/* 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^28 - 6*x^27 + 18*x^26 + 6*x^25 - 69*x^24 + 47*x^23 + 257*x^22 - 674*x^21 + 321*x^20 + 545*x^19 - 15*x^18 - 692*x^17 + 1854*x^16 - 6800*x^15 + 5094*x^14 + 6261*x^13 - 5929*x^12 + 6262*x^11 - 14458*x^10 - 7839*x^9 + 27851*x^8 - 6775*x^7 + 6005*x^6 - 1487*x^5 - 35142*x^4 + 22011*x^3 + 18446*x^2 - 12525*x + 2675, 28, 10, [0, 14], 20444429365013571404907915184985572799247638801, [7, 449], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, 1/7*a^12 - 2/7*a^6 + 1/7, 1/7*a^13 - 2/7*a^7 + 1/7*a, 1/7*a^14 - 2/7*a^8 + 1/7*a^2, 1/7*a^15 - 2/7*a^9 + 1/7*a^3, 1/35*a^16 + 1/35*a^13 + 1/7*a^10 + 1/7*a^7 + 1/35*a^4 + 1/35*a, 1/35*a^17 + 1/35*a^14 + 1/7*a^11 + 1/7*a^8 + 1/35*a^5 + 1/35*a^2, 1/35*a^18 + 1/35*a^15 + 1/7*a^9 + 11/35*a^6 + 1/35*a^3 - 1/7, 1/245*a^19 + 3/245*a^18 - 1/245*a^17 + 3/245*a^15 - 16/245*a^14 - 6/245*a^13 - 3/49*a^12 + 20/49*a^11 - 3/7*a^10 + 3/49*a^9 - 2/49*a^8 - 19/245*a^7 + 4/35*a^6 - 106/245*a^5 + 3/7*a^4 + 3/245*a^3 - 86/245*a^2 - 46/245*a + 8/49, 1/245*a^20 - 3/245*a^18 + 3/245*a^17 + 3/245*a^16 + 17/245*a^15 + 1/35*a^14 + 3/245*a^13 + 1/49*a^12 + 17/49*a^11 + 17/49*a^10 - 18/49*a^9 + 81/245*a^8 + 17/49*a^7 - 78/245*a^6 - 67/245*a^5 - 67/245*a^4 - 53/245*a^3 - 68/245*a^2 - 67/245*a - 10/49, 1/1225*a^21 + 2/1225*a^20 + 2/1225*a^19 - 16/1225*a^18 - 17/1225*a^17 + 2/1225*a^16 + 4/175*a^15 - 12/175*a^14 - 3/49*a^13 + 11/245*a^12 - 66/245*a^11 + 86/245*a^10 - 409/1225*a^9 + 582/1225*a^8 - 38/1225*a^7 + 274/1225*a^6 - 17/1225*a^5 + 317/1225*a^4 + 58/1225*a^3 - 409/1225*a^2 + 4/245*a + 11/49, 1/1225*a^22 - 2/1225*a^20 + 1/245*a^18 + 16/1225*a^17 - 11/1225*a^16 + 1/49*a^15 - 52/1225*a^14 + 2/49*a^13 - 8/245*a^12 - 117/245*a^11 + 131/1225*a^10 - 9/49*a^9 - 527/1225*a^8 - 41/245*a^7 + 11/49*a^6 - 544/1225*a^5 + 264/1225*a^4 - 72/245*a^3 + 74/175*a^2 + 101/245*a + 3/49, 1/1225*a^23 - 1/1225*a^20 - 1/1225*a^19 + 4/1225*a^18 - 3/245*a^17 + 2/175*a^16 - 76/1225*a^15 + 6/175*a^14 + 6/245*a^13 - 554/1225*a^11 + 1/35*a^10 + 71/245*a^9 - 396/1225*a^8 - 386/1225*a^7 - 201/1225*a^6 + 87/245*a^5 - 9/25*a^4 - 321/1225*a^3 - 303/1225*a^2 - 4/35*a + 23/49, 1/8575*a^24 + 2/8575*a^23 - 2/8575*a^22 - 2/8575*a^21 - 1/8575*a^20 + 1/1715*a^19 + 1/175*a^18 + 69/8575*a^17 + 1/1225*a^16 - 138/8575*a^15 + 327/8575*a^14 + 78/1715*a^13 - 254/8575*a^12 - 2223/8575*a^11 - 617/8575*a^10 - 1027/8575*a^9 - 208/1225*a^8 - 229/1715*a^7 - 138/1225*a^6 - 2566/8575*a^5 + 962/8575*a^4 + 3442/8575*a^3 + 3202/8575*a^2 + 129/1715*a - 152/343, 1/317275*a^25 + 13/317275*a^24 + 34/317275*a^23 + 88/317275*a^22 - 1/8575*a^21 + 78/317275*a^20 + 587/317275*a^19 - 1212/317275*a^18 + 4336/317275*a^17 + 818/63455*a^16 + 4493/317275*a^15 + 3777/317275*a^14 - 7654/317275*a^13 - 18842/317275*a^12 - 48226/317275*a^11 - 157572/317275*a^10 + 96118/317275*a^9 + 153723/317275*a^8 - 96343/317275*a^7 + 105423/317275*a^6 + 20336/317275*a^5 - 20536/63455*a^4 - 41872/317275*a^3 + 19067/317275*a^2 - 11619/63455*a + 3970/12691, 1/239902679140075*a^26 - 372079181/239902679140075*a^25 - 1669085671/47980535828015*a^24 - 13096528929/239902679140075*a^23 + 4060398581/47980535828015*a^22 + 27458434343/239902679140075*a^21 - 17153736906/47980535828015*a^20 + 37491778448/239902679140075*a^19 + 19888439/31880754703*a^18 - 3125399970408/239902679140075*a^17 - 1009391376933/239902679140075*a^16 - 224447750206/5579132073025*a^15 - 8921329677032/239902679140075*a^14 + 15368694854459/239902679140075*a^13 + 2721791037421/47980535828015*a^12 + 9808378115153/34271811305725*a^11 - 3495246989928/9596107165603*a^10 - 65723651702222/239902679140075*a^9 + 89431643986/195838921747*a^8 + 15412654789428/239902679140075*a^7 + 21576088607649/47980535828015*a^6 - 1952172573088/5851284857075*a^5 - 4439796119548/239902679140075*a^4 - 15902389951734/34271811305725*a^3 + 107187720306407/239902679140075*a^2 - 10224426888601/47980535828015*a - 3361885110408/9596107165603, 1/25974637773290955737442125*a^27 - 314849447/633527750568072091157125*a^26 - 47391558836009694/120812268712981189476475*a^25 + 1260363234268205255186/25974637773290955737442125*a^24 - 153098375144052646149/5194927554658191147488425*a^23 + 7224169299395329353827/25974637773290955737442125*a^22 + 129211431934504875307/5194927554658191147488425*a^21 - 3414811189977577279004/25974637773290955737442125*a^20 - 18689322019588240262/15145561383843122878975*a^19 + 52533451903175870390964/5194927554658191147488425*a^18 - 21160207840310393390447/5194927554658191147488425*a^17 + 367336420210594628003828/25974637773290955737442125*a^16 + 36727865296166722183411/25974637773290955737442125*a^15 - 230460392031535652070606/25974637773290955737442125*a^14 + 36114056255241525781172/1038985510931638229497685*a^13 - 1120963118776252889276569/25974637773290955737442125*a^12 - 446591093297662333312507/1038985510931638229497685*a^11 - 11652570999457683460235953/25974637773290955737442125*a^10 + 113926294469806835449633/1038985510931638229497685*a^9 - 4143666150335868965602859/25974637773290955737442125*a^8 - 1299272957749327239248924/5194927554658191147488425*a^7 - 45645616744665658536731/140403447423194355337525*a^6 - 1454747202573961108124507/5194927554658191147488425*a^5 - 324277694356358538197931/3710662539041565105348875*a^4 + 455529277338756412579327/5194927554658191147488425*a^3 - 2278806181125286183753649/25974637773290955737442125*a^2 + 422813904623347664778272/1038985510931638229497685*a + 295641202301014397180982/1038985510931638229497685], 0, 1, [], 1, [ (40603611874649439518491)/(25974637773290955737442125)*a^(27) - (5269634338290712596937)/(633527750568072091157125)*a^(26) + (114159211189962590467951)/(5194927554658191147488425)*a^(25) + (706451731775966739989011)/(25974637773290955737442125)*a^(24) - (8306878006945618860367)/(85162746797675264712925)*a^(23) + (20096068037725773156797)/(25974637773290955737442125)*a^(22) + (2267240751366317082028864)/(5194927554658191147488425)*a^(21) - (19962429187171367572038604)/(25974637773290955737442125)*a^(20) - (3267603298016871360334)/(20057635346170622191075)*a^(19) + (5395404337246912863838968)/(5194927554658191147488425)*a^(18) + (3408102744991121427243383)/(5194927554658191147488425)*a^(17) - (25528448550219241284716777)/(25974637773290955737442125)*a^(16) + (54340909133448712128964571)/(25974637773290955737442125)*a^(15) - (227329488050952565011623446)/(25974637773290955737442125)*a^(14) + (6518474076240