/* 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^24 - 4*x^23 + 8*x^22 - 12*x^21 + 12*x^20 - 4*x^19 - 8*x^18 + 24*x^17 - 56*x^16 + 88*x^15 - 88*x^14 + 56*x^13 - 28*x^12 + 112*x^11 - 352*x^10 + 704*x^9 - 896*x^8 + 768*x^7 - 512*x^6 - 512*x^5 + 3072*x^4 - 6144*x^3 + 8192*x^2 - 8192*x + 4096, 24, 400, [0, 12], 7404154726819150028835278894923776, [2, 3, 31, 37], [1, a, a^2, a^3, a^4, a^5, 1/2*a^6, 1/2*a^7, 1/4*a^8 - 1/2*a^5 - 1/2*a^2, 1/4*a^9 - 1/2*a^3, 1/4*a^10 - 1/2*a^4, 1/8*a^11 - 1/4*a^5 - 1/2*a^2, 1/8*a^12 - 1/4*a^6 - 1/2*a^3, 1/8*a^13 - 1/4*a^7 - 1/2*a^4, 1/8*a^14 - 1/2*a^2, 1/16*a^15 + 1/4*a^3, 1/32*a^16 + 1/8*a^4, 1/64*a^17 - 1/16*a^14 - 1/16*a^13 - 1/16*a^12 - 1/8*a^10 - 1/8*a^9 - 1/8*a^8 + 1/8*a^7 - 1/8*a^6 + 5/16*a^5 - 1/2*a^3, 1/256*a^18 - 1/64*a^15 - 1/64*a^14 + 3/64*a^13 + 1/32*a^12 - 1/32*a^11 + 1/32*a^10 - 1/32*a^9 + 1/32*a^8 - 5/32*a^7 - 15/64*a^6 - 1/2*a^5 - 1/4*a^4 - 1/8*a^3 - 1/2, 1/512*a^19 - 1/128*a^16 - 1/128*a^15 + 3/128*a^14 + 1/64*a^13 - 1/64*a^12 + 1/64*a^11 - 1/64*a^10 + 1/64*a^9 - 5/64*a^8 - 15/128*a^7 - 1/4*a^6 + 3/8*a^5 - 1/16*a^4 - 1/2*a^3 - 1/2*a^2 + 1/4*a, 1/512*a^20 - 1/128*a^17 - 1/128*a^16 + 3/128*a^15 + 1/64*a^14 - 1/64*a^13 + 1/64*a^12 - 1/64*a^11 + 1/64*a^10 - 5/64*a^9 - 15/128*a^8 - 1/4*a^7 - 1/8*a^6 - 1/16*a^5 - 1/2*a^4 - 1/2*a^3 + 1/4*a^2, 1/1024*a^21 - 1/256*a^17 + 3/256*a^16 - 1/128*a^15 + 5/128*a^14 - 1/128*a^13 + 3/128*a^12 - 3/128*a^11 + 15/128*a^10 - 23/256*a^9 + 1/32*a^8 - 3/32*a^7 + 15/64*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2, 1/174080*a^22 - 33/87040*a^21 - 19/21760*a^20 + 3/21760*a^19 + 47/43520*a^18 + 133/43520*a^17 + 41/5440*a^16 + 327/21760*a^15 - 719/21760*a^14 + 49/4352*a^13 + 7/21760*a^12 + 613/21760*a^11 + 3853/43520*a^10 + 111/4352*a^9 - 39/2720*a^8 - 2399/10880*a^7 + 377/5440*a^6 - 329/1360*a^5 - 123/340*a^4 + 3/85*a^3 - 38/85*a^2 + 123/340*a - 83/170, 1/348160*a^23 - 11/43520*a^21 - 37/87040*a^20 - 67/87040*a^19 - 33/17408*a^18 + 133/43520*a^17 + 271/43520*a^16 + 973/43520*a^15 - 37/2560*a^14 - 1503/43520*a^13 - 193/8704*a^12 - 3631/87040*a^11 + 7/160*a^10 - 823/10880*a^9 + 99/2176*a^8 + 443/2176*a^7 + 81/680*a^6 + 149/2720*a^5 + 363/1360*a^4 - 1/17*a^3 - 38/85*a^2 + 151/340*a + 33/85], 1, 3, [3], 1, [ (1811)/(348160)*a^(23) - (57)/(10880)*a^(22) - (1303)/(43520)*a^(21) + (1107)/(17408)*a^(20) - (4441)/(87040)*a^(19) + (2037)/(87040)*a^(18) + (227)/(43520)*a^(17) - (363)/(8704)*a^(16) + (503)/(8704)*a^(15) - (12623)/(43520)*a^(14) + (31267)/(43520)*a^(13) - (14823)/(43520)*a^(12) - (13705)/(17408)*a^(11) + (4271)/(5440)*a^(10) + (16987)/(10880)*a^(9) - (119)/(40)*a^(8) + (27233)/(10880)*a^(7) - (16471)/(5440)*a^(6) + (1811)/(544)*a^(5) - (5533)/(1360)*a^(4) + (447)/(680)*a^(3) + (7597)/(340)*a^(2) - (3307)/(68)*a + (5077)/(170) , (257)/(10240)*a^(23) - (833)/(10240)*a^(22) + (821)/(5120)*a^(21) - (53)/(256)*a^(20) + (323)/(2560)*a^(19) + (21)/(640)*a^(18) - (527)/(2560)*a^(17) + (125)/(256)*a^(16) - (69)/(64)*a^(15) + (947)/(640)*a^(14) - (217)/(160)*a^(13) + (23)/(160)*a^(12) + (115)/(512)*a^(11) + (7387)/(2560)*a^(10) - (10619)/(1280)*a^(9) + (8303)/(640)*a^(8) - (7383)/(640)*a^(7) + (3251)/(320)*a^(6) - (79)/(16)*a^(5) - (363)/(20)*a^(4) + (1339)/(20)*a^(3) - (2337)/(20)*a^(2) + (547)/(4)*a - (877)/(10) , (1227)/(348160)*a^(23) - (3157)/(174080)*a^(22) + (3747)/(87040)*a^(21) - (4537)/(87040)*a^(20) + (2477)/(87040)*a^(19) + (587)/(87040)*a^(18) - (203)/(4352)*a^(17) + (4901)/(43520)*a^(16) - (10607)/(43520)*a^(15) + (17443)/(43520)*a^(14) - (16951)/(43520)*a^(13) - (1533)/(43520)*a^(12) + (22039)/(87040)*a^(11) + (29567)/(43520)*a^(10) - (49457)/(21760)*a^(9) + (4149)/(1360)*a^(8) - (28827)/(10880)*a^(7) + (14097)/(5440)*a^(6) - (3931)/(2720)*a^(5) - (59)/(17)*a^(4) + (77)/(5)*a^(3) - (2103)/(68)*a^(2) + (11931)/(340)*a - (3107)/(170) , (2581)/(348160)*a^(23) - (83)/(4352)*a^(22) + (503)/(87040)*a^(21) + (1953)/(87040)*a^(20) - (2477)/(87040)*a^(19) + (515)/(17408)*a^(18) - (1557)/(43520)*a^(17) + (2001)/(43520)*a^(16) - (5067)/(43520)*a^(15) + (1631)/(43520)*a^(14) + (16577)/(43520)*a^(13) - (3481)/(8704)*a^(12) - (46451)/(87040)*a^(11) + (14041)/(10880)*a^(10) - (7561)/(21760)*a^(9) - (691)/(1088)*a^(8) + (35)/(136)*a^(7) - (5427)/(5440)*a^(6) + (6549)/(2720)*a^(5) - (4321)/(680)*a^(4) + (25)/(2)*a^(3) - (1317)/(340)*a^(2) - (1661)/(85)*a + (3141)/(170) , (301)/(43520)*a^(23) - (567)/(43520)*a^(22) + (1043)/(87040)*a^(21) - (609)/(43520)*a^(20) + (329)/(43520)*a^(19) + (287)/(21760)*a^(18) - (127)/(4352)*a^(17) + (1337)/(21760)*a^(16) - (1737)/(10880)*a^(15) + (489)/(5440)*a^(14) + (139)/(10880)*a^(13) + (97)/(10880)*a^(12) - (1579)/(5440)*a^(11) + (2891)/(5440)*a^(10) - (13253)/(21760)*a^(9) + (14153)/(10880)*a^(8) - (12103)/(10880)*a^(7) + (203)/(340)*a^(6) + (107)/(340)*a^(5) - (1151)/(272)*a^(4) + (7093)/(680)*a^(3) - (567)/(68)*a^(2) + (2449)/(340)*a - (834)/(85) , (447)/(43520)*a^(23) - (5147)/(174080)*a^(22) + (2707)/(43520)*a^(21) - (385)/(4352)*a^(20) + (623)/(10880)*a^(19) + (441)/(43520)*a^(18) - (3413)/(43520)*a^(17) + (865)/(4352)*a^(16) - (1827)/(4352)*a^(15) + (12271)/(21760)*a^(14) - (13389)/(21760)*a^(13) + (3321)/(21760)*a^(12) + (433)/(4352)*a^(11) + (39093)/(43520)*a^(10) - (35363)/(10880)*a^(9) + (437)/(80)*a^(8) - (52457)/(10880)*a^(7) + (22719)/(5440)*a^(6) - (575)/(272)*a^(5) - (4689)/(680)*a^(4) + (17077)/(680)*a^(3) - (7679)/(170)*a^(2) + (4057)/(68)*a - (6583)/(170) , (3369)/(348160)*a^(23) - (2187)/(43520)*a^(22) + (2429)/(21760)*a^(21) - (2087)/(17408)*a^(20) + (5391)/(87040)*a^(19) + (1863)/(87040)*a^(18) - (5487)/(43520)*a^(17) + (2519)/(8704)*a^(16) - (303)/(512)*a^(15) + (44623)/(43520)*a^(14) - (38207)/(43520)*a^(13) - (12317)/(43520)*a^(12) + (9285)/(17408)*a^(11) + (22523)/(10880)*a^(10) - (31811)/(5440)*a^(9) + (38659)/(5440)*a^(8) - (18177)/(2720)*a^(7) + (34061)/(5440)*a^(6) - (1505)/(544)*a^(5) - (6371)/(680)*a^(4) + (27333)/(680)*a^(3) - (27037)/(340)*a^(2) + (1390)/(17)*a - (5517)/(170) , (5331)/(348160)*a^(23) - (959)/(21760)*a^(22) + (3209)/(87040)*a^(21) + (53)/(17408)*a^(20) - (2651)/(87040)*a^(19) + (4697)/(87040)*a^(18) - (3823)/(43520)*a^(17) + (1319)/(8704)*a^(16) - (189)/(512)*a^(15) + (14177)/(43520)*a^(14) + (17727)/(43520)*a^(13) - (29763)/(43520)*a^(12) - (13233)/(17408)*a^(11) + (28797)/(10880)*a^(10) - (43851)/(21760)*a^(9) + (9487)/(10880)*a^(8) - (757)/(680)*a^(7) + (39)/(5440)*a^(6) + (1551)/(544)*a^(5) - (9059)/(680)*a^(4) + (10671)/(340)*a^(3) - (4409)/(170)*a^(2) - (172)/(17)*a + (3047)/(170) , (29)/(2720)*a^(23) - (4143)/(174080)*a^(22) + (7)/(136)*a^(21) - (1859)/(21760)*a^(20) + (65)/(1088)*a^(19) + (369)/(43520)*a^(18) - (3093)/(43520)*a^(17) + (3979)/(21760)*a^(16) - (8723)/(21760)*a^(15) + (10243)/(21760)*a^(14) - (13433)/(21760)*a^(13) + (7629)/(21760)*a^(12) + (143)/(21760)*a^(11) + (21849)/(43520)*a^(10) - (14283)/(5440)*a^(9) + (7401)/(1360)*a^(8) - (48413)/(10880)*a^(7) + (4133)/(1088)*a^(6) - (1347)/(680)*a^(5) - (2187)/(340)*a^(4) + (15163)/(680)*a^(3) - (3257)/(85)*a^(2) + (20153)/(340)*a - (8009)/(170) , (437)/(348160)*a^(23) - (1331)/(174080)*a^(22) + (311)/(21760)*a^(21) - (1203)/(87040)*a^(20) + (819)/(87040)*a^(19) + (321)/(87040)*a^(18) - (47)/(2720)*a^(17) + (1629)/(43520)*a^(16) - (3613)/(43520)*a^(15) + (1149)/(8704)*a^(14) - (3741)/(43520)*a^(13) - (2079)/(43520)*a^(12) + (1441)/(87040)*a^(11) + (2777)/(8704)*a^(10) - (2019)/(2720)*a^(9) + (4533)/(5440)*a^(8) - (10861)/(10880)*a^(7) + (5279)/(5440)*a^(6) - (889)/(2720)*a^(5) - (219)/(170)*a^(4) + (4041)/(680)*a^(3) - (3427)/(340)*a^(2) + (2829)/(340)*a - (7)/(2) , (13)/(640)*a^(23) - (9723)/(174080)*a^(22) + (95)/(1088)*a^(21) - (4543)/(43520)*a^(20) + (535)/(8704)*a^(19) + (1339)/(43520)*a^(18) - (5613)/(43520)*a^(17) + (6539)/(21760)*a^(16) - (15143)/(21760)*a^(15) + (17233)/(21760)*a^(14) - (10873)/(21760)*a^(13) - (231)/(21760)*a^(12) - (7717)/(21760)*a^(11) + (97149)/(43520)*a^(10) - (24473)/(5440)*a^(9) + (77653)/(10880)*a^(8) - (35089)/(5440)*a^(7) + (353)/(68)*a^(6) - (1057)/(680)*a^(5) - (19413)/(1360)*a^(4) + (3811)/(85)*a^(3) - (21453)/(340)*a^(2) + (5492)/(85)*a - (3977)/(85) ], 39316667.48906936, [[x^2 - x + 1, 1], [x^2 - 3, 1], [x^2 + 1, 1], [x^3 - x^2 - 3*x + 1, 1], [x^4 - x^2 + 1, 1], [x^6 - 2*x^5 + 23*x^4 - 6*x^3 + 141*x^2 + 152*x + 361, 1], [x^6 - 2*x^5 - 10*x^4 + 6*x^3 + 12*x^2 - 4*x - 2, 1], [x^6 - 3*x^5 - 8*x^4 + 13*x^3 + 22*x^2 - x - 5, 1], [x^6 - x^5 + 4*x^4 + x^3 + 10*x^2 - 3*x + 1, 1], [x^6 - 3*x^5 + 5*x^4 - 3*x^3 + 4*x^2 + 2*x + 2, 1], [x^6 - 2*x^5 + 2*x^4 + 2*x^3 + 4*x^2 - 4*x + 2, 1], [x^6 - 2*x^5 - 9*x^4 + 6*x^3 + 25*x^2 + 12*x + 1, 1], [x^12 - 4*x^11 + 8*x^10 - 10*x^9 + 12*x^8 - 20*x^7 + 34*x^6 - 40*x^5 + 48*x^4 - 80*x^3 + 128*x^2 - 128*x + 64, 1], [x^12 - 4*x^11 + 16*x^10 - 46*x^9 + 92*x^8 - 148*x^7 + 158*x^6 + 296*x^5 + 368*x^4 + 368*x^3 + 256*x^2 + 128*x + 64, 1], [x^12 - 3*x^11 + 4*x^10 - x^9 - 6*x^8 + 13*x^7 - 21*x^6 + 26*x^5 - 24*x^4 - 8*x^3 + 64*x^2 - 96*x + 64, 1], [x^12 + 25*x^10 + 234*x^8 + 1017*x^6 + 2078*x^4 + 1757*x^2 + 361, 1], [x^12 - 2*x^11 + 2*x^10 - 8*x^9 + 4*x^8 + 16*x^7 - 8*x^6 + 20*x^5 + 20*x^4 - 24*x^3 + 8*x^2 - 8*x + 4, 1], [x^12 - 19*x^10 + 118*x^8 - 287*x^6 + 310*x^4 - 147*x^2 + 25, 1], [x^12 - 2*x^11 + 13*x^10 + 6*x^9 + 68*x^8 + 58*x^7 + 287*x^6 + 364*x^5 + 562*x^4 + 288*x^3 + 119*x^2 + 12*x + 1, 1]]]