/* 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^22 - 4*x^21 + 5*x^20 + 4*x^19 - 26*x^18 + 31*x^17 + 15*x^16 - 79*x^15 + 76*x^14 + 60*x^13 - 153*x^12 + 84*x^11 + 83*x^10 - 192*x^9 + 24*x^8 + 58*x^7 - 150*x^6 + 30*x^5 + 19*x^4 - 23*x^3 + 6*x^2 + 29*x + 1, 22, 52, [4, 9], -931263224878297608080470016, [2, 11, 19, 547], [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, 1/11*a^17 + 3/11*a^15 + 3/11*a^13 - 4/11*a^12 - 1/11*a^11 + 1/11*a^10 - 2/11*a^9 - 5/11*a^8 - 4/11*a^7 + 1/11*a^6 - 4/11*a^5 - 4/11*a^4 - 2/11*a^3 - 1/11*a^2 - 5/11*a - 1/11, 1/11*a^18 + 3/11*a^16 + 3/11*a^14 - 4/11*a^13 - 1/11*a^12 + 1/11*a^11 - 2/11*a^10 - 5/11*a^9 - 4/11*a^8 + 1/11*a^7 - 4/11*a^6 - 4/11*a^5 - 2/11*a^4 - 1/11*a^3 - 5/11*a^2 - 1/11*a, 1/242*a^19 + 5/242*a^18 - 5/121*a^17 - 117/242*a^16 - 51/121*a^15 + 5/22*a^14 + 83/242*a^13 - 31/121*a^12 - 105/242*a^11 - 3/121*a^10 + 63/242*a^9 + 56/121*a^8 + 53/242*a^7 + 53/121*a^6 + 48/121*a^5 + 107/242*a^4 + 93/242*a^3 - 57/242*a^2 - 39/242*a - 9/242, 1/242*a^20 + 9/242*a^18 - 1/242*a^17 - 111/242*a^16 + 37/242*a^15 - 30/121*a^14 + 29/242*a^13 - 103/242*a^12 + 13/242*a^11 + 71/242*a^10 - 71/242*a^9 - 45/242*a^8 + 105/242*a^7 - 30/121*a^6 - 87/242*a^5 - 34/121*a^4 + 14/121*a^3 - 20/121*a^2 + 27/121*a - 21/242, 1/406526742211766*a^21 - 288595015055/203263371105883*a^20 + 255666951553/406526742211766*a^19 - 10643548821841/406526742211766*a^18 - 10810179676633/406526742211766*a^17 + 92462124524021/406526742211766*a^16 - 5406253665840/203263371105883*a^15 - 139971702813821/406526742211766*a^14 - 14585103833331/406526742211766*a^13 + 13764050961235/36956976564706*a^12 + 163921142487191/406526742211766*a^11 - 193045451521693/406526742211766*a^10 + 27509531970517/406526742211766*a^9 - 57330290235511/406526742211766*a^8 - 31001972030638/203263371105883*a^7 + 98468543453281/406526742211766*a^6 - 36295292169886/203263371105883*a^5 + 52852929139063/203263371105883*a^4 + 75738032908635/203263371105883*a^3 - 52209940478345/203263371105883*a^2 - 295786960287/36956976564706*a - 92399281118454/203263371105883], 0, 1, [], 1, [ (4115115668275)/(203263371105883)*a^(21) - (36217864001663)/(406526742211766)*a^(20) + (42623957066059)/(406526742211766)*a^(19) + (30352628641251)/(203263371105883)*a^(18) - (265238532033837)/(406526742211766)*a^(17) + (122180384755895)/(203263371105883)*a^(16) + (348064011768861)/(406526742211766)*a^(15) - (933952628700649)/(406526742211766)*a^(14) + (203910682678299)/(203263371105883)*a^(13) + (117345185580525)/(36956976564706)*a^(12) - (935219496279468)/(203263371105883)*a^(11) - (257815505528925)/(406526742211766)*a^(10) + (1112584768074438)/(203263371105883)*a^(9) - (1657506961038323)/(406526742211766)*a^(8) - (525357975035906)/(203263371105883)*a^(7) + (1053517868100584)/(203263371105883)*a^(6) - (614923361666769)/(406526742211766)*a^(5) - (470902278088683)/(406526742211766)*a^(4) + (1037191219067321)/(406526742211766)*a^(3) - (139444654007467)/(406526742211766)*a^(2) - (2767222751515)/(3359725142246)*a + (212136542349154)/(203263371105883) , (20237559936547)/(406526742211766)*a^(21) - (43330777141568)/(203263371105883)*a^(20) + (136259300898627)/(406526742211766)*a^(19) + (13373028669289)/(406526742211766)*a^(18) - (535954302110965)/(406526742211766)*a^(17) + (893177466666807)/(406526742211766)*a^(16) - (71618145619632)/(203263371105883)*a^(15) - (1628164933356085)/(406526742211766)*a^(14) + (2581123219961467)/(406526742211766)*a^(13) + (3360983133265)/(36956976564706)*a^(12) - (3582798296287631)/(406526742211766)*a^(11) + (4147856712351355)/(406526742211766)*a^(10) + (216517934003923)/(406526742211766)*a^(9) - (5507462774755811)/(406526742211766)*a^(8) + (1568142024091743)/(203263371105883)*a^(7) + (162877126021101)/(406526742211766)*a^(6) - (2498172620807374)/(203263371105883)*a^(5) + (1245026391276245)/(203263371105883)*a^(4) + (90850976191960)/(203263371105883)*a^(3) - (380008083365270)/(203263371105883)*a^(2) + (8583769093215)/(3359725142246)*a + (559713515710311)/(203263371105883) , (2146482683207)/(406526742211766)*a^(21) - (6113397812629)/(203263371105883)*a^(20) + (28920784481841)/(406526742211766)*a^(19) - (27662678848865)/(406526742211766)*a^(18) - (39784824147279)/(406526742211766)*a^(17) + (161344926785609)/(406526742211766)*a^(16) - (88783581648204)/(203263371105883)*a^(15) - (63799750311259)/(406526742211766)*a^(14) + (443361481622179)/(406526742211766)*a^(13) - (39842873864947)/(36956976564706)*a^(12) - (189794453329839)/(406526742211766)*a^(11) + (820918625859855)/(406526742211766)*a^(10) - (735025945549199)/(406526742211766)*a^(9) - (185221319315287)/(406526742211766)*a^(8) + (374197392761029)/(203263371105883)*a^(7) - (540296972242649)/(406526742211766)*a^(6) + (89116735403169)/(203263371105883)*a^(5) + (238581883961081)/(203263371105883)*a^(4) - (421039483103645)/(203263371105883)*a^(3) + (303729529910560)/(203263371105883)*a^(2) - (26941151494127)/(36956976564706)*a - (153290567465254)/(203263371105883) , (1563086874244)/(203263371105883)*a^(21) - (15869702645895)/(406526742211766)*a^(20) + (33209185878273)/(406526742211766)*a^(19) - (6889507996321)/(203263371105883)*a^(18) - (105962860444401)/(406526742211766)*a^(17) + (122949937192814)/(203263371105883)*a^(16) - (135474343672449)/(406526742211766)*a^(15) - (384799365898575)/(406526742211766)*a^(14) + (419730961460425)/(203263371105883)*a^(13) - (2265171496323)/(3359725142246)*a^(12) - (521508973567676)/(203263371105883)*a^(11) + (1609858904779071)/(406526742211766)*a^(10) - (53296123609824)/(203263371105883)*a^(9) - (1824303252052615)/(406526742211766)*a^(8) + (715699479503991)/(203263371105883)*a^(7) + (104243482347988)/(203263371105883)*a^(6) - (1818983064996313)/(406526742211766)*a^(5) + (872711166596185)/(406526742211766)*a^(4) - (50997770185193)/(406526742211766)*a^(3) - (608194737341849)/(406526742211766)*a^(2) + (43202030362505)/(36956976564706)*a + (201826872297932)/(203263371105883) , (15266327456177)/(406526742211766)*a^(21) - (61308269857247)/(406526742211766)*a^(20) + (85497635203905)/(406526742211766)*a^(19) + (10408871047935)/(203263371105883)*a^(18) - (170490611689826)/(203263371105883)*a^(17) + (254413488441186)/(203263371105883)*a^(16) - (26328054702757)/(406526742211766)*a^(15) - (874507660898437)/(406526742211766)*a^(14) + (655498120818206)/(203263371105883)*a^(13) + (3936379381447)/(18478488282353)*a^(12) - (801533934984714)/(203263371105883)*a^(11) + (947569978108333)/(203263371105883)*a^(10) - (231024898964741)/(203263371105883)*a^(9) - (1135110563821145)/(203263371105883)*a^(8) + (1302217358930671)/(406526742211766)*a^(7) - (858801485663379)/(406526742211766)*a^(6) - (1921128291832807)/(406526742211766)*a^(5) + (839531771558358)/(203263371105883)*a^(4) - (219762449324364)/(203263371105883)*a^(3) + (104909378060602)/(203263371105883)*a^(2) + (5076300725349)/(3359725142246)*a + (457820031523787)/(406526742211766) , (144582543784)/(203263371105883)*a^(21) - (1994273802353)/(203263371105883)*a^(20) + (1579238246481)/(203263371105883)*a^(19) + (4695283362300)/(203263371105883)*a^(18) - (1993351287005)/(203263371105883)*a^(17) - (10547737196620)/(203263371105883)*a^(16) + (34115665712884)/(203263371105883)*a^(15) + (23524897165173)/(203263371105883)*a^(14) - (130358363862029)/(203263371105883)*a^(13) + (4195937616440)/(18478488282353)*a^(12) + (135512758256983)/(203263371105883)*a^(11) - (363124626815981)/(203263371105883)*a^(10) - (145114952251905)/(203263371105883)*a^(9) + (495894938761914)/(203263371105883)*a^(8) - (54523508329079)/(203263371105883)*a^(7) - (106174486030451)/(203263371105883)*a^(6) + (799838155083276)/(203263371105883)*a^(5) + (380426936502383)/(203263371105883)*a^(4) - (48345226169767)/(203263371105883)*a^(3) + (371025409732742)/(203263371105883)*a^(2) + (10608837302533)/(18478488282353)*a - (100152015582134)/(203263371105883) , (20721894289066)/(203263371105883)*a^(21) - (169992439324791)/(406526742211766)*a^(20) + (218609861014381)/(406526742211766)*a^(19) + (82638640436756)/(203263371105883)*a^(18) - (1116268693013065)/(406526742211766)*a^(17) + (682281438385742)/(203263371105883)*a^(16) + (631145442532479)/(406526742211766)*a^(15) - (3480976415104479)/(406526742211766)*a^(14) + (1681033766440903)/(203263371105883)*a^(13) + (235544388000811)/(36956976564706)*a^(12) - (3463652235389453)/(203263371105883)*a^(11) + (3732084897224843)/(406526742211766)*a^(10) + (1932009987353037)/(203263371105883)*a^(9) - (8518635802280723)/(406526742211766)*a^(8) + (626622029253779)/(203263371105883)*a^(7) + (1603952385374067)/(203263371105883)*a^(6) - (6345614366824603)/(406526742211766)*a^(5) + (1370742053179497)/(406526742211766)*a^(4) + (841635626037039)/(406526742211766)*a^(3) - (1335899291773201)/(406526742211766)*a^(2) + (17635461832739)/(36956976564706)*a + (552664253418331)/(203263371105883) , (51352388734319)/(406526742211766)*a^(21) - (180719931552745)/(406526742211766)*a^(20) + (80798916028030)/(203263371105883)*a^(19) + (307247252975881)/(406526742211766)*a^(18) - (605113228622767)/(203263371105883)*a^(17) + (1003952019757289)/(406526742211766)*a^(16) + (1352705936179985)/(406526742211766)*a^(15) - (1768624119992014)/(203263371105883)*a^(14) + (2272059679015977)/(406526742211766)*a^(13) + (192914300650253)/(18478488282353)*a^(12) - (6277259089463789)/(406526742211766)*a^(11) + (806756618077090)/(203263371105883)*a^(10) + (4935159744073719)/(406526742211766)*a^(9) - (4274535408238344)/(203263371105883)*a^(8) - (746484021624008)/(203263371105883)*a^(7) + (2903755527318197)/(406526742211766)*a^(6) - (6931777624709495)/(406526742211766)*a^(5) + (175191514238689)/(406526742211766)*a^(4) + (2025152646546021)/(406526742211766)*a^(3) - (1107913323843913)/(406526742211766)*a^(2) + (26175687928846)/(18478488282353)*a + (508126367028023)/(203263371105883) , (2023821221483)/(406526742211766)*a^(21) + (5565190016273)/(203263371105883)*a^(20) - (42309125836213)/(203263371105883)*a^(19) + (74663948256015)/(203263371105883)*a^(18) + (34668257828305)/(406526742211766)*a^(17) - (300128417708089)/(203263371105883)*a^(16) + (456823318900204)/(203263371105883)*a^(15) + (109825234017238)/(203263371105883)*a^(14) - (1070416168056526)/(203263371105883)*a^(13) + (197222629260883)/(36956976564706)*a^(12) + (665082984919147)/(203263371105883)*a^(11) - (4589685800503535)/(406526742211766)*a^(10) + (1032741646405104)/(203263371105883)*a^(9) + (2703957872926037)/(406526742211766)*a^(8) - (4559757520158163)/(406526742211766)*a^(7) + (1304289465787215)/(406526742211766)*a^(6) + (1516157817842403)/(203263371105883)*a^(5) - (2461612051519447)/(406526742211766)*a^(4) + (913994294006803)/(406526742211766)*a^(3) + (442579574970873)/(406526742211766)*a^(2) - (35479156652151)/(18478488282353)*a - (325093544964663)/(406526742211766) , (2704001463122)/(203263371105883)*a^(21) - (6405227232297)/(203263371105883)*a^(20) - (5647504773371)/(406526742211766)*a^(19) + (48119977667371)/(406526742211766)*a^(18) - (38527773464509)/(203263371105883)*a^(17) - (30174356942461)/(406526742211766)*a^(16) + (101516203373863)/(203263371105883)*a^(15) - (142047641725775)/(406526742211766)*a^(14) - (72824935914983)/(406526742211766)*a^(13) + (16342191285635)/(18478488282353)*a^(12) - (56196788930221)/(406526742211766)*a^(11) - (49258326624026)/(203263371105883)*a^(10) - (91942308507031)/(406526742211766)*a^(9) - (190990370983037)/(203263371105883)*a^(8) - (142260453945603)/(406526742211766)*a^(7) - (83169046410282)/(203263371105883)*a^(6) - (101431630180189)/(203263371105883)*a^(5) - (176680334769677)/(406526742211766)*a^(4) - (274317453904859)/(406526742211766)*a^(3) + (131506949109667)/(406526742211766)*a^(2) + (8589363571301)/(36956976564706)*a - (245144617662771)/(406526742211766) , (5793855784066)/(203263371105883)*a^(21) - (37699991092243)/(406526742211766)*a^(20) + (32477587372057)/(406526742211766)*a^(19) + (28788684647802)/(203263371105883)*a^(18) - (246065824866867)/(406526742211766)*a^(17) + (106445469566053)/(203263371105883)*a^(16) + (223251651478907)/(406526742211766)*a^(15) - (676366843362049)/(406526742211766)*a^(14) + (282000046752849)/(203263371105883)*a^(13) + (6167539644577)/(3359725142246)*a^(12) - (590676552361326)/(203263371105883)*a^(11) + (618390590407297)/(406526742211766)*a^(10) + (463397904145423)/(203263371105883)*a^(9) - (2022725473412825)/(406526742211766)*a^(8) - (230463547025487)/(203263371105883)*a^(7) + (201264490864259)/(203263371105883)*a^(6) - (2012919700900543)/(406526742211766)*a^(5) - (491305417552263)/(406526742211766)*a^(4) + (209417098891555)/(406526742211766)*a^(3) - (525386407288537)/(406526742211766)*a^(2) - (1647659842747)/(3359725142246)*a + (212449209038723)/(203263371105883) , (56996998546933)/(406526742211766)*a^(21) - (106965314402570)/(203263371105883)*a^(20) + (110684655528177)/(203263371105883)*a^(19) + (155984543750984)/(203263371105883)*a^(18) - (1409034347704183)/(406526742211766)*a^(17) + (673188771353915)/(203263371105883)*a^(16) + (665634100818002)/(203263371105883)*a^(15) - (2072143085290292)/(203263371105883)*a^(14) + (1490408245780734)/(203263371105883)*a^(13) + (35725003220601)/(3359725142246)*a^(12) - (3692964073634135)/(203263371105883)*a^(11) + (2290679985597031)/(406526742211766)*a^(10) + (2491156817955687)/(203263371105883)*a^(9) - (8953238186211123)/(406526742211766)*a^(8) - (501037183884739)/(406526742211766)*a^(7) + (2898435377356381)/(406526742211766)*a^(6) - (3412388004643595)/(203263371105883)*a^(5) + (1146436519442689)/(406526742211766)*a^(4) + (1164221960527749)/(406526742211766)*a^(3) - (1179731342266487)/(406526742211766)*a^(2) + (2096064997681)/(1679862571123)*a + (1062420543660181)/(406526742211766) ], 56735.8548792, [[x^11 - x^9 + x^7 - x^6 + 2*x^5 + x^4 - 2*x^3 - x - 1, 1]]]