/* 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^31 + 3*x^30 - 2*x^29 - 12*x^27 + 17*x^26 - 24*x^25 + 3*x^24 + 8*x^23 + 101*x^22 - 128*x^21 + 208*x^20 - 34*x^19 + 39*x^18 - 726*x^17 + 877*x^16 - 1452*x^15 + 156*x^14 - 272*x^13 + 3328*x^12 - 4096*x^11 + 6464*x^10 + 1024*x^9 + 768*x^8 - 12288*x^7 + 17408*x^6 - 24576*x^5 - 16384*x^3 + 49152*x^2 - 65536*x + 65536, 32, 204, [0, 16], 5037920877776643425304576000000000000000000000000, [2, 3, 5, 17], [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 - 1/2*a^11 - 1/4*a^10 - 1/2*a^9 + 1/4*a^8 - 1/2*a^7 - 1/2*a^5 - 1/4*a^4 + 1/4*a^2 - 1/2*a, 1/8*a^19 - 1/8*a^17 - 1/2*a^16 - 1/2*a^15 - 1/2*a^14 + 1/8*a^13 + 1/4*a^12 + 3/8*a^11 - 1/4*a^10 - 3/8*a^9 + 1/4*a^8 - 1/4*a^6 + 3/8*a^5 + 1/8*a^3 - 1/4*a^2 - 1/2*a, 1/48*a^20 + 1/16*a^18 - 1/4*a^17 - 1/2*a^16 - 1/4*a^15 + 3/16*a^14 - 1/8*a^13 - 3/16*a^12 + 1/8*a^11 + 17/48*a^10 + 3/8*a^9 - 1/4*a^8 + 1/8*a^7 + 1/16*a^6 - 1/16*a^4 - 3/8*a^3 - 1/2*a^2 + 1/3, 1/96*a^21 + 1/32*a^19 - 1/8*a^18 - 1/4*a^17 - 1/8*a^16 - 13/32*a^15 - 1/16*a^14 - 3/32*a^13 + 1/16*a^12 + 17/96*a^11 + 3/16*a^10 - 1/8*a^9 - 7/16*a^8 - 15/32*a^7 - 1/2*a^6 + 15/32*a^5 + 5/16*a^4 + 1/4*a^3 - 1/2*a^2 - 1/3*a, 1/192*a^22 - 1/192*a^20 - 1/16*a^19 + 1/16*a^18 + 3/16*a^17 - 29/64*a^16 + 7/32*a^15 - 15/64*a^14 - 11/32*a^13 - 91/192*a^12 + 15/32*a^11 - 1/6*a^10 - 3/32*a^9 - 15/64*a^8 - 3/8*a^7 + 11/64*a^6 + 5/32*a^5 - 1/16*a^4 - 3/8*a^3 + 1/12*a^2 - 1/3, 1/384*a^23 - 1/384*a^21 - 1/96*a^20 + 1/32*a^19 - 3/32*a^18 + 3/128*a^17 + 23/64*a^16 + 17/128*a^15 + 1/64*a^14 + 53/384*a^13 - 13/64*a^12 + 1/24*a^11 - 85/192*a^10 + 33/128*a^9 + 5/16*a^8 + 27/128*a^7 - 23/64*a^6 - 1/32*a^5 - 1/2*a^4 + 1/6*a^3 - 1/4*a^2 - 1/6*a + 1/3, 1/768*a^24 - 1/768*a^22 - 1/192*a^21 - 1/192*a^20 - 3/64*a^19 - 13/256*a^18 - 9/128*a^17 - 111/256*a^16 - 31/128*a^15 - 91/768*a^14 - 61/128*a^13 - 7/24*a^12 - 133/384*a^11 + 211/768*a^10 + 9/32*a^9 - 37/256*a^8 + 25/128*a^7 - 5/64*a^6 + 1/4*a^5 + 7/48*a^4 - 1/4*a^3 + 5/12*a^2 + 1/6*a - 1/3, 1/1536*a^25 - 1/1536*a^23 - 1/384*a^22 - 1/384*a^21 - 1/384*a^20 - 13/512*a^19 + 7/256*a^18 + 17/512*a^17 + 97/256*a^16 - 475/1536*a^15 - 13/256*a^14 + 11/48*a^13 - 277/768*a^12 + 403/1536*a^11 + 95/192*a^10 + 155/512*a^9 + 89/256*a^8 - 53/128*a^7 - 5/16*a^6 - 41/96*a^5 + 5/16*a^4 + 1/3*a^3 - 5/12*a^2 - 1/6*a + 1/3, 1/1373184*a^26 + 1/171648*a^25 + 823/1373184*a^24 + 13/114432*a^23 + 169/343296*a^22 - 1523/343296*a^21 + 8953/1373184*a^20 - 9469/228864*a^19 - 2807/457728*a^18 + 10345/228864*a^17 + 646541/1373184*a^16 + 220865/686592*a^15 + 14959/171648*a^14 - 39011/228864*a^13 + 214163/1373184*a^12 - 4669/21456*a^11 + 556457/1373184*a^10 + 80441/228864*a^9 + 937/114432*a^8 + 11353/57216*a^7 + 413/2682*a^6 + 16675/42912*a^5 - 127/10728*a^4 - 925/3576*a^3 - 433/2682*a^2 - 85/2682*a + 157/1341, 1/2746368*a^27 + 253/915456*a^25 + 181/686592*a^24 - 143/686592*a^23 - 1087/686592*a^22 + 473/2746368*a^21 + 1/9216*a^20 - 22951/915456*a^19 + 10767/152576*a^18 + 278717/2746368*a^17 + 50685/152576*a^16 - 13447/38144*a^15 + 301855/1373184*a^14 - 874237/2746368*a^13 + 115025/343296*a^12 - 1244087/2746368*a^11 + 85999/1373184*a^10 + 72533/228864*a^9 - 743/38144*a^8 - 30667/85824*a^7 - 521/2384*a^6 - 1333/3576*a^5 - 1103/10728*a^4 - 397/1341*a^3 + 1591/5364*a^2 + 472/1341*a - 628/1341, 1/38449152*a^28 + 1/19224576*a^27 - 5/38449152*a^26 - 1837/6408192*a^25 + 1973/4806144*a^24 - 1643/1373184*a^23 - 11609/5492736*a^22 - 16127/3204096*a^21 - 90431/12816384*a^20 + 111989/3204096*a^19 - 677677/5492736*a^18 - 1827365/9612288*a^17 + 978989/2403072*a^16 + 1469/43008*a^15 - 3040801/38449152*a^14 - 1209101/19224576*a^13 + 7150469/38449152*a^12 - 44875/400512*a^11 + 143827/457728*a^10 - 583157/1602048*a^9 - 388285/1201536*a^8 + 42985/300384*a^7 + 20471/42912*a^6 + 2737/7152*a^5 + 4721/18774*a^4 + 937/37548*a^3 + 3287/18774*a^2 - 843/2086*a + 373/1043, 1/2383847424*a^29 + 13/1191923712*a^28 - 79/794615808*a^27 + 25/132435968*a^26 + 18209/74495232*a^25 - 37327/66217984*a^24 + 48191/37838848*a^23 + 1527193/595961856*a^22 + 1234429/340549632*a^21 + 1453511/595961856*a^20 + 110473373/2383847424*a^19 + 32293267/595961856*a^18 + 6813511/33108992*a^17 + 58222167/132435968*a^16 - 1074248401/2383847424*a^15 + 26402679/132435968*a^14 + 338108095/794615808*a^13 + 13246097/148990464*a^12 + 192172733/595961856*a^11 - 10804051/74495232*a^10 - 34551901/74495232*a^9 + 683359/2660544*a^8 + 1796261/6207936*a^7 - 5493/73904*a^6 + 202639/9311904*a^5 - 10553/64666*a^4 + 31847/96999*a^3 + 132326/290997*a^2 + 214321/581994*a - 98162/290997, 1/4767694848*a^30 - 5/529743872*a^28 - 83/1191923712*a^27 + 89/595961856*a^26 + 17813/1191923712*a^25 + 1764617/4767694848*a^24 + 1286669/2383847424*a^23 + 619407/529743872*a^22 - 1662463/794615808*a^21 - 31592527/4767694848*a^20 + 4017521/264871936*a^19 - 14768321/397307904*a^18 - 235972133/2383847424*a^17 - 2139106717/4767694848*a^16 - 57621611/297980928*a^15 + 1427736349/4767694848*a^14 - 650459153/2383847424*a^13 + 89377301/198653952*a^12 + 34284473/99326976*a^11 + 138967555/297980928*a^10 - 2848789/16554496*a^9 + 698255/12415872*a^8 + 2019749/9311904*a^7 + 3603437/9311904*a^6 + 534445/9311904*a^5 - 1309339/4655952*a^4 - 712855/2327976*a^3 - 463/193998*a^2 + 44092/96999*a + 46559/96999, 1/9535389696*a^31 - 1/9535389696*a^29 + 17/2383847424*a^28 - 197/2383847424*a^27 - 611/2383847424*a^26 - 724279/9535389696*a^25 - 698153/1589231616*a^24 - 978319/3178463232*a^23 - 1402873/4767694848*a^22 + 2443901/1059487744*a^21 - 1527295/227033088*a^20 - 12304021/297980928*a^19 - 468423601/4767694848*a^18 - 2141092141/9535389696*a^17 + 18693379/1191923712*a^16 + 283693441/9535389696*a^15 - 254467377/529743872*a^14 + 1418833/113516544*a^13 + 343342645/1191923712*a^12 - 32342927/66217984*a^11 + 5905783/33108992*a^10 - 10560919/148990464*a^9 - 32321279/74495232*a^8 - 3720133/18623808*a^7 + 8143193/18623808*a^6 - 2264785/9311904*a^5 - 