/* 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 - 2*x^15 - 35*x^14 + 140*x^13 + 95*x^12 - 3201*x^11 + 13312*x^10 + 22360*x^9 - 285830*x^8 + 81435*x^7 + 2562842*x^6 - 1161819*x^5 - 9809590*x^4 - 2753750*x^3 + 6343430*x^2 + 35305612*x + 35181701, 16, 1113, [4, 6], 48763989276665152618408203125, [5, 41, 18341], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, 1/41*a^12 - 17/41*a^11 + 17/41*a^10 - 12/41*a^9 + 8/41*a^8 + 14/41*a^7 - 11/41*a^6 + 10/41*a^5 - 7/41*a^4 + 13/41*a^2 + 18/41*a - 20/41, 1/451*a^13 + 3/451*a^12 - 36/451*a^11 - 2/11*a^10 - 150/451*a^9 - 72/451*a^8 - 100/451*a^7 + 200/451*a^6 + 193/451*a^5 - 17/451*a^4 - 151/451*a^3 - 50/451*a^2 + 217/451*a + 133/451, 1/451*a^14 - 1/451*a^12 + 180/451*a^11 - 58/451*a^10 - 150/451*a^9 + 17/451*a^8 + 214/451*a^7 + 1/41*a^6 - 156/451*a^5 + 43/451*a^4 - 48/451*a^3 + 37/451*a^2 - 177/451*a + 74/451, 1/96369274152460342808809446769170520420045337731*a^15 - 1047429188840985139856415706826315300317348/2350470101279520556312425530955378546830374091*a^14 + 73885030168100454158903996871350969530965422/96369274152460342808809446769170520420045337731*a^13 + 430252114499816687868967158102069337457488455/96369274152460342808809446769170520420045337731*a^12 - 1740968234593827830961033302656860929957774600/8760843104769122073528131524470047310913212521*a^11 + 47332795995969008347663161773369067116880545903/96369274152460342808809446769170520420045337731*a^10 - 37911257024389313571456297849691808351042635233/96369274152460342808809446769170520420045337731*a^9 + 14704270466334110952122293919470750662894559582/96369274152460342808809446769170520420045337731*a^8 + 5022325916020578807141603740670341312794682773/96369274152460342808809446769170520420045337731*a^7 - 34507051783698421674356220998710279058710821584/96369274152460342808809446769170520420045337731*a^6 + 8383105543488629125551097134146442766239319921/96369274152460342808809446769170520420045337731*a^5 - 48180794563456065822887104869523627483366758751/96369274152460342808809446769170520420045337731*a^4 + 44354135776139295309570603458446565348169508314/96369274152460342808809446769170520420045337731*a^3 + 1282316192278448926989019666759742664128238328/8760843104769122073528131524470047310913212521*a^2 - 32958053404234444865931553679924367359440257416/96369274152460342808809446769170520420045337731*a - 35747644249411588400067319688142249172956867495/96369274152460342808809446769170520420045337731], 0, 1, [], 1, [ (1027148725675910706273251)/(51628336260146331814382515611919)*a^(15) + (19487550426810643805047082)/(51628336260146331814382515611919)*a^(14) - (105104909795338872871576980)/(51628336260146331814382515611919)*a^(13) - (248189244350115692028946543)/(51628336260146331814382515611919)*a^(12) + (2783836328634530855391493135)/(51628336260146331814382515611919)*a^(11) - (10471090923990935973417151907)/(51628336260146331814382515611919)*a^(10) - (10395716564875333273632980613)/(51628336260146331814382515611919)*a^(9) + (261599983555959499028080299354)/(51628336260146331814382515611919)*a^(8) - (525053127891372653684881137342)/(51628336260146331814382515611919)*a^(7) - (2424638810446764476839142022387)/(51628336260146331814382515611919)*a^(6) + (5380731895180836929405749928449)/(51628336260146331814382515611919)*a^(5) + (10607495860062335773095462592398)/(51628336260146331814382515611919)*a^(4) - (4033647384679022466228942611798)/(51628336260146331814382515611919)*a^(3) - (26220820273453408116394447734349)/(51628336260146331814382515611919)*a^(2) - (61435413035866634316284653821206)/(51628336260146331814382515611919)*a - (12771615778261785581155763779935)/(51628336260146331814382515611919) , (9535370340893431865819585344142996727319)/(96369274152460342808809446769170520420045337731)*a^(15) - (16616475436816760294873918659587982676051)/(96369274152460342808809446769170520420045337731)*a^(14) - (270857242100227138992858751610077053840699)/(96369274152460342808809446769170520420045337731)*a^(13) + (1141964309859415174854492110890977333249814)/(96369274152460342808809446769170520420045337731)*a^(12) - (562509259955013805618721207436284565008650)/(96369274152460342808809446769170520420045337731)*a^(11) - (23300707785533338145408161367634280995073458)/(96369274152460342808809446769170520420045337731)*a^(10) + (114372490644115887649046892107111542843440898)/(96369274152460342808809446769170520420045337731)*a^(9) + (106004404654084388000636464146713713777782523)/(96369274152460342808809446769