/* 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 - 4*x^31 + 8*x^30 - 16*x^29 + 25*x^28 - 24*x^27 + 24*x^26 - 20*x^25 - 36*x^23 + 152*x^22 - 256*x^21 + 425*x^20 - 584*x^19 + 296*x^18 + 4*x^17 + 113*x^16 + 8*x^15 + 1184*x^14 - 4672*x^13 + 6800*x^12 - 8192*x^11 + 9728*x^10 - 4608*x^9 - 10240*x^7 + 24576*x^6 - 49152*x^5 + 102400*x^4 - 131072*x^3 + 131072*x^2 - 131072*x + 65536, 32, 12882, [0, 16], 1033818800357475102568684143000990752577071087616, [2, 3, 41, 113], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, 1/2*a^13 - 1/2*a, 1/4*a^14 + 1/4*a^2, 1/8*a^15 - 1/2*a^12 - 1/2*a^6 + 1/8*a^3, 1/16*a^16 - 1/4*a^13 - 1/2*a^10 - 1/4*a^7 - 7/16*a^4, 1/16*a^17 - 1/2*a^11 - 1/4*a^8 - 7/16*a^5 + 1/4*a^2, 1/16*a^18 - 1/2*a^12 - 1/4*a^9 - 7/16*a^6 + 1/4*a^3, 1/16*a^19 - 1/4*a^10 - 7/16*a^7 + 1/4*a^4 - 1/2*a, 1/16*a^20 - 1/4*a^11 - 7/16*a^8 + 1/4*a^5 - 1/2*a^2, 1/32*a^21 - 1/32*a^17 - 1/8*a^14 - 1/8*a^12 - 1/4*a^11 + 9/32*a^9 + 1/8*a^8 - 3/8*a^6 - 9/32*a^5 + 1/4*a^3 + 1/4*a^2 - 1/2*a, 1/64*a^22 + 1/64*a^18 - 1/16*a^15 - 1/16*a^13 + 1/8*a^12 - 1/2*a^11 - 23/64*a^10 - 1/16*a^9 - 3/16*a^7 - 23/64*a^6 + 1/8*a^4 + 1/4*a^3 - 1/4*a^2, 1/128*a^23 + 1/128*a^19 - 1/32*a^18 - 1/32*a^16 - 1/32*a^14 + 1/16*a^13 + 41/128*a^11 + 15/32*a^10 + 1/8*a^9 - 3/32*a^8 + 41/128*a^7 - 9/32*a^6 + 1/16*a^5 + 1/8*a^4 - 1/4*a^3, 1/256*a^24 - 7/256*a^20 - 1/64*a^19 - 1/64*a^17 - 1/64*a^15 + 1/32*a^14 + 41/256*a^12 + 23/64*a^11 + 1/16*a^10 - 3/64*a^9 - 31/256*a^8 + 23/64*a^7 + 1/32*a^6 - 1/16*a^5 + 3/8*a^4 - 1/2*a^3 + 1/4*a^2 - 1/2*a, 1/512*a^25 - 7/512*a^21 + 3/128*a^20 - 1/128*a^18 - 1/32*a^17 - 1/128*a^16 + 1/64*a^15 - 1/8*a^14 + 41/512*a^13 - 41/128*a^12 + 5/32*a^11 + 61/128*a^10 + 225/512*a^9 + 11/128*a^8 + 1/64*a^7 + 15/32*a^6 - 15/32*a^5 - 1/4*a^4 + 1/8*a^3 + 1/4*a^2 - 1/2*a, 1/5120*a^26 - 1/1280*a^24 + 1/640*a^23 + 9/5120*a^22 - 1/256*a^21 + 7/1280*a^20 - 3/1280*a^19 - 1/40*a^18 - 21/1280*a^17 - 3/640*a^16 - 3/64*a^15 + 617/5120*a^14 - 21/256*a^13 + 619/1280*a^12 - 105/256*a^11 - 623/5120*a^10 + 191/1280*a^9 - 151/1280*a^8 - 99/640*a^7 + 17/40*a^6 - 15/32*a^5 - 27/80*a^4 + 11/40*a^3 - 2/5*a^2 + 2/5, 1/10240*a^27 - 1/2560*a^25 + 1/1280*a^24 + 9/10240*a^23 - 1/512*a^22 + 7/2560*a^21 + 77/2560*a^20 - 1/80*a^19 - 21/2560*a^18 - 3/1280*a^17 - 3/128*a^16 + 617/10240*a^15 - 21/512*a^14 + 619/2560*a^13 - 105/512*a^12 - 1903/10240*a^11 - 1089/2560*a^10 - 151/2560*a^9 - 379/1280*a^8 - 23/80*a^7 - 15/64*a^6 - 7/160*a^5 - 29/80*a^4 + 3/10*a^3 - 1/4*a^2 - 3/10*a, 1/2293760*a^28 - 11/573440*a^27 + 1/286720*a^26 + 89/143360*a^25 - 4471/2293760*a^24 + 5/7168*a^23 + 1847/286720*a^22 - 8861/573440*a^21 + 4241/143360*a^20 + 7031/573440*a^19 - 8793/286720*a^18 + 113/8960*a^17 - 5591/2293760*a^16 + 431/20480*a^15 - 5419/57344*a^14 + 8687/81920*a^13 - 124991/2293760*a^12 + 12083/71680*a^11 - 10929/35840*a^10 + 26591/71680*a^9 + 419/2240*a^8 - 341/1120*a^7 - 1033/4480*a^6 - 11/224*a^5 - 241/560*a^4 - 249/1120*a^3 - 3/35*a^2 - 43/140*a - 199/560, 1/4587520*a^29 - 17/573440*a^27 - 1/286720*a^26 - 2743/4587520*a^25 + 279/229376*a^24 + 273/81920*a^23 - 2677/1146880*a^22 - 807/143360*a^21 - 26073/1146880*a^20 + 685/114688*a^19 - 303/28672*a^18 - 58839/4587520*a^17 - 20761/1146880*a^16 + 289/573440*a^15 + 79073/1146880*a^14 + 74749/917504*a^13 + 113863/229376*a^12 - 7267/71680*a^11 + 49711/143360*a^10 - 10439/35840*a^9 - 11/448*a^8 - 681/8960*a^7 - 93/560*a^6 - 9/140*a^5 - 1073/2240*a^4 + 191/560*a^3 - 67/280*a^2 - 151/1120*a + 107/280, 1/211658997760*a^30 + 8699/105829498880*a^29 - 10923/52914749440*a^28 - 55279/1889812480*a^27 - 1823313/30236999680*a^26 - 55653543/105829498880*a^25 + 16121887/52914749440*a^24 - 53452033/52914749440*a^23 - 13262617/3779624960*a^22 - 21535173/3112632320*a^21 + 86307243/13228687360*a^20 - 74738773/6614343680*a^19 + 5183540233/211658997760*a^18 - 1892741887/105829498880*a^17 + 477832011/52914749440*a^16 - 14377399/622526464*a^15 + 3348841897/211658997760*a^14 - 6050051447/105829498880*a^13 - 13135916631/52914749440*a^12 - 2401429377/6614343680*a^11 - 194399689/3307171840*a^10 - 31941589/97269760*a^9 - 12753041/59056640*a^8 - 57050797/206698240*a^7 - 1779657/103349120*a^6 - 51178157/103349120*a^5 + 1845089/7382080*a^4 + 1195667/3691040*a^3 - 9384191/51674560*a^2 + 8731809/25837280*a - 2329967/12918640, 1/423317995520*a^31 + 3/54132736*a^29 + 4203/26457374720*a^28 - 12312599/423317995520*a^27 - 3208253/105829498880*a^26 - 41543407/105829498880*a^25 - 156940673/105829498880*a^24 + 21846471/6614343680*a^23 + 584132363/105829498880*a^22 + 93143943/7559249920*a^21 - 12326463/1150320640*a^20 - 2236834379/84663599104*a^19 + 227616731/21165899776*a^18 - 901330683/105829498880*a^17 - 1979489851/105829498880*a^16 + 173101137/423317995520*a^15 + 7756402319/105829498880*a^14 + 22206553323/105829498880*a^13 - 1982054257/5291474944*a^12 + 172213997/3307171840*a^11 - 1715089/472453120*a^10 + 67881517/413396480*a^9 + 83802111/206698240*a^8 + 47205517/206698240*a^7 + 80913831/206698240*a^6 + 124569/875840*a^5 - 18928597/51674560*a^4 + 3985041/103349120*a^3 + 10828623/25837280*a^2 + 1766133/3691040*a + 1098613/6459320], 1, 18, [3, 6], 1, [ (3703794851)/(211658997760)*a^(31) - (1197894699)/(26457374720)*a^(30) + (402671777)/(5291474944)*a^(29) - (1826811157)/(10582949888)*a^(28) + (5852074109)/(30236999680)*a^(27) - (7750748149)/(52914749440)*a^(26) + (804498087)/(3779624960)*a^(25) - (634377313)/(13228687360)*a^(24) - (45209289)/(661434368)*a^(23) - (7697360423)/(10582949888)*a^(22) + (6171099447)/(3779624960)*a^(21) - (14402412217)/(6614343680)*a^(20) + (184857860015)/(42331799552)*a^(19) - (213875554313)/(52914749440)*a^(18) - (14379874553)/(26457374720)*a^(17) - (2612486103)/(3779624960)*a^(16) + (204972245843)/(211658997760)*a^(15) + (4717923387)/(3112632320)*a^(14) + (303292561377)/(13228687360)*a^(13) - (2613800806821)/(52914749440)*a^(12) + (11630827107)/(236226560)*a^(11) - (6106489071)/(82679296)*a^(10) + (4716296847)/(71895040)*a^(9) + (152085309)/(12158720)*a^(8) + (5652523)/(320960)*a^(7) - (7967541093)/(51674560)*a^(6) + (1097168817)/(5167456)*a^(5) - (1036063411)/(1845520)*a^(4) + (51644954237)/(51674560)*a^(3) - (11379333309)/(12918640)*a^(2) + (3387108433)/(3229660)*a - (10443159413)/(12918640) , (1799647)/(188981248)*a^(31) - (310992513)/(12450529280)*a^(30) + (259816279)/(6225264640)*a^(29) - (5020445981)/(52914749440)*a^(28) + (284665253)/(2645737472)*a^(27) - (3400326277)/(42331799552)*a^(26) + (12481414041)/(105829498880)*a^(25) - (301016447)/(10582949888)*a^(24) - (420888395)/(10582949888)*a^(23) - (10512546859)/(26457374720)*a^(22) + (47742830757)/(52914749440)*a^(21) - (3951500387)/(3307171840)*a^(20) + (15876079967)/(6614343680)*a^(19) - (95774979077)/(42331799552)*a^(18) - (31759430351)/(105829498880)*a^(17) - (19174548567)/(52914749440)*a^(16) + (6234469639)/(10582949888)*a^(15) + (188632755543)/(211658997760)*a^(14) + (263991035493)/(21165899776)*a^(13) - (1447754989061)/(52914749440)*a^(12) + (35847690341)/(1322868736)*a^(11) - (26860607581)/(661434368)*a^(10) + (528688227)/(14379008)*a^(9) + (554453469)/(82679296)*a^(8) + (81473739)/(8986880)*a^(7) - (8792961057)/(103349120)*a^(6) + (12103225489)/(103349120)*a^(5) - (3167776905)/(10334912)*a^(4) + (14298116207)/(25837280)*a^(3) - (25164534561)/(51674560)*a^(2) + (14906636993)/(25837280)*a - (5861479037)/(12918640) , (86053767)/(60473999360)*a^(31) - (936425449)/(211658997760)*a^(30) + (95797407)/(13228687360)*a^(29) - (861504649)/(52914749440)*a^(28) + (1755989797)/(84663599104)*a^(27) - (3092894923)/(211658997760)*a^(26) + (1144517489)/(52914749440)*a^(25) - (171568623)/(21165899776)*a^(24) - (28365143)/(3112632320)*a^(23) - (6462130833)/(105829498880)*a^(22) + (606055461)/(3779624960)*a^(21) - (161201243)/(755924992)*a^(20) + (176132612729)/(423317995520)*a^(19) - (19276787111)/(42331799552)*a^(18) - (60735001)/(3112632320)*a^(17) - (390168731)/(15118499840)*a^(16) + (60024717849)/(423317995520)*a^(15) + (45766733629)/(211658997760)*a^(14) + (10142962463)/(5291474944)*a^(13) - (263356548817)/(52914749440)*a^(12) + (32937956903)/(6614343680)*a^(11) - (5991199759)/(826792960)*a^(10) + (529966057)/(71895040)*a^(9) + (296118779)/(413396480)*a^(8) + (1332943)/(2246720)*a^(7) - (2969730447)/(206698240)*a^(6) + (436079395)/(20669824)*a^(5) - (1302397577)/(25837280)*a^(4) + (10523281317)/(103349120)*a^(3) - (4719598507)/(51674560)*a^(2) + (666767179)/(6459320)*a - (1222491493)/(12918640) , (1260740877)/(423317995520)*a^(31) - (771759291)/(105829498880)*a^(30) + (652754147)/(52914749440)*a^(29) - (3231703)/(115032064)*a^(28) + (12900234421)/(423317995520)*a^(27) - (614315511)/(26457374720)*a^(26) + (1801431529)/(52914749440)*a^(25) - (698807429)/(105829498880)*a^(24) - (275068287)/(26457374720)*a^(23) - (2600209665)/(21165899776)*a^(22) + (13976962731)/(52914749440)*a^(21) - (2303695729)/(6614343680)*a^(20) + (298937238613)/(423317995520)*a^(19) - (8341185787)/(13228687360)*a^(18