/* 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 - 3*x^30 + 4*x^28 - 9*x^26 + 27*x^24 - 93*x^22 + 188*x^20 - 279*x^18 + 581*x^16 - 1116*x^14 + 3008*x^12 - 5952*x^10 + 6912*x^8 - 9216*x^6 + 16384*x^4 - 49152*x^2 + 65536, 32, 34, [0, 16], 366225584701948244050176000000000000000000000000, [2, 3, 5, 7], [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, a^15, a^16, 1/2*a^17 - 1/2*a^15 - 1/2*a^11 - 1/2*a^9 - 1/2*a^7 - 1/2*a^3 - 1/2*a, 1/4*a^18 + 1/4*a^16 - 1/4*a^12 - 1/4*a^10 - 1/4*a^8 + 1/4*a^4 + 1/4*a^2, 1/8*a^19 + 1/8*a^17 - 1/8*a^13 - 1/8*a^11 - 1/8*a^9 + 1/8*a^5 + 1/8*a^3, 1/176*a^20 - 1/16*a^18 + 1/4*a^16 + 5/16*a^14 - 7/16*a^12 + 43/176*a^10 - 1/4*a^8 - 5/16*a^6 + 7/16*a^4 + 1/4*a^2 - 2/11, 1/352*a^21 - 1/32*a^19 + 1/8*a^17 - 11/32*a^15 + 9/32*a^13 - 133/352*a^11 - 1/8*a^9 + 11/32*a^7 - 9/32*a^5 + 1/8*a^3 + 9/22*a, 1/704*a^22 + 1/704*a^20 - 1/8*a^18 + 5/64*a^16 + 5/64*a^14 + 351/704*a^12 - 29/88*a^10 + 27/64*a^8 + 27/64*a^6 - 1/8*a^4 + 5/11*a^2 + 5/11, 1/1408*a^23 + 1/1408*a^21 - 1/16*a^19 + 5/128*a^17 - 59/128*a^15 + 351/1408*a^13 - 29/176*a^11 + 27/128*a^9 - 37/128*a^7 + 7/16*a^5 - 3/11*a^3 + 5/22*a, 1/14080*a^24 + 1/2816*a^22 - 1/704*a^20 - 27/1280*a^18 - 123/256*a^16 - 1153/2816*a^14 - 59/3520*a^12 + 565/2816*a^10 + 27/256*a^8 - 7/320*a^6 - 31/88*a^4 - 3/22*a^2 - 14/55, 1/28160*a^25 + 1/5632*a^23 - 1/1408*a^21 - 27/2560*a^19 - 123/512*a^17 - 1153/5632*a^15 - 59/7040*a^13 + 565/5632*a^11 + 27/512*a^9 - 7/640*a^7 + 57/176*a^5 - 3/44*a^3 - 7/55*a, 1/25062400*a^26 + 193/25062400*a^24 - 237/626560*a^22 + 27463/25062400*a^20 + 48389/2278400*a^18 + 1266179/5012480*a^16 + 767593/3132800*a^14 - 1794663/25062400*a^12 - 1911467/5012480*a^10 + 141669/284800*a^8 + 411321/1566400*a^6 - 20597/78320*a^4 - 8869/97900*a^2 + 11667/24475, 1/50124800*a^27 + 193/50124800*a^25 - 237/1253120*a^23 + 27463/50124800*a^21 + 48389/4556800*a^19 + 1266179/10024960*a^17 + 767593/6265600*a^15 - 1794663/50124800*a^13 - 1911467/10024960*a^11 + 141669/569600*a^9 + 411321/3132800*a^7 - 20597/156640*a^5 - 8869/195800*a^3 + 11667/48950*a, 1/100249600*a^28 + 1/100249600*a^26 + 413/12531200*a^24 - 39177/100249600*a^22 + 100983/100249600*a^20 - 10419553/100249600*a^18 - 13933/140800*a^16 + 5837289/100249600*a^14 + 12111721/100249600*a^12 + 2466949/12531200*a^10 - 628117/1566400*a^8 + 741977/1566400*a^6 - 143039/391600*a^4 + 19079/97900*a^2 - 651/24475, 1/200499200*a^29 + 1/200499200*a^27 + 413/25062400*a^25 - 39177/200499200*a^23 + 100983/200499200*a^21 - 10419553/200499200*a^19 - 13933/281600*a^17 - 94412311/200499200*a^15 - 88137879/200499200*a^13 + 2466949/25062400*a^11 - 628117/3132800*a^9 - 824423/3132800*a^7 + 248561/783200*a^5 - 78821/195800*a^3 - 651/48950*a, 1/400998400*a^30 + 1/400998400*a^28 - 1/50124800*a^26 + 5127/400998400*a^24 + 170743/400998400*a^22 + 581391/400998400*a^20 + 3644777/50124800*a^18 - 128966951/400998400*a^16 - 162762007/400998400*a^14 + 9092791/50124800*a^12 + 9525477/25062400*a^10 - 1900949/6265600*a^8 + 655029/1566400*a^6 + 55237/195800*a^4 - 6217/24475*a^2 + 11961/24475, 1/801996800*a^31 + 1/801996800*a^29 - 1/100249600*a^27 + 5127/801996800*a^25 + 170743/801996800*a^23 + 581391/801996800*a^21 + 3644777/100249600*a^19 - 128966951/801996800*a^17 - 162762007/801996800*a^15 - 41032009/100249600*a^13 + 9525477/50124800*a^11 - 1900949/12531200*a^9 - 911371/3132800*a^7 - 140563/391600*a^5 + 9129/24475*a^3 + 11961/48950*a], 1, 0,0,0,0,0, [[x^2 + 1, 1], [x^2 - 35, 1], [x^2 - x + 9, 1], [x^2 - x - 26, 1], [x^2 + 105, 1], [x^2 - 3, 1], [x^2 - x + 1, 1], [x^2 - x - 1, 1], [x^2 + 5, 1], [x^2 - 7, 1], [x^2 - x + 2, 1], [x^2 - x - 5, 1], [x^2 + 21, 1], [x^2 - 15, 1], [x^2 - x + 4, 1], [x^4 - 17*x^2 + 81, 1], [x^4 + 53*x^2 + 676, 1], [x^4 - x^2 + 1, 1], [x^4 - 19*x^2 + 64, 1], [x^4 + 35*x^2 + 1225, 1], [x^4 - x^3 - 8*x^2 - 9*x + 81, 1], [x^4 - 2*x^3 + 13*x^2 - 12*x + 141, 1], [x^4 + 3*x^2 + 1, 1], [x^4 - 3*x^2 + 4, 1], [x^4 + 11*x^2 + 25, 1], [x^4 - 7*x^2 + 16, 1], [x^4 - 2*x^3 - 15*x^2 + 16*x + 29, 1], [x^4 - 2*x^3 + 15*x^2 - 14*x + 14, 1], [x^4 - 25*x^2 + 25, 1], [x^4 - 7*x^2 + 196, 1], [x^4 - x^3 + 5*x^2 + 2*x + 4, 1], [x^4 - x^2 + 9, 1], [x^4 - x^3 + 4*x^2 - 15*x + 15, 1], [x^4 + 3*x^2 + 81, 1], [x^4 - 13*x^2 + 16, 1], [x^4 + 13*x^2 + 16, 1], [x^4 - 11*x^2 + 4, 1], [x^4 + 11*x^2 + 4, 1], [x^4 - 2*x^3 + 41*x^2 - 40*x + 505, 1], [x^4 - 2*x^3 + x^2 + 105, 1], [x^4 - 2*x^3 - 5*x^2 + 6*x + 114, 1], [x^4 - 2*x^3 - 25*x^2 + 26*x + 274, 1], [x^4 - 2*x^3 - 7*x^2 + 8*x + 1, 1], [x^4 + x^2 + 4, 1], [x^4 - 5*x^2 + 1, 1], [x^4 - 2*x^3 - x^2 + 2*x + 22, 1], [x^4 - x^3 + 2*x^2 + x + 1, 1], [x^4 - 5*x^2 + 25, 1], [x^4 + 7*x^2 + 49, 1], [x^4 - x^3 - x^2 - 2*x + 4, 1], [x^4 - 105*x^2 + 2205, 1], [x^4 - x^3 + 26*x^2 - 26*x + 151, 1], [x^4 - x^3 - 4*x^2 + 4*x + 1, 1], [x^4 + 15*x^2 + 45, 1], [x^4 - 5*x^2 + 5, 1], [x^4 - x^3 + x^2 - x + 1, 1], [x^4 - x^3 - 9*x^2 + 9*x + 11, 1], [x^4 + 35*x^2 + 245, 1], [x^8 + 17*x^6 + 208*x^4 + 1377*x^2 + 6561, 1], [x^8 - 9*x^6 + 37*x^4 - 36*x^2 + 16, 1], [x^8 - 7*x^6 + 16*x^4 + 105*x^2 + 225, 1], [x^8 - 4*x^7 - 8*x^6 + 38*x^5 + 93*x^4 - 254*x^3 - 566*x^2 + 700*x + 1780, 1], [x^8 - 4*x^7 + 14*x^5 + 53*x^4 - 134*x^3 - 218*x^2 + 288*x + 904, 1], [x^8 - 3*x^6 + 8*x^4 - 3*x^2 + 1, 1], [x^8 + 3*x^6 + 5*x^4 + 12*x^2 + 16, 1], [x^8 - 15*x^6 + 32*x^4 - 15*x^2 + 1, 1], [x^8 - 4*x^7 + 16*x^6 - 34*x^5 + 69*x^4 - 86*x^3 - 2*x^2 + 40*x + 16, 1], [x^8 - 2*x^7 - 23*x^6 + 40*x^5 + 249*x^4 - 208*x^3 - 1388*x^2 + 128*x + 3844, 1], [x^8 - 2*x^7 - 11*x^6 - 2*x^5 + 183*x^4 - 154*x^3 - 14*x^2 - 196*x + 196, 1], [x^8 - x^7 - 4*x^6 - 9*x^5 + 23*x^4 + 18*x^3 - 16*x^2 + 8*x + 16, 1], [x^8 + x^6 - 8*x^4 + 9*x^2 + 81, 1], [x^8 - 10*x^6 + 67*x^4 + 210*x^2 + 441, 1], [x^8 - 14*x^6 + 79*x^4 + 210*x^2 + 225, 1], [x^8 - 51*x^6 + 926*x^4 - 7176*x^2 + 22801, 1], [x^8 + 9*x^6 + 26*x^4 + 24*x^2 + 1, 1], [x^8 - x^6 + x^4 - x^2 + 1, 1], [x^8 + 19*x^6 + 121*x^4 + 279*x^2 + 121, 1], [x^8 - 2*x^7 - 35*x^6 + 58*x^5 + 339*x^4 - 328*x^3 - 965*x^2 + 92*x + 421, 1], [x^8 - 3*x^6 + 14*x^4 + 48*x^2 + 361, 1], [x^8 - 12*x^6 + 34*x^4 - 23*x^2 + 1, 1], [x^8 + 7*x^6 + 49*x^4 + 343*x^2 + 2401, 1], [x^8 - 4*x^7 + 44*x^6 - 118*x^5 + 529*x^4 - 866*x^3 + 1736*x^2 - 1322*x + 781, 1], [x^8 - 2*x^7 - 2*x^5 + 29*x^4 + 2*x^3 + 55*x^2 + 27*x + 151, 1], [x^8 - 4*x^7 + 4*x^6 + 2*x^5 + 29*x^4 - 66*x^3 + 36*x^2 - 2*x + 281, 1], [x^8 - x^7 - x^6 + 3*x^5 - x^4 + 6*x^3 - 4*x^2 - 8*x + 16, 1], [x^8 - 4*x^7 - 24*x^6 + 86*x^5 + 141*x^4 - 430*x^3 + 50*x^2 + 180*x - 20, 1], [x^8 - x^7 + 6*x^6 - 11*x^5 + 41*x^4 + 55*x^3 + 150*x^2 + 125*x + 625, 1], [x^8 - x^7 - 14*x^6 + 9*x^5 + 61*x^4 - 5*x^3 - 90*x^2 - 45*x - 5, 1], [x^8 + 25*x^6 + 