/* 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^27 - 7*x^26 + 21*x^25 - 50*x^24 + 110*x^23 - 244*x^22 + 734*x^21 - 2140*x^20 + 5743*x^19 - 13591*x^18 + 28791*x^17 - 54584*x^16 + 93410*x^15 - 138060*x^14 + 176010*x^13 - 189870*x^12 + 169389*x^11 - 127135*x^10 + 89765*x^9 - 72912*x^8 + 70628*x^7 - 65648*x^6 + 50256*x^5 - 29876*x^4 + 13340*x^3 - 4224*x^2 + 848*x - 80, 27, 8, [1, 13], -149674927005884133619412112407487159468032, [2, 563], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^3, 1/2*a^10 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^3, 1/2*a^11 - 1/2*a^7 - 1/2*a^3, 1/2*a^12 - 1/2*a^8 - 1/2*a^4, 1/2*a^13 - 1/2*a^8 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3, 1/2*a^14 - 1/2*a^8 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3, 1/4*a^15 - 1/4*a^14 - 1/4*a^13 - 1/4*a^11 - 1/4*a^10 - 1/4*a^9 - 1/4*a^7 + 1/4*a^6 - 1/4*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2, 1/4*a^16 - 1/4*a^13 - 1/4*a^12 - 1/4*a^9 - 1/4*a^8 - 1/2*a^7 - 1/2*a^6 + 1/4*a^5 - 1/2*a^3 - 1/2*a^2, 1/20*a^17 + 1/10*a^16 - 1/20*a^15 - 1/10*a^14 + 1/5*a^13 - 1/10*a^12 - 1/20*a^11 - 1/5*a^10 - 1/10*a^8 - 1/4*a^7 - 1/20*a^5 - 2/5*a^4 + 1/10*a^2 - 2/5*a, 1/20*a^18 - 1/10*a^14 - 1/4*a^13 - 1/10*a^12 - 1/10*a^11 - 1/10*a^10 + 3/20*a^9 - 3/10*a^8 - 1/20*a^6 + 9/20*a^5 - 1/5*a^4 - 2/5*a^3 - 1/10*a^2 - 1/5*a, 1/20*a^19 - 1/10*a^15 - 1/4*a^14 - 1/10*a^13 - 1/10*a^12 - 1/10*a^11 + 3/20*a^10 + 1/5*a^9 - 1/2*a^8 - 1/20*a^7 - 1/20*a^6 - 1/5*a^5 + 1/10*a^4 + 2/5*a^3 - 1/5*a^2, 1/40*a^20 - 1/40*a^19 - 1/40*a^17 + 1/40*a^16 - 1/20*a^15 + 1/8*a^14 - 9/40*a^13 - 3/40*a^12 - 1/10*a^11 + 1/8*a^10 - 9/40*a^9 - 1/10*a^8 + 1/8*a^7 + 17/40*a^6 + 3/10*a^5 + 1/10*a^4 + 9/20*a^3 + 3/10*a^2 + 1/5*a, 1/40*a^21 - 1/40*a^19 - 1/40*a^18 - 1/40*a^16 + 3/40*a^15 - 1/10*a^14 + 1/5*a^13 - 7/40*a^12 + 1/40*a^11 - 1/10*a^10 + 7/40*a^9 + 1/40*a^8 - 9/20*a^7 - 11/40*a^6 - 1/10*a^5 - 9/20*a^4 - 1/4*a^3 - 1/2*a^2 + 1/5*a, 1/40*a^22 - 1/20*a^16 - 1/20*a^15 + 9/40*a^14 + 1/5*a^13 - 1/10*a^11 + 1/10*a^8 - 1/5*a^7 - 19/40*a^6 + 1/10*a^5 - 9/20*a^4 - 3/20*a^3 + 2/5*a^2 - 1/5*a, 1/40*a^23 + 1/20*a^16 - 3/40*a^15 - 3/20*a^14 - 1/20*a^13 - 1/5*a^12 + 1/5*a^11 + 1/20*a^10 - 3/20*a^9 + 1/5*a^8 + 1/40*a^7 - 3/20*a^6 - 1/4*a^5 - 1/20*a^4 + 2/5*a^3 + 2/5*a^2 - 2/5*a, 1/40*a^24 + 3/40*a^16 - 1/10*a^15 + 1/20*a^14 - 3/20*a^13 + 1/20*a^12 + 1/10*a^11 + 1/20*a^10 - 1/20*a^9 + 3/8*a^8 - 2/5*a^7 - 1/4*a^6 - 1/4*a^5 + 3/10*a^4 + 2/5*a^3 + 2/5*a, 1/973400*a^25 - 137/97340*a^24 - 737/97340*a^23 - 4/785*a^22 + 489/97340*a^21 - 5739/973400*a^20 - 14249/973400*a^19 + 2012/121675*a^18 + 77/15700*a^17 + 621/31400*a^16 - 4869/243350*a^15 - 173167/973400*a^14 + 4707/31400*a^13 + 160601/973400*a^12 + 277/24335*a^11 - 209751/973400*a^10 + 27823/243350*a^9 - 2227/19468*a^8 + 120443/973400*a^7 - 325971/973400*a^6 - 26279/121675*a^5 + 2821/7850*a^4 + 177613/486700*a^3 - 40787/243350*a^2 - 56989/121675*a + 5748/24335, 1/36780145240738430396201552959538777000*a^26 - 71229904979266566300430724512/148307037261042058049199810320720875*a^25 - 55930775430782559388279940543055987/7356029048147686079240310591907755400*a^24 - 6902941856408461776965683635737411/3678014524073843039620155295953877700*a^23 - 7903911116310811080278450687257691/1471205809629537215848062118381551080*a^22 - 50023599997166183298482387857148968/4597518155092303799525194119942347125*a^21 + 20208106414630741400362409024458309/7356029048147686079240310591907755400*a^20 + 120821099224319928917148331018931001/7356029048147686079240310591907755400*a^19 + 