224478124498)/(5194927554658191147488425)*a^(13) + (348476376986478165096751181)/(25974637773290955737442125)*a^(12) - (7610409515365787578713878)/(5194927554658191147488425)*a^(11) + (133929992829277014011845517)/(25974637773290955737442125)*a^(10) - (88663366953739062527153518)/(5194927554658191147488425)*a^(9) - (680893984790891401939911959)/(25974637773290955737442125)*a^(8) + (164735844466698196894697246)/(5194927554658191147488425)*a^(7) + (79045518747042417532159997)/(5194927554658191147488425)*a^(6) + (50482511077143936536785453)/(5194927554658191147488425)*a^(5) + (15733262744862385985561254)/(3710662539041565105348875)*a^(4) - (281208404947445075694036554)/(5194927554658191147488425)*a^(3) - (94618816249980907502300299)/(25974637773290955737442125)*a^(2) + (40907218756884689868136441)/(1038985510931638229497685)*a + (4794765685626888433245867)/(1038985510931638229497685) ,   (90871594338554832111)/(702017237115971776687625)*a^(27) - (25954531947426398930804)/(25974637773290955737442125)*a^(26) + (19980867952561861269131)/(5194927554658191147488425)*a^(25) - (113403685575793142172213)/(25974637773290955737442125)*a^(24) - (75457574765229510533)/(11673994504849867747165)*a^(23) + (535003495912505514748719)/(25974637773290955737442125)*a^(22) + (63958829547452687841676)/(5194927554658191147488425)*a^(21) - (3269498578881025648485908)/(25974637773290955737442125)*a^(20) + (169033160166555107835253)/(742132507808313021069775)*a^(19) - (143460989038508113265773)/(1038985510931638229497685)*a^(18) + (78678362530102904152839)/(5194927554658191147488425)*a^(17) - (1771857732499136162839094)/(25974637773290955737442125)*a^(16) + (8306463597631921614280037)/(25974637773290955737442125)*a^(15) - (35848060744490573157006807)/(25974637773290955737442125)*a^(14) + (520674157178845103749958)/(207797102186327645899537)*a^(13) - (32069127753116360356625573)/(25974637773290955737442125)*a^(12) - (3257524924381825720460692)/(5194927554658191147488425)*a^(11) + (53017731580532582086548309)/(25974637773290955737442125)*a^(10) - (29472767163864124813792053)/(5194927554658191147488425)*a^(9) + (2259808260981152411553312)/(425813733988376323564625)*a^(8) + (1250482273074359250871348)/(1038985510931638229497685)*a^(7) - (14721057849030848144979257)/(5194927554658191147488425)*a^(6) + (24690922686923820918617364)/(5194927554658191147488425)*a^(5) - (3967893549000372561739716)/(530094648434509300764125)*a^(4) - (1009901441694797591949189)/(5194927554658191147488425)*a^(3) + (2828927710105513249615712)/(425813733988376323564625)*a^(2) - (1398914780201372825345077)/(1038985510931638229497685)*a - (131915118157600786717291)/(1038985510931638229497685) ,   (797112559954164457971)/(3710662539041565105348875)*a^(27) - (4889478566963608609067)/(3710662539041565105348875)*a^(26) + (3511097934814511129093)/(742132507808313021069775)*a^(25) - (13755505340324865526764)/(3710662539041565105348875)*a^(24) - (53854851899893755937)/(742132507808313021069775)*a^(23) + (25818140520746803772612)/(3710662539041565105348875)*a^(22) + (2359252679734183901806)/(148426501561662604213955)*a^(21) - (4340949800285934411666)/(41692837517320956239875)*a^(20) + (168726600679338954818