/* 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 - 2*x^21 - x^20 + 18*x^19 - 17*x^18 - 44*x^17 + 110*x^16 - 3*x^15 - 254*x^14 + 59*x^13 + 240*x^12 - 102*x^11 - 552*x^10 - 230*x^9 + 307*x^8 + 320*x^7 - 3*x^6 - 154*x^5 - 62*x^4 + 18*x^3 + 19*x^2 + 2*x - 1, 22, 46, [6, 8], 1447402975463751668017578125, [5, 7, 83, 127], [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, a^17, 1/5*a^18 + 2/5*a^17 - 1/5*a^14 + 2/5*a^12 - 1/5*a^11 - 1/5*a^10 - 1/5*a^9 - 2/5*a^6 - 2/5*a^5 - 2/5*a^4 - 1/5*a^3 + 2/5*a^2 + 1/5*a - 1/5, 1/5*a^19 + 1/5*a^17 - 1/5*a^15 + 2/5*a^14 + 2/5*a^13 + 1/5*a^11 + 1/5*a^10 + 2/5*a^9 - 2/5*a^7 + 2/5*a^6 + 2/5*a^5 - 2/5*a^4 - 1/5*a^3 + 2/5*a^2 + 2/5*a + 2/5, 1/5*a^20 - 2/5*a^17 - 1/5*a^16 + 2/5*a^15 - 2/5*a^14 - 1/5*a^12 + 2/5*a^11 - 2/5*a^10 + 1/5*a^9 - 2/5*a^8 + 2/5*a^7 - 1/5*a^6 + 1/5*a^4 - 2/5*a^3 + 1/5*a + 1/5, 1/56519985376604065507145*a^21 - 1332303350785640714766/56519985376604065507145*a^20 - 3535365261660196536029/56519985376604065507145*a^19 - 4919424422287081949599/56519985376604065507145*a^18 - 18552319389979348044422/56519985376604065507145*a^17 - 5480146535618417328722/56519985376604065507145*a^16 + 2979282937667072444890/11303997075320813101429*a^15 - 3979740765573833739454/56519985376604065507145*a^14 + 2618457838077731340976/56519985376604065507145*a^13 + 12954503807196842959579/56519985376604065507145*a^12 + 18695186257425511168174/56519985376604065507145*a^11 + 24886967222611872102271/56519985376604065507145*a^10 + 23198866140311044023326/56519985376604065507145*a^9 - 21710420089587276733561/56519985376604065507145*a^8 + 4307330292767668606748/11303997075320813101429*a^7 - 2365804169949362957548/56519985376604065507145*a^6 - 20038793996407534264328/56519985376604065507145*a^5 - 13162204338885356986351/56519985376604065507145*a^4 - 8629938208056997339052/56519985376604065507145*a^3 + 27563790421963051834119/56519985376604065507145*a^2 + 582428447918856776305/11303997075320813101429*a + 10260943314429562231528/56519985376604065507145], 0, 1, [], 1, [ (3889606748078687352138)/(56519985376604065507145)*a^(21) - (5361371855440919173188)/(56519985376604065507145)*a^(20) - (1451168833915740788442)/(11303997075320813101429)*a^(19) + (67296658376268153086154)/(56519985376604065507145)*a^(18) - (32601793496650157732642)/(56519985376604065507145)*a^(17) - (179839889053267715211746)/(56519985376604065507145)*a^(16) + (343265763521639937518513)/(56519985376604065507145)*a^(15) + (82025314522442247885281)/(56519985376604065507145)*a^(14) - (852029519793239857998868)/(56519985376604065507145)*a^(13) + (10719650796797218098419)/(56519985376604065507145)*a^(12) + (209369955229447467343938)/(56519985376604065507145)*a^(11) - (111486184543142919201751)/(56519985376604065507145)*a^(10) - (999610056843056797273769)/(56519985376604065507145)*a^(9) - (2727747327543201052791158)/(56519985376604065507145)*a^(8) - (951144580698794603681039)/(56519985376604065507145)*a^(7) + (1444734207213739112280853)/(56519985376604065507145)*a^(6) + (1689608369037097406826788)/(56519985376604065507145)*a^(5) + (85745008767270883000866)/(56519985376604065507145)*a^(4) - (743567999425154242582234)/(56519985376604065507145)*a^(3) - (238716106429694080466622)/(56519985376604065507145)*a^(2) + (5187301626723989679373)/(11303997075320813101429)*a + (50429063078073577745352)/(56519985376604065507145) , (4087395172025587485777)/(56519985376604065507145)*a^(21) - (18250758599204074128816)/(56519985376604065507145)*a^(20) + (5744248935974404358740)/(11303997075320813101429)*a^(19) + (52482543598776551394846)/(56519985376604065507145)*a^(18) - (50005259980417423708042)/(11303997075320813101429)*a^(17) + (44761365579575139460040)/(11303997075320813101429)*a^(16) + (564013513585900640568814)/(56519985376604065507145)*a^(15) - (1542998776348805068018133)/(56519985376604065507145)*a^(14) + (652650818198132680635368)/(56519985376604065507145)*a^(13) + (392169845821695710199310)/(11303997075320813101429)*a^(12) - (2658648283750185869740796)/(56519985376604065507145)*a^(11) - (273383636686598429054161)/(56519985376604065507145)*a^(10) + (140840750219262489513904)/(11303997075320813101429)*a^(9) + (1573079829053418399207116)/(56519985376604065507145)*a^(8) - (1632498117898600258350779)/(56519985376604065507145)*a^(7) - (1587814276583882557133089)/(56519985376604065507145)*a^(6) + (251641400273393926734512)/(56519985376604065507145)*a^(5) + (141916152146165260913262)/(11303997075320813101429)*a^(4) + (432305835210343993937687)/(56519985376604065507145)*a^(3) - (263622912424024219306408)/(56519985376604065507145)*a^(2) - (115436903502929554128519)/(56519985376604065507145)*a - (22464382940840820838691)/(56519985376604065507145) , (17389629249939428223643)/(56519985376604065507145)*a^(21) - (43035748090083439602021)/(56519985376604065507145)*a^(20) + (610328996692479734414)/(11303997075320813101429)*a^(19) + (311530230208666167998644)/(56519985376604065507145)*a^(18) - (443512881632167725851166)/(56519985376604065507145)*a^(17) - (554439487489021831083253)/(56519985376604065507145)*a^(16) + (2175775094128142747605747)/(56519985376604065507145)*a^(15) - (1085368017215257347780998)/(56519985376604065507145)*a^(14) - (3900562832465947608753803)/(56519985376604065507145)*a^(13) + (2877221130554671213595347)/(56519985376604065507145)*a^(12) + (2806356975805849493343162)/(56519985376604065507145)*a^(11) - (620999732752367007817460)/(11303997075320813101429)*a^(10) - (8121298453259953792577982)/(56519985376604065507145)*a^(9) - (142397691717399493931262)/(56519985376604065507145)*a^(8) + (1080825252047006047981197)/(11303997075320813101429)*a^(7) + (2996784329864890670894946)/(56519985376604065507145)*a^(6) - (1474995371373348743807912)/(56519985376604065507145)*a^(5) - (1976673903482553915560862)/(56519985376604065507145)*a^(4) - (139224360563907800751253)/(56519985376604065507145)*a^(3) + (379003236296215569067798)/(56519985376604065507145)*a^(2) + (58875304642488488775882)/(56519985376604065507145)*a - (36610665880731125395391)/(56519985376604065507145) , (36610665880731125395391)/(56519985376604065507145)*a^(21) - (18122192202280335802885)/(11303997075320813101429)*a^(20) + (1285016441870462841326)/(11303997075320813101429)*a^(19) + (655940340869697858444968)/(56519985376604065507145)*a^(18) - (933911550181095299720291)/(56519985376604065507145)*a^(17) - (1167356417120001791546038)/(56519985376604065507145)*a^(16) + (4581612734369445624576263)/(56519985376604065507145)*a^(15) - (457121418354067224758384)/(11303997075320813101429)*a^(14) - (8213741116490448502648316)/(56519985376604065507145)*a^(13) + (6060592119429084007081872)/(56519985376604065507145)*a^(12) + (5909338680820798881298493)/(56519985376604065507145)*a^(11) - (6540644895640424283673044)/(56519985376604065507145)*a^(10) - (17104088902401746179168532)/(56519985376604065507145)*a^(9) - (299154699308205048361948)/(56519985376604065507145)*a^(8) + (11381872117101854990316299)/(56519985376604065507145)*a^(7) + (1262257364319785977323827)/(11303997075320813101429)*a^(6) - (3106616327507084047081119)/(56519985376604065507145)*a^(5) - (4163047174259244567082302)/(56519985376604065507145)*a^(4) - (58637476224555171790676)/(11303997075320813101429)*a^(3) + (798216346417068057868291)/(56519985376604065507145)*a^(2) + (316599415437675813444631)/(56519985376604065507145)*a - (8434791651526060698449)/(11303997075320813101429) , (11943985278010908658263)/(56519985376604065507145)*a^(21) - (37729930360100320492146)/(56519985376604065507145)*a^(20) + (6035300232168424653138)/(11303997075320813101429)*a^(19) + (193170296548446745647934)/(56519985376604065507145)*a^(18) - (450765630570479150146856)/(56519985376604065507145)*a^(17) - (26163721187994134878238)/(56519985376604065507145)*a^(16) + (1547280570082007461743442)/(56519985376604065507145)*a^(15) - (2034829478556243413822693)/(56519985376604065507145)*a^(14) - (1107391498516953067768218)/(56519985376604065507145)*a^(13) + (3261451271870651744717922)/(56519985376604065507145)*a^(12) - (1387418374738699659560828)/(56519985376604065507145)*a^(11) - (334822814547024047373669)/(11303997075320813101429)*a^(10) - (2962761299390544253113412)/(56519985376604065507145)*a^(9) + (1506770377207579734872778)/(56519985376604065507145)*a^(8) + (161200450517054408481131)/(11303997075320813101429)*a^(7) - (234695212108873994301179)/(56519985376604065507145)*a^(6) - (413492087644944186694642)/(56519985376604065507145)*a^(5) - (182244128859930284536382)/(56519985376604065507145)*a^(4) + (129964172868383627054332)/(56519985376604065507145)*a^(3) - (92656156757470023111832)/(56519985376604065507145)*a^(2) - (47631686642232365062293)/(56519985376604065507145)*a - (38977362121249987148161)/(56519985376604065507145) , (22114556022362452413393)/(56519985376604065507145)*a^(21) - (11717419929087288621986)/(11303997075320813101429)*a^(20) + (1632325380119936184814)/(11303997075320813101429)*a^(19) + (413328127871683364944109)/(56519985376604065507145)*a^(18) - (646781066615593004747008)/(56519985376604065507145)*a^(17) - (698708457357324349270244)/(56519985376604065507145)*a^(16) + (3112641743630522459178174)/(56519985376604065507145)*a^(15) - (367033674853724521668709)/(11303997075320813101429)*a^(14) - (5522112199547893787758678)/(56519985376604065507145)*a^(13) + (5518416239003638484917806)/(56519985376604065507145)*a^(12) + (3700389765752249306467364)/(56519985376604065507145)*a^(11) - (6599342451484436972710287)/(56519985376604065507145)*a^(10) - (9300858829960004466471541)/(56519985376604065507145)*a^(9) + (3303612826502890369058006)/(56519985376604065507145)*a^(8) + (7870458803284344753411167)/(56519985376604065507145)*a^(7) + (150890548061983478473541)/(11303997075320813101429)*a^(6) - (3352756698491741110507592)/(56519985376604065507145)*a^(5) - (1794573897400051714870526)/(56519985376604065507145)*a^(4) + (153976009744651392197498)/(11303997075320813101429)*a^(3) + (504495711248358358125568)/(56519985376604065507145)*a^(2) - (24035743235386092834667)/(56519985376604065507145)*a - (12363201028026257880960)/(11303997075320813101429) , (1413321902017114131621)/(11303997075320813101429)*a^(21) - (2576558763833071685520)/(11303997075320813101429)*a^(20) - (1481236550547778770970)/(11303997075320813101429)*a^(19) + (25080136710219058639079)/(11303997075320813101429)*a^(18) - (22200348053332256088334)/(11303997075320813101429)*a^(17) - (57232344210082933483312)/(11303997075320813101429)*a^(16) + (149665984743890849018080)/(11303997075320813101429)*a^(15) - (21739582799625446640293)/(11303997075320813101429)*a^(14) - (319808149582301323891170)/(11303997075320813101429)*a^(13) + (115201903922727629528788)/(11303997075320813101429)*a^(12) + (137195592652550534268744)/(11303997075320813101429)*a^(11) - (154290272171868296627655)/(11303997075320813101429)*a^(10) - (517926575669664075087994)/(11303997075320813101429)*a^(9) - (541914870245487030564634)/(11303997075320813101429)*a^(8) + (27402343076101566606125)/(11303997075320813101429)*a^(7) + (202394768930331320759001)/(11303997075320813101429)*a^(6) + (276912609336730112464930)/(11303997075320813101429)*a^(5) + (15523162072162215779388)/(11303997075320813101429)*a^(4) - (105924487910940043804786)/(11303997075320813101429)*a^(3) - (62047520382007148822064)/(11303997075320813101429)*a^(2) - (7069392697033030738001)/(11303997075320813101429)*a + (19915111960346797812506)/(11303997075320813101429) , (2856291801118944244921)/(11303997075320813101429)*a^(21) - (18941639073950259065589)/(56519985376604065507145)*a^(20) - (35887028022692364165722)/(56519985376604065507145)*a^(19) + (252757439356968941940554)/(56519985376604065507145)*a^(18) - (66008541531406582463771)/(56519985376604065507145)*a^(17) - (841949486676655142836006)/(56519985376604065507145)*a^(16) + (1201267676227987138587509)/(56519985376604065507145)*a^(15) + (230500289719325587746308)/(11303997075320813101429)*a^(14) - (4021664392778184925892584)/(56519985376604065507145)*a^(13) - (1578447275840190926645663)/(56519985376604065507145)*a^(12) + (4929299274036318997530836)/(56519985376604065507145)*a^(11) + (273075326981406371108282)/(56519985376604065507145)*a^(10) - (9864967725811474185231682)/(56519985376604065507145)*a^(9) - (7542859607487205857436132)/(56519985376604065507145)*a^(8) + (3536151882206715966082606)/(56519985376604065507145)*a^(7) + (7098128277725063174517122)/(56519985376604065507145)*a^(6) + (1410971462649786217284598)/(56519985376604065507145)*a^(5) - (2436970567473032582653593)/(56519985376604065507145)*a^(4) - (1646533817156155807910579)/(56519985376604065507145)*a^(3) + (24517467494936863429514)/(56519985376604065507145)*a^(2) + (272325927022792950697781)/(56519985376604065507145)*a + (28001976431222475495923)/(56519985376604065507145) , (16903946918226199275173)/(56519985376604065507145)*a^(21) - (22384216210615616202901)/(56519985376604065507145)*a^(20) - (10269566156911530861708)/(11303997075320813101429)*a^(19) + (322420806716511343152117)/(56519985376604065507145)*a^(18) - (17441473591644634803603)/(11303997075320813101429)*a^(17) - (1143363520477764965952413)/(56519985376604065507145)*a^(16) + (1670880824034104234676482)/(56519985376604065507145)*a^(15) + (1527502189631455943109729)/(56519985376604065507145)*a^(14) - (5786435931844921320391203)/(56519985376604065507145)*a^(13) - (998904112686130195766552)/(56519985376604065507145)*a^(12) + (7106929113895471136424414)/(56519985376604065507145)*a^(11) - (1099682580625616800535818)/(56519985376604065507145)*a^(10) - (2357013745634715260869170)/(11303997075320813101429)*a^(9) - (8232843918856273271140442)/(56519985376604065507145)*a^(8) + (1509840437818613977641131)/(11303997075320813101429)*a^(7) + (1806232655081796091042964)/(11303997075320813101429)*a^(6) + (380496523869219556866637)/(56519985376604065507145)*a^(5) - (3979656582759283475715908)/(56519985376604065507145)*a^(4) - (1951873455278751218489251)/(56519985376604065507145)*a^(3) + (667613758365692643942364)/(56519985376604065507145)*a^(2) + (95229934745731229841460)/(11303997075320813101429)*a + (62848225501685751452226)/(56519985376604065507145) , (3884688851767918528146)/(11303997075320813101429)*a^(21) - (48742656687522431867922)/(56519985376604065507145)*a^(20) + (1623694506118349237052)/(56519985376604065507145)*a^(19) + (357514090819114070140703)/(56519985376604065507145)*a^(18) - (510340698566133455958368)/(56519985376604065507145)*a^(17) - (665253869696240699080838)/(56519985376604065507145)*a^(16) + (2559914400673786306002824)/(56519985376604065507145)*a^(15) - (240704273638051325688991)/(11303997075320813101429)*a^(14) - (4803608532917692956752701)/(56519985376604065507145)*a^(13) + (3701521277094067743699233)/(56519985376604065507145)*a^(12) + (766818698614293218315285)/(11303997075320813101429)*a^(11) - (4485491373074967367542442)/(56519985376604065507145)*a^(10) - (9511367853468719111774171)/(56519985376604065507145)*a^(9) + (1297219784224555361159289)/(56519985376604065507145)*a^(8) + (7454836075149638102013867)/(56519985376604065507145)*a^(7) + (448602417955763037370811)/(11303997075320813101429)*a^(6) - (2733923776910363516505912)/(56519985376604065507145)*a^(5) - (2199456898478856809730067)/(56519985376604065507145)*a^(4) + (544917300546696323656829)/(56519985376604065507145)*a^(3) + (111507999319981822525539)/(11303997075320813101429)*a^(2) + (19352647277941567245374)/(11303997075320813101429)*a - (100185431426058851266311)/(56519985376604065507145) , (5005038061297551619294)/(56519985376604065507145)*a^(21) - (1887818270595516226891)/(11303997075320813101429)*a^(20) - (2526436277978490608978)/(56519985376604065507145)*a^(19) + (79749864864903444311553)/(56519985376604065507145)*a^(18) - (14255886811743299481339)/(11303997075320813101429)*a^(17) - (167259317914799808593357)/(56519985376604065507145)*a^(16) + (83797522377145831642354)/(11303997075320813101429)*a^(15) - (33274010604651884544757)/(56519985376604065507145)*a^(14) - (162275164567193228831866)/(11303997075320813101429)*a^(13) - (40180065228669856104558)/(11303997075320813101429)*a^(12) + (552602548254334249933998)/(56519985376604065507145)*a^(11) + (77000120710286464978578)/(11303997075320813101429)*a^(10) - (502153373557045859869047)/(11303997075320813101429)*a^(9) - (2273215762231620538047187)/(56519985376604065507145)*a^(8) + (61540335063397906075652)/(56519985376604065507145)*a^(7) + (2127047159340810217650242)/(56519985376604065507145)*a^(6) + (670123434121369392758406)/(56519985376604065507145)*a^(5) - (415536720160287981672889)/(56519985376604065507145)*a^(4) - (721286184813860198480978)/(56519985376604065507145)*a^(3) - (9347895305137429155965)/(11303997075320813101429)*a^(2) + (111065851017260736256834)/(56519985376604065507145)*a + (28257137396033151900383)/(56519985376604065507145) , (42860870917695887970136)/(56519985376604065507145)*a^(21) - (16720002058484183500634)/(11303997075320813101429)*a^(20) - (49583257633441913262996)/(56519985376604065507145)*a^(19) + (155905492019345963496601)/(11303997075320813101429)*a^(18) - (696379066158018651046293)/(56519985376604065507145)*a^(17) - (1978723690851651659927558)/(56519985376604065507145)*a^(16) + (4764637884557139633179129)/(56519985376604065507145)*a^(15) + (155437056537967816947211)/(56519985376604065507145)*a^(14) - (11482483031831693778493688)/(56519985376604065507145)*a^(13) + (2599649995034027207688456)/(56519985376604065507145)*a^(12) + (2257075944474512013950982)/(11303997075320813101429)*a^(11) - (5795338824006323959644447)/(56519985376604065507145)*a^(10) - 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