/* 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^16 - 3*x^15 - 59*x^14 + 177*x^13 + 1203*x^12 - 3371*x^11 - 11052*x^10 + 25557*x^9 + 53804*x^8 - 84215*x^7 - 137046*x^6 + 109014*x^5 + 148448*x^4 - 32074*x^3 - 32876*x^2 - 4698*x - 67, 16, 22, [16, 0], 179594836941784276350012113, [17, 89], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, 1/67*a^13 - 5/67*a^12 + 33/67*a^11 + 14/67*a^10 - 29/67*a^9 - 10/67*a^8 + 17/67*a^7 + 15/67*a^6 - 21/67*a^5 + 31/67*a^4 - 1/67*a^3 - 4/67*a^2 + 24/67*a, 1/67*a^14 + 8/67*a^12 - 22/67*a^11 - 26/67*a^10 - 21/67*a^9 - 33/67*a^8 + 33/67*a^7 - 13/67*a^6 - 7/67*a^5 + 20/67*a^4 - 9/67*a^3 + 4/67*a^2 - 14/67*a, 1/16529681543978371585987202239*a^15 - 105584950941387831643068685/16529681543978371585987202239*a^14 + 54920849472778948993354107/16529681543978371585987202239*a^13 + 1863555253709387484093466137/16529681543978371585987202239*a^12 + 3780521972495617398828012336/16529681543978371585987202239*a^11 - 6676124600565621848527478965/16529681543978371585987202239*a^10 - 8058283812787967485022177865/16529681543978371585987202239*a^9 + 3540217780520032372332905042/16529681543978371585987202239*a^8 - 1177885760423882371412638343/16529681543978371585987202239*a^7 - 6153682512348614214897494907/16529681543978371585987202239*a^6 - 1450045851492115511059076687/16529681543978371585987202239*a^5 + 6381162574421113005849211686/16529681543978371585987202239*a^4 + 3744039332865653523908140270/16529681543978371585987202239*a^3 + 1264974038102167884094621249/16529681543978371585987202239*a^2 - 923823844458563618277222993/16529681543978371585987202239*a - 107733437102736885846397888/246711664835498083372943317], 0, 1, [], 1, [ (30414569112767888583831213)/(16529681543978371585987202239)*a^(15) - (157903032005782533280501113)/(16529681543978371585987202239)*a^(14) - (1483995549526013677144599494)/(16529681543978371585987202239)*a^(13) + (8805633966569780514467770421)/(16529681543978371585987202239)*a^(12) + (285053643345350495558906461)/(246711664835498083372943317)*a^(11) - (153931970805594392896082461200)/(16529681543978371585987202239)*a^(10) - (25159017086887106453423057670)/(16529681543978371585987202239)*a^(9) + (1001615442765247758732542833924)/(16529681543978371585987202239)*a^(8) - (457943884144148261089435508348)/(16529681543978371585987202239)*a^(7) - (2689326695925209041814092886101)/(16529681543978371585987202239)*a^(6) + (1783975162834016318756637182348)/(16529681543978371585987202239)*a^(5) + (2584592384723270717387120986588)/(16529681543978371585987202239)*a^(4) - (1891409611280961228880415175825)/(16529681543978371585987202239)*a^(3) - (2321160870717066212662007462)/(246711664835498083372943317)*a^(2) + (159776256654005491076747506799)/(16529681543978371585987202239)*a - (181234910772580411484506417)/(246711664835498083372943317) , (15371623781759026207734059)/(16529681543978371585987202239)*a^(15) + (13816285497969331357491966)/(16529681543978371585987202239)*a^(14) - (1204315403711598222330149781)/(16529681543978371585987202239)*a^(13) - (268127885703280930556908423)/(16529681543978371585987202239)*a^(12) + (35134847656037472419938036105)/(16529681543978371585987202239)*a^(11) - (10516242140110684747438851609)/(16529681543978371585987202239)*a^(10) - (462504038026779235119260768388)/(16529681543978371585987202239)*a^(9) + (277257489103373769334544837768)/(16529681543978371585987202239)*a^(8) + (2753808657113144085182175143186)/(16529681543978371585987202239)*a^(7) - (1741248650775441679300768444678)/(16529681543978371585987202239)*a^(6) - (7388247475682785479195170151702)/(16529681543978371585987202239)*a^(5) + (3853239872413552464977997482922)/(16529681543978371585987202239)*a^(4) + (7589725376401198382414847127419)/(16529681543978371585987202239)*a^(3) - (2734631444832192448975071477330)/(16529681543978371585987202239)*a^(2) - (1093629341742326703663806495035)/(16529681543978371585987202239)*a - (296219843170172221214524283)/(246711664835498083372943317) , (31098339818912421338000312)/(16529681543978371585987202239)*a^(15) - (87375449092490089172465595)/(16529681543978371585987202239)*a^(14) - (1872297187780094264892879148)/(16529681543978371585987202239)*a^(13) + (5251666663880276520823740237)/(16529681543978371585987202239)*a^(12) + (39449843189389660197773397442)/(16529681543978371585987202239)*a^(11) - (103111724222016718978007912753)/(16529681543978371585987202239)*a^(10) - (377653613490577313549421034313)/(16529681543978371585987202239)*a^(9) + (824260481741664380841953447250)/(16529681543978371585987202239)*a^(8) + (1870855553103251887081641663286)/(16529681543978371585987202239)*a^(7) - (2925271247447990192316422355801)/(16529681543978371585987202239)*a^(6) - (4685813102891468715338977312687)/(16529681543978371585987202239)*a^(5) + (4303059916562345261552282445976)/(16529681543978371585987202239)*a^(4) + (4819385223355115536929396338799)/(16529681543978371585987202239)*a^(3) - (1920438417396902376078209077723)/(16529681543978371585987202239)*a^(2) - (843959351491033352738547474944)/(16529681543978371585987202239)*a - (244896274835053712100514107)/(246711664835498083372943317) , (91706156384785375066004900)/(16529681543978371585987202239)*a^(15) - (355895687850817714940115666)/(16529681543978371585987202239)*a^(14) - (5052616583303816058568358782)/(16529681543978371585987202239)*a^(13) + (20472176213300674485575696105)/(16529681543978371585987202239)*a^(12) + (90023371926176408142934067695)/(16529681543978371585987202239)*a^(11) - (376623405932569582041432134068)/(16529681543978371585987202239)*a^(10) - (648635695990484705638371802127)/(16529681543978371585987202239)*a^(9) + (2706217085580408594475626366540)/(16529681543978371585987202239)*a^(8) + (2422717738778513703165039561761)/(16529681543978371585987202239)*a^(7) - (8468023940189152947796475444260)/(16529681543978371585987202239)*a^(6) - (5187244771072580616917890420221)/(16529681543978371585987202239)*a^(5) + (10708862666330508855200288672349)/(16529681543978371585987202239)*a^(4) + (5207018852101210505655561055071)/(16529681543978371585987202239)*a^(3) - (3561203133754835624084254469446)/(16529681543978371585987202239)*a^(2) - (1082645712562956654175085801875)/(16529681543978371585987202239)*a - (370540715082760915914901637)/(246711664835498083372943317) , (30193247453105065144173375)/(16529681543978371585987202239)*a^(15) - (110617206752545092487148958)/(16529681543978371585987202239)*a^(14) - (1696323845997708116530880140)/(16529681543978371585987202239)*a^(13) + (6414875582850617450284185447)/(16529681543978371585987202239)*a^(12) + (31474934632648264742713937366)/(16529681543978371585987202239)*a^(11) - (119579710904958470167341760115)/(16529681543978371585987202239)*a^(10) - (245823065413020285635527710144)/(16529681543978371585987202239)*a^(9) + (880341161073496454901130085366)/(16529681543978371585987202239)*a^(8) + (1009806069819410077172833406823)/(16529681543978371585987202239)*a^(7) - (2853425996815953713665960202358)/(16529681543978371585987202239)*a^(6) - (2285406831015128220335550289882)/(16529681543978371585987202239)*a^(5) + (3821210365044892876260885239785)/(16529681543978371585987202239)*a^(4) + (2279043240027056197606579892097)/(16529681543978371585987202239)*a^(3) - (1485246938019889811757690891769)/(16529681543978371585987202239)*a^(2) - (398462617725928792513285833730)/(16529681543978371585987202239)*a + (55590470524873207670118887)/(246711664835498083372943317) , (31098339818912421338000312)/(16529681543978371585987202239)*a^(15) - (87375449092490089172465595)/(16529681543978371585987202239)*a^(14) - (1872297187780094264892879148)/(16529681543978371585987202239)*a^(13) + (5251666663880276520823740237)/(16529681543978371585987202239)*a^(12) + (39449843189389660197773397442)/(16529681543978371585987202239)*a^(11) - (103111724222016718978007912753)/(16529681543978371585987202239)*a^(10) - (377653613490577313549421034313)/(16529681543978371585987202239)*a^(9) + (824260481741664380841953447250)/(16529681543978371585987202239)*a^(8) + (1870855553103251887081641663286)/(16529681543978371585987202239)*a^(7) - (2925271247447990192316422355801)/(16529681543978371585987202239)*a^(6) - (4685813102891468715338977312687)/(16529681543978371585987202239)*a^(5) + (4303059916562345261552282445976)/(16529681543978371585987202239)*a^(4) + (4819385223355115536929396338799)/(16529681543978371585987202239)*a^(3) - (1920438417396902376078209077723)/(16529681543978371585987202239)*a^(2) - (843959351491033352738547474944)/(16529681543978371585987202239)*a - (491607939670551795473457424)/(246711664835498083372943317) , (70507959001989944800763235)/(16529681543978371585987202239)*a^(15) - (344624091469791192057517621)/(16529681543978371585987202239)*a^(14) - (3533649784982092021616163246)/(16529681543978371585987202239)*a^(13) + (19277384055345340865612283559)/(16529681543978371585987202239)*a^(12) + (49605135661178510441079577490)/(16529681543978371585987202239)*a^(11) - (338380953732407539761641110822)/(16529681543978371585987202239)*a^(10) - (155275553241029190962445903531)/(16529681543978371585987202239)*a^(9) + (2217822646253767726783213952021)/(16529681543978371585987202239)*a^(8) - (379745810301132411667112296880)/(16529681543978371585987202239)*a^(7) - (6010828806271740825246028277291)/(16529681543978371585987202239)*a^(6) + (31094181598265670272993595053)/(246711664835498083372943317)*a^(5) + (5839375672319048379745016551083)/(16529681543978371585987202239)*a^(4) - (2025525737986239004813762860927)/(16529681543978371585987202239)*a^(3) - (399396450865569545614650441072)/(16529681543978371585987202239)*a^(2) - (111917952389030894458912640807)/(16529681543978371585987202239)*a - (390018310168414769210937522)/(246711664835498083372943317) , (71481737110374042747733434)/(16529681543978371585987202239)*a^(15) - (249524730830831126856831670)/(16529681543978371585987202239)*a^(14) - (4079421453355369458548012055)/(16529681543978371585987202239)*a^(13) + (14559970580196745395486743114)/(16529681543978371585987202239)*a^(12) + (78115003276290652573739515740)/(16529681543978371585987202239)*a^(11) - (274006036243211739802300875368)/(16529681543978371585987202239)*a^(10) - (647249181511100860092547510019)/(16529681543978371585987202239)*a^(9) + (2049955375897582029450485286946)/(16529681543978371585987202239)*a^(8) + (2850588918513997718213588829862)/(16529681543978371585987202239)*a^(7) - (6770457860787404662098812301554)/(16529681543978371585987202239)*a^(6) - (6816487918576442251359476241298)/(16529681543978371585987202239)*a^(5) + (9225908928192861333147545428871)/(16529681543978371585987202239)*a^(4) + (7021218611833455808668984865661)/(16529681543978371585987202239)*a^(3) - (3663755364903904490978439840002)/(16529681543978371585987202239)*a^(2) - (1228568906772666821801872956439)/(16529681543978371585987202239)*a + (81424554811699863009487845)/(246711664835498083372943317) , (118554847060338885131828811)/(16529681543978371585987202239)*a^(15) - (388496100461405337626728639)/(16529681543978371585987202239)*a^(14) - (6892369555181483086594370702)/(16529681543978371585987202239)*a^(13) + (22912179387126597258275387302)/(16529681543978371585987202239)*a^(12) + (136571258339086478172079152964)/(16529681543978371585987202239)*a^(11) - (438590111443158877311531965666)/(16529681543978371585987202239)*a^(10) - (1194315693529572956535128135823)/(16529681543978371585987202239)*a^(9) + (3381691236369681505918148180057)/(16529681543978371585987202239)*a^(8) + (5485193247787957649569719808730)/(16529681543978371585987202239)*a^(7) - (11659428725156123985371417566724)/(16529681543978371585987202239)*a^(6) - (13187346266893583126903822173770)/(16529681543978371585987202239)*a^(5) + (17079475804845019838092768462622)/(16529681543978371585987202239)*a^(4) + (13211077879182696013680569868560)/(16529681543978371585987202239)*a^(3) - (8109728803382545290642728039101)/(16529681543978371585987202239)*a^(2) - (1953498403068228072396478129330)/(16529681543978371585987202239)*a + (2834090501445619179391158741)/(246711664835498083372943317) , (133113690633251670682410357)/(16529681543978371585987202239)*a^(15) - (499666167176923213683446443)/(16529681543978371585987202239)*a^(14) - (7421153968056049024374683504)/(16529681543978371585987202239)*a^(13) + (28872074925514105787719443295)/(16529681543978371585987202239)*a^(12) + (135602562300810000980425469980)/(16529681543978371585987202239)*a^(11) - (535148439344447617768700499440)/(16529681543978371585987202239)*a^(10) - (1030262334242935555472126660677)/(16529681543978371585987202239)*a^(9) + (3901385618434847960591200525118)/(16529681543978371585987202239)*a^(8) + (4129825281718314665118376237406)/(16529681543978371585987202239)*a^(7) - (12500608581518180734807168428352)/(16529681543978371585987202239)*a^(6) - (139159319017602079836503331316)/(246711664835498083372943317)*a^(5) + (16530667140601267939746860982503)/(16529681543978371585987202239)*a^(4) + (9445107220579357257776348628203)/(16529681543978371585987202239)*a^(3) - (6279980184458281908773136795772)/(16529681543978371585987202239)*a^(2) - (1596172470309059031525251204037)/(16529681543978371585987202239)*a - (335373717140657260859735928)/(246711664835498083372943317) , (162504801208008534806719279)/(16529681543978371585987202239)*a^(15) - (824767922070530568614357274)/(16529681543978371585987202239)*a^(14) - (8010100375297353940121652133)/(16529681543978371585987202239)*a^(13) + (46037442183786671743062627288)/(16529681543978371585987202239)*a^(12) + (106692518796352121015485949795)/(16529681543978371585987202239)*a^(11) - (805676725786854672159587946467)/(16529681543978371585987202239)*a^(10) - (219650747063656061376010354384)/(16529681543978371585987202239)*a^(9) + (5251159035924647035486583642761)/(16529681543978371585987202239)*a^(8) - (1837663463141844941455014081312)/(16529681543978371585987202239)*a^(7) - (14115111138754660662236207403440)/(16529681543978371585987202239)*a^(6) + (7649056244396454748289159562643)/(16529681543978371585987202239)*a^(5) + (13523251764649686947493353041017)/(16529681543978371585987202239)*a^(4) - (7849434007305895015656565504637)/(16529681543978371585987202239)*a^(3) - (754744823002951720199019512929)/(16529681543978371585987202239)*a^(2) + (349638616619174691032821972665)/(16529681543978371585987202239)*a + (115769526101182731800802874)/(246711664835498083372943317) , (1862855199312014126727411)/(16529681543978371585987202239)*a^(15) + (79664698693785567944372602)/(16529681543978371585987202239)*a^(14) - (7630228331411522118623197)/(246711664835498083372943317)*a^(13) - (4015297469935952881007625863)/(16529681543978371585987202239)*a^(12) + (24763047253028558073634880295)/(16529681543978371585987202239)*a^(11) + (57776959773117235678619915348)/(16529681543978371585987202239)*a^(10) - (418048364968200309142063662307)/(16529681543978371585987202239)*a^(9) - (212612538775095120564540633663)/(16529681543978371585987202239)*a^(8) + (2733855333814702453866956730360)/(16529681543978371585987202239)*a^(7) - (130061525480791691848567430438)/(16529681543978371585987202239)*a^(6) - (7527236881380060899929639303601)/(16529681543978371585987202239)*a^(5) + (1377339407817720945846788933143)/(16529681543978371585987202239)*a^(4) + (7628251272366343223554756105881)/(16529681543978371585987202239)*a^(3) - (1249025355565687500363740269290)/(16529681543978371585987202239)*a^(2) - (885517367633764091323337685031)/(16529681543978371585987202239)*a - (481138340390541050097640455)/(246711664835498083372943317) , (106561355193864339758591834)/(16529681543978371585987202239)*a^(15) - (372335006243689556782201328)/(16529681543978371585987202239)*a^(14) - (6084466438654702892713680590)/(16529681543978371585987202239)*a^(13) + (21766234058679181221497629160)/(16529681543978371585987202239)*a^(12) + (116545041999370333271657548692)/(16529681543978371585987202239)*a^(11) - (411180652627281208274667343321)/(16529681543978371585987202239)*a^(10) - (963751159839249787156205357795)/(16529681543978371585987202239)*a^(9) + (3102252162059408687855807871460)/(16529681543978371585987202239)*a^(8) + (4198712248706388856606309131622)/(16529681543978371585987202239)*a^(7) - (10426210351416549777987885746237)/(16529681543978371585987202239)*a^(6) - (9785981261439382569314087194707)/(16529681543978371585987202239)*a^(5) + (14806620587228805902456363122509)/(16529681543978371585987202239)*a^(4) + (9624132241891139719552539630025)/(16529681543978371585987202239)*a^(3) - (6638828323384077997653161938369)/(16529681543978371585987202239)*a^(2) - (1284608422336403491740283371531)/(16529681543978371585987202239)*a + (1349013708886798412302828639)/(246711664835498083372943317) , (132746408087594849707629518)/(16529681543978371585987202239)*a^(15) - 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