/* 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 - x^15 - 3*x^14 + 10*x^13 - 10*x^12 + 31*x^11 + 66*x^10 - 310*x^9 + 229*x^8 + 930*x^7 + 594*x^6 - 837*x^5 - 810*x^4 - 2430*x^3 - 2187*x^2 + 2187*x + 6561, 16, 2, [0, 8], 1306642885859619140625, [3, 5, 13], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/3*a^9 - 1/3*a^8 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^2 + 1/3*a, 1/171*a^10 - 1/9*a^9 - 1/3*a^8 + 1/9*a^7 - 1/9*a^6 + 40/171*a^5 + 1/3*a^4 - 4/9*a^3 + 4/9*a^2 + 1/3*a - 8/19, 1/513*a^11 - 1/513*a^10 - 1/9*a^9 - 8/27*a^8 + 8/27*a^7 - 131/513*a^6 + 31/171*a^5 + 5/27*a^4 - 5/27*a^3 + 4/9*a^2 - 9/19*a + 9/19, 1/6156*a^12 - 1/1539*a^11 + 1/324*a^9 + 8/81*a^8 + 238/1539*a^7 - 1/228*a^6 - 28/81*a^5 - 5/81*a^4 + 1/4*a^3 + 74/171*a^2 - 10/57*a - 1/4, 1/18301788*a^13 - 223/4575447*a^12 - 1165/1525149*a^11 + 17551/18301788*a^10 - 29104/240813*a^9 + 1734976/4575447*a^8 - 2087333/6100596*a^7 - 508438/4575447*a^6 - 1349639/4575447*a^5 + 124579/321084*a^4 + 113029/508383*a^3 + 5381/56487*a^2 - 75347/225948*a + 2400/18829, 1/54905364*a^14 - 1/54905364*a^13 + 959/18301788*a^12 + 47971/54905364*a^11 - 59491/54905364*a^10 + 3745111/54905364*a^9 - 1129709/18301788*a^8 + 4566191/54905364*a^7 - 8243519/54905364*a^6 + 336913/18301788*a^5 - 527239/6100596*a^4 - 126157/677844*a^3 - 221963/677844*a^2 - 19689/75316*a - 15763/75316, 1/164716092*a^15 - 1/164716092*a^14 - 1/54905364*a^13 - 5255/164716092*a^12 - 39619/164716092*a^11 + 76495/164716092*a^10 + 985333/54905364*a^9 - 29341345/164716092*a^8 + 3975709/164716092*a^7 - 11706593/54905364*a^6 - 37349/6100596*a^5 + 1441805/6100596*a^4 - 260639/677844*a^3 - 212371/677844*a^2 + 695/75316*a - 16797/37658], 1, 4, [4], 1, [ (22939)/(164716092)*a^(15) - (21803)/(82358046)*a^(14) + (5)/(112974)*a^(13) + (252961)/(164716092)*a^(12) - (275675)/(82358046)*a^(11) + (745931)/(82358046)*a^(10) + (3127)/(2033532)*a^(9) - (3345431)/(82358046)*a^(8) + (8039351)/(82358046)*a^(7) + (7699)/(677844)*a^(6) + (169169)/(3050298)*a^(5) + (114695)/(1016766)*a^(4) + (105133)/(677844)*a^(3) + (945)/(37658)*a^(2) + (52283)/(112974)*a - (3891)/(18829) , (235)/(27452682)*a^(15) - (485)/(9150894)*a^(14) + (26101)/(54905364)*a^(13) - (15035)/(27452682)*a^(12) - (12875)/(9150894)*a^(11) + (123137)/(18301788)*a^(10) - (272045)/(27452682)*a^(9) + (367265)/(27452682)*a^(8) + (713119)/(18301788)*a^(7) - (4856681)/(27452682)*a^(6) + (1900625)/(9150894)*a^(5) + (1846843)/(6100596)*a^(4) - (11255)/(112974)*a^(3) - (2715)/(37658)*a^(2) + (5781)/(75316)*a - (12610)/(18829) , (1)/(225948)*a^(15) - (173)/(3050298)*a^(14) - (307)/(2033532)*a^(13) - (1)/(112974)*a^(12) + (5)/(37658)*a^(11) - (3)/(75316)*a^(10) - (11309)/(3050298)*a^(9) - (8135)/(1016766)*a^(8) - (337)/(75316)*a^(7) + (923)/(112974)*a^(6) + (719)/(37658)*a^(5) - (1972159)/(6100596)*a^(4) - (448805)/(1016766)*a^(3) - (945)/(37658)*a^(2) - (3969)/(75316)*a - (2187)/(75316) , (365)/(18301788)*a^(15) + (2)/(4617)*a^(10) + (365)/(4617)*a^(5) - (22265)/(75316) , (2263)/(164716092)*a^(15) + (11441)/(164716092)*a^(14) - (3245)/(18301788)*a^(13) - (13793)/(164716092)*a^(12) + (163199)/(164716092)*a^(11) - (56807)/(164716092)*a^(10) + (20489)/(18301788)*a^(9) + (1227377)/(164716092)*a^(8) - (6708005)/(164716092)*a^(7) + (1352711)/(18301788)*a^(6) + (185863)/(2033532)*a^(5) - (754517)/(6100596)*a^(4) - (14381)/(677844)*a^(3) + (126083)/(677844)*a^(2) - (108005)/(225948)*a + (12805)/(37658) , (2507)/(18301788)*a^(15) - (572)/(13726341)*a^(14) - (9745)/(13726341)*a^(13) + (1193)/(1016766)*a^(12) + (6862)/(13726341)*a^(11) + (17603)/(13726341)*a^(10) + (249329)/(27452682)*a^(9) - (21631)/(508383)*a^(8) - (226816)/(13726341)*a^(7) + (5021921)/(27452682)*a^(6) + (804542)/(4575447)*a^(5) - (77875)/(169461)*a^(4) - (63749)/(112974)*a^(3) + (42665)/(169461)*a^(2) + (27490)/(56487)*a - (3909)/(75316) , (29491)/(82358046)*a^(15) - (52031)/(164716092)*a^(14) - (13237)/(18301788)*a^(13) + (600755)/(164716092)*a^(12) - (811397)/(164716092)*a^(11) + (2273165)/(164716092)*a^(10) + (472357)/(18301788)*a^(9) - (17260499)/(164716092)*a^(8) + (19515059)/(164716092)*a^(7) + (4218787)/(18301788)*a^(6) + (1134173)/(6100596)*a^(5) + (620681)/(2033532)*a^(4) - (51221)/(677844)*a^(3) - (657641)/(677844)*a^(2) - (56795)/(75316)*a - (71169)/(75316) ], 24866.4840857, [[x^2 - x - 16, 1], [x^2 - x + 1, 1], [x^2 - x + 49, 1], [x^2 - x - 1, 1], [x^2 - x - 3, 1], [x^2 - x + 4, 1], [x^2 - x + 10, 1], [x^4 - x^3 + 17*x^2 + 16*x + 256, 1], [x^4 - 9*x^2 + 4, 1], [x^4 - x^3 - x^2 + 25*x + 40, 1], [x^4 - x^3 + 2*x^2 + x + 1, 1], [x^4 - x^3 + 4*x^2 + 3*x + 9, 1], [x^4 + 17*x^2 + 121, 1], [x^4 + x^2 + 49, 1], [x^4 - x^3 - 4*x^2 + 4*x + 1, 1], [x^4 - x^3 - 49*x^2 + 49*x + 451, 1], [x^4 - x^3 + x^2 - x + 1, 1], [x^4 - x^3 + 16*x^2 - 16*x + 61, 1], [x^8 + 9*x^6 + 77*x^4 + 36*x^2 + 16, 1], [x^8 - 2*x^7 - 20*x^6 + 28*x^5 + 99*x^4 - 118*x^3 - 65*x^2 + 107*x - 29, 1], [x^8 - x^7 + 4*x^6 - 7*x^5 + 19*x^4 + 21*x^3 + 36*x^2 + 27*x + 81, 1], [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1, 1], [x^8 - x^7 - 15*x^6 + 16*x^5 + 179*x^4 - 134*x^3 - 720*x^2 - 976*x + 3721, 1], [x^8 - x^7 + 21*x^6 - 11*x^5 + 116*x^4 + 55*x^3 + 135*x^2 + 230*x + 445, 1], [x^8 - x^7 - 9*x^6 + 19*x^5 + 71*x^4 + 190*x^3 - 900*x^2 - 1000*x + 10000, 1]]]