/* 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 - x^15 + 52*x^14 - 52*x^13 + 1072*x^12 - 1395*x^11 + 11748*x^10 - 13839*x^9 + 86310*x^8 - 83556*x^7 + 540278*x^6 - 463965*x^5 + 1553597*x^4 - 771733*x^3 + 3292187*x^2 - 1949034*x + 2213401, 16, 1, [0, 8], 4585048252186499369597900390625, [3, 5, 17], [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, 1/289034445079918768974533783036378799974459625164723*a^15 - 7805059681154855318417728924119045946318528872880/289034445079918768974533783036378799974459625164723*a^14 + 139421278639331645414297196489737606004470479679180/289034445079918768974533783036378799974459625164723*a^13 + 37135064956533850334366520060328602647135011429108/289034445079918768974533783036378799974459625164723*a^12 - 127317722405057512291145412440779026779535404574539/289034445079918768974533783036378799974459625164723*a^11 + 15506641334413197413843062501780127517421217998640/289034445079918768974533783036378799974459625164723*a^10 + 83252585739488419017947772572439068244862566449089/289034445079918768974533783036378799974459625164723*a^9 - 96795861642757680756201663079753241428964024245772/289034445079918768974533783036378799974459625164723*a^8 - 129484990356321113194159276588720023209883618025216/289034445079918768974533783036378799974459625164723*a^7 - 133738533940126421812790530054608978851819731939013/289034445079918768974533783036378799974459625164723*a^6 + 90871878891179884722960847541927411593620119148138/289034445079918768974533783036378799974459625164723*a^5 - 80685588460940467254233631493707288531404436488694/289034445079918768974533783036378799974459625164723*a^4 - 29179282860179436161656724368953597311278075696658/289034445079918768974533783036378799974459625164723*a^3 + 96835165990098560863202421181736244314785044444869/289034445079918768974533783036378799974459625164723*a^2 - 132729208814143006860330249003391962149330256830075/289034445079918768974533783036378799974459625164723*a - 135826115220380632656635164545256289922518634717000/289034445079918768974533783036378799974459625164723], 1, 2824, [2, 1412], 1, [ (16199104922109930431157677261614681944)/(26429686627899708363919728711607458572239099)*a^(15) - (54689247385072636661921817684668140105)/(26429686627899708363919728711607458572239099)*a^(14) + (865938650996759894929407947728624865590)/(26429686627899708363919728711607458572239099)*a^(13) - (2816603012477758120809838586301241433680)/(26429686627899708363919728711607458572239099)*a^(12) + (18540413123394103919641966114761508446620)/(26429686627899708363919728711607458572239099)*a^(11) - (62320337699118048981268265388952813705516)/(26429686627899708363919728711607458572239099)*a^(10) + (225230684935647791935097892399354458874020)/(26429686627899708363919728711607458572239099)*a^(9) - (636788205457627411107738533643390309715400)/(26429686627899708363919728711607458572239099)*a^(8) + (1691728175010700960139035887129702014287285)/(26429686627899708363919728711607458572239099)*a^(7) - (4225983493772788347177707820694118907124050)/(26429686627899708363919728711607458572239099)*a^(6) + (9983696091689799071583297211187042143662736)/(26429686627899708363919728711607458572239099)*a^(5) - (25228931255308726108561582395951589598312065)/(26429686627899708363919728711607458572239099)*a^(4) + (30428741495335264112963752758816939341177050)/(26429686627899708363919728711607458572239099)*a^(3) - (53510684533583560702725615666264614840625125)/(26429686627899708363919728711607458572239099)*a^(2) + (34312861913239563173066132107978784301203700)/(26429686627899708363919728711607458572239099)*a - (103135997652676448508544640444034510839844494)/(26429686627899708363919728711607458572239099) , (2188329801833273603060041712286146557)/(26429686627899708363919728711607458572239099)*a^(15) - (15884681117150793575993032541489932155)/(26429686627899708363919728711607458572239099)*a^(14) + (156855546520859012288470220507852085965)/(26429686627899708363919728711607458572239099)*a^(13) - (848407614021117618429277395924906996605)/(26429686627899708363919728711607458572239099)*a^(12) + (4479207849384143062157392985998179290775)/(26429686627899708363919728711607458572239099)*a^(11) - (18600440052456289382914297280635818984990)/(26429686627899708363919728711607458572239099)*a^(10) + (70826198272849270722826439766099423376785)/(26429686627899708363919728711607458572239099)*a^(9) - (209009064230297995490944391019122965467935)/(26429686627899708363919728711607458572239099)*a^(8) + (607023621281200720492750277796681084475315)/(26429686627899708363919728711607458572239099)*a^(7) - (1334766177520426005355687543994748818805980)/(26429686627899708363919728711607458572239099)*a^(6) + (3519357787615108855260704626406538681610223)/(26429686627899708363919728711607458572239099)*a^(5) - (6723623233397473159961350434684400044250960)/(26429686627899708363919728711607458572239099)*a^(4) + (16035126889569943553532020847961821853272330)/(26429686627899708363919728711607458572239099)*a^(3) - (13521144079238713517426408854047333227471260)/(26429686627899708363919728711607458572239099)*a^(2) + (10219456570740772959516143835878528397468980)/(26429686627899708363919728711607458572239099)*a + (11965000406276013792721806239927567581119896)/(26429686627899708363919728711607458572239099) , (14010775120276656828097635549328535387)/(26429686627899708363919728711607458572239099)*a^(15) - (38804566267921843085928785143178207950)/(26429686627899708363919728711607458572239099)*a^(14) + (709083104475900882640937727220772779625)/(26429686627899708363919728711607458572239099)*a^(13) - (1968195398456640502380561190376334437075)/(26429686627899708363919728711607458572239099)*a^(12) + (14061205274009960857484573128763329155845)/(26429686627899708363919728711607458572239099)*a^(11) - (43719897646661759598353968108316994720526)/(26429686627899708363919728711607458572239099)*a^(10) + (154404486662798521212271452633255035497235)/(26429686627899708363919728711607458572239099)*a^(9) - (427779141227329415616794142624267344247465)/(26429686627899708363919728711607458572239099)*a^(8) + (1084704553729500239646285609333020929811970)/(26429686627899708363919728711607458572239099)*a^(7) - (2891217316252362341822020276699370088318070)/(26429686627899708363919728711607458572239099)*a^(6) + (6464338304074690216322592584780503462052513)/(26429686627899708363919728711607458572239099)*a^(5) - (18505308021911252948600231961267189554061105)/(26429686627899708363919728711607458572239099)*a^(4) + (14393614605765320559431731910855117487904720)/(26429686627899708363919728711607458572239099)*a^(3) - (39989540454344847185299206812217281613153865)/(26429686627899708363919728711607458572239099)*a^(2) + (24093405342498790213549988272100255903734720)/(26429686627899708363919728711607458572239099)*a - (115100998058952462301266446683962078420964390)/(26429686627899708363919728711607458572239099) , (4747449890209690179644903524238763449521497)/(22233418852301443767271829464336830767266125012671)*a^(15) - (12022350659773310394643423657028284321203346)/(22233418852301443767271829464336830767266125012671)*a^(14) + (255678287455452309020360804669725687701123132)/(22233418852301443767271829464336830767266125012671)*a^(13) - (626858569640546233019633862689364669105962664)/(22233418852301443767271829464336830767266125012671)*a^(12) + (5501328851051938840993111008211530770297594714)/(22233418852301443767271829464336830767266125012671)*a^(11) - (14429186003266178328559570394921051751428176315)/(22233418852301443767271829464336830767266125012671)*a^(10) + (65566145920049476454083094122131110030700585273)/(22233418852301443767271829464336830767266125012671)*a^(9) - (151601058390600070221427091744823654797591254417)/(22233418852301443767271829464336830767266125012671)*a^(8) + (487549524765857911205700871637910323715229266584)/(22233418852301443767271829464336830767266125012671)*a^(7) - (1029300218146120373942510733880147499465800499786)/(22233418852301443767271829464336830767266125012671)*a^(6) + (2715359488765743211947581510492036901158592383016)/(22233418852301443767271829464336830767266125012671)*a^(5) - (6502643335675744451177212250189098523400409227905)/(22233418852301443767271829464336830767266125012671)*a^(4) + (7813614264302145747202735193943463995676799406657)/(22233418852301443767271829464336830767266125012671)*a^(3) - (13957898533904712904922786103001563930094020741423)/(22233418852301443767271829464336830767266125012671)*a^(2) + (9012848094790898043822439269661698889520774937761)/(22233418852301443767271829464336830767266125012671)*a - (30312325793853723138070611502833689132765330848568)/(22233418852301443767271829464336830767266125012671) , (10745604159321381169023838322268410223558942)/(22233418852301443767271829464336830767266125012671)*a^(15) - (33925439781814351903586930802612324303377750)/(22233418852301443767271829464336830767266125012671)*a^(14) + (542640169506841356526364012167796429474920362)/(22233418852301443767271829464336830767266125012671)*a^(13) - (1712958950517897395433891100263803125491006336)/(22233418852301443767271829464336830767266125012671)*a^(12) + (10745906177212599680223429079745523171007528516)/(22233418852301443767271829464336830767266125012671)*a^(11) - (37439766895276222107977348160279659551321755365)/(22233418852301443767271829464336830767266125012671)*a^(10) + (119638642410520171769177081213314869173869050397)/(22233418852301443767271829464336830767266125012671)*a^(9) - (365175245888835124784963358709540302645745944512)/(22233418852301443767271829464336830767266125012671)*a^(8) + (844735704837921547160757999381298497772974706888)/(22233418852301443767271829464336830767266125012671)*a^(7) - (2437905893929466516469197887091030090462812902277)/(22233418852301443767271829464336830767266125012671)*a^(6) + (5072660853490154645928370118815847058091283470050)/(22233418852301443767271829464336830767266125012671)*a^(5) - (14872137625450970808954731293524038028372965376544)/(22233418852301443767271829464336830767266125012671)*a^(4) + (11134558156437029084743657448412187355921067686329)/(22233418852301443767271829464336830767266125012671)*a^(3) - (32007503829272965274534028966153232190949975581118)/(22233418852301443767271829464336830767266125012671)*a^(2) + (19164359779264195454402413305220269103234855623025)/(22233418852301443767271829464336830767266125012671)*a - (94803545625096973501856170786394626511953906092911)/(22233418852301443767271829464336830767266125012671) , (459216089868619249567649222960005976598322)/(22233418852301443767271829464336830767266125012671)*a^(15) - (2879512708980609150264995748045051955502175)/(22233418852301443767271829464336830767266125012671)*a^(14) + (33668065277636432973402095478512767564074087)/(22233418852301443767271829464336830767266125012671)*a^(13) - (185639173863975249917407265695146538947697135)/(22233418852301443767271829464336830767266125012671)*a^(12) + (1011590011053167316446106128200504057503056466)/(22233418852301443767271829464336830767266125012671)*a^(11) - (4804255718551523617234873648435287773841659178)/(22233418852301443767271829464336830767266125012671)*a^(10) + (16413300793562318135042158219841162112916985730)/(22233418852301443767271829464336830767266125012671)*a^(9) - (59822679473898094996132937093426615141713732377)/(22233418852301443767271829464336830767266125012671)*a^(8) + (139558692890035702012834516500177589758371878797)/(22233418852301443767271829464336830767266125012671)*a^(7) - (356868725234384600841674313684244607383662483726)/(22233418852301443767271829464336830767266125012671)*a^(6) + (444286594183742629577746639125938224581845283252)/(22233418852301443767271829464336830767266125012671)*a^(5) - (1067154231604573877893056714425653076811982109271)/(22233418852301443767271829464336830767266125012671)*a^(4) - (98504111114017758400453002046032608901342519699)/(22233418852301443767271829464336830767266125012671)*a^(3) - (2244079138252751294088704020037407024034643599553)/(22233418852301443767271829464336830767266125012671)*a^(2) + (1242960529952343977646686820274826432545477456167)/(22233418852301443767271829464336830767266125012671)*a + (5536599650773100287029927516886697907915428900008)/(22233418852301443767271829464336830767266125012671) , (5781495199440770529801203080936196043023341)/(22233418852301443767271829464336830767266125012671)*a^(15) - (30121527729394505092496323434315393410167036)/(22233418852301443767271829464336830767266125012671)*a^(14) + (352262621167912841672969482103391298916455837)/(22233418852301443767271829464336830767266125012671)*a^(13) - (1532975749466523672530153397800437688039088844)/(22233418852301443767271829464336830767266125012671)*a^(12) + (8805926704861789396860678856942594044172666358)/(22233418852301443767271829464336830767266125012671)*a^(11) - (32667690610260865132370500543582444465234872448)/(22233418852301443767271829464336830767266125012671)*a^(10) + (125871734914945895287745999223163086158940596735)/(22233418852301443767271829464336830767266125012671)*a^(9) - (347156705800932429504662318649294177154051729886)/(22233418852301443767271829464336830767266125012671)*a^(8) + (1003173196739632214384423765630949913024986232657)/(22233418852301443767271829464336830767266125012671)*a^(7) - (2308646934720232230591985607403308437521428849963)/(22233418852301443767271829464336830767266125012671)*a^(6) + (5802553511936719389455726090527718045128165500967)/(22233418852301443767271829464336830767266125012671)*a^(5) - (12230306312590776315456898712246927630344697263702)/(22233418852301443767271829464336830767266125012671)*a^(4) + (22621869075030705293995182776293991377190642031455)/(22233418852301443767271829464336830767266125012671)*a^(3) - (25444743744563072521054000455931807925274887239844)/(22233418852301443767271829464336830767266125012671)*a^(2) + (17967005210212883154376925618087933130850478652846)/(22233418852301443767271829464336830767266125012671)*a - (21706613201265179719742184552629216792547485527441)/(22233418852301443767271829464336830767266125012671) ], 81485.0410293661, [[x^2 - x - 4, 1], [x^4 - x^3 - 6*x^2 + x + 1, 1], [x^8 - x^7 - 24*x^6 + 23*x^5 + 151*x^4 - 197*x^3 - 214*x^2 + 429*x - 169, 1]]]