318495498524937405890390504192716723/36780145240738430396201552959538777000*a^18 + 11840379126968696074718097017070587/1186456298088336464393598482565767000*a^17 - 227749930802853890200765610549494801/18390072620369215198100776479769388500*a^16 + 1807485432875035154488869825775803077/18390072620369215198100776479769388500*a^15 - 565695241699780992525278367374063729/9195036310184607599050388239884694250*a^14 + 4262525231837336397756830574368420219/36780145240738430396201552959538777000*a^13 + 5075644638805319627808081934587175999/36780145240738430396201552959538777000*a^12 + 748359368691465578433331388763999681/9195036310184607599050388239884694250*a^11 + 945872447522729370973144930221996326/4597518155092303799525194119942347125*a^10 + 4700402157486075254911752090656895463/36780145240738430396201552959538777000*a^9 - 9532466378859860213929350944933769957/36780145240738430396201552959538777000*a^8 - 4475202718578510749523357325657256279/36780145240738430396201552959538777000*a^7 + 2121727607180706448400995205902423277/18390072620369215198100776479769388500*a^6 - 6212173002965935698759031628099623087/18390072620369215198100776479769388500*a^5 - 4392006291370127650358930641832926169/18390072620369215198100776479769388500*a^4 - 1264526551414922658515745850498254651/9195036310184607599050388239884694250*a^3 - 3152349305454504139724675129548697371/9195036310184607599050388239884694250*a^2 - 2137599926502749520296877232776359216/4597518155092303799525194119942347125*a - 445885343244733984234298607402289833/919503631018460759905038823988469425], 0, 2, [2], 1, [ (4625352697890381580547216733006914947)/(36780145240738430396201552959538777000)*a^(26) - (29202088788946265134537123859778084637)/(36780145240738430396201552959538777000)*a^(25) + (1900021527472692868440825697367674632)/(919503631018460759905038823988469425)*a^(24) - (17246549946872292706681026002593210577)/(3678014524073843039620155295953877700)*a^(23) + (2990518946620645241383449548576905781)/(294241161925907443169612423676310216)*a^(22) - (834395448288221857311137758812428440193)/(36780145240738430396201552959538777000)*a^(21) + (109647146992792378424595685148890898827)/(1471205809629537215848062118381551080)*a^(20) - (783490094530321348076521207699103825973)/(3678014524073843039620155295953877700)*a^(19) + (2571751725495321766699262881719090075177)/(4597518155092303799525194119942347125)*a^(18) - (189574356748550706037007008688967745287)/(148307037261042058049199810320720875)*a^(17) + (48188049846961055627314870406050446343383)/(18390072620369215198100776479769388500)*a^(16) - (176089193019741492966093787444372439361197)/(36780145240738430396201552959538777000)*a^(15) + (145177933782826867558484522708618039889189)/(18390072620369215198100776479769388500)*a^(14) - (401563552578904948226504852436454352312487)/(36780145240738430396201552959538777000)*a^(13) + (238390702298127771625101952457341036210919)/(18390072620369215198100776479769388500)*a^(12) - (467152366343159160196060081737766255559497)/(36780145240738430396201552959538777000)*a^(11) + (45585181894152961176451844931955774468952)/(4597518155092303799525194119942347125)*a^(10) - (1554269803668411237990896741424254385867)/(234268441023811658574532184455661000)*a^(9) + (176677168199263756388348934113579056323971)/(36780145240738430396201552959538777000)*a^(8) - (169437536996674517092801748559594450744933)/(36780145240738430396201552959538777000)*a^(7) + (5673502402620023772244732390261679335063)/(1186456298088336464393598482565767000)*a^(6) - (37120932831859239496944925273632992983037)/(9195036310184607599050388239884694250)*a^(5) + (11844483079044607651366796070725609553688)/(4597518155092303799525194119942347125)*a^(4) - (708686124756917704818519083269980621069)/(593228149044168232196799241282883500)*a^(3) + (1718229066078811060732326406544957191309)/(4597518155092303799525194119942347125)*a^(2) - (297866614722390811083868644518922333867)/(4597518155092303799525194119942347125)*a + (2606658053706986646766470548594427654)/(919503631018460759905038823988469425) , (1132067060520813134651030707718248873)/(7356029048147686079240310591907755400)*a^(26) - (24081609110543966658556055879681573)/(23729125961766729287871969651315340)*a^(25) + (2056629522206375157468349658475931611)/(735602904814768607924031059190775540)*a^(24) - (9439152775176080233908615028827531031)/(1471205809629537215848062118381551080)*a^(23) + (20563490507225173355166275852850662127)/(1471205809629537215848062118381551080)*a^(22) - (228707994439484922361341629099734372247)/(7356029048147686079240310591907755400)*a^(21) + (725648117732335247450708665544173191053)/(7356029048147686079240310591907755400)*a^(20) - (262520634743089175554152500726720481324)/(919503631018460759905038823988469425)*a^(19) + (1388225474104241693665598022211447913153)/(1839007262036921519810077647976938850)*a^(18) - (414955192453235085800056169493410241847)/(237291259617667292878719696513153400)*a^(17) + (3333882063385156490351165567591601672264)/(919503631018460759905038823988469425)*a^(16) - (24696703117743524725459588546082553067423)/(3678014524073843039620155295953877700)*a^(15) + (20627525369086433802469593710767603939049)/(1839007262036921519810077647976938850)*a^(14) - (117071809617692664023047526302869293032007)/(7356029048147686079240310591907755400)*a^(13) + (7120771264246939974216048639039956655353)/(367801452407384303962015529595387770)*a^(12) - (144668121647500082491079369099767013384753)/(7356029048147686079240310591907755400)*a^(11) + (59287756422350766727386294878037440800113)/(3678014524073843039620155295953877700)*a^(10) - (8222615507001352968389743489577540749981)/(735602904814768607924031059190775540)*a^(9) + (58174221111348198585068985611105298344069)/(7356029048147686079240310591907755400)*a^(8) - (13080308796489033834830978286721068272007)/(1839007262036921519810077647976938850)*a^(7) + (53674516779335917063811649711303425804049)/(7356029048147686079240310591907755400)*a^(6) - (5928821727677507142536706038222251958146)/(919503631018460759905038823988469425)*a^(5) + (16206182709544750738563915215471282222729)/(3678014524073843039620155295953877700)*a^(4) - (8257524927705036042332640074526071680437)/(3678014524073843039620155295953877700)*a^(3) + (1478721907519684162550046200918792764071)/(1839007262036921519810077647976938850)*a^(2) - (33074683925049006982464367556719550788)/(183900726203692151981007764797693885)*a + (647453198057644523027792908445547720)/(36780145240738430396201552959538777) , (5668116980764557170656025101885803577)/(36780145240738430396201552959538777000)*a^(26) - (18605953930875850428342546701995869921)/(18390072620369215198100776479769388500)*a^(25) + (2565395051196868815524778525612910197)/(919503631018460759905038823988469425)*a^(24) - (23733279146692593391035210427175687127)/(3678014524073843039620155295953877700)*a^(23) + (4131702386497840999671877541566171137)/(294241161925907443169612423676310216)*a^(22) - (1149490649665983377507120141343245225563)/(36780145240738430396201552959538777000)*a^(21) + (145658768377449036676480523437