/* 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 - 6*x^14 + 33*x^13 - 30*x^12 - 74*x^11 + 204*x^10 - 45*x^9 - 383*x^8 + 321*x^7 + 305*x^6 - 432*x^5 - 59*x^4 + 216*x^3 - 17*x^2 - 16*x + 1, 16, 388, [8, 4], 17334529279969140625, [5, 29, 89], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, 1/2*a^11 - 1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^3 - 1/2, 1/4*a^12 - 1/4*a^8 - 1/4*a^7 - 1/4*a^6 - 1/4*a^5 - 1/4*a^3 - 1/2*a^2 - 1/4*a - 1/4, 1/4*a^13 - 1/4*a^9 - 1/4*a^8 - 1/4*a^7 - 1/4*a^6 - 1/4*a^4 - 1/2*a^3 - 1/4*a^2 - 1/4*a, 1/436*a^14 + 21/436*a^13 - 35/218*a^11 - 75/436*a^10 + 17/109*a^9 + 41/109*a^8 + 1/218*a^7 - 39/436*a^6 - 85/436*a^5 - 189/436*a^4 - 25/436*a^3 + 25/218*a^2 + 23/436*a - 29/218, 1/5171257352*a^15 + 2825337/2585628676*a^14 - 57388978/646407169*a^13 - 526630191/5171257352*a^12 + 1034819795/5171257352*a^11 + 2088990301/5171257352*a^10 - 1829598079/5171257352*a^9 + 446677911/1292814338*a^8 - 87180451/5171257352*a^7 - 204293907/2585628676*a^6 + 626197015/5171257352*a^5 - 1371219181/5171257352*a^4 + 497453495/1292814338*a^3 - 112965151/1292814338*a^2 + 741098967/5171257352*a - 1520800753/5171257352], 0, 1, [], 1, [ (56333)/(7847128)*a^(15) - (24399)/(3923564)*a^(14) - (81948)/(980891)*a^(13) + (1312561)/(7847128)*a^(12) + (1674371)/(7847128)*a^(11) - (8317339)/(7847128)*a^(10) + (6477449)/(7847128)*a^(9) + (4012909)/(1961782)*a^(8) - (32345043)/(7847128)*a^(7) - (2253839)/(3923564)*a^(6) + (42555087)/(7847128)*a^(5) - (7629741)/(7847128)*a^(4) - (5089627)/(1961782)*a^(3) + (684085)/(1961782)*a^(2) + (1546431)/(7847128)*a + (12596195)/(7847128) , (496686135)/(5171257352)*a^(15) - (661290155)/(2585628676)*a^(14) - (847887925)/(1292814338)*a^(13) + (15044613793)/(5171257352)*a^(12) - (9884545195)/(5171257352)*a^(11) - (38372084377)/(5171257352)*a^(10) + (85581457823)/(5171257352)*a^(9) + (2710919997)/(2585628676)*a^(8) - (178083100487)/(5171257352)*a^(7) + (11291965427)/(646407169)*a^(6) + (169353679403)/(5171257352)*a^(5) - (139189194527)/(5171257352)*a^(4) - (34983901865)/(2585628676)*a^(3) + (8393643644)/(646407169)*a^(2) + (15821561891)/(5171257352)*a - (4583622089)/(5171257352) , (37163006)/(646407169)*a^(15) - (467843835)/(2585628676)*a^(14) - (809991967)/(2585628676)*a^(13) + (2562210431)/(1292814338)*a^(12) - (2748897789)/(1292814338)*a^(11) - (10830793727)/(2585628676)*a^(10) + (8575746754)/(646407169)*a^(9) - (6556706291)/(1292814338)*a^(8) - (15289600463)/(646407169)*a^(7) + (69297946239)/(2585628676)*a^(6) + (39259704689)/(2585628676)*a^(5) - (92710895493)/(2585628676)*a^(4) + (9006217757)/(2585628676)*a^(3) + (24007167081)/(1292814338)*a^(2) - (17143963323)/(2585628676)*a - (1524307648)/(646407169) , (540461661)/(5171257352)*a^(15) - (185802583)/(646407169)*a^(14) - (478669980)/(646407169)*a^(13) + (17121083509)/(5171257352)*a^(12) - (10223457293)/(5171257352)*a^(11) - (46328032617)/(5171257352)*a^(10) + (98429600827)/(5171257352)*a^(9) + (6935596657)/(2585628676)*a^(8) - (221244393557)/(5171257352)*a^(7) + (51247024339)/(2585628676)*a^(6) + (226340121653)/(5171257352)*a^(5) - (174742568873)/(5171257352)*a^(4) - (50889398843)/(2585628676)*a^(3) + (48191453491)/(2585628676)*a^(2) + (23259158307)/(5171257352)*a + (884939311)/(5171257352) , (496686135)/(5171257352)*a^(15) - (661290155)/(2585628676)*a^(14) - (847887925)/(1292814338)*a^(13) + (15044613793)/(5171257352)*a^(12) - (9884545195)/(5171257352)*a^(11) - (38372084377)/(5171257352)*a^(10) + (85581457823)/(5171257352)*a^(9) + (2710919997)/(2585628676)*a^(8) - (178083100487)/(5171257352)*a^(7) + (11291965427)/(646407169)*a^(6) + (169353679403)/(5171257352)*a^(5) - (139189194527)/(5171257352)*a^(4) - (34983901865)/(2585628676)*a^(3) + (8393643644)/(646407169)*a^(2) + (15821561891)/(5171257352)*a + (587635263)/(5171257352) , (392339761)/(5171257352)*a^(15) - (135434286)/(646407169)*a^(14) - (1214501243)/(2585628676)*a^(13) + (12071137049)/(5171257352)*a^(12) - (10471137853)/(5171257352)*a^(11) - (27344793705)/(5171257352)*a^(10) + (73829848401)/(5171257352)*a^(9) - (3962352781)/(1292814338)*a^(8) - (132910487147)/(5171257352)*a^(7) + (14334109039)/(646407169)*a^(6) + (88888600033)/(5171257352)*a^(5) - (145503759203)/(5171257352)*a^(4) + (2127207677)/(2585628676)*a^(3) + (15644911641)/(1292814338)*a^(2) - (20729453939)/(5171257352)*a - (6049903473)/(5171257352) , (104712021)/(2585628676)*a^(15) - (283148095)/(2585628676)*a^(14) - (312318875)/(1292814338)*a^(13) + (3041230253)/(2585628676)*a^(12) - (2734478335)/(2585628676)*a^(11) - (1523835374)/(646407169)*a^(10) + (8565370117)/(1292814338)*a^(9) - (4275008971)/(2585628676)*a^(8) - (6832873056)/(646407169)*a^(7) + (10401017037)/(1292814338)*a^(6) + (4209100055)/(646407169)*a^(5) - (20851981279)/(2585628676)*a^(4) - (568517413)/(2585628676)*a^(3) + (1820248723)/(2585628676)*a^(2) + (23850425)/(2585628676)*a + (5409704981)/(2585628676) , (456996641)/(5171257352)*a^(15) - (259794127)/(1292814338)*a^(14) - (414403581)/(646407169)*a^(13) + (12566064741)/(5171257352)*a^(12) - (6372652841)/(5171257352)*a^(11) - (35692775481)/(5171257352)*a^(10) + (70894521483)/(5171257352)*a^(9) + (7573677577)/(2585628676)*a^(8) - (153758995617)/(5171257352)*a^(7) + (34191417381)/(2585628676)*a^(6) + (145954946457)/(5171257352)*a^(5) - (117622335981)/(5171257352)*a^(4) - (30213591419)/(2585628676)*a^(3) + (31241510277)/(2585628676)*a^(2) + (4593022491)/(5171257352)*a - (7347268393)/(5171257352) , (295720407)/(2585628676)*a^(15) - (190326699)/(646407169)*a^(14) - (2102979365)/(2585628676)*a^(13) + (8881703355)/(2585628676)*a^(12) - (5053767273)/(2585628676)*a^(11) - (24205296849)/(2585628676)*a^(10) + (12497879779)/(646407169)*a^(9) + (8538395297)/(2585628676)*a^(8) - (54911067277)/(1292814338)*a^(7) + (45676858125)/(2585628676)*a^(6) + (113649917387)/(2585628676)*a^(5) - (18903170258)/(646407169)*a^(4) - (31166978865)/(1292814338)*a^(3) + (43197732695)/(2585628676)*a^(2) + (10552276299)/(1292814338)*a - (2483090529)/(2585628676) , (238447629)/(2585628676)*a^(15) - (205013727)/(646407169)*a^(14) - (1147537679)/(2585628676)*a^(13) + (8493409507)/(2585628676)*a^(12) - (10194659123)/(2585628676)*a^(11) - (14910646211)/(2585628676)*a^(10) + (13684664453)/(646407169)*a^(9) - (27860883539)/(2585628676)*a^(8) - (21762608234)/(646407169)*a^(7) + (103873181133)/(2585628676)*a^(6) + (51924492771)/(2585628676)*a^(5) - (29961443987)/(646407169)*a^(4) + (1695892792)/(646407169)*a^(3) + (52073205277)/(2585628676)*a^(2) - (2114871773)/(646407169)*a - (3839012489)/(2585628676) , (111356487)/(1292814338)*a^(15) - (669317023)/(2585628676)*a^(14) - (377542661)/(646407169)*a^(13) + (1912348523)/(646407169)*a^(12) - (2686977649)/(1292814338)*a^(11) - (20322413183)/(2585628676)*a^(10) + (46602863229)/(2585628676)*a^(9) + (1746889637)/(2585628676)*a^(8) - (105325355057)/(2585628676)*a^(7) + (31604267211)/(1292814338)*a^(6) + (107985465499)/(2585628676)*a^(5) - (26832575082)/(646407169)*a^(4) - (44010388763)/(2585628676)*a^(3) + (64915964371)/(2585628676)*a^(2) + (1212585700)/(646407169)*a - (1303859469)/(646407169) ], 3571.7751314, [[x^2 - x - 1, 1], [x^4 - x^3 - 3*x^2 + x + 1, 1], [x^4 - x^3 - 5*x^2 + 2*x + 4, 1], [x^4 - x^3 - 27*x^2 + 23*x + 149, 1], [x^8 - 2*x^7 + 3*x^4 - 5*x^2 + x + 1, 2], [x^8 - x^7 - 4*x^6 + 8*x^5 - 9*x^4 + 8*x^3 - 4*x^2 - x + 1, 2], [x^8 - 15*x^6 + 57*x^4 - 15*x^2 + 1, 1]]]