170520420045337731)*a^(8) - (1955321686642871954264037777277154950039582190)/(96369274152460342808809446769170520420045337731)*a^(7) + (789495413599524610696175748521588531305830977)/(96369274152460342808809446769170520420045337731)*a^(6) + (13153008612087327691023561690617928507478621837)/(96369274152460342808809446769170520420045337731)*a^(5) - (6057861695125919156995536577802532108441209228)/(96369274152460342808809446769170520420045337731)*a^(4) - (27204738649095193130856208492629009778863215037)/(96369274152460342808809446769170520420045337731)*a^(3) + (924097684675891901721506234453181435276916078)/(8760843104769122073528131524470047310913212521)*a^(2) - (20481365991221427167311281529624199641480730589)/(96369274152460342808809446769170520420045337731)*a - (87332894482425090897381121678594233358444641547)/(96369274152460342808809446769170520420045337731) , (15895690111575411383378725663840867194299)/(96369274152460342808809446769170520420045337731)*a^(15) - (59774888984794682723208835883546198473889)/(96369274152460342808809446769170520420045337731)*a^(14) - (396956633471451086487278060396970722529054)/(96369274152460342808809446769170520420045337731)*a^(13) + (2733134155374547873218667629138738002582481)/(96369274152460342808809446769170520420045337731)*a^(12) - (4218009042123677950899927219886410548428775)/(96369274152460342808809446769170520420045337731)*a^(11) - (36016852145230653403759859239919237976101454)/(96369274152460342808809446769170520420045337731)*a^(10) + (6171809515288872192950299191314016766786804)/(2350470101279520556312425530955378546830374091)*a^(9) - (146090670372048651008398677704885586480835580)/(96369274152460342808809446769170520420045337731)*a^(8) - (3613680447890019325325899735368856848670147362)/(96369274152460342808809446769170520420045337731)*a^(7) + (6613968863983376890553507410168191248461494405)/(96369274152460342808809446769170520420045337731)*a^(6) + (23034866448509401602773859805840887818757603888)/(96369274152460342808809446769170520420045337731)*a^(5) - (1111177752295860600569860047594916736673322561)/(2350470101279520556312425530955378546830374091)*a^(4) - (64453933661367610035653307944661411520711562027)/(96369274152460342808809446769170520420045337731)*a^(3) + (57212824578447945639288650548678159270869075968)/(96369274152460342808809446769170520420045337731)*a^(2) + (67820748093582369867170377773351019065605188567)/(96369274152460342808809446769170520420045337731)*a + (128463515342249716549075236693898981467031722511)/(96369274152460342808809446769170520420045337731) , (14480684829239000257490534106040680218464)/(96369274152460342808809446769170520420045337731)*a^(15) - (42244560243400643085954354386020139104085)/(96369274152460342808809446769170520420045337731)*a^(14) - (385066765059534513417461728412018168759274)/(96369274152460342808809446769170520420045337731)*a^(13) + (2161014547116837822598359905494726462660206)/(96369274152460342808809446769170520420045337731)*a^(12) - (2953730026422433333561380651672096089079173)/(96369274152460342808809446769170520420045337731)*a^(11) - (31426184256120525114409794150571334587006949)/(96369274152460342808809446769170520420045337731)*a^(10) + (207018068506987374940451405331857679990613453)/(96369274152460342808809446769170520420045337731)*a^(9) - (54811184239009409024041340363839060159732332)/(96369274152460342808809446769170520420045337731)*a^(8) - (2893809282005166720887589162269674601083857068)/(96369274152460342808809446769170520420045337731)*a^(7) + (3694819525702939086284702634543725988903991752)/(96369274152460342808809446769170520420045337731)*a^(6) + (16941679810219501937697929559377571273815548196)/(96369274152460342808809446769170520420045337731)*a^(5) - (14032170483201293598946555880791653795825592708)/(96369274152460342808809446769170520420045337731)*a^(4) - (31122478774909541843298396616095913310199878534)/(96369274152460342808809446769170520420045337731)*a^(3) - (52421168517675841038485795792269341545399168318)/(96369274152460342808809446769170520420045337731)*a^(2) - (3590958773035104062739458287341284113493837245)/(8760843104769122073528131524470047310913212521)*a + (103133119198141034574239755173635599360643303243)/(96369274152460342808809446769170520420045337731) , (27468936213640742448823988955581631021402)/(96369274152460342808809446769170520420045337731)*a^(15) - (35182377645964509915556995508043950818316)/(96369274152460342808809446769170520420045337731)*a^(14) - (838275228781802751069548555522651717692210)/(96369274152460342808809446769170520420045337731)*a^(13) + (3167418582378051821090943094964989157016374)/(96369274152460342808809446769170520420045337731)*a^(12) - (59193699049847020173147321096993777450509)/(8760843104769122073528131524470047310913212521)*a^(11) - (70041875986703344076916401248438331441740483)/(96369274152460342808809446769170520420045337731)*a^(10) + (328829807769933374777376398463974496939704893)/(96369274152460342808809446769170520420045337731)*a^(9) + (358091725571362945506434090616744264764427025)/(96369274152460342808809446769170520420045337731)*a^(8) - (5560349991229572081771055483258591631674974526)/(96369274152460342808809446769170520420045337731)*a^(7) + (1155191576615373460922112056847964402278641282)/(96369274152460342808809446769170520420045337731)*a^(6) + (3132073859647977773089909139215146756282995225)/(8760843104769122073528131524470047310913212521)*a^(5) + (3786492000884101015244033433039243497370517636)/(96369274152460342808809446769170520420045337731)*a^(4) - (45629140994673529636373619154417477097337024204)/(96369274152460342808809446769170520420045337731)*a^(3) - (111425048662856801115820964503490105733364543338)/(96369274152460342808809446769170520420045337731)*a^(2) - (159941201090578302560558764366845334109201996965)/(96369274152460342808809446769170520420045337731)*a - (24321506635203966636097244268658128086056715562)/(96369274152460342808809446769170520420045337731) , (18736894391062392219984108470901944354527504)/(96369274152460342808809446769170520420045337731)*a^(15) - (149849437129727231339473607561702571843089116)/(96369274152460342808809446769170520420045337731)*a^(14) - (257261141908858020529183759893184977925753274)/(96369274152460342808809446769170520420045337731)*a^(13) + (5888590596317478353809707829511092454869648160)/(96369274152460342808809446769170520420045337731)*a^(12) - (15645283787395265697618581611164507466376786837)/(96369274152460342808809446769170520420045337731)*a^(11) - (36365615079453345051705608616587470075277448299)/(96369274152460342808809446769170520420045337731)*a^(10) + (480008170566472293568306705050920429229457460561)/(96369274152460342808809446769170520420045337731)*a^(9) - (129789873996360607319900085058897274706497540945)/(8760843104769122073528131524470047310913212521)*a^(8) - (4956916606523493101915903756562344709251963724283)/(96369274152460342808809446769170520420045337731)*a^(7) + (25374419201249872356580296040100911107343977110268)/(96369274152460342808809446769170520420045337731)*a^(6) + (18026567065598582270245057867958623791803875368786)/(96369274152460342808809446769170520420045337731)*a^(5) - (127155336028333774689952351566156528579303021180613)/(96369274152460342808809446769170520420045337731)*a^(4) - (28294689315322733656471225343361398408095867543344)/(96369274152460342808809446769170520420045337731)*a^(3) + (6201338314767668542282379776349188995297997486971)/(96369274152460342808809446769170520420045337731)*a^(2) + (346877108277350753311514073433560750981323630187027)/(96369274152460342808809446769170520420045337731)*a + (479051874609255681375149180899953691908365686504028)/(96369274152460342808809446769170520420045337731) , (115777353125134813147748912566917441190201352)/(8760843104769122073528131524470047310913212521)*a^(15) - (8974763304633759477210397298699450360944421265)/(96369274152460342808809446769170520420045337731)*a^(14) - (2430692552870112826209471748834088825494445151)/(96369274152460342808809446769170520420045337731)*a^(13) + (217602807028731377778223456603705585849593500100)/(96369274152460342808809446769170520420045337731)*a^(12) - (93409587219080837836607478623428400959074777831)/(8760843104769122073528131524470047310913212521)*a^(11) + (720062733448043719451310242177225871841577085443)/(96369274152460342808809446769170520420045337731)*a^(10) + (16489227126622090858969654250621268574252018496988)/(96369274152460342808809446769170520420045337731)*a^(9) - (63100169460039265369992280357801115546145805939553)/(96369274152460342808809446769170520420045337731)*a^(8) - (5907505329134150276774392574334792508975494420560)/(8760843104769122073528131524470047310913212521)*a^(7) + (609954596145724117916488898234128665929887361103550)/(96369274152460342808809446769170520420045337731)*a^(6) - (46494810171271423647639950258783739483428005773901)/(96369274152460342808809446769170520420045337731)*a^(5) - 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