284702587)/(1471205809629537215848062118381551080)*a^(20) - (1050356449112515473436451749284608403373)/(3678014524073843039620155295953877700)*a^(19) + (13922620719839471105736060550413015777603)/(18390072620369215198100776479769388500)*a^(18) - (2081700224373849768524295371594160269511)/(1186456298088336464393598482565767000)*a^(17) + (33519640005226751057253898219415015055089)/(9195036310184607599050388239884694250)*a^(16) - (248686798164815000705788362145134765949627)/(36780145240738430396201552959538777000)*a^(15) + (208183449776786824496229578640931382058549)/(18390072620369215198100776479769388500)*a^(14) - (592415423740425016003432154215035588528767)/(36780145240738430396201552959538777000)*a^(13) + (5846797954061830260648089761864207824417)/(296614074522084116098399620641441750)*a^(12) - (740049244150496658167459372798081828243127)/(36780145240738430396201552959538777000)*a^(11) + (306582408890815388783147705098657596985703)/(18390072620369215198100776479769388500)*a^(10) - (214760543025258509648853443003363332853727)/(18390072620369215198100776479769388500)*a^(9) + (302764410554571443105949934810271200577061)/(36780145240738430396201552959538777000)*a^(8) - (269200777903971097967418433366916781507703)/(36780145240738430396201552959538777000)*a^(7) + (274974846893880341967834923563314009734373)/(36780145240738430396201552959538777000)*a^(6) - (30540799365296338720188425898499172445771)/(4597518155092303799525194119942347125)*a^(5) + (21191272089584114337866807935080569864958)/(4597518155092303799525194119942347125)*a^(4) - (43920637605762881392223977823958022274399)/(18390072620369215198100776479769388500)*a^(3) + (4060782570601162532412256991507773696869)/(4597518155092303799525194119942347125)*a^(2) - (964363660417549424504930709510252177297)/(4597518155092303799525194119942347125)*a + (22766609642174537220833935666180949964)/(919503631018460759905038823988469425) , (2280085727132034134644192886348119683)/(36780145240738430396201552959538777000)*a^(26) - (7619849237926421550872649102006653769)/(18390072620369215198100776479769388500)*a^(25) + (4291373972545735444644126132550714157)/(3678014524073843039620155295953877700)*a^(24) - (19892028236771039441017269239038411881)/(7356029048147686079240310591907755400)*a^(23) + (8670417129539360794293459787873405763)/(1471205809629537215848062118381551080)*a^(22) - (482015096104982233966274147029852274077)/(36780145240738430396201552959538777000)*a^(21) + (301719061035002050517751155787415742961)/(7356029048147686079240310591907755400)*a^(20) - (437438719757205258142965787535963566709)/(3678014524073843039620155295953877700)*a^(19) + (1452543392122537866495117760897759998513)/(4597518155092303799525194119942347125)*a^(18) - (872577605372266805991927579429647585949)/(1186456298088336464393598482565767000)*a^(17) + (7050152864355186441591946173046797152688)/(4597518155092303799525194119942347125)*a^(16) - (26258891859887467895557924455894614542547)/(9195036310184607599050388239884694250)*a^(15) + (22065477670238087511996968324670657723954)/(4597518155092303799525194119942347125)*a^(14) - (253036527247520799278783862207913876112533)/(36780145240738430396201552959538777000)*a^(13) + (77886129146003684494488138396082425943553)/(9195036310184607599050388239884694250)*a^(12) - (320892339866000335140164119048028920903033)/(36780145240738430396201552959538777000)*a^(11) + (33612442549521753579031852244126702014118)/(4597518155092303799525194119942347125)*a^(10) - 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