/* 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 - 249*x^14 + 1468*x^13 + 14951*x^12 - 127824*x^11 - 146116*x^10 + 3524299*x^9 - 6618428*x^8 - 25092711*x^7 + 111980624*x^6 - 122939949*x^5 - 71984014*x^4 + 233617078*x^3 - 109771874*x^2 - 52840783*x + 40491571, 16, 22, [16, 0], 54377966460580450275755400738525390625, [5, 73], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/5*a^8 + 1/5*a^7 - 1/5*a^5 - 1/5*a^4 - 1/5*a^3 + 1/5*a + 1/5, 1/5*a^9 - 1/5*a^7 - 1/5*a^6 + 1/5*a^3 + 1/5*a^2 - 1/5, 1/5*a^10 - 1/5*a^5 + 1/5, 1/5*a^11 - 1/5*a^6 + 1/5*a, 1/15*a^12 - 1/15*a^11 - 1/15*a^10 - 1/15*a^9 - 1/15*a^8 + 4/15*a^7 + 7/15*a^6 + 2/15*a^5 + 2/5*a^4 - 1/3*a^3 - 1/3*a^2 - 7/15*a - 1/15, 1/15*a^13 + 1/15*a^11 + 1/15*a^10 + 1/15*a^9 + 1/3*a^7 + 1/5*a^6 - 7/15*a^5 + 4/15*a^4 - 4/15*a^3 + 2/5*a^2 + 7/15*a - 4/15, 1/1635*a^14 + 2/327*a^13 - 5/327*a^12 + 121/1635*a^11 + 4/1635*a^10 + 41/545*a^9 - 152/1635*a^8 + 253/545*a^7 + 43/109*a^6 - 532/1635*a^5 - 74/545*a^4 + 47/545*a^3 + 389/1635*a^2 - 661/1635*a + 133/1635, 1/261236987487992030198280695159045794111186305*a^15 + 22087419264295624135445885849402609769452/261236987487992030198280695159045794111186305*a^14 + 1039307852952930647146600399034563930051826/87078995829330676732760231719681931370395435*a^13 + 4006211087324096671968264801529177554847436/261236987487992030198280695159045794111186305*a^12 - 5941671373268854164683085214892528197889317/87078995829330676732760231719681931370395435*a^11 - 2654790616160829418190588660642169059190064/261236987487992030198280695159045794111186305*a^10 + 19211103241354389688468919031586893209020649/261236987487992030198280695159045794111186305*a^9 - 928434962376635664358096803555315594357935/52247397497598406039656139031809158822237261*a^8 + 6111984390391135563190430098795349660037551/261236987487992030198280695159045794111186305*a^7 - 10991190189158790916274457983758354773899068/52247397497598406039656139031809158822237261*a^6 + 2793741270065420390538032303564401734912392/87078995829330676732760231719681931370395435*a^5 - 6003488684257877991985038523932776011957817/87078995829330676732760231719681931370395435*a^4 - 123158590282372844488566075376979933580321614/261236987487992030198280695159045794111186305*a^3 - 9270834658936739265957063717490398573843666/87078995829330676732760231719681931370395435*a^2 + 97959159891088258686708426115417747416385852/261236987487992030198280695159045794111186305*a + 261671342438709537347955970539812292699364/1040784810709131594415460936888628661797555], 0, 2, [2], 1, [ (236692062326775843644544417781598464882927)/(52247397497598406039656139031809158822237261)*a^(15) - (2129914814995653153711612550811135932700972)/(261236987487992030198280695159045794111186305)*a^(14) - (99080195073505392357455292774926512950363782)/(87078995829330676732760231719681931370395435)*a^(13) + (460183705599455753172542020638091397962873367)/(87078995829330676732760231719681931370395435)*a^(12) + (19351568823817474494591085872430334348614316059)/(261236987487992030198280695159045794111186305)*a^(11) - (128049132577709655465532843421138713998371436916)/(261236987487992030198280695159045794111186305)*a^(10) - (326659669751574418543454490918234193668015969358)/(261236987487992030198280695159045794111186305)*a^(9) + (3778960919782790553235422128378856531941954023931)/(261236987487992030198280695159045794111186305)*a^(8) - (1098607409542182413110152199955635391021539586067)/(87078995829330676732760231719681931370395435)*a^(7) - (33657643841831530128316502397710379549512125015499)/(261236987487992030198280695159045794111186305)*a^(6) + (92121146172392910135727127789932843245602297853646)/(261236987487992030198280695159045794111186305)*a^(5) - (11622239896494957338763112098727957282414030584229)/(87078995829330676732760231719681931370395435)*a^(4) - (127103683607300943547789188841886253120726279174671)/(261236987487992030198280695159045794111186305)*a^(3) + (123856562745066042566951756315316482604502506074696)/(261236987487992030198280695159045794111186305)*a^(2) + (6286396904342263252946370089921902055631553092273)/(87078995829330676732760231719681931370395435)*a - (158923028293155058174758196098615697602424001786)/(1040784810709131594415460936888628661797555) , (134920411229500182646716870149552830291619)/(261236987487992030198280695159045794111186305)*a^(15) - (218072622408655292996662656841192080048599)/(261236987487992030198280695159045794111186305)*a^(14) - (33896656963123033984981406103495468018217882)/(261236987487992030198280695159045794111186305)*a^(13) + (50386902047429265777784254795322107098404021)/(87078995829330676732760231719681931370395435)*a^(12) + (742095366509868450310857510172202902317872134)/(87078995829330676732760231719681931370395435)*a^(11) - (14165415873041831037861300782552036943847424894)/(261236987487992030198280695159045794111186305)*a^(10) - (39309499484537040500902558177397044869849270791)/(261236987487992030198280695159045794111186305)*a^(9) + (421089576183150197583380191773031591019166908117)/(261236987487992030198280695159045794111186305)*a^(8) - (310442097438205138622761492413871137280506065783)/(261236987487992030198280695159045794111186305)*a^(7) - (3814450439628752291286327664109447802861695635742)/(261236987487992030198280695159045794111186305)*a^(6) + (9831650950167045282740153147710122594929885652194)/(261236987487992030198280695159045794111186305)*a^(5) - (2990849982971369743856223284182413170883127110994)/(261236987487992030198280695159045794111186305)*a^(4) - (13848596542404627968922218936611309295725489272067)/(261236987487992030198280695159045794111186305)*a^(3) + (12382333729704889136384334252519620638225481602553)/(261236987487992030198280695159045794111186305)*a^(2) + (2303719697315205711812813766129124415627567325392)/(261236987487992030198280695159045794111186305)*a - (1052442114509943038766164548150402862938404192)/(69385654047275439627697395792575244119837) , (89184551338717383969087895023183849785936)/(17415799165866135346552046343936386274079087)*a^(15) - (784174066676696483480723207696062794881237)/(87078995829330676732760231719681931370395435)*a^(14) - (67205090044832338044141795698852157697268464)/(52247397497598406039656139031809158822237261)*a^(13) + (515560979079860001278016020132482338072967214)/(87078995829330676732760231719681931370395435)*a^(12) + (21921263115295234334452661822044339389955801501)/(261236987487992030198280695159045794111186305)*a^(11) - (28757023983605097368179010643991895107090837426)/(52247397497598406039656139031809158822237261)*a^(10) - (373982430628937400890033094795459505610846656139)/(261236987487992030198280695159045794111186305)*a^(9) + (283364409484017656965264583140300357457791292052)/(17415799165866135346552046343936386274079087)*a^(8) - (3576952624082359791687807270456547760029818345172)/(261236987487992030198280695159045794111186305)*a^(7) - (12670171791691822539894254113336555056192974245267)/(87078995829330676732760231719681931370395435)*a^(6) + (20523237356603111050735992287224686690146300725054)/(52247397497598406039656139031809158822237261)*a^(5) - (37056078724270911811544781140601878129046153946751)/(261236987487992030198280695159045794111186305)*a^(4) - (28466934540227426456174201620977042319304207504258)/(52247397497598406039656139031809158822237261)*a^(3) + (45276145424296196322798260302140628606551054103049)/(87078995829330676732760231719681931370395435)*a^(2) + (21816144954621793160199290985496131701387868581791)/(261236987487992030198280695159045794111186305)*a - (34768189282169206292434136333574167122255232554)/(208156962141826318883092187377725732359511) , (20792334588778215246271185046300315435282)/(52247397497598406039656139031809158822237261)*a^(15) - (208625792672391201882970356216062976505793)/(261236987487992030198280695159045794111186305)*a^(14) - (5220466329787924767689582620654739306261161)/(52247397497598406039656139031809158822237261)*a^(13) + (42231082525848520517543176003671008642526933)/(87078995829330676732760231719681931370395435)*a^(12) + (336469624821996331316603962545898623001993486)/(52247397497598406039656139031809158822237261)*a^(11) - (3874956016459990394473605376919892813477303796)/(87078995829330676732760231719681931370395435)*a^(10) - (8962766593191514427655856291538989374220435169)/(87078995829330676732760231719681931370395435)*a^(9) + (68082098309786666379408936989878588776879334309)/(52247397497598406039656139031809158822237261)*a^(8) - (346544416092376849029211318151670870624036636694)/(261236987487992030198280695159045794111186305)*a^(7) - (595155677475868735441584200105041123954717500442)/(52247397497598406039656139031809158822237261)*a^(6) + (2892680599361704254059055241306812884901346962531)/(87078995829330676732760231719681931370395435)*a^(5) - (3926202225719051853413531215623500718924044020373)/(261236987487992030198280695159045794111186305)*a^(4) - (781852835335090025449776670787792336297068254324)/(17415799165866135346552046343936386274079087)*a^(3) + (12409254695600361200728747163955522798160880514104)/(261236987487992030198280695159045794111186305)*a^(2) + (305206742663047944111102563620000235110405678211)/(52247397497598406039656139031809158822237261)*a - (16041563287871532629060563286827224571185744523)/(1040784810709131594415460936888628661797555) , (3953077416288041382017670254240652598279666)/(17415799165866135346552046343936386274079087)*a^(15) - (7101682744815843763545541569496371206742491)/(17415799165866135346552046343936386274079087)*a^(14) - (2978589128646463533540716012085784850601207082)/(52247397497598406039656139031809158822237261)*a^(13) + (23041008421104870151186247686805001903341691648)/(87078995829330676732760231719681931370395435)*a^(12) + (969726278640723073714710786618400705734287119192)/(261236987487992030198280695159045794111186305)*a^(11) - (6412400045603664624475307565785576071774112869712)/(261236987487992030198280695159045794111186305)*a^(10) - (3276287321683778527085469167078194235110927908154)/(52247397497598406039656139031809158822237261)*a^(9) + (12617471550172023104969783995870456946126400291609)/(17415799165866135346552046343936386274079087)*a^(8) - (164670343247577145439095462254494352182688839168854)/(261236987487992030198280695159045794111186305)*a^(7) - (562025760136596005555758909292337457676758242290094)/(87078995829330676732760231719681931370395435)*a^(6) + (4610820466378200942637949879565971954323154084117567)/(261236987487992030198280695159045794111186305)*a^(5) - (348155943588208293185640511566731688235810479988813)/(52247397497598406039656139031809158822237261)*a^(4) - (1272665557621447292493936834692639587382323529948441)/(52247397497598406039656139031809158822237261)*a^(3) + (2064785013183049428936604309433576652411640163381593)/(87078995829330676732760231719681931370395435)*a^(2) + (945737820841987372455010336379228950839942902427922)/(261236987487992030198280695159045794111186305)*a - (7948382313164829404888922370484612358936983243672)/(1040784810709131594415460936888628661797555) , (739571784734106108792299065792923999181166)/(87078995829330676732760231719681931370395435)*a^(15) - (1315120583218679634134688742278486059367856)/(87078995829330676732760231719681931370395435)*a^(14) - (111454927328435869409627011495307592054687043)/(52247397497598406039656139031809158822237261)*a^(13) + (171747100943912099039353185257949117323380827)/(17415799165866135346552046343936386274079087)*a^(12) + (36318105247650239577171432231879604820710836856)/(261236987487992030198280695159045794111186305)*a^(11) - (47845619469544011453003103011156723951609486202)/(52247397497598406039656139031809158822237261)*a^(10) - (616371478126444516773373547711114353504718554097)/(261236987487992030198280695159045794111186305)*a^(9) + (471059790351279184278128739632654366239997979978)/(17415799165866135346552046343936386274079087)*a^(8) - (1210761478969169110876625516170314572635989006506)/(52247397497598406039656139031809158822237261)*a^(7) - (21018570127560144130411224951709436547383617676612)/(87078995829330676732760231719681931370395435)*a^(6) + (34284230489619211023379004537205150908072178029620)/(52247397497598406039656139031809158822237261)*a^(5) - (63476808509935914366181245539316678199694879382908)/(261236987487992030198280695159045794111186305)*a^(4) - (47413778101742208921598804623749790833018742255491)/(52247397497598406039656139031809158822237261)*a^(3) + (15254701707793335034949662857703057715162974494009)/(17415799165866135346552046343936386274079087)*a^(2) + (35681556836964704166716377787860769064384457698061)/(261236987487992030198280695159045794111186305)*a - (293315361123648411849124108743700370605266673787)/(1040784810709131594415460936888628661797555) , (69425816102974510253608523618371583673821981)/(261236987487992030198280695159045794111186305)*a^(15) - (124874166102491751124177666571204328383784392)/(261236987487992030198280695159045794111186305)*a^(14) - (5812348099378978377182410451257746002814275511)/(87078995829330676732760231719681931370395435)*a^(13) + (5397964187077953187384787543637442203807895577)/(17415799165866135346552046343936386274079087)*a^(12) + (1135256650960817618745133343226325511963745333979)/(261236987487992030198280695159045794111186305)*a^(11) - (7510469153610183086305686467946832338612026639707)/(261236987487992030198280695159045794111186305)*a^(10) - (19166789280773665845013399042952328297295567802587)/(261236987487992030198280695159045794111186305)*a^(9) + (44330360134762149373287028736940078329698151587348)/(52247397497598406039656139031809158822237261)*a^(8) - (64404172955218041736660824115848644785018764946758)/(87078995829330676732760231719681931370395435)*a^(7) - (394839368534143409012633340107990593399173735654706)/(52247397497598406039656139031809158822237261)*a^(6) + (1080537015028493823972724956486997456947151297811966)/(52247397497598406039656139031809158822237261)*a^(5) - (681590267366606222430881814216524193550028697162148)/(87078995829330676732760231719681931370395435)*a^(4) - (7454043357309581597103029433820009419511756481229509)/(261236987487992030198280695159045794111186305)*a^(3) + (7264269146966263756558042332321965122511645000798216)/(261236987487992030198280695159045794111186305)*a^(2) + (368622738424344725638228249592552506686977415831532)/(87078995829330676732760231719681931370395435)*a - (1864553403977387677679980095930285165908811676003)/(208156962141826318883092187377725732359511) , (975198725092895591279813657857457367730839)/(87078995829330676732760231719681931370395435)*a^(15) - (5247611548723219477872048576743394483342904)/(261236987487992030198280695159045794111186305)*a^(14) - (244933786394340056030090100072534084425463418)/(87078995829330676732760231719681931370395435)*a^(13) + (681675229599005942901560448627693137331919933)/(52247397497598406039656139031809158822237261)*a^(12) + (47851560082619903641969421093193448090389006368)/(261236987487992030198280695159045794111186305)*a^(11) - 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