471277/1551984*a^4 - 14351/96999*a^3 - 363739/1163988*a^2 + 195613/581994*a - 47933/96999], 1, 16, [4, 4], 1, [ (2995)/(170274816)*a^(31) + (3953)/(56758272)*a^(30) - (3953)/(170274816)*a^(29) + (3953)/(170274816)*a^(28) + (3953)/(85137408)*a^(27) - (223)/(2364928)*a^(26) - (146261)/(170274816)*a^(25) - (27671)/(170274816)*a^(24) - (27671)/(170274816)*a^(23) - (43483)/(56758272)*a^(22) - (2575)/(56758272)*a^(21) + (359723)/(56758272)*a^(20) + (98825)/(42568704)*a^(19) + (264851)/(85137408)*a^(18) + (976391)/(170274816)*a^(17) + (131973)/(18919424)*a^(16) - (6257599)/(170274816)*a^(15) - (1656307)/(170274816)*a^(14) - (992203)/(42568704)*a^(13) - (51389)/(1182464)*a^(12) - (261171)/(4729856)*a^(11) + (573185)/(3547392)*a^(10) + (51389)/(1330272)*a^(9) + (146261)/(2660544)*a^(8) + (75107)/(332568)*a^(7) + (73495)/(295616)*a^(6) - (43483)/(83142)*a^(5) - (3953)/(41571)*a^(4) - (3953)/(41571)*a^(3) - (3953)/(13857)*a^(2) - (58283)/(41571)*a + (29669)/(13857) , (27379)/(340549632)*a^(31) - (1330361)/(4767694848)*a^(30) + (3709)/(16554496)*a^(29) - (12443)/(227033088)*a^(28) - (9209)/(794615808)*a^(27) - (1139609)/(1191923712)*a^(26) + (6668527)/(2383847424)*a^(25) - (3597077)/(4767694848)*a^(24) - (1052059)/(794615808)*a^(23) + (1521181)/(4767694848)*a^(22) + (20808449)/(2383847424)*a^(21) - (104713589)/(4767694848)*a^(20) + (788495)/(198653952)*a^(19) + (220603)/(66217984)*a^(18) + (134381)/(16554496)*a^(17) - (302983039)/(4767694848)*a^(16) + (379315)/(2660544)*a^(15) - (141166021)/(4767694848)*a^(14) - (3960169)/(397307904)*a^(13) - (4980001)/(297980928)*a^(12) + (95393351)/(297980928)*a^(11) - (6396827)/(9311904)*a^(10) + (511547)/(12415872)*a^(9) + (5236289)/(24831744)*a^(8) - (20431)/(775992)*a^(7) - (1633085)/(1163988)*a^(6) + (11949431)/(4655952)*a^(5) + (95251)/(4655952)*a^(4) - (75977)/(387996)*a^(3) - (261275)/(166284)*a^(2) + (580592)/(96999)*a - (2243380)/(290997) , (26249)/(4767694848)*a^(31) - (18895)/(153796608)*a^(30) + (1248517)/(4767694848)*a^(29) + (480749)/(4767694848)*a^(28) + (177749)/(2383847424)*a^(27) + (49501)/(595961856)*a^(26) + (1181027)/(681099264)*a^(25) - (1103759)/(529743872)*a^(24) - (13430177)/(4767694848)*a^(23) - (6366721)/(4767694848)*a^(22) - (6591799)/(4767694848)*a^(21) - (80680687)/(4767694848)*a^(20) + (13637087)/(1191923712)*a^(19) + (41147033)/(2383847424)*a^(18) + (12893387)/(681099264)*a^(17) + (7917151)/(681099264)*a^(16) + (585773707)/(4767694848)*a^(15) - (29102499)/(529743872)*a^(14) - (86784295)/(1191923712)*a^(13) - (782729)/(9612288)*a^(12) - (3761251)/(37247616)*a^(11) - (50205413)/(74495232)*a^(10) + (12234679)/(74495232)*a^(9) + (852959)/(2660544)*a^(8) + (2567233)/(18623808)*a^(7) + (929255)/(4655952)*a^(6) + (13599659)/(4655952)*a^(5) - (5435)/(64666)*a^(4) - (177749)/(290997)*a^(3) - (203998)/(290997)*a^(2) + (62035)/(41571)*a - (361283)/(41571) , (8321)/(397307904)*a^(31) - (8623)/(85137408)*a^(30) - (8321)/(397307904)*a^(29) - (8321)/(595961856)*a^(28) - (8321)/(297980928)*a^(27) - (91531)/(297980928)*a^(26) + (326065)/(397307904)*a^(25) + (158099)/(297980928)*a^(24) + (307877)/(1191923712)*a^(23) + (108173)/(297980928)*a^(22) + (1206545)/(397307904)*a^(21) - (358817)/(99326976)*a^(20) - (108173)/(33108992)*a^(19) - (2088571)/(595961856)*a^(18) - (3486499)/(1191923712)*a^(17) - (13172143)/(595961856)*a^(16) + (10078577)/(397307904)*a^(15) + (2055287)/(148990464)*a^(14) + (557507)/(37247616)*a^(13) + (208025)/(9311904)*a^(12) + (108173)/(886848)*a^(11) - (733981)/(8277248)*a^(10) - (91531)/(1551984)*a^(9) - (8321)/(332568)*a^(8) - (8321)/(166284)*a^(7) - (307877)/(581994)*a^(6) + (495449)/(3103968)*a^(5) + (33284)/(290997)*a^(4) + (33284)/(290997)*a^(3) - (66568)/(290997)*a^(2) + (133136)/(96999)*a - (378233)/(290997) , (130561)/(1362198528)*a^(31) - (16339)/(681099264)*a^(30) + (87091)/(3178463232)*a^(29) + (326327)/(4767694848)*a^(28) - (19613)/(264871936)*a^(27) - (960095)/(794615808)*a^(26) - (3064937)/(9535389696)*a^(25) - (546677)/(2383847424)*a^(24) - (1501225)/(1362198528)*a^(23) + (519947)/(2383847424)*a^(22) + (84923815)/(9535389696)*a^(21) + (3283193)/(794615808)*a^(20) + (114575)/(25632768)*a^(19) + (40935661)/(4767694848)*a^(18) + (3204769)/(1059487744)*a^(17) - (27113859)/(529743872)*a^(16) - (26280031)/(1362198528)*a^(15) - (2879983)/(85137408)*a^(14) - (19366609)/(297980928)*a^(13) - (36632305)/(1191923712)*a^(12) + (133625333)/(595961856)*a^(11) + (3923243)/(49663488)*a^(10) + (4198177)/(49663488)*a^(9) + (12498007)/(37247616)*a^(8) + (1449599)/(4138624)*a^(7) - (315535)/(443424)*a^(6) - (521489)/(2327976)*a^(5) - (326327)/(2327976)*a^(4) - (1109089)/(2327976)*a^(3) - (2194505)/(1163988)*a^(2) + (27383)/(18774)*a + (65054)/(290997) , (1363147)/(9535389696)*a^(31) - (133993)/(595961856)*a^(30) + (2412433)/(9535389696)*a^(29) + (354143)/(2383847424)*a^(28) - (42185)/(1191923712)*a^(27) - (4122709)/(2383847424)*a^(26) + (18173123)/(9535389696)*a^(25) - (6617881)/(4767694848)*a^(24) - (33590611)/(9535389696)*a^(23) - (859369)/(681099264)*a^(22) + (127205563)/(9535389696)*a^(21) - (23251183)/(1589231616)*a^(20) + (3536561)/(340549632)*a^(19) + (96162497)/(4767694848)*a^(18) + (235519201)/(9535389696)*a^(17) - (6044197)/(74495232)*a^(16) + (1010837407)/(9535389696)*a^(15) - (316023707)/(4767694848)*a^(14) - (4430413)/(38449152)*a^(13) - (8081765)/(74495232)*a^(12) + (208386641)/(595961856)*a^(11) - (55750157)/(99326976)*a^(10) + (22340389)/(148990464)*a^(9) + (23524001)/(37247616)*a^(8) + (18054899)/(37247616)*a^(7) - (1967731)/(1330272)*a^(6) + (2583793)/(1163988)*a^(5) - (70631)/(2327976)*a^(4) - (2141269)/(2327976)*a^(3) - (4097845)/(1163988)*a^(2) + (3159743)/(581994)*a - (1843763)/(290997) , (396563)/(9535389696)*a^(31) - (16331)/(113516544)*a^(30) + (286085)/(9535389696)*a^(29) - (167)/(4806144)*a^(28) - (13233)/(264871936)*a^(27) - (1352011)/(2383847424)*a^(26) + (1370435)/(1059487744)*a^(25) + (233911)/(681099264)*a^(24) + (56195)/(3178463232)*a^(23) + (3425375)/(4767694848)*a^(22) + (55371727)/(9535389696)*a^(21) - (13747001)/(1589231616)*a^(20) - (181775)/(85137408)*a^(19) - (2947673)/(681099264)*a^(18) - (9621445)/(3178463232)*a^(17) - (103490591)/(2383847424)*a^(16) + (151914649)/(3178463232)*a^(15) + (61712411)/(4767694848)*a^(14) + (828245)/(37838848)*a^(13) + (20844791)/(595961856)*a^(12) + (75202255)/(297980928)*a^(11) - (2393623)/(12415872)*a^(10) - (344491)/(21284352)*a^(9) + (674435)/(74495232)*a^(8) - (1550665)/(12415872)*a^(7) - (309521)/(290997)*a^(6) + (1356823)/(3103968)*a^(5) - (14123)/(290997)*a^(4) + (6569)/(55428)*a^(3) - (722947)/(1163988)*a^(2) + (669175)/(193998)*a - (135214)/(96999) , (266345)/(4767694848)*a^(31) - (449)/(31997952)*a^(30) + (224909)/(4767694848)*a^(29) + (753005)/(4767694848)*a^(28) + (9323)/(76898304)*a^(27) - (629785)/(1191923712)*a^(26) - (49253)/(681099264)*a^(25) - (773147)/(4767694848)*a^(24) - (878537)/(529743872)*a^(23) - (8207233)/(4767694848)*a^(22) + (15219961)/(4767694848)*a^(21) + (603217)/(4767694848)*a^(20) + (4117291)/(1191923712)*a^(19) + (24370079)/(2383847424)*a^(18) + (9936467)/(681099264)*a^(17) - (9328661)/(681099264)*a^(16) + (33065387)/(4767694848)*a^(15) - (81577339)/(4767694848)*a^(14) - (7863937)/(132435968)*a^(13) - (101399093)/(1191923712)*a^(12) + (6920029)/(148990464)*a^(11) - (4231327)/(74495232)*a^(10) - (5490101)/(148990464)*a^(9) + (592637)/(2660544)*a^(8) + (7034887)/(18623808)*a^(7) - (871699)/(4655952)*a^(6) + (1235893)/(4655952)*a^(5) + (291457)/(4655952)*a^(4) - (7039)/(64666)*a^(3) - (336454)/(290997)*a^(2) + (1627)/(4619)*a - (14465)/(13857) , (22595)/(3178463232)*a^(31) - (4495)/(51265536)*a^(30) + (592561)/(3178463232)*a^(29) + (31385)/(529743872)*a^(28) + (58375)/(1191923712)*a^(27) + (30145)/(2383847424)*a^(26) + (1632335)/(1362198528)*a^(25) - (466691)/(264871936)*a^(24) - (17542645)/(9535389696)*a^(23) - (2024305)/(2383847424)*a^(22) - (5295715)/(9535389696)*a^(21) - (9187415)/(794615808)*a^(20) + (1242761)/(99326976)*a^(19) + (17828885)/(1589231616)*a^(18) + (17122945)/(1362198528)*a^(17) + (3473185)/(681099264)*a^(16) + (798708445)/(9535389696)*a^(15) - (2126629)/(33108992)*a^(14) - (112705385)/(2383847424)*a^(13) - (1046495)/(19224576)*a^(12) - (2037545)/(37247616)*a^(11) - (1891215)/(4138624)*a^(10) + (2979679)/(16554496)*a^(9) + (5935)/(27714)*a^(8) + (3472355)/(37247616)*a^(7) + (102635)/(1163988)*a^(6) + (18431345)/(9311904)*a^(5) - (113737)/(517328)*a^(4) - (116750)/(290997)*a^(3) - (301285)/(581994)*a^(2) + (95765)/(83142)*a - (24390)/(4619) , (319601)/(4767694848)*a^(31) + (32783)/(595961856)*a^(30) - (203641)/(1589231616)*a^(29) - (64853)/(1191923712)*a^(28) - (48383)/(340549632)*a^(27) - (959809)/(1191923712)*a^(26) - (5980999)/(4767694848)*a^(25) + (2335141)/(2383847424)*a^(24) + (7912585)/(4767694848)*a^(23) - 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