519)/(742132507808313021069775)*a^(19) - (8072409542272843904466)/(20057635346170622191075)*a^(18) + (373201037400549991156613)/(742132507808313021069775)*a^(17) - (933716284034604959146382)/(3710662539041565105348875)*a^(16) + (2730575071785602161320391)/(3710662539041565105348875)*a^(15) - (8555818243167480679565026)/(3710662539041565105348875)*a^(14) + (93192969343027986934989)/(29685300312332520842791)*a^(13) - (2402326923840983127157192)/(530094648434509300764125)*a^(12) + (4157125103405550007264347)/(742132507808313021069775)*a^(11) - (2437863061358608931001193)/(3710662539041565105348875)*a^(10) - (2177968587920065490760902)/(742132507808313021069775)*a^(9) + (6068236533694514603176871)/(3710662539041565105348875)*a^(8) - (3027626968651517880458029)/(742132507808313021069775)*a^(7) - (41836115152928068348443)/(742132507808313021069775)*a^(6) + (9215862048815753713255133)/(742132507808313021069775)*a^(5) - (5034489757980746852535961)/(530094648434509300764125)*a^(4) + (3801900451954978138506549)/(742132507808313021069775)*a^(3) - (18638370521160897903910629)/(3710662539041565105348875)*a^(2) - (1303874485846892891796)/(268402353637726228235)*a + (183039210119543427716016)/(21203785937380372030565) ,   (460314035626754127442)/(25974637773290955737442125)*a^(27) - (308921213134600708569)/(25974637773290955737442125)*a^(26) - (1679180531759766183706)/(5194927554658191147488425)*a^(25) + (49945058374559792958617)/(25974637773290955737442125)*a^(24) - (3501570771057211535748)/(5194927554658191147488425)*a^(23) - (237389619757444226807141)/(25974637773290955737442125)*a^(22) + (23086602763600740469394)/(5194927554658191147488425)*a^(21) + (446590332891350128025332)/(25974637773290955737442125)*a^(20) - (10464905289304842759651)/(148426501561662604213955)*a^(19) + (777692320466821854272)/(126705550113614418231425)*a^(18) + (20698500202641951827378)/(207797102186327645899537)*a^(17) + (50559470563661244209823)/(702017237115971776687625)*a^(16) - (3365744159231553954123063)/(25974637773290955737442125)*a^(15) - (1125300520476139165055832)/(25974637773290955737442125)*a^(14) - (3155083814364466784751842)/(5194927554658191147488425)*a^(13) + (13490016159039487103020457)/(25974637773290955737442125)*a^(12) + (894940731538130047046649)/(1038985510931638229497685)*a^(11) + (4438069893988791278814399)/(25974637773290955737442125)*a^(10) - (55501125977386179001523)/(1038985510931638229497685)*a^(9) - (43785855288481840892574953)/(25974637773290955737442125)*a^(8) - (4582768590103995084534381)/(5194927554658191147488425)*a^(7) + (437638325307808564121305)/(207797102186327645899537)*a^(6) + (651236551161656423677409)/(1038985510931638229497685)*a^(5) + (1400471473804425195918173)/(3710662539041565105348875)*a^(4) - (2463581645564762687466151)/(5194927554658191147488425)*a^(3) - (57775416238899563026211278)/(25974637773290955737442125)*a^(2) + (11335297610312229902959)/(25341110022722883646285)*a + (30333999458907506965557)/(28080689484638871067505) ,   (7453966285538325246446)/(25974637773290955737442125)*a^(27) - (31530358777015787052492)/(25974637773290955737442125)*a^(26) + (11599229435593740431667)/(5194927554658191147488425)*a^(25) + (4152679159390898562766)/(425813733988376323564625)*a^(24) - (61564244070276080007253)/(5194927554658191147488425)*a^(23) - (773806820879499278243523)/(25974637773290955737442125)*a^(22) + (459723923637496749076819)/(5194927554658191147488425)*a^(21) - (353036831112935427806164)/(25974637773290955737442125)*a^(20) - (196149668992006130838748)/(742132507808313021069775)*a^(19) + (337505559949150592885419)/(5194927554658191147488425)*a^(18) + (3840011337610923677619276)/(5194927554658191147488425)*a^(17) - (5584904989058913240817352)/(25974637773290955737442125)*a^(16) - (17175306453064049840146809)/(25974637773290955737442125)*a^(15) - (21317959821950090746013751)/(25974637773290955737442125)*a^(14) + (802584729465115407926289)/(5194927554658191147488425)*a^(13) + (53941401948789955795172021)/(25974637773290955737442125)*a^(12) + (11621432253212386280164536)/(5194927554658191147488425)*a^(11) - (81335290331301539823458753)/(25974637773290955737442125)*a^(10) - (15990238162131687760350853)/(5194927554658191147488425)*a^(9) - (9001920838974186798870644)/(25974637773290955737442125)*a^(8) + (21561839656902690419393061)/(5194927554658191147488425)*a^(7) + (25541539335951140219677233)/(5194927554658191147488425)*a^(6) - (22138474555830229897101119)/(5194927554658191147488425)*a^(5) - (28106148933718740110249596)/(3710662539041565105348875)*a^(4) + (30163266517779070199776179)/(5194927554658191147488425)*a^(3) + (71005038623362323413902321)/(25974637773290955737442125)*a^(2) - (2107872527482628645237556)/(1038985510931638229497685)*a + (226123856753520982242542)/(1038985510931638229497685) ,   (7616368724723650059993)/(25974637773290955737442125)*a^(27) - (1227585733168545542013)/(702017237115971776687625)*a^(26) + (27497682981192122349838)/(5194927554658191147488425)*a^(25) + (45223726648836153310258)/(25974637773290955737442125)*a^(24) - (104962548328776922465673)/(5194927554658191147488425)*a^(23) + (10997936526604113861361)/(633527750568072091157125)*a^(22) + (388234988033655753046397)/(5194927554658191147488425)*a^(21) - (5436725347234232032887427)/(25974637773290955737442125)*a^(20) + (15330381340594945517493)/(148426501561662604213955)*a^(19) + (966725701678037643236674)/(5194927554658191147488425)*a^(18) - (601431049484079757058058)/(5194927554658191147488425)*a^(17) - (5657300722116189834913451)/(25974637773290955737442125)*a^(16) + (19245104061918621656421663)/(25974637773290955737442125)*a^(15) - (46270431895376348140057643)/(25974637773290955737442125)*a^(14) + (6429519181361361059506219)/(5194927554658191147488425)*a^(13) + (1140886416151507369246648)/(633527750568072091157125)*a^(12) - (12894748090330202869615846)/(5194927554658191147488425)*a^(11) + (60558603202592238031010136)/(25974637773290955737442125)*a^(10) - (18732508586534197395766524)/(5194927554658191147488425)*a^(9) - (13456777599959230253758)/(7118289332225529114125)*a^(8) + (38673924496048460162599311)/(5194927554658191147488425)*a^(7) - (13639079460737406394599834)/(5194927554658191147488425)*a^(6) + (6788811953602488921795872)/(5194927554658191147488425)*a^(5) + (765607772107359453929561)/(530094648434509300764125)*a^(4) - 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