/* 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 - 11*x^14 + 3*x^13 - 61*x^12 - 6*x^11 + 1089*x^10 + 3823*x^9 + 9018*x^8 + 11451*x^7 + 12158*x^6 + 20640*x^5 + 25240*x^4 + 24216*x^3 + 15859*x^2 + 3807*x + 1899, 16, 681, [4, 6], 7561037361641682928770951437, [13, 53], [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, 1/3*a^14 + 1/3*a^13 - 1/3*a^12 - 1/3*a^11 + 1/3*a^10 + 1/3*a^9 + 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 + 1/3*a^4 + 1/3*a^3 - 1/3*a^2 - 1/3*a, 1/11332402123027909427992913252931759*a^15 + 45202019834878827685778612934950/3777467374342636475997637750977253*a^14 + 2110941076125190104786917377604728/11332402123027909427992913252931759*a^13 - 879505998682102442200889261198521/3777467374342636475997637750977253*a^12 + 4288242745556912407868912851077590/11332402123027909427992913252931759*a^11 - 1220005106529677537255733143591489/3777467374342636475997637750977253*a^10 - 1040822169541852999263348922795940/3777467374342636475997637750977253*a^9 + 2725819788948092929590788250532795/11332402123027909427992913252931759*a^8 - 1148410211257104041900216189615887/3777467374342636475997637750977253*a^7 - 210610509996492891032385633574530/3777467374342636475997637750977253*a^6 + 4890745260934868747279183518768241/11332402123027909427992913252931759*a^5 + 694921414201271987540496207862192/3777467374342636475997637750977253*a^4 + 864904087412557142436601256158594/11332402123027909427992913252931759*a^3 + 1702775107435880838942539301799292/3777467374342636475997637750977253*a^2 - 4554792789473730458724510348598631/11332402123027909427992913252931759*a - 1583328468646915977237725088158123/3777467374342636475997637750977253], 0, 1, [], 1, [ (23154074296282412067137637)/(320695082294136724339726441207)*a^(15) - (196109736113032904413035898)/(962085246882410173019179323621)*a^(14) - (928692026970438928799815885)/(962085246882410173019179323621)*a^(13) + (721011583847865063025562707)/(962085246882410173019179323621)*a^(12) - (4197772559484435865986831056)/(962085246882410173019179323621)*a^(11) - (1696313812471867910177158675)/(962085246882410173019179323621)*a^(10) + (87058007102341489349477815031)/(962085246882410173019179323621)*a^(9) + (255541297294151373124146334043)/(962085246882410173019179323621)*a^(8) + (579948514287983454245211514669)/(962085246882410173019179323621)*a^(7) + (641841612962016536474462533732)/(962085246882410173019179323621)*a^(6) + (248478545676661211694400837375)/(962085246882410173019179323621)*a^(5) + (1119931133763894949889257800716)/(962085246882410173019179323621)*a^(4) + (460196286154541017722180922670)/(962085246882410173019179323621)*a^(3) + (1180418885482003804060390558795)/(962085246882410173019179323621)*a^(2) + (102437783236950600975631362238)/(962085246882410173019179323621)*a - (655730045348919343759304514098)/(320695082294136724339726441207) , (62864892498544887840689348)/(320695082294136724339726441207)*a^(15) - (742551072926999941174340803)/(962085246882410173019179323621)*a^(14) - (1356487523299381385964609388)/(962085246882410173019179323621)*a^(13) + (1656899949591181215166354807)/(962085246882410173019179323621)*a^(12) - (13215207705074304627700148810)/(962085246882410173019179323621)*a^(11) + (13385538511614697822834477745)/(962085246882410173019179323621)*a^(10) + (194429645652733429884567539693)/(962085246882410173019179323621)*a^(9) + (542121027618409201879693412360)/(962085246882410173019179323621)*a^(8) + (1228823052058627310571911212027)/(962085246882410173019179323621)*a^(7) + (977570417334088752411478696498)/(962085246882410173019179323621)*a^(6) + (809251058894985018692906416021)/(962085246882410173019179323621)*a^(5) + (1426149520742347812420243335678)/(962085246882410173019179323621)*a^(4) + (909289911154822955873800966607)/(962085246882410173019179323621)*a^(3) + (1507279961177178920493546168991)/(962085246882410173019179323621)*a^(2) + (173376981243124028500682970349)/(962085246882410173019179323621)*a - (394261797871676817507001570319)/(320695082294136724339726441207) , (347286732438490713607343251946)/(3777467374342636475997637750977253)*a^(15) - (3060353799750836805981576526807)/(11332402123027909427992913252931759)*a^(14) - (10980358324971342483696432709669)/(11332402123027909427992913252931759)*a^(13) - (1047451021968164563223105264534)/(11332402123027909427992913252931759)*a^(12) - (63644555434411086317054911003508)/(11332402123027909427992913252931759)*a^(11) - (6051041213187286930113682904167)/(11332402123027909427992913252931759)*a^(10) + (1080808377186253289412972496678163)/(11332402123027909427992913252931759)*a^(9) + (4158407781540045035334544878905276)/(11332402123027909427992913252931759)*a^(8) + (10170575005124950712532607154652838)/(11332402123027909427992913252931759)*a^(7) + (13909527788711882761732387085603086)/(11332402123027909427992913252931759)*a^(6) + (16824750313277565631752460660027225)/(11332402123027909427992913252931759)*a^(5) + (23800461359230953960418542682987571)/(11332402123027909427992913252931759)*a^(4) + (31840684213468602346137598336953809)/(11332402123027909427992913252931759)*a^(3) + (30440532424603941017748297890336170)/(11332402123027909427992913252931759)*a^(2) + (15638675011016462565374131899639397)/(11332402123027909427992913252931759)*a + (3119711525837957009941454646120215)/(3777467374342636475997637750977253) , (1286848965678171107629300915403)/(3777467374342636475997637750977253)*a^(15) - (16507111037235969539435000201474)/(11332402123027909427992913252931759)*a^(14) - (22262716856808556590262781959685)/(11332402123027909427992913252931759)*a^(13) + (43969942990822470752303942610116)/(11332402123027909427992913252931759)*a^(12) - (287201799829214860863555609576742)/(11332402123027909427992913252931759)*a^(11) + (333971240453437092337552934013799)/(11332402123027909427992913252931759)*a^(10) + (3809010167170076025032868982521115)/(11332402123027909427992913252931759)*a^(9) + (9816417716661235060411566350805181)/(11332402123027909427992913252931759)*a^(8) + (21455248903003475845371392350517225)/(11332402123027909427992913252931759)*a^(7) + (14591527664058480775607634780255467)/(11332402123027909427992913252931759)*a^(6) + (26260630002728606367872188043455505)/(11332402123027909427992913252931759)*a^(5) + (51165301859731899137750550075862972)/(11332402123027909427992913252931759)*a^(4) + (43359081935344620847913354357343682)/(11332402123027909427992913252931759)*a^(3) + (48521562068441913609430137433059026)/(11332402123027909427992913252931759)*a^(2) + (6902734108825442672824833836150525)/(11332402123027909427992913252931759)*a + (2705384424401275233627917642236533)/(3777467374342636475997637750977253) , (3752646346403615589813084975030)/(3777467374342636475997637750977253)*a^(15) - (16654748240915923497027805537842)/(3777467374342636475997637750977253)*a^(14) - (17222403672123437178337011437064)/(3777467374342636475997637750977253)*a^(13) + (35927265396652125191697331285179)/(3777467374342636475997637750977253)*a^(12) - (281909453159836874048458691388136)/(3777467374342636475997637750977253)*a^(11) + (379200894294387954429194704347494)/(3777467374342636475997637750977253)*a^(10) + (3529715764430907580707051536616866)/(3777467374342636475997637750977253)*a^(9) + (9265012186621487222161109725945836)/(3777467374342636475997637750977253)*a^(8) + (20607706702421520057649889289378786)/(3777467374342636475997637750977253)*a^(7) + (13965711618886480625597711481375683)/(3777467374342636475997637750977253)*a^(6) + (27971689689547210830683013503018016)/(3777467374342636475997637750977253)*a^(5) + (41959294347802537437683556059053170)/(3777467374342636475997637750977253)*a^(4) + (40152588041446412627925450779416476)/(3777467374342636475997637750977253)*a^(3) + (38443366123896776287261568822678529)/(3777467374342636475997637750977253)*a^(2) + (7183022101265570877709310754417055)/(3777467374342636475997637750977253)*a + (5675460357443453761622115846758780)/(3777467374342636475997637750977253) , (1234790730414413903006476400322)/(3777467374342636475997637750977253)*a^(15) - (27439192738779235426728071363041)/(11332402123027909427992913252931759)*a^(14) + (32953351598688833699782128355691)/(11332402123027909427992913252931759)*a^(13) + (103864310182153834782278984678686)/(11332402123027909427992913252931759)*a^(12) - (494407396711797759285040791424439)/(11332402123027909427992913252931759)*a^(11) + (1121351619691808131522999358673953)/(11332402123027909427992913252931759)*a^(10) + (2516502293662260901746467176018133)/(11332402123027909427992913252931759)*a^(9) - (2827077411503180681944062947163937)/(11332402123027909427992913252931759)*a^(8) - (3001205518782861208401404954947451)/(11332402123027909427992913252931759)*a^(7) - (22351899085319230196146747675580309)/(11332402123027909427992913252931759)*a^(6) + (46684313206083316989690913996782592)/(11332402123027909427992913252931759)*a^(5) + (81178506510920481703755746610249353)/(11332402123027909427992913252931759)*a^(4) - (21039419870350461744300004367095966)/(11332402123027909427992913252931759)*a^(3) + (31959821661634328114404978641047452)/(11332402123027909427992913252931759)*a^(2) - (2479105152419272475042172517461206)/(11332402123027909427992913252931759)*a + (759047426048027435583529097925469)/(3777467374342636475997637750977253) , (1064994979406474151288816044791)/(3777467374342636475997637750977253)*a^(15) - (7308921012286379405780780050888)/(11332402123027909427992913252931759)*a^(14) - (58664578131404128269199558933147)/(11332402123027909427992913252931759)*a^(13) + (65822772707321806651514314317340)/(11332402123027909427992913252931759)*a^(12) - (123789041537508077151452903132420)/(11332402123027909427992913252931759)*a^(11) - (428753285685375763204533484164283)/(11332402123027909427992913252931759)*a^(10) + (4650567612490303503287315048452097)/(11332402123027909427992913252931759)*a^(9) + (12606438518958509504858013755792246)/(11332402123027909427992913252931759)*a^(8) + (21326975970263684698037078217872062)/(11332402123027909427992913252931759)*a^(7) + (24241601663396634158167271913498757)/(11332402123027909427992913252931759)*a^(6) + (10838822095541220053495452434003538)/(11332402123027909427992913252931759)*a^(5) + (129545855132712580099221968543638913)/(11332402123027909427992913252931759)*a^(4) + (151162804569409601874707614472356391)/(11332402123027909427992913252931759)*a^(3) + (64045866770916873280101543240136816)/(11332402123027909427992913252931759)*a^(2) + (3043870540336872825439149477701626)/(11332402123027909427992913252931759)*a - (32557001570957897262304480511606087)/(3777467374342636475997637750977253) , (3815459663955904065075149012879)/(11332402123027909427992913252931759)*a^(15) - (13714621973041698780518438057729)/(11332402123027909427992913252931759)*a^(14) - (11771277655434329470526055312578)/(3777467374342636475997637750977253)*a^(13) + (37062998908171746895366046071250)/(11332402123027909427992913252931759)*a^(12) - (79770597428623320579328285694226)/(3777467374342636475997637750977253)*a^(11) + (110748031262442733037785491764404)/(11332402123027909427992913252931759)*a^(10) + (4181014192530462224578730166177811)/(11332402123027909427992913252931759)*a^(9) + (4042539070240408652694751580311920)/(3777467374342636475997637750977253)*a^(8) + (25722668785651749345341935081174019)/(11332402123027909427992913252931759)*a^(7) + (23508231933011274177528060733032125)/(11332402123027909427992913252931759)*a^(6) + (7260196028076183679857562999011380)/(3777467374342636475997637750977253)*a^(5) + (54965485485187660857868562390413903)/(11332402123027909427992913252931759)*a^(4) + (17925128610738791112204468577708358)/(3777467374342636475997637750977253)*a^(3) + (35664030958818906734460821171312900)/(11332402123027909427992913252931759)*a^(2) + (2842567837542178453540712552572396)/(11332402123027909427992913252931759)*a - (8418032661597165828792493406674572)/(3777467374342636475997637750977253) , (68246975285617773909099349846066)/(11332402123027909427992913252931759)*a^(15) - (361963033878967941496889960309554)/(11332402123027909427992913252931759)*a^(14) - (73339859939637405668652460695815)/(3777467374342636475997637750977253)*a^(13) + (1837523642447960512959790465482769)/(11332402123027909427992913252931759)*a^(12) - (1864070100000441785746790925407903)/(3777467374342636475997637750977253)*a^(11) + (8579286194914466217807786613577111)/(11332402123027909427992913252931759)*a^(10) + (73132392368325666920918610410683157)/(11332402123027909427992913252931759)*a^(9) + (28149279676076364915363026658160322)/(3777467374342636475997637750977253)*a^(8) + (80304245379543024449949792448860673)/(11332402123027909427992913252931759)*a^(7) - (314604502441055969337352445523455447)/(11332402123027909427992913252931759)*a^(6) - (72017375169403592100573521946659118)/(3777467374342636475997637750977253)*a^(5) + (552764249772325704223862835561635492)/(11332402123027909427992913252931759)*a^(4) - (204742814546553797343979629515003525)/(3777467374342636475997637750977253)*a^(3) - (1089530910840728551393725418994613860)/(11332402123027909427992913252931759)*a^(2) - (141671164118238272210105558100781489)/(11332402123027909427992913252931759)*a - (65596036996596661818356433897163347)/(3777467374342636475997637750977253) ], 51881134.8593, [[x^2 - x - 13, 1], [x^4 - 2*x^3 - 6*x^2 + 7*x - 1, 1], [x^8 - 2*x^7 - 5*x^6 + 6*x^5 + 10*x^4 - x^3 - 3*x^2 - 13, 1]]]