/* 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 + 2*x^30 + 9*x^28 + 4*x^26 + 26*x^24 - 45*x^22 + 10*x^20 - 403*x^18 - 171*x^16 - 1612*x^14 + 160*x^12 - 2880*x^10 + 6656*x^8 + 4096*x^6 + 36864*x^4 + 32768*x^2 + 65536, 32, 405, [0, 16], 44580746322432044939368312527587514829553937678336, [2, 3, 61], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/3*a^8 - 1/3*a^6 - 1/3*a^2 + 1/3, 1/3*a^9 - 1/3*a^7 - 1/3*a^3 + 1/3*a, 1/3*a^10 - 1/3*a^6 - 1/3*a^4 + 1/3, 1/3*a^11 - 1/3*a^7 - 1/3*a^5 + 1/3*a, 1/3*a^12 + 1/3*a^6 + 1/3, 1/3*a^13 + 1/3*a^7 + 1/3*a, 1/3*a^14 + 1/3*a^6 - 1/3*a^2 - 1/3, 1/3*a^15 + 1/3*a^7 - 1/3*a^3 - 1/3*a, 1/9*a^16 + 1/9*a^14 + 1/9*a^12 + 1/9*a^10 + 1/9*a^8 + 1/9*a^6 - 2/9*a^4 - 2/9*a^2 - 2/9, 1/18*a^17 - 1/9*a^15 + 1/18*a^13 - 1/9*a^11 - 1/9*a^9 - 5/18*a^7 - 4/9*a^5 - 5/18*a^3 - 5/18*a, 1/36*a^18 - 1/18*a^16 + 1/36*a^14 + 1/9*a^12 - 1/18*a^10 - 5/36*a^8 - 1/18*a^6 + 13/36*a^4 + 13/36*a^2 - 1/3, 1/72*a^19 - 1/36*a^17 + 1/72*a^15 - 1/9*a^13 + 5/36*a^11 - 5/72*a^9 - 13/36*a^7 - 35/72*a^5 - 23/72*a^3 + 1/3*a, 1/144*a^20 - 1/72*a^18 + 1/144*a^16 + 1/9*a^14 + 5/72*a^12 - 5/144*a^10 - 1/72*a^8 + 37/144*a^6 + 49/144*a^4 + 1/3*a^2, 1/288*a^21 - 1/144*a^19 + 1/288*a^17 - 1/9*a^15 + 5/144*a^13 + 43/288*a^11 - 1/144*a^9 - 59/288*a^7 + 1/288*a^5 + 1/3*a^3 - 1/6*a, 1/1728*a^22 - 1/864*a^20 + 1/1728*a^18 - 1/18*a^16 + 23/288*a^14 - 71/576*a^12 + 7/96*a^10 + 29/192*a^8 + 89/192*a^6 - 17/54*a^4 + 41/108*a^2 - 13/27, 1/3456*a^23 - 1/1728*a^21 + 1/3456*a^19 - 1/36*a^17 + 23/576*a^15 - 71/1152*a^13 - 25/192*a^11 - 35/384*a^9 + 25/384*a^7 - 53/108*a^5 - 31/216*a^3 - 2/27*a, 1/6912*a^24 - 1/3456*a^22 + 1/6912*a^20 - 1/72*a^18 + 23/1152*a^16 - 71/2304*a^14 + 13/128*a^12 - 35/768*a^10 + 25/768*a^8 - 17/216*a^6 + 185/432*a^4 - 1/27*a^2 - 1/3, 1/13824*a^25 - 1/6912*a^23 + 1/13824*a^21 - 1/144*a^19 + 23/2304*a^17 - 71/4608*a^15 + 13/256*a^13 + 221/1536*a^11 + 25/1536*a^9 - 89/432*a^7 + 41/864*a^5 + 13/27*a^3 - 1/2*a, 1/27648*a^26 - 1/13824*a^24 + 1/27648*a^22 - 1/288*a^20 + 23/4608*a^18 - 71/9216*a^16 - 217/1536*a^14 + 221/3072*a^12 - 487/3072*a^10 - 89/864*a^8 - 823/1728*a^6 - 5/54*a^4 - 1/12*a^2, 1/55296*a^27 - 1/27648*a^25 + 1/55296*a^23 - 1/576*a^21 + 23/9216*a^19 - 71/18432*a^17 - 217/3072*a^15 - 803/6144*a^13 + 179/2048*a^11 - 89/1728*a^9 - 247/3456*a^7 - 23/108*a^5 - 1/24*a^3 - 1/2*a, 1/110592*a^28 - 1/55296*a^26 + 1/110592*a^24 - 1/3456*a^22 + 5/55296*a^20 - 149/110592*a^18 - 217/6144*a^16 + 287/4096*a^14 - 295/12288*a^12 + 355/3456*a^10 - 1123/6912*a^8 - 439/1728*a^6 + 23/432*a^4 + 19/54*a^2 + 2/27, 1/221184*a^29 - 1/110592*a^27 + 1/221184*a^25 - 1/6912*a^23 + 5/110592*a^21 - 149/221184*a^19 - 217/12288*a^17 + 287/8192*a^15 - 295/24576*a^13 - 797/6912*a^11 - 1123/13824*a^9 + 137/3456*a^7 + 167/864*a^5 + 19/108*a^3 + 10/27*a, 1/269402112*a^30 + 7/6414336*a^28 - 613/89800704*a^26 - 193/4810752*a^24 - 881/4988928*a^22 - 5493/3325952*a^20 - 1088293/134701056*a^18 - 248083/29933568*a^16 + 704779/9977856*a^14 - 778427/33675264*a^12 + 35941/5612544*a^10 - 32171/1403136*a^8 - 73/150336*a^6 + 533/14616*a^4 - 367/1044*a^2 + 3971/16443, 1/538804224*a^31 + 7/12828672*a^29 - 613/179601408*a^27 - 193/9621504*a^25 - 881/9977856*a^23 - 5493/6651904*a^21 - 1088293/269402112*a^19 - 248083/59867136*a^17 - 2621173/19955712*a^15 + 10446661/67350528*a^13 + 35941/11225088*a^11 + 435541/2806272*a^9 - 50185/300672*a^7 + 533/29232*a^5 + 677/2088*a^3 + 3971/32886*a], 1, 20, [2, 10], 1, [ (3713)/(44900352)*a^(31) + (259)/(801792)*a^(29) + (16141)/(44900352)*a^(27) + (491)/(356352)*a^(25) - (27499)/(22450176)*a^(23) + (123119)/(44900352)*a^(21) - (205325)/(11225088)*a^(19) + (1051)/(14966784)*a^(17) - (1341583)/(14966784)*a^(15) + (390101)/(22450176)*a^(13) - (696347)/(2806272)*a^(11) + (125497)/(350784)*a^(9) - (7705)/(33408)*a^(7) + (92447)/(43848)*a^(5) + (1279)/(1566)*a^(3) + (31519)/(5481)*a - 1 , (50893)/(269402112)*a^(30) + (1117)/(6414336)*a^(28) + (37229)/(29933568)*a^(26) - (1751)/(9621504)*a^(24) + (108107)/(44900352)*a^(22) - (69499)/(9977856)*a^(20) - (90547)/(134701056)*a^(18) - (1444543)/(29933568)*a^(16) - (790927)/(29933568)*a^(14) - (9107617)/(67350528)*a^(12) + (71059)/(5612544)*a^(10) - (16067)/(155904)*a^(8) + (101327)/(150336)*a^(6) + (118913)/(87696)*a^(4) + (2735)/(1044)*a^(2) + (84104)/(16443) , (1241)/(7483392)*a^(30) - (803)/(1069056)*a^(28) + (32261)/(22450176)*a^(26) - (5845)/(1069056)*a^(24) + (117083)/(11225088)*a^(22) - (622273)/(22450176)*a^(20) + (1307767)/(22450176)*a^(18) - (822421)/(7483392)*a^(16) + (336703)/(1247232)*a^(14) - (1014073)/(2494464)*a^(12) + (299479)/(311808)*a^(10) - (1984253)/(1403136)*a^(8) + (22423)/(8352)*a^(6) - (95407)/(21924)*a^(4) + (13675)/(3132)*a^(2) - (57856)/(5481) , (41)/(442