140*x^4 + 125*x^2 + 25, 1], [x^8 - 21*x^6 + 441*x^4 - 9261*x^2 + 194481, 1], [x^8 + 16*x^6 + 146*x^4 + 761*x^2 + 1681, 1], [x^8 + 49*x^6 + 686*x^4 + 2744*x^2 + 2401, 1], [x^8 + 36*x^6 + 306*x^4 + 621*x^2 + 81, 1], [x^8 - 2*x^7 - 29*x^6 + 54*x^5 + 184*x^4 - 238*x^3 - 126*x^2 + 216*x - 59, 1], [x^8 + 13*x^6 + 74*x^4 + 272*x^2 + 841, 1], [x^8 - 7*x^6 + 14*x^4 - 8*x^2 + 1, 1], [x^8 + 3*x^6 + 9*x^4 + 27*x^2 + 81, 1], [x^8 - 35*x^6 + 980*x^4 - 8575*x^2 + 60025, 1], [x^8 - x^7 + 10*x^6 - 9*x^5 + 79*x^4 - 59*x^3 + 180*x^2 + 99*x + 121, 1], [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1, 1], [x^8 + 5*x^6 + 20*x^4 + 25*x^2 + 25, 1], [x^16 + 9*x^14 + 44*x^12 + 261*x^10 + 1029*x^8 + 1044*x^6 + 704*x^4 + 576*x^2 + 256, 1], [x^16 + 4*x^14 + 50*x^12 - 114*x^10 + 1259*x^8 - 3294*x^6 + 11675*x^4 - 15881*x^2 + 22801, 1], [x^16 + 3*x^14 + 5*x^12 + 3*x^10 - 11*x^8 + 12*x^6 + 80*x^4 + 192*x^2 + 256, 1], [x^16 - 11*x^14 + 96*x^12 - 781*x^10 + 6191*x^8 - 19525*x^6 + 60000*x^4 - 171875*x^2 + 390625, 1], [x^16 + 29*x^14 + 336*x^12 + 1979*x^10 + 6231*x^8 + 10055*x^6 + 7040*x^4 + 1125*x^2 + 25, 1], [x^16 - 19*x^14 + 240*x^12 - 1741*x^10 + 9219*x^8 - 29161*x^6 + 63200*x^4 - 33759*x^2 + 14641, 1], [x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1, 1], [x^16 - 28*x^14 + 274*x^12 - 1262*x^10 + 3051*x^8 - 3970*x^6 + 2635*x^4 - 725*x^2 + 25, 1], [x^16 + 5*x^14 + 24*x^12 + 115*x^10 + 551*x^8 + 115*x^6 + 24*x^4 + 5*x^2 + 1, 1], [x^16 - 7*x^14 + 343*x^10 - 2401*x^8 + 16807*x^6 - 823543*x^2 + 5764801, 1], [x^16 + 12*x^14 + 110*x^12 + 362*x^10 + 879*x^8 + 758*x^6 + 495*x^4 + 23*x^2 + 1, 1], [x^16 - 8*x^15 + 54*x^14 - 238*x^13 + 898*x^12 - 2658*x^11 + 6506*x^10 - 12884*x^9 + 19818*x^8 - 23198*x^7 + 16454*x^6 - 1434*x^5 - 3247*x^4 - 2796*x^3 + 2356*x^2 + 376*x + 316, 1], [x^16 - x^15 + 2*x^14 - 5*x^13 + 5*x^12 + x^11 + 6*x^10 + 5*x^9 - 21*x^8 + 10*x^7 + 24*x^6 + 8*x^5 + 80*x^4 - 160*x^3 + 128*x^2 - 128*x + 256, 1], [x^16 - 2*x^15 - 25*x^14 + 50*x^13 + 254*x^12 - 442*x^11 - 1452*x^10 + 2200*x^9 + 4686*x^8 - 7282*x^7 - 5457*x^6 + 3214*x^5 + 30374*x^4 + 11566*x^3 + 3134*x^2 - 9304*x + 2101, 1], [x^16 + 21*x^14 + 210*x^12 + 1104*x^10 + 3329*x^8 + 5124*x^6 + 4320*x^4 + 1536*x^2 + 256, 1]]]