519026352)*a^(15) - (18512739485)/(174759513176)*a^(14) + (33393408109)/(87379756588)*a^(13) - (62749312447)/(87379756588)*a^(12) - (58171568729)/(349519026352)*a^(11) + (16121718295)/(21844939147)*a^(10) + (39294624417)/(87379756588)*a^(9) - (945675439457)/(174759513176)*a^(8) + (4770803291181)/(349519026352)*a^(7) - (410089787191)/(21844939147)*a^(6) + (3659398325991)/(174759513176)*a^(5) - (2328941821555)/(87379756588)*a^(4) + (2253452574575)/(87379756588)*a^(3) - (876485292493)/(43689878294)*a^(2) + (221907993485)/(21844939147)*a - (62592589752)/(21844939147) , (4413677441)/(87379756588)*a^(15) - (10285431405)/(87379756588)*a^(14) + (9247000110)/(21844939147)*a^(13) - (61361744421)/(87379756588)*a^(12) + (70941691763)/(87379756588)*a^(11) + (27408454917)/(87379756588)*a^(10) - (45162620907)/(43689878294)*a^(9) - (287716666227)/(87379756588)*a^(8) + (1235661023681)/(87379756588)*a^(7) - (2311936381849)/(87379756588)*a^(6) + (1540925397353)/(43689878294)*a^(5) - (3311746376489)/(87379756588)*a^(4) + (925328455074)/(21844939147)*a^(3) - (1847818454745)/(43689878294)*a^(2) + (556224184469)/(21844939147)*a - (158539709630)/(21844939147) , (5913193161)/(21844939147)*a^(15) - (31121888325)/(174759513176)*a^(14) + (197547460165)/(174759513176)*a^(13) - (128008851885)/(87379756588)*a^(12) - (38279036327)/(21844939147)*a^(11) + (471999486703)/(174759513176)*a^(10) + (725021621799)/(174759513176)*a^(9) - (383499141659)/(21844939147)*a^(8) + (2963409088081)/(87379756588)*a^(7) - (5950752277449)/(174759513176)*a^(6) + (5735955066773)/(174759513176)*a^(5) - (4116106354319)/(87379756588)*a^(4) + (3498436446853)/(87379756588)*a^(3) - (296297182151)/(21844939147)*a^(2) - (79459948781)/(43689878294)*a + (42132767676)/(21844939147) , (28823985875)/(174759513176)*a^(15) - (43349722643)/(174759513176)*a^(14) + (73290810077)/(87379756588)*a^(13) - (134694975411)/(87379756588)*a^(12) - (11827385593)/(174759513176)*a^(11) + (370835583715)/(174759513176)*a^(10) + (37719648767)/(43689878294)*a^(9) - (524524148205)/(43689878294)*a^(8) + (5339087779499)/(174759513176)*a^(7) - (7440347023863)/(174759513176)*a^(6) + (4033607890525)/(87379756588)*a^(5) - (1212717987561)/(21844939147)*a^(4) + (2529823575267)/(43689878294)*a^(3) - (1813713079379)/(43689878294)*a^(2) + (417224102333)/(21844939147)*a - (83895122594)/(21844939147) , (285587332863)/(349519026352)*a^(15) - (171028128791)/(174759513176)*a^(14) + (87953833584)/(21844939147)*a^(13) - (570874107143)/(87379756588)*a^(12) - (553646226777)/(349519026352)*a^(11) + (779329235637)/(87379756588)*a^(10) + (258667912703)/(43689878294)*a^(9) - (9877262702533)/(174759513176)*a^(8) + (47408530792805)/(349519026352)*a^(7) - (15710843055847)/(87379756588)*a^(6) + (34502464910725)/(174759513176)*a^(5) - (21106828299227)/(87379756588)*a^(4) + (21048151293159)/(87379756588)*a^(3) - (3711969054728)/(21844939147)*a^(2) + (1557971986648)/(21844939147)*a - (318434838633)/(21844939147) , (24990300817)/(174759513176)*a^(15) - (20865664853)/(87379756588)*a^(14) + (96867853343)/(174759513176)*a^(13) - (58551633277)/(43689878294)*a^(12) - (116310374483)/(174759513176)*a^(11) + (64038799953)/(21844939147)*a^(10) + (353354337215)/(174759513176)*a^(9) - (542493869433)/(43689878294)*a^(8) + (4272434396923)/(174759513176)*a^(7) - (2474042393611)/(87379756588)*a^(6) + (3853338746775)/(174759513176)*a^(5) - (2768838984447)/(87379756588)*a^(4) + (3165520042555)/(87379756588)*a^(3) - (200707002683)/(21844939147)*a^(2) - (210959633567)/(43689878294)*a + (11830332386)/(21844939147) ], 5053.51427492, [[x^2 - x - 1, 1], [x^4 - x^2 - 1, 1], [x^8 - 2*x^7 + 2*x^6 - 4*x^5 + 16*x^4 - 28*x^3 + 28*x^2 - 16*x + 4, 1]]]