368)*a^(30) - (229)/(221184)*a^(28) + (505)/(442368)*a^(26) - (137)/(18432)*a^(24) + (2749)/(221184)*a^(22) - (14605)/(442368)*a^(20) + (17795)/(221184)*a^(18) - (5899)/(49152)*a^(16) + (18665)/(49152)*a^(14) - (25303)/(55296)*a^(12) + (36347)/(27648)*a^(10) - (13699)/(6912)*a^(8) + (233)/(72)*a^(6) - (2993)/(432)*a^(4) + (421)/(108)*a^(2) - (469)/(27) , (87389)/(269402112)*a^(30) + (1505)/(6414336)*a^(28) + (154087)/(89800704)*a^(26) - (6169)/(9621504)*a^(24) + (67609)/(14966784)*a^(22) - (36713)/(3325952)*a^(20) + (48745)/(134701056)*a^(18) - (691573)/(9977856)*a^(16) - (530263)/(29933568)*a^(14) - (14639735)/(67350528)*a^(12) + (347105)/(5612544)*a^(10) - (58987)/(350784)*a^(8) + (20147)/(18792)*a^(6) + (50927)/(29232)*a^(4) + (358)/(87)*a^(2) + (96952)/(16443) , (207983)/(269402112)*a^(30) + (2111)/(6414336)*a^(28) + (128351)/(29933568)*a^(26) - (28549)/(9621504)*a^(24) + (560369)/(44900352)*a^(22) - (3192817)/(89800704)*a^(20) + (2298271)/(134701056)*a^(18) - (5994853)/(29933568)*a^(16) + (855707)/(29933568)*a^(14) - (42193895)/(67350528)*a^(12) + (629273)/(1403136)*a^(10) - (377921)/(467712)*a^(8) + (249017)/(75168)*a^(6) + (234599)/(87696)*a^(4) + (36883)/(3132)*a^(2) + (174445)/(16443) , (949)/(44900352)*a^(30) - (883)/(801792)*a^(28) + (10211)/(14966784)*a^(26) - (21809)/(3207168)*a^(24) + (84631)/(7483392)*a^(22) - (1213733)/(44900352)*a^(20) + (862471)/(11225088)*a^(18) - (1368305)/(14966784)*a^(16) + (5459333)/(14966784)*a^(14) - (8483459)/(22450176)*a^(12) + (6709453)/(5612544)*a^(10) - (53147)/(29232)*a^(8) + (127811)/(50112)*a^(6) - (8657)/(1218)*a^(4) + (3311)/(1566)*a^(2) - (98684)/(5481) , (2321)/(44900352)*a^(31) + (4201)/(29933568)*a^(30) + (1231)/(6414336)*a^(29) + (119)/(2138112)*a^(28) + (9703)/(44900352)*a^(27) + (64147)/(89800704)*a^(26) + (4981)/(6414336)*a^(25) - (191)/(356352)*a^(24) - (19205)/(22450176)*a^(23) + (75919)/(44900352)*a^(22) + (69353)/(44900352)*a^(21) - (508799)/(89800704)*a^(20) - (142619)/(14966784)*a^(19) + (63775)/(44900352)*a^(18) - (24991)/(14966784)*a^(17) - (856715)/(29933568)*a^(16) - (46999)/(935424)*a^(15) + (2213)/(3325952)*a^(14) + (513895)/(44900352)*a^(13) - (184909)/(2494464)*a^(12) - (1565329)/(11225088)*a^(11) + (31609)/(467712)*a^(10) + (544529)/(2806272)*a^(9) - (11507)/(701568)*a^(8) - (8933)/(50112)*a^(7) + (1697)/(4176)*a^(6) + (99257)/(87696)*a^(5) + (14689)/(21924)*a^(4) + (2245)/(6264)*a^(3) + (2563)/(1566)*a^(2) + (3985)/(1218)*a + (13306)/(5481) , (431)/(3207168)*a^(31) - (15815)/(29933568)*a^(30) + (367)/(712704)*a^(29) - (703)/(2138112)*a^(28) + (923)/(1603584)*a^(27) - (275749)/(89800704)*a^(26) + (13819)/(6414336)*a^(25) + (89)/(66816)*a^(24) - (139)/(66816)*a^(23) - (367249)/(44900352)*a^(22) + (3437)/(801792)*a^(21) + (2026361)/(89800704)*a^(20) - (178451)/(6414336)*a^(19) - (261019)/(44900352)*a^(18) - (95)/(59392)*a^(17) + (4009997)/(29933568)*a^(16) - (299081)/(2138112)*a^(15) + (129683)/(9977856)*a^(14) + (184871)/(6414336)*a^(13) + (780667)/(1870848)*a^(12) - (69059)/(178176)*a^(11) - (66895)/(311808)*a^(10) + (221215)/(400896)*a^(9) + (639103)/(1403136)*a^(8) - (40981)/(100224)*a^(7) - (17093)/(8352)*a^(6) + (13531)/(4176)*a^(5) - (54613)/(21924)*a^(4) + (7361)/(6264)*a^(3) - (26393)/(3132)*a^(2) + (14129)/(1566)*a - (51763)/(5481) , (2213)/(6193152)*a^(31) - (71)/(442368)*a^(30) - (113)/(442368)*a^(29) - (275)/(221184)*a^(28) + (14093)/(6193152)*a^(27) - (127)/(442368)*a^(26) - (791)/(221184)*a^(25) - (247)/(36864)*a^(24) + (9347)/(1032192)*a^(23) + (1805)/(221184)*a^(22) - (5923)/(229376)*a^(21) - (8885)/(442368)*a^(20) + (103093)/(3096576)*a^(19) + (16873)/(221184)*a^(18) - (253045)/(2064384)*a^(17) - (897)/(16384)*a^(16) + (278939)/(2064384)*a^(15) + (18605)/(49152)*a^(14) - (617657)/(1548288)*a^(13) - (25981)/(110592)*a^(12) + (232759)/(387072)*a^(11) + (31891)/(27648)*a^(10) - (92663)/(96768)*a^(9) - (2873)/(1728)*a^(8) + (509)/(216)*a^(7) + (587)/(288)*a^(6) - (41)/(42)*a^(5) - (1703)/(216)*a^(4) + (103)/(18)*a^(3) - (25)/(108)*a^(2) - (160)/(189)*a - (566)/(27) , (4513)/(9977856)*a^(31) - (3883)/(7483392)*a^(30) + (265)/(267264)*a^(29) + (5)/(50112)*a^(28) + (192037)/(89800704)*a^(27) - (71941)/(22450176)*a^(26) + (20023)/(6414336)*a^(25) + (6073)/(1603584)*a^(24) - (42227)/(44900352)*a^(23) - (130969)/(11225088)*a^(22) - (86153)/(89800704)*a^(21) + (672433)/(22450176)*a^(20) - (362045)/(7483392)*a^(19) - (177641)/(5612544)*a^(18) - (1432829)/(29933568)*a^(17) + (378703)/(2494464)*a^(16) - (2564965)/(9977856)*a^(15) - (273715)/(2494464)*a^(14) - (1341077)/(14966784)*a^(13) + (1900697)/(3741696)*a^(12) - (1177433)/(1870848)*a^(11) - (1695061)/(2806272)*a^(10) + (2433211)/(2806272)*a^(9) + (1469365)/(1403136)*a^(8) - (8485)/(100224)*a^(7) - (17221)/(6264)*a^(6) + (1231373)/(175392)*a^(5) + (6809)/(87696)*a^(4) + (30697)/(6264)*a^(3) - (12503)/(1566)*a^(2) + (12260)/(609)*a - (15268)/(5481) , (34625)/(89800704)*a^(31) + (15)/(59392)*a^(30) + (863)/(2138112)*a^(29) + (761)/(1069056)*a^(28) + (193297)/(89800704)*a^(27) + (175)/(133632)*a^(26) - (155)/(1603584)*a^(25) + (10103)/(3207168)*a^(24) + (60535)/(14966784)*a^(23) - (13)/(33408)*a^(22) - (1112773)/(89800704)*a^(21) + (373)/(89088)*a^(20) - (260381)/(44900352)*a^(19) - (117671)/(3207168)*a^(18) - (2380153)/(29933568)*a^(17) - (2677)/(133632)*a^(16) - (1740653)/(29933568)*a^(15) - (209729)/(1069056)*a^(14) - (2737417)/(11225088)*a^(13) - (23239)/(1069056)*a^(12) - (28691)/(1870848)*a^(11) - (144007)/(267264)*a^(10) - (52517)/(2806272)*a^(9) + (19615)/(33408)*a^(8) + (115247)/(100224)*a^(7) - (5735)/(12528)*a^(6) + (2265)/(812)*a^(5) + (424)/(87)*a^(4) + (30647)/(6264)*a^(3) + (3163)/(1044)*a^(2) + (46402)/(5481)*a + (11558)/(783) , (39047)/(538804224)*a^(31) - (114379)/(269402112)*a^(30) - (6173)/(12828672)*a^(29) + (1037)/(2138112)*a^(28) + (114005)/(179601408)*a^(27) - (250345)/(89800704)*a^(26) - (67339)/(19243008)*a^(25) + (13499)/(2405376)*a^(24) + (59249)/(9977856)*a^(23) - (578485)/(44900352)*a^(22) - (112299)/(6651904)*a^(21) + (3143789)/(89800704)*a^(20) + (9851083)/(269402112)*a^(19) - (7077101)/(134701056)*a^(18) - (3688093)/(59867136)*a^(17) + (538729)/(3325952)*a^(16) + (10495339)/(59867136)*a^(15) - (753035)/(3325952)*a^(14) - (30240593)/(134701056)*a^(13) + (4622585)/(8418816)*a^(12) + (1781401)/(2806272)*a^(11) - (455201)/(467712)*a^(10) - (78643)/(87696)*a^(9) + (2008483)/(1403136)*a^(8) + (249143)/(150336)*a^(7) - (498929)/(150336)*a^(6) - (184763)/(58464)*a^(5) + (28069)/(10962)*a^(4) + (265)/(116)*a^(3) - (22043)/(3132)*a^(2) - (272249)/(32886)*a + (71143)/(16443) , (4999)/(269402112)*a^(31) - (8399)/(269402112)*a^(30) + (161)/(2138112)*a^(29) + (2165)/(6414336)*a^(28) + (3823)/(29933568)*a^(27) - (14447)/(29933568)*a^(26) + (4657)/(9621504)*a^(25) + (22579)/(9621504)*a^(24) - (2539)/(44900352)*a^(23) - (210817)/(44900352)*a^(22) + (171799)/(89800704)*a^(21) + (1002881)/(89800704)*a^(20) - (716845)/(134701056)*a^(19) - (3624211)/(134701056)*a^(18) + (29915)/(29933568)*a^(17) + (1273493)/(29933568)*a^(16) - (275095)/(9977856)*a^(15) - (3847955)/(29933568)*a^(14) + (381761)/(67350528)*a^(13) + (11967377)/(67350528)*a^(12) - (137645)/(1247232)*a^(11) - (1143473)/(2806272)*a^(10) + (90107)/(935424)*a^(9) + (326107)/(467712)*a^(8) - (57257)/(300672)*a^(7) - (165175)/(150336)*a^(6) + (105649)/(175392)*a^(5) + (106039)/(43848)*a^(4) + (11)/(3132)*a^(3) - (5615)/(3132)*a^(2) + (38432)/(16443)*a + (85325)/(16443) , (4999)/(269402112)*a^(31) + (8399)/(269402112)*a^(30) + (161)/(2138112)*a^(29) - (2165)/(6414336)*a^(28) + (3823)/(29933568)*a^(27) + (14447)/(29933568)*a^(26) + (4657)/(9621504)*a^(25) - (22579)/(9621504)*a^(24) - (2539)/(44900352)*a^(23) + (210817)/(44900352)*a^(22) + (171799)/(89800704)*a^(21) - (1002881)/(89800704)*a^(20) - (716845)/(134701056)*a^(19) + (3624211)/(134701056)*a^(18) + (29915)/(29933568)*a^(17) - (1273493)/(29933568)*a^(16) - (275095)/(9977856)*a^(15) + (3847955)/(29933568)*a^(14) + (381761)/(67350528)*a^(13) - (11967377)/(67350528)*a^(12) - (137645)/(1247232)*a^(11) + (1143473)/(2806272)*a^(10) + (90107)/(935424)*a^(9) - (326107)/(467712)*a^(8) - (57257)/(300672)*a^(7) + (165175)/(150336)*a^(6) + (105649)/(175392)*a^(5) - (106039)/(43848)*a^(4) + (11)/(3132)*a^(3) + (5615)/(3132)*a^(2) + (38432)/(16443)*a - (85325)/(16443) ], 333896890255.2903, [[x^2 - 3, 1], [x^2 - x + 1, 1], [x^2 + 1, 1], [x^4 - 7*x^2 - 3*x + 1, 1], [x^4 - x^2 + 1, 1], [x^8 + 15*x^6 + 63*x^4 + 54*x^2 + 9, 1], [x^8 + 14*x^6 + 51*x^4 + 23*x^2 + 1, 1], [x^8 - 4*x^7 - 4*x^6 + 23*x^5 + 4*x^4 - 38*x^3 - x^2 + 16*x + 4, 1], [x^8 - 15*x^6 + 74*x^4 - 147*x^2 + 100, 1], [x^8 + x^6 - 3*x^5 - 3*x^4 - 6*x^3 + 4*x^2 + 16, 1], [x^8 - 3*x^7 + 4*x^6 - 4*x^5 + 8*x^4 + 16*x^3 + 18*x^2 + 28*x + 13, 1], [x^8 - 18*x^6 + 63*x^4 - 45*x^2 + 9, 1], [x^16 + 24*x^14 + 226*x^12 + 1059*x^10 + 2595*x^8 + 3204*x^6 + 1651*x^4 + 123*x^2 + 1, 1], [x^16 - x^14 - 5*x^12 + 2*x^10 + 25*x^8 + 8*x^6 - 80*x^4 - 64*x^2 + 256, 1], [x^16 + 6*x^14 + 9*x^12 - 45*x^10 - 234*x^8 - 405*x^6 + 729*x^4 + 4374*x^2 + 6561, 1], [x^16 + x^14 + 8*x^12 - 180*x^10 + 530*x^8 - 360*x^6 - 364*x^4 + 316*x^2 + 169, 1], [x^16 - 2*x^14 - 5*x^12 + 7*x^10 + 13*x^8 + 28*x^6 - 80*x^4 - 128*x^2 + 256, 1], [x^16 - 18*x^14 + 115*x^12 - 342*x^10 + 519*x^8 - 405*x^6 + 154*x^4 - 24*x^2 + 1, 1], [x^16 - 3*x^15 + 4*x^14 - 3*x^13 + 4*x^12 - 6*x^11 + 7*x^10 - 18*x^9 + 37*x^8 - 36*x^7 + 28*x^6 - 48*x^5 + 64*x^4 - 96*x^3 + 256*x^2 - 384*x + 256, 1]]]