/* 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 + 3*x^14 - x^13 + 2*x^12 - 8*x^11 + 14*x^10 - 18*x^9 + 29*x^8 - 49*x^7 + 66*x^6 - 71*x^5 + 57*x^4 - 33*x^3 + 17*x^2 - 6*x + 1, 16, 388, [0, 8], 36005299687890625, [5, 19, 29], [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, a^14, 1/12651607*a^15 + 31251/12651607*a^14 + 2545018/12651607*a^13 + 1339362/12651607*a^12 - 3747613/12651607*a^11 + 680896/12651607*a^10 + 720624/12651607*a^9 + 2522018/12651607*a^8 + 3638991/12651607*a^7 - 4922265/12651607*a^6 + 3070876/12651607*a^5 + 2067731/12651607*a^4 + 456175/12651607*a^3 - 1067672/12651607*a^2 + 5918595/12651607*a + 622177/12651607], 0, 1, [], 0, [ (12061026)/(12651607)*a^(15) - (35507039)/(12651607)*a^(14) + (34894177)/(12651607)*a^(13) - (10628075)/(12651607)*a^(12) + (22207787)/(12651607)*a^(11) - (94124937)/(12651607)*a^(10) + (165036220)/(12651607)*a^(9) - (209949274)/(12651607)*a^(8) + (338479101)/(12651607)*a^(7) - (570831561)/(12651607)*a^(6) + (765940914)/(12651607)*a^(5) - (813933705)/(12651607)*a^(4) + (640263740)/(12651607)*a^(3) - (350888837)/(12651607)*a^(2) + (166002370)/(12651607)*a - (43247557)/(12651607) , (611945)/(12651607)*a^(15) - (5336589)/(12651607)*a^(14) + (10869917)/(12651607)*a^(13) - (5828798)/(12651607)*a^(12) - (1539609)/(12651607)*a^(11) - (9773825)/(12651607)*a^(10) + (35794909)/(12651607)*a^(9) - (45884527)/(12651607)*a^(8) + (52999425)/(12651607)*a^(7) - (98815686)/(12651607)*a^(6) + (165238966)/(12651607)*a^(5) - (189949808)/(12651607)*a^(4) + (160772811)/(12651607)*a^(3) - (90814595)/(12651607)*a^(2) + (28474957)/(12651607)*a - (12008400)/(12651607) , (12008400)/(12651607)*a^(15) - (35413255)/(12651607)*a^(14) + (30688611)/(12651607)*a^(13) - (1138483)/(12651607)*a^(12) + (18188002)/(12651607)*a^(11) - (97606809)/(12651607)*a^(10) + (158343775)/(12651607)*a^(9) - (180356291)/(12651607)*a^(8) + (302359073)/(12651607)*a^(7) - (535412175)/(12651607)*a^(6) + (693738714)/(12651607)*a^(5) - (687357434)/(12651607)*a^(4) + (494528992)/(12651607)*a^(3) - (235504389)/(12651607)*a^(2) + (113328205)/(12651607)*a - (43575443)/(12651607) , (3122743)/(12651607)*a^(15) - (5654905)/(12651607)*a^(14) + (1265542)/(12651607)*a^(13) + (1203443)/(12651607)*a^(12) + (5425397)/(12651607)*a^(11) - (16461120)/(12651607)*a^(10) + (20169363)/(12651607)*a^(9) - (23953733)/(12651607)*a^(8) + (48826162)/(12651607)*a^(7) - (75770743)/(12651607)*a^(6) + (81233113)/(12651607)*a^(5) - (71416492)/(12651607)*a^(4) + (22249467)/(12651607)*a^(3) + (76807)/(12651607)*a^(2) - (799149)/(12651607)*a + (16887735)/(12651607) , (5158034)/(12651607)*a^(15) - (13055860)/(12651607)*a^(14) + (7254626)/(12651607)*a^(13) + (1473923)/(12651607)*a^(12) + (11804423)/(12651607)*a^(11) - (39339557)/(12651607)*a^(10) + (49517865)/(12651607)*a^(9) - (56666570)/(12651607)*a^(8) + (115158494)/(12651607)*a^(7) - (193028336)/(12651607)*a^(6) + (225098780)/(12651607)*a^(5) - (219493535)/(12651607)*a^(4) + (159457767)/(12651607)*a^(3) - (84330281)/(12651607)*a^(2) + (62460872)/(12651607)*a - (9163209)/(12651607) , (3122743)/(12651607)*a^(15) - (5654905)/(12651607)*a^(14) + (1265542)/(12651607)*a^(13) + (1203443)/(12651607)*a^(12) + (5425397)/(12651607)*a^(11) - (16461120)/(12651607)*a^(10) + (20169363)/(12651607)*a^(9) - (23953733)/(12651607)*a^(8) + (48826162)/(12651607)*a^(7) - (75770743)/(12651607)*a^(6) + (81233113)/(12651607)*a^(5) - (71416492)/(12651607)*a^(4) + (22249467)/(12651607)*a^(3) + (76807)/(12651607)*a^(2) - (13450756)/(12651607)*a + (16887735)/(12651607) , (611945)/(12651607)*a^(15) - (5336589)/(12651607)*a^(14) + (10869917)/(12651607)*a^(13) - (5828798)/(12651607)*a^(12) - (1539609)/(12651607)*a^(11) - (9773825)/(12651607)*a^(10) + (35794909)/(12651607)*a^(9) - (45884527)/(12651607)*a^(8) + (52999425)/(12651607)*a^(7) - (98815686)/(12651607)*a^(6) + (165238966)/(12651607)*a^(5) - (189949808)/(12651607)*a^(4) + (160772811)/(12651607)*a^(3) - (90814595)/(12651607)*a^(2) + (28474957)/(12651607)*a + (643207)/(12651607) ], 30.5819893814, [[x^2 - x - 1, 1], [x^4 - x^3 - 3*x^2 + x + 1, 1], [x^4 - 2*x^3 + 2*x^2 - x - 1, 1], [x^4 - x^3 - 13*x - 31, 1], [x^8 - 2*x^7 + 2*x^6 - 3*x^5 + 3*x^4 - 3*x^3 + 2*x^2 - 2*x + 1, 2], [x^8 - x^7 - x^5 + x^4 + 2*x^3 - 2*x + 1, 2], [x^8 - x^7 - 2*x^6 - 9*x^5 - 7*x^4 - 3*x^3 - 8*x^2 - 3*x + 1, 1]]]