/* 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^32 + 40*x^24 + 16*x^20 + 784*x^16 + 256*x^12 + 10240*x^8 + 65536, 32, 96908, [0, 16], 385049567410499609358247677435067162906957579288576, [2, 17, 997], [1, a, a^2, a^3, 1/2*a^4, 1/2*a^5, 1/4*a^6 - 1/2*a^3 - 1/2*a^2, 1/4*a^7 - 1/2*a^3, 1/4*a^8, 1/4*a^9, 1/8*a^10 - 1/2*a^2, 1/8*a^11 - 1/2*a^3, 1/16*a^12 - 1/4*a^4 - 1/2*a^3 - 1/2*a^2, 1/16*a^13 - 1/4*a^5 - 1/2*a^3, 1/16*a^14 - 1/2*a^3 - 1/2*a^2, 1/32*a^15 - 1/16*a^11 - 1/8*a^9 - 1/8*a^7 - 1/4*a^5 + 1/4*a^3, 1/32*a^16 - 1/8*a^8 - 1/2*a^2, 1/32*a^17 - 1/8*a^9 - 1/2*a^3, 1/64*a^18 - 1/32*a^14 - 1/16*a^11 - 1/16*a^10 - 1/8*a^8 - 1/8*a^6 - 1/4*a^5 - 1/4*a^4 + 1/4*a^3, 1/64*a^19 + 1/4*a^3, 1/128*a^20 - 1/8*a^8 - 1/8*a^4 - 1/2*a^3 - 1/2*a^2, 1/256*a^21 - 1/32*a^13 - 1/16*a^9 - 3/16*a^5 - 1/2*a, 1/512*a^22 - 1/64*a^14 - 1/16*a^11 - 1/32*a^10 - 1/8*a^9 - 1/8*a^8 - 3/32*a^6 - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 - 1/4*a^2 - 1/2*a, 1/512*a^23 - 1/64*a^15 - 1/32*a^11 - 1/8*a^9 - 3/32*a^7 - 1/4*a^5 - 1/4*a^3, 1/2048*a^24 - 3/256*a^16 - 1/32*a^14 + 1/128*a^12 - 1/16*a^11 - 1/16*a^10 - 1/8*a^9 + 1/128*a^8 - 1/8*a^6 - 1/4*a^5 - 1/8*a^4 + 1/4*a^3 - 1/4*a^2 - 1/2*a - 1/2, 1/2048*a^25 - 3/256*a^17 + 1/128*a^13 - 15/128*a^9 + 1/8*a^5 - 1/2*a, 1/4096*a^26 - 3/512*a^18 + 1/256*a^14 - 15/256*a^10 + 1/16*a^6 - 1/2*a^3 + 1/4*a^2, 1/8192*a^27 - 3/1024*a^19 + 1/512*a^15 + 17/512*a^11 - 1/8*a^9 - 3/32*a^7 - 3/8*a^3 - 1/2*a, 1/638976*a^28 + 7/79872*a^24 - 227/79872*a^20 - 115/39936*a^16 + 1097/39936*a^12 - 1/8*a^9 + 193/4992*a^8 + 35/624*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a + 11/78, 1/1277952*a^29 + 7/159744*a^25 - 1/1024*a^23 - 227/159744*a^21 - 1/128*a^19 + 1133/79872*a^17 - 1/128*a^15 + 1097/79872*a^13 - 1/64*a^11 - 431/9984*a^9 - 1/64*a^7 - 277/1248*a^5 - 1/8*a^3 - 67/156*a, 1/2555904*a^30 + 7/319488*a^26 - 1/4096*a^25 - 1/1024*a^23 - 227/319488*a^22 - 1/256*a^20 + 1133/159744*a^18 + 3/512*a^17 - 1/128*a^15 + 1097/159744*a^14 - 1/256*a^13 - 1/32*a^12 + 3/64*a^11 - 431/19968*a^10 - 17/256*a^9 + 1/16*a^8 + 7/64*a^7 + 35/2496*a^6 - 1/16*a^5 - 1/16*a^4 - 1/2*a^3 + 11/312*a^2 + 1/4*a - 1/2, 1/2555904*a^31 + 7/319488*a^27 - 227/319488*a^23 + 1133/159744*a^19 + 1097/159744*a^15 - 431/19968*a^11 + 35/2496*a^7 - 145/312*a^3], 1, 40, [2, 20], 1, [ (9)/(212992)*a^(30) - (53)/(638976)*a^(29) + (9)/(53248)*a^(26) + (19)/(79872)*a^(25) + (37)/(26624)*a^(22) - (137)/(79872)*a^(21) + (83)/(13312)*a^(18) + (167)/(39936)*a^(17) + (253)/(13312)*a^(14) - (1357)/(39936)*a^(13) + (237)/(3328)*a^(10) + (457)/(4992)*a^(9) + (21)/(104)*a^(6) - (16)/(39)*a^(5) + (29)/(52)*a^(2) + (40)/(39)*a + 1 , (31)/(1277952)*a^(31) - (11)/(851968)*a^(30) - (49)/(1277952)*a^(29) - (1)/(16384)*a^(28) - (17)/(159744)*a^(27) + (1)/(106496)*a^(26) + (1)/(19968)*a^(25) + (139)/(159744)*a^(23) + (1)/(106496)*a^(22) - (109)/(159744)*a^(21) - (5)/(2048)*a^(20) - (133)/(79872)*a^(19) - (87)/(53248)*a^(18) + (175)/(79872)*a^(17) - (1)/(1024)*a^(16) + (935)/(79872)*a^(15) + (205)/(53248)*a^(14) - (1025)/(79872)*a^(13) - (49)/(1024)*a^(12) - (179)/(9984)*a^(11) - (173)/(6656)*a^(10) + (439)/(4992)*a^(9) - (1)/(64)*a^(8) + (55)/(624)*a^(7) - (21)/(832)*a^(6) - (233)/(1248)*a^(5) - (3)/(8)*a^(4) - (59)/(312)*a^(3) - (17)/(104)*a^(2) + (31)/(39)*a - (1)/(2) , (67)/(1277952)*a^(31) - (85)/(851968)*a^(30) + (5)/(39936)*a^(29) - (1)/(4096)*a^(28) - (19)/(79872)*a^(27) + (29)/(106496)*a^(26) - (11)/(159744)*a^(25) + (235)/(159744)*a^(23) - (257)/(106496)*a^(22) + (31)/(9984)*a^(21) - (3)/(512)*a^(20) - (373)/(79872)*a^(19) + (207)/(53248)*a^(18) + (41)/(19968)*a^(17) - (1)/(256)*a^(16) + (1427)/(79872)*a^(15) - (1725)/(53248)*a^(14) + (529)/(9984)*a^(13) - (25)/(256)*a^(12) - (209)/(2496)*a^(11) + (651)/(6656)*a^(10) - (203)/(9984)*a^(9) + (595)/(2496)*a^(7) - (323)/(832)*a^(6) + (191)/(312)*a^(5) - (15)/(16)*a^(4) - (121)/(156)*a^(3) + (105)/(104)*a^(2) + (5)/(156)*a - (1)/(2) , (49)/(1277952)*a^(30) - (11)/(638976)*a^(28) + (31)/(159744)*a^(26) - (19)/(39936)*a^(24) + (109)/(159744)*a^(22) + (1)/(79872)*a^(20) + (605)/(79872)*a^(18) - (451)/(39936)*a^(16) + (1337)/(79872)*a^(14) + (725)/(39936)*a^(12) + (1033)/(9984)*a^(10) - (209)/(1248)*a^(8) + (311)/(1248)*a^(6) + (161)/(624)*a^(4) + (55)/(78)*a^(2) - (41)/(39) , (5)/(1277952)*a^(30) - (11)/(638976)*a^(28) - (1)/(39936)*a^(26) - (19)/(39936)*a^(24) + (113)/(159744)*a^(22) + (1)/(79872)*a^(20) - (107)/(79872)*a^(18) - (451)/(39936)*a^(16) + (181)/(79872)*a^(14) + (725)/(39936)*a^(12) - (161)/(4992)*a^(10) - (209)/(1248)*a^(8) - (59)/(1248)*a^(6) + (161)/(624)*a^(4) - (23)/(156)*a^(2) - (80)/(39) , (67)/(1277952)*a^(31) + (193)/(2555904)*a^(30) - (9)/(212992)*a^(29) + (1)/(4096)*a^(28) + (41)/(319488)*a^(27) + (25)/(319488)*a^(26) - (9)/(53248)*a^(25) + (235)/(159744)*a^(23) + (493)/(319488)*a^(22) - (37)/(26624)*a^(21) + (3)/(512)*a^(20) + (173)/(79872)*a^(19) - (43)/(159744)*a^(18) - (83)/(13312)*a^(17) + (1)/(256)*a^(16) + (1895)/(79872)*a^(15) + (3929)/(159744)*a^(14) - (253)/(13312)*a^(13) + (25)/(256)*a^(12) + (317)/(19968)*a^(11) - (269)/(19968)*a^(10) - (237)/(3328)*a^(9) + (517)/(2496)*a^(7) + (593)/(2496)*a^(6) - (21)/(104)*a^(5) + (15)/(16)*a^(4) - (47)/(312)*a^(3) - (61)/(312)*a^(2) - (55)/(52)*a - (1)/(2) , (31)/(851968)*a^(31) + (49)/(851968)*a^(30) - (19)/(159744)*a^(29) + (31)/(638976)*a^(28) + (9)/(106496)*a^(27) - (47)/(106496)*a^(26) - (11)/(159744)*a^(25) + (61)/(79872)*a^(24) + (139)/(106496)*a^(23) + (109)/(106496)*a^(22) - (55)/(19968)*a^(21) + (139)/(79872)*a^(20) + (179)/(53248)*a^(19) - (539)/(53248)*a^(18) - (37)/(19968)*a^(17) + (803)/(39936)*a^(16) + (1143)/(53248)*a^(15) + (713)/(53248)*a^(14) - (223)/(4992)*a^(13) + (1559)/(39936)*a^(12) + (263)/(6656)*a^(11) - (1125)/(6656)*a^(10) - (203)/(9984)*a^(9) + (1771)/(4992)*a^(8) + (107)/(416)*a^(7) + (155)/(832)*a^(6) - (359)/(624)*a^(5) + (133)/(312)*a^(4) + (29)/(104)*a^(3) - (163)/(104)*a^(2) + (5)/(156)*a + (151)/(39) , (31)/(851968)*a^(31) + (5)/(196608)*a^(30) + (9)/(212992)*a^(29) + (25)/(319488)*a^(28) + (9)/(106496)*a^(27) + (5)/(24576)*a^(26) + (9)/(53248)*a^(25) + (19)/(39936)*a^(24) + (139)/(106496)*a^(23) + (17)/(24576)*a^(22) + (37)/(26624)*a^(21) + (97)/(39936)*a^(20) + (179)/(53248)*a^(19) + (73)/(12288)*a^(18) + (83)/(13312)*a^(17) + (245)/(19968)*a^(16) + (1143)/(53248)*a^(15) + (253)/(12288)*a^(14) + (253)/(13312)*a^(13) + (593)/(19968)*a^(12) + (263)/(6656)*a^(11) + (119)/(1536)*a^(10) + (237)/(3328)*a^(9) + (457)/(2496)*a^(8) + (107)/(416)*a^(7) + (43)/(192)*a^(6) + (21)/(104)*a^(5) + (73)/(624)*a^(4) + (29)/(104)*a^(3) + (13)/(24)*a^(2) + (3)/(52)*a + (121)/(78) , (31)/(851968)*a^(31) - (5)/(196608)*a^(30) - (9)/(212992)*a^(29) - (25)/(319488)*a^(28) + (9)/(106496)*a^(27) - (5)/(24576)*a^(26) - (9)/(53248)*a^(25) - (19)/(39936)*a^(24) + (139)/(106496)*a^(23) - (17)/(24576)*a^(22) - (37)/(26624)*a^(21) - (97)/(39936)*a^(20) + (179)/(53248)*a^(19) - (73)/(12288)*a^(18) - (83)/(13312)*a^(17) - (245)/(19968)*a^(16) + (1143)/(53248)*a^(15) - (253)/(12288)*a^(14) - (253)/(13312)*a^(13) - (593)/(19968)*a^(12) + (263)/(6656)*a^(11) - (119)/(1536)*a^(10) - (237)/(3328)*a^(9) - (457)/(2496)*a^(8) + (107)/(416)*a^(7) - (43)/(192)*a^(6) - (21)/(104)*a^(5) - (73)/(624)*a^(4) + (29)/(104)*a^(3) - (13)/(24)*a^(2) - (3)/(52)*a - (121)/(78) , (7)/(851968)*a^(31) - (11)/(851968)*a^(30) - (49)/(1277952)*a^(29) + (1)/(16384)*a^(28) + (23)/(106496)*a^(27) + (1)/(106496)*a^(26) + (1)/(19968)*a^(25) + (75)/(106496)*a^(23) + (1)/(106496)*a^(22) - (109)/(159744)*a^(21) + (5)/(2048)*a^(20) + (339)/(53248)*a^(19) - (87)/(53248)*a^(18) + (175)/(79872)*a^(17) + (1)/(1024)*a^(16) + (815)/(53248)*a^(15) + (205)/(53248)*a^(14) - (1025)/(79872)*a^(13) + (49)/(1024)*a^(12) + (701)/(6656)*a^(11) - (173)/(6656)*a^(10) + (439)/(4992)*a^(9) + (1)/(64)*a^(8) + (89)/(832)*a^(7) - (21)/(832)*a^(6) - (233)/(1248)*a^(5) + (3)/(8)*a^(4) + (45)/(52)*a^(3) - (17)/(104)*a^(2) + (31)/(39)*a - (1)/(2) , (7)/(851968)*a^(31) + (11)/(851968)*a^(30) - (49)/(1277952)*a^(29) - (1)/(16384)*a^(28) + (23)/(106496)*a^(27) - (1)/(106496)*a^(26) + (1)/(19968)*a^(25) + (75)/(106496)*a^(23) - (1)/(106496)*a^(22) - (109)/(159744)*a^(21) - (5)/(2048)*a^(20) + (339)/(53248)*a^(19) + (87)/(53248)*a^(18) + (175)/(79872)*a^(17) - (1)/(1024)*a^(16) + (815)/(53248)*a^(15) - (205)/(53248)*a^(14) - (1025)/(79872)*a^(13) - (49)/(1024)*a^(12) + (701)/(6656)*a^(11) + (173)/(6656)*a^(10) + (439)/(4992)*a^(9) - (1)/(64)*a^(8) + (89)/(832)*a^(7) + (21)/(832)*a^(6) - (233)/(1248)*a^(5) - (3)/(8)*a^(4) + (45)/(52)*a^(3) + (17)/(104)*a^(2) + (31)/(39)*a + (1)/(2) , (21)/(425984)*a^(31) - (379)/(2555904)*a^(30) + (179)/(638976)*a^(29) - (121)/(638976)*a^(28) + (47)/(106496)*a^(27) - (79)/(319488)*a^(26) + (49)/(159744)*a^(25) + (25)/(39936)*a^(24) + (69)/(53248)*a^(23) - (1327)/(319488)*a^(22) + (551)/(79872)*a^(21) - (301)/(79872)*a^(20) + (315)/(26624)*a^(19) - (1031)/(159744)*a^(18) + (397)/(39936)*a^(17) + (655)/(39936)*a^(16) + (625)/(26624)*a^(15) - (10787)/(159744)*a^(14) + (4327)/(39936)*a^(13) - (2009)/(39936)*a^(12) + (1099)/(6656)*a^(11) - (1309)/(19968)*a^(10) + (1117)/(9984)*a^(9) + (49)/(156)*a^(8) + (209)/(832)*a^(7) - (1877)/(2496)*a^(6) + (43)/(39)*a^(5) - (113)/(156)*a^(4) + (163)/(104)*a^(3) - (113)/(312)*a^(2) + (77)/(156)*a + (307)/(78) , (59)/(2555904)*a^(31) - (25)/(851968)*a^(30) - (5)/(39936)*a^(29) - (23)/(638976)*a^(28) - (1)/(19968)*a^(27) - (19)/(106496)*a^(26) + (11)/(159744)*a^(25) + (17)/(39936)*a^(24) + (23)/(319488)*a^(23) - (149)/(106496)*a^(22) - (31)/(9984)*a^(21) - (83)/(79872)*a^(20) - (389)/(159744)*a^(19) - (245)/(53248)*a^(18) - (41)/(19968)*a^(17) + (305)/(39936)*a^(16) + (139)/(159744)*a^(15) - (1217)/(53248)*a^(14) - (529)/(9984)*a^(13) + (41)/(39936)*a^(12) - (293)/(9984)*a^(11) - (301)/(6656)*a^(10) + (203)/(9984)*a^(9) + (265)/(1248)*a^(8) + (19)/(624)*a^(7) - (147)/(832)*a^(6) - (113)/(312)*a^(5) + (7)/(312)*a^(4) - (7)/(156)*a^(3) + (11)/(104)*a^(2) + (73)/(156)*a + (137)/(78) , (1)/(19968)*a^(31) - (11)/(851968)*a^(30) + (37)/(1277952)*a^(29) - (29)/(319488)*a^(28) - (1)/(319488)*a^(27) + (1)/(106496)*a^(26) - (7)/(79872)*a^(25) + (23)/(79872)*a^(24) + (17)/(19968)*a^(23) + (1)/(106496)*a^(22) + (337)/(159744)*a^(21) - (125)/(39936)*a^(20) - (53)/(39936)*a^(19) - (87)/(53248)*a^(18) + (269)/(79872)*a^(17) + (137)/(19968)*a^(16) + (119)/(19968)*a^(15) + (205)/(53248)*a^(14) + (3461)/(79872)*a^(13) - (769)/(19968)*a^(12) - (1153)/(19968)*a^(11) - (173)/(6656)*a^(10) + (157)/(2496)*a^(9) + (779)/(4992)*a^(8) + (7)/(156)*a^(7) - (21)/(832)*a^(6) + (593)/(1248)*a^(5) - (353)/(624)*a^(4) - (37)/(156)*a^(3) - (17)/(104)*a^(2) - (11)/(78)*a + (71)/(39) , (31)/(638976)*a^(31) - (23)/(1277952)*a^(30) + (1)/(9984)*a^(29) - (1)/(106496)*a^(28) + (49)/(319488)*a^(27) + (17)/(79872)*a^(26) + (19)/(79872)*a^(25) - (7)/(13312)*a^(24) + (139)/(79872)*a^(23) - (83)/(159744)*a^(22) + (17)/(9984)*a^(21) + (19)/(13312)*a^(20) + (35)/(9984)*a^(19) + (305)/(79872)*a^(18) + (71)/(9984)*a^(17) - (93)/(6656)*a^(16) + (1169)/(39936)*a^(15) + (41)/(79872)*a^(14) + (79)/(4992)*a^(13) + (151)/(6656)*a^(12) + (1273)/(19968)*a^(11) + (109)/(2496)*a^(10) + (379)/(4992)*a^(9) - (89)/(832)*a^(8) + (181)/(1248)*a^(7) + (85)/(624)*a^(6) + (95)/(624)*a^(5) + (17)/(104)*a^(4) + (233)/(312)*a^(3) + (59)/(156)*a^(2) + (1)/(39)*a - (11)/(13) ], 901078689200.9504, [[x^2 + 1, 1], [x^2 - 2, 1], [x^2 + 2, 1], [x^4 - 6*x^2 - 2*x + 1, 1], [x^4 + 1, 1], [x^8 - 16*x^6 - 2*x^5 + 70*x^4 + 16*x^3 - 46*x^2 - 6*x + 1, 1], [x^8 - 16*x^6 + 90*x^4 - 206*x^2 + 153, 1], [x^8 + 16*x^6 + 90*x^4 + 206*x^2 + 153, 1], [x^8 - 2*x^7 + 2*x^6 + 2*x^5 - 6*x^4 + 4*x^3 + 8*x^2 - 16*x + 16, 1], [x^8 - 10*x^6 + 30*x^4 - 32*x^2 + 9, 1], [x^8 + 10*x^6 + 30*x^4 + 32*x^2 + 9, 1], [x^8 - 2*x^7 + 2*x^6 + 4*x^5 + 10*x^4 - 10*x^3 + 8*x^2 + 12*x + 9, 1], [x^16 + 68*x^12 + 1062*x^8 + 180*x^4 + 1, 1], [x^16 - 28*x^14 + 300*x^12 - 1540*x^10 + 3884*x^8 - 4448*x^6 + 1924*x^4 - 224*x^2 + 4, 1], [x^16 + 10*x^12 - 2*x^10 + 49*x^8 - 8*x^6 + 160*x^4 + 256, 1], [x^16 + 28*x^14 + 300*x^12 + 1540*x^10 + 3884*x^8 + 4448*x^6 + 1924*x^4 + 224*x^2 + 4, 1], [x^16 + 10*x^12 + 2*x^10 + 49*x^8 + 8*x^6 + 160*x^4 + 256, 1], [x^16 - 2*x^13 - 10*x^12 - 4*x^11 + 2*x^10 + 10*x^9 + 57*x^8 + 20*x^7 + 8*x^6 - 32*x^5 - 160*x^4 - 64*x^3 + 256, 1], [x^16 - 8*x^15 + 48*x^14 - 176*x^13 + 530*x^12 - 1380*x^11 + 2874*x^10 - 5044*x^9 + 7508*x^8 - 9740*x^7 + 11460*x^6 - 11388*x^5 + 9730*x^4 - 6632*x^3 + 3360*x^2 - 1232*x + 242, 1]]]