) - (5805861133)/(52914749440)*a^(17) - (13573768727)/(105829498880)*a^(16) + (12799815657)/(84663599104)*a^(15) + (342967319)/(1556316160)*a^(14) + (20277898267)/(5291474944)*a^(13) - (210159930461)/(26457374720)*a^(12) + (923533807)/(118113280)*a^(11) - (1950305491)/(165358592)*a^(10) + (531651849)/(51674560)*a^(9) + (6827361)/(3039680)*a^(8) + (342542001)/(103349120)*a^(7) - (1050992897)/(41339648)*a^(6) + (44228627)/(1291864)*a^(5) - (2377634877)/(25837280)*a^(4) + (16528970589)/(103349120)*a^(3) - (902819441)/(6459320)*a^(2) + (1080898583)/(6459320)*a - (160747935)/(1291864) , (639327637)/(52914749440)*a^(31) - (719748529)/(21165899776)*a^(30) + (1480018437)/(26457374720)*a^(29) - (6709201987)/(52914749440)*a^(28) + (7979155817)/(52914749440)*a^(27) - (11500911637)/(105829498880)*a^(26) + (2123229043)/(13228687360)*a^(25) - (2505789399)/(52914749440)*a^(24) - (1600015567)/(26457374720)*a^(23) - (962549259)/(1889812480)*a^(22) + (32559058039)/(26457374720)*a^(21) - (4288025391)/(2645737472)*a^(20) + (33981766085)/(10582949888)*a^(19) - (340862707893)/(105829498880)*a^(18) - (4335471839)/(13228687360)*a^(17) - (3542832187)/(10582949888)*a^(16) + (9964222559)/(10582949888)*a^(15) + (8253618627)/(6225264640)*a^(14) + (105911116971)/(6614343680)*a^(13) - (1986261188911)/(52914749440)*a^(12) + (122852880581)/(3307171840)*a^(11) - (22625033019)/(413396480)*a^(10) + (85976117699)/(1653585920)*a^(9) + (18675399)/(2431744)*a^(8) + (227479991)/(25837280)*a^(7) - (11742605717)/(103349120)*a^(6) + (1659592653)/(10334912)*a^(5) - (5204449963)/(12918640)*a^(4) + (19633104401)/(25837280)*a^(3) - (2476188067)/(3691040)*a^(2) + (1258536387)/(1614830)*a - (8387150967)/(12918640) , (399914983)/(15118499840)*a^(31) - (3694808717)/(52914749440)*a^(30) + (209203251)/(1793720320)*a^(29) - (175036579)/(661434368)*a^(28) + (31854563761)/(105829498880)*a^(27) - (2379296011)/(10582949888)*a^(26) + (34767732689)/(105829498880)*a^(25) - (1060504167)/(13228687360)*a^(24) - (365718797)/(3307171840)*a^(23) - (14590940907)/(13228687360)*a^(22) + (16663064469)/(6614343680)*a^(21) - (88512072877)/(26457374720)*a^(20) + (708457655681)/(105829498880)*a^(19) - (334667639447)/(52914749440)*a^(18) - (84972968991)/(105829498880)*a^(17) - (279550197)/(287580160)*a^(16) + (7456724039)/(4601282560)*a^(15) + (7602764171)/(3112632320)*a^(14) + (3673729968577)/(105829498880)*a^(13) - (2020223687509)/(26457374720)*a^(12) + (125548406677)/(1653585920)*a^(11) - (375031901609)/(3307171840)*a^(10) + (84808255551)/(826792960)*a^(9) + (11160357)/(607936)*a^(8) + (1028267493)/(41339648)*a^(7) - (3060075623)/(12918640)*a^(6) + (8468943359)/(25837280)*a^(5) - (8837806329)/(10334912)*a^(4) + (39919379779)/(25837280)*a^(3) - (3519622697)/(2583728)*a^(2) + (41643826713)/(25837280)*a - (8193613333)/(6459320) , (1776376131)/(211658997760)*a^(31) - (894936793)/(42331799552)*a^(30) + (1892063689)/(52914749440)*a^(29) - (4293287647)/(52914749440)*a^(28) + (2693547501)/(30236999680)*a^(27) - (14524115553)/(211658997760)*a^(26) + (2618396861)/(26457374720)*a^(25) - (74621069)/(3779624960)*a^(24) - (92649839)/(3112632320)*a^(23) - (3676351307)/(10582949888)*a^(22) + (40255472063)/(52914749440)*a^(21) - (3850440209)/(3779624960)*a^(20) + (433891325131)/(211658997760)*a^(19) - (390281104337)/(211658997760)*a^(18) - (425146223)/(1556316160)*a^(17) - (2385585957)/(6614343680)*a^(16) + (12198808969)/(30236999680)*a^(15) + (141424346759)/(211658997760)*a^(14) + (145095091889)/(13228687360)*a^(13) - (1214229803169)/(52914749440)*a^(12) + (151573864049)/(6614343680)*a^(11) - (510629373)/(14764160)*a^(10) + (49612214213)/(1653585920)*a^(9) + (2575741997)/(413396480)*a^(8) + (951084513)/(103349120)*a^(7) - (16728201)/(230690)*a^(6) + (10200467717)/(103349120)*a^(5) - (490671099)/(1845520)*a^(4) + (4798959293)/(10334912)*a^(3) - (21097192657)/(51674560)*a^(2) + (1583790969)/(3229660)*a - (206707703)/(561680) , (2190043)/(661434368)*a^(31) - (168678915)/(21165899776)*a^(30) + (703213023)/(52914749440)*a^(29) - (1628131909)/(52914749440)*a^(28) + (434619471)/(13228687360)*a^(27) - (155656391)/(6225264640)*a^(26) + (1991733901)/(52914749440)*a^(25) - (21593897)/(3112632320)*a^(24) - (62413213)/(5291474944)*a^(23) - (1807213973)/(13228687360)*a^(22) + (1088960663)/(3779624960)*a^(21) - (493235817)/(1322868736)*a^(20) + (10245871767)/(13228687360)*a^(19) - (14490849003)/(21165899776)*a^(18) - (1008937997)/(7559249920)*a^(17) - (8482514049)/(52914749440)*a^(16) + (142150735)/(755924992)*a^(15) + (29791850313)/(105829498880)*a^(14) + (9718691959)/(2300641280)*a^(13) - (459585140717)/(52914749440)*a^(12) + (27683039159)/(3307171840)*a^(11) - (21302270009)/(1653585920)*a^(10) + (18680036749)/(1653585920)*a^(9) + (540559763)/(206698240)*a^(8) + (22121691)/(6079360)*a^(7) - (582560397)/(20669824)*a^(6) + (110516447)/(3039680)*a^(5) - (2590902249)/(25837280)*a^(4) + (4511328621)/(25837280)*a^(3) - (3883244543)/(25837280)*a^(2) + (2355820153)/(12918640)*a - (1759661413)/(12918640) , (1063437)/(1314652160)*a^(31) - (497513111)/(211658997760)*a^(30) + (59445701)/(15118499840)*a^(29) - (94833143)/(10582949888)*a^(28) + (2278416069)/(211658997760)*a^(27) - (1653196723)/(211658997760)*a^(26) + (1174306353)/(105829498880)*a^(25) - (87908847)/(26457374720)*a^(24) - (2844493)/(622526464)*a^(23) - (1773262331)/(52914749440)*a^(22) + (650914667)/(7559249920)*a^(21) - (1540738253)/(13228687360)*a^(20) + (9636322897)/(42331799552)*a^(19) - (9772349255)/(42331799552)*a^(18) - (118270063)/(6225264640)*a^(17) - (120922021)/(13228687360)*a^(16) + (2191337149)/(42331799552)*a^(15) + (19681790861)/(211658997760)*a^(14) + (116993343637)/(105829498880)*a^(13) - (139729652283)/(52914749440)*a^(12) + (3559101095)/(1322868736)*a^(11) - (1836213479)/(472453120)*a^(10) + (6040257211)/(1653585920)*a^(9) + (40080443)/(82679296)*a^(8) + (69154083)/(206698240)*a^(7) - 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