/* 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 + 9*x^14 - 146*x^13 + 132*x^12 + 301*x^11 + 933*x^10 + 10461*x^9 - 8365*x^8 - 30971*x^7 - 18709*x^6 + 7320*x^5 + 37149*x^4 + 36402*x^3 + 55167*x^2 + 22519*x - 6323, 16, 22, [8, 4], 135845792016352372555063553, [17, 83], [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, 1/101027817112911349340933203396635467012540983*a^15 + 35384239452906246659506338851359451831045699/101027817112911349340933203396635467012540983*a^14 - 48828758563064584239141036743459235213066379/101027817112911349340933203396635467012540983*a^13 - 43459624113321872946199779191602482477212891/101027817112911349340933203396635467012540983*a^12 + 18501582442607918721330400878531056200409319/101027817112911349340933203396635467012540983*a^11 + 33362759455347288372156492084765579537763859/101027817112911349340933203396635467012540983*a^10 - 4759229989427912665780967855616188913001553/101027817112911349340933203396635467012540983*a^9 + 154393955886402745298519661984974523602041/980852593329236401368283528122674437014961*a^8 - 6518530649822942737766677755537844172617184/101027817112911349340933203396635467012540983*a^7 - 25545804739469019625010217054467144600856650/101027817112911349340933203396635467012540983*a^6 - 32675501080098342506612543123426873725732135/101027817112911349340933203396635467012540983*a^5 - 25568974840978702654816211751055430574219296/101027817112911349340933203396635467012540983*a^4 + 32969735589270881130698693734523369097682484/101027817112911349340933203396635467012540983*a^3 - 47163811759127315858414324857090760283610674/101027817112911349340933203396635467012540983*a^2 - 25432151693595854740653361788466736821779807/101027817112911349340933203396635467012540983*a + 16281425127346125838647768658086953988940730/101027817112911349340933203396635467012540983], 0, 1, [], 1, [ (2848512102825821025978005383246940855717)/(101027817112911349340933203396635467012540983)*a^(15) - (11441674147145326628144920024436661002352)/(101027817112911349340933203396635467012540983)*a^(14) + (37633014070677400703834477674274694011408)/(101027817112911349340933203396635467012540983)*a^(13) - (452555535078034876578308501630586615894892)/(101027817112911349340933203396635467012540983)*a^(12) + (831773442126410501562937245555785265262464)/(101027817112911349340933203396635467012540983)*a^(11) - (13953200746799471923072268225182264567007)/(101027817112911349340933203396635467012540983)*a^(10) + (2323237231788557111832133093838484130350879)/(101027817112911349340933203396635467012540983)*a^(9) + (270584938204035554396770376163900811166228)/(980852593329236401368283528122674437014961)*a^(8) - (51601102695403701213230481324707165036032377)/(101027817112911349340933203396635467012540983)*a^(7) - (29338330631607276690082263599583363670516883)/(101027817112911349340933203396635467012540983)*a^(6) + (3013368011263101896034279318619264336275203)/(101027817112911349340933203396635467012540983)*a^(5) - (4945009264711956637292135606318796843919399)/(101027817112911349340933203396635467012540983)*a^(4) + (71237072727823356415531818736791032080649536)/(101027817112911349340933203396635467012540983)*a^(3) - (8831002284536134953522132092048897568243042)/(101027817112911349340933203396635467012540983)*a^(2) + (79951530264135542378622337245698750312450994)/(101027817112911349340933203396635467012540983)*a - (98744919940713975217381197948046003324859890)/(101027817112911349340933203396635467012540983) , (5066450123793911390724138495417667297271)/(101027817112911349340933203396635467012540983)*a^(15) - (17631785257789246557108786728069128375203)/(101027817112911349340933203396635467012540983)*a^(14) + (56808810735089136852850358449172192952944)/(101027817112911349340933203396635467012540983)*a^(13) - (773128627451160109976624000386919113526329)/(101027817112911349340933203396635467012540983)*a^(12) + (1060300482283068344605133536158905258577600)/(101027817112911349340933203396635467012540983)*a^(11) + (636044494671798499009202953673766016057177)/(101027817112911349340933203396635467012540983)*a^(10) + (4481357835979122250654689991710434618413003)/(101027817112911349340933203396635467012540983)*a^(9) + (502279865718157964199481024734882625638604)/(980852593329236401368283528122674437014961)*a^(8) - (64849527595474450317103972226330658330758355)/(101027817112911349340933203396635467012540983)*a^(7) - (94639899457544324696757997133482130114401506)/(101027817112911349340933203396635467012540983)*a^(6) - (47035198020346316328694793396098992090176308)/(101027817112911349340933203396635467012540983)*a^(5) - (17713042407614902530023050015734509433648156)/(101027817112911349340933203396635467012540983)*a^(4) + (156891707450347894762649351949164947520773963)/(101027817112911349340933203396635467012540983)*a^(3) + (69614274891183196755546093860864378700672526)/(101027817112911349340933203396635467012540983)*a^(2) + (210582217473348201591466155790236865294564530)/(101027817112911349340933203396635467012540983)*a + (47795579337883535056078230830503495136822852)/(101027817112911349340933203396635467012540983) , (3896300889803079980074642574500652429382)/(101027817112911349340933203396635467012540983)*a^(15) - (16480067391576295191894927933514003849526)/(101027817112911349340933203396635467012540983)*a^(14) + (52552752912730690736426953994971313790018)/(101027817112911349340933203396635467012540983)*a^(13) - (621534888265063000315692368466433626547950)/(101027817112911349340933203396635467012540983)*a^(12) + (1246994579026979855426605573378273066000490)/(101027817112911349340933203396635467012540983)*a^(11) + (69953570886189933356582371436802624136008)/(101027817112911349340933203396635467012540983)*a^(10) + (2683698586052132444574957375499831466224337)/(101027817112911349340933203396635467012540983)*a^(9) + (354569017233477735630007633341720428763513)/(980852593329236401368283528122674437014961)*a^(8) - (79148546744666140741375893860581258214467180)/(101027817112911349340933203396635467012540983)*a^(7) - (47822625356834465663315268246724695618871429)/(101027817112911349340933203396635467012540983)*a^(6) + (51792734674423747909267275388457651194944475)/(101027817112911349340933203396635467012540983)*a^(5) + (70136831738262207543674411011733804491449678)/(101027817112911349340933203396635467012540983)*a^(4) + (23499996263445587648792098197974479110959432)/(101027817112911349340933203396635467012540983)*a^(3) - (93969857311486196776558864542027282293044326)/(101027817112911349340933203396635467012540983)*a^(2) + (84379236111523229824403594158453241136021689)/(101027817112911349340933203396635467012540983)*a - (67922436963930540636696809175213121404571840)/(101027817112911349340933203396635467012540983) , (6432122089886931577817332669518553218854)/(101027817112911349340933203396635467012540983)*a^(15) - (20897243576347172302543381358604062176475)/(101027817112911349340933203396635467012540983)*a^(14) + (66230517718091752543424385916647364545790)/(101027817112911349340933203396635467012540983)*a^(13) - (965799952065849715777071255197096114444112)/(101027817112911349340933203396635467012540983)*a^(12) + (1126250799889130058160788885842599240218273)/(101027817112911349340933203396635467012540983)*a^(11) + (1172173349430769299379965725971615518682558)/(101027817112911349340933203396635467012540983)*a^(10) + (6307314804347383067232595799316639373039394)/(101027817112911349340933203396635467012540983)*a^(9) + (637231980821111698687582583496108245500281)/(980852593329236401368283528122674437014961)*a^(8) - (66632981657302328616141091806528232056944468)/(101027817112911349340933203396635467012540983)*a^(7) - (150311829266073946729920245584579490667038278)/(101027817112911349340933203396635467012540983)*a^(6) - (111414329886920253045010505723373333883862621)/(101027817112911349340933203396635467012540983)*a^(5) + (52325316919906171025258624718001519696820886)/(101027817112911349340933203396635467012540983)*a^(4) + (159317498588740307908143829803935207403070826)/(101027817112911349340933203396635467012540983)*a^(3) + (186901122446365771637239207744937490066078723)/(101027817112911349340933203396635467012540983)*a^(2) + (303087419625684764166120930535265605294853730)/(101027817112911349340933203396635467012540983)*a + (56210427400807786218118231797322230673625711)/(101027817112911349340933203396635467012540983) , (2935468277474894122839886454390129901513)/(101027817112911349340933203396635467012540983)*a^(15) - (6464503916659438781864315834200739881355)/(101027817112911349340933203396635467012540983)*a^(14) + (20274873050407705550838492080072683651213)/(101027817112911349340933203396635467012540983)*a^(13) - (410321980310467347244465445725883460982631)/(101027817112911349340933203396635467012540983)*a^(12) + (54732212960940661777954902065988273000540)/(101027817112911349340933203396635467012540983)*a^(11) + (1063609123223794168285035662544693080327642)/(101027817112911349340933203396635467012540983)*a^(10) + (3589686017010460853531159546528623566259283)/(101027817112911349340933203396635467012540983)*a^(9) + (320858794278538699208115026160751167928910)/(980852593329236401368283528122674437014961)*a^(8) + (377765345137360092009291669679722942927865)/(101027817112911349340933203396635467012540983)*a^(7) - (101787516446611323681127176677246985923170114)/(101027817112911349340933203396635467012540983)*a^(6) - (135308532635731601315190824455600544414445046)/(101027817112911349340933203396635467012540983)*a^(5) - (35974511076400112162720209672543381607486298)/(101027817112911349340933203396635467012540983)*a^(4) + (151210739526733012757479939722723060993075015)/(101027817112911349340933203396635467012540983)*a^(3) + (226948888505717182731932353376572833064394164)/(101027817112911349340933203396635467012540983)*a^(2) + (218724854879755156272656668076336580533552515)/(101027817112911349340933203396635467012540983)*a + (55514031083652213298682779188932851121874548)/(101027817112911349340933203396635467012540983) , (1578516078391148475004255995353277835133)/(101027817112911349340933203396635467012540983)*a^(15) - (3589282975158218925116226224459267382410)/(101027817112911349340933203396635467012540983)*a^(14) + (12302762401694830535282096736447613841495)/(101027817112911349340933203396635467012540983)*a^(13) - (226812770368911844205924474592418756764244)/(101027817112911349340933203396635467012540983)*a^(12) + (62214712945314951700928105851569144153065)/(101027817112911349340933203396635467012540983)*a^(11) + (379714892878305079813365185911728671855795)/(101027817112911349340933203396635467012540983)*a^(10) + (2338444856174105825412174913539449578856796)/(101027817112911349340933203396635467012540983)*a^(9) + (170658527329529985975623262018317930347345)/(980852593329236401368283528122674437014961)*a^(8) - (143065084455209819868384962942823375401309)/(101027817112911349340933203396635467012540983)*a^(7) - (44744075245886123478970103828121292317127222)/(101027817112911349340933203396635467012540983)*a^(6) - (97904868233979891775282773736417032558145963)/(101027817112911349340933203396635467012540983)*a^(5) - (25229939988784592661825596701366645947601864)/(101027817112911349340933203396635467012540983)*a^(4) + (91135882375957355940696307252234858778272077)/(101027817112911349340933203396635467012540983)*a^(3) + (171598628619503937878909910744131581268866058)/(101027817112911349340933203396635467012540983)*a^(2) + (116298165619296142137859281210682841820714472)/(101027817112911349340933203396635467012540983)*a - (47190726254370681733352628501174368045076960)/(101027817112911349340933203396635467012540983) , (1765319043484062712190390533473115033624)/(101027817112911349340933203396635467012540983)*a^(15) - (5312786050446487416650457039645615355678)/(101027817112911349340933203396635467012540983)*a^(14) + (16018815228049259434415087625871804488287)/(101027817112911349340933203396635467012540983)*a^(13) - (258728241124370237583533813805397974004252)/(101027817112911349340933203396635467012540983)*a^(12) + (241426309704852172599426939285356080423430)/(101027817112911349340933203396635467012540983)*a^(11) + (497518199438185602632415080307729688406473)/(101027817112911349340933203396635467012540983)*a^(10) + (1792026767083471047451426930318020414070617)/(101027817112911349340933203396635467012540983)*a^(9) + (173147945793858470638641634767588971053819)/(980852593329236401368283528122674437014961)*a^(8) - (13921253804054330332262629964570876940780960)/(101027817112911349340933203396635467012540983)*a^(7) - (54970242345901464647684447790489551427640037)/(101027817112911349340933203396635467012540983)*a^(6) - (36480599940961537077228755671043901129324263)/(101027817112911349340933203396635467012540983)*a^(5) + (51875363069476997910977251354924932317611536)/(101027817112911349340933203396635467012540983)*a^(4) + (17819028339830705643622685971532592583260484)/(101027817112911349340933203396635467012540983)*a^(3) + (63364756303047789199827394973681172070677312)/(101027817112911349340933203396635467012540983)*a^(2) + (92521873517930184505594106444552956375009674)/(101027817112911349340933203396635467012540983)*a - (60203985218161862394092260816783765419520144)/(101027817112911349340933203396635467012540983) , (42483667296837596953988181272388018006059)/(101027817112911349340933203396635467012540983)*a^(15) - (115157774533181565973233557023018188087977)/(101027817112911349340933203396635467012540983)*a^(14) + (354629823886643003656949249992447822413556)/(101027817112911349340933203396635467012540983)*a^(13) - (6107119741255931843500787909584674669766143)/(101027817112911349340933203396635467012540983)*a^(12) + (3879266751585423270060627434747156583813835)/(101027817112911349340933203396635467012540983)*a^(11) + (13142160312877772537078042127086442785624486)/(101027817112911349340933203396635467012540983)*a^(10) + (42903173430577618531796555157970442088866645)/(101027817112911349340933203396635467012540983)*a^(9) + (4439362799599022634315522202937088073579207)/(980852593329236401368283528122674437014961)*a^(8) - (214675673686230704003099265690101578756444198)/(101027817112911349340933203396635467012540983)*a^(7) - (1308977006703525096834211986686077624561474429)/(101027817112911349340933203396635467012540983)*a^(6) - (1091467939078525258500847734542825198618963271)/(101027817112911349340933203396635467012540983)*a^(5) - (57884599892380400729507221436195889299785507)/(101027817112911349340933203396635467012540983)*a^(4) + (1289745796879060719965990006182553176667559608)/(101027817112911349340933203396635467012540983)*a^(3) + (1545024289812093452110672710141483277686174650)/(101027817112911349340933203396635467012540983)*a^(2) + (2466557406571125708343159525967574129259309235)/(101027817112911349340933203396635467012540983)*a + (1369167496225699191414485317330352226311777053)/(101027817112911349340933203396635467012540983) , (16153285665889949615032201499724994520178)/(101027817112911349340933203396635467012540983)*a^(15) - 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