/* 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 - 8*x^27 + 24*x^26 - 48*x^25 + 18*x^24 - 48*x^23 + 288*x^22 - 240*x^21 - 1242*x^20 + 528*x^19 + 3504*x^18 + 576*x^17 - 9312*x^16 - 1344*x^15 + 16704*x^14 + 9600*x^13 - 25056*x^12 - 24192*x^11 + 18816*x^10 + 28416*x^9 - 21408*x^8 - 55296*x^7 - 25344*x^6 + 14592*x^5 + 5088*x^4 - 17664*x^3 - 16128*x^2 - 5120*x - 512, 28, 393, [4, 12], 21140839391697569190758072549457521572728274944, [2, 3], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/2*a^8, 1/2*a^9, 1/2*a^10, 1/2*a^11, 1/4*a^12 - 1/2*a^4, 1/8*a^13 + 1/4*a^5 - 1/2*a, 1/16*a^14 - 1/4*a^10 + 1/8*a^6 - 1/4*a^2, 1/32*a^15 - 1/8*a^11 - 1/4*a^10 - 1/4*a^9 - 7/16*a^7 - 1/2*a^6 - 1/2*a^5 - 1/8*a^3 - 1/2*a^2 - 1/2*a, 1/32*a^16 - 1/8*a^12 - 1/4*a^11 - 1/4*a^10 + 1/16*a^8 - 1/2*a^7 - 1/2*a^6 - 1/8*a^4 - 1/2*a^3 - 1/2*a^2, 1/32*a^17 - 1/4*a^11 + 1/16*a^9 - 1/2*a^7 + 1/8*a^5 - 1/2*a^3 - 1/2*a, 1/64*a^18 - 1/32*a^14 - 1/8*a^12 - 1/4*a^11 + 5/32*a^10 - 1/2*a^7 - 1/2*a^6 + 1/4*a^4 - 1/8*a^2 - 1/2, 1/256*a^19 - 1/128*a^18 - 1/64*a^17 - 1/128*a^15 + 1/64*a^14 - 1/32*a^13 - 27/128*a^11 - 5/64*a^10 - 1/32*a^9 + 1/8*a^8 - 3/8*a^7 - 1/4*a^6 + 1/8*a^4 + 7/32*a^3 + 1/16*a^2 - 3/8*a - 1/4, 1/1024*a^20 - 1/64*a^17 - 1/512*a^16 - 1/64*a^15 - 1/32*a^14 + 1/64*a^13 + 37/512*a^12 + 1/8*a^11 + 7/32*a^10 + 1/8*a^9 + 7/32*a^8 - 13/32*a^7 - 5/32*a^6 + 1/16*a^5 - 17/128*a^4 - 3/16*a^3 + 3/16*a^2 + 1/4*a + 3/8, 1/2048*a^21 - 1/128*a^18 - 1/1024*a^17 + 1/128*a^16 - 1/64*a^15 - 3/128*a^14 + 37/1024*a^13 - 1/64*a^11 + 1/16*a^10 + 7/64*a^9 - 11/64*a^8 + 11/64*a^7 - 9/32*a^6 - 17/256*a^5 - 5/32*a^4 - 5/32*a^3 - 5/16*a - 1/2, 1/2048*a^22 - 1/1024*a^18 + 1/128*a^17 - 1/64*a^16 - 1/128*a^15 - 27/1024*a^14 - 1/16*a^13 + 7/64*a^12 + 1/64*a^11 + 7/64*a^10 + 5/64*a^9 - 5/64*a^8 - 15/32*a^7 + 79/256*a^6 + 15/32*a^5 - 5/32*a^4 - 3/16*a^3 + 7/16*a^2 - 1/4*a, 1/2048*a^23 - 1/1024*a^19 - 1/128*a^18 - 1/64*a^17 - 1/128*a^16 + 5/1024*a^15 - 1/32*a^14 - 1/64*a^13 - 7/64*a^12 + 15/64*a^11 + 11/64*a^10 + 11/64*a^9 + 1/32*a^8 + 95/256*a^7 + 15/32*a^6 + 3/32*a^5 + 1/16*a^4 + 5/16*a^3 + 3/8*a^2 - 1/2, 1/16384*a^24 - 1/4096*a^23 - 1/4096*a^22 + 3/2048*a^19 + 9/2048*a^18 - 15/1024*a^17 - 61/8192*a^16 - 25/2048*a^15 - 57/2048*a^14 - 13/256*a^13 - 483/4096*a^12 + 69/512*a^11 + 27/512*a^10 + 21/256*a^9 + 503/2048*a^8 - 103/512*a^7 + 229/512*a^6 + 25/64*a^5 - 329/1024*a^4 + 51/128*a^3 - 43/128*a^2 - 5/32*a - 17/64, 1/16384*a^25 - 1/4096*a^23 - 1/2048*a^20 + 1/2048*a^19 + 1/1024*a^18 + 99/8192*a^17 + 9/1024*a^16 - 9/2048*a^15 + 1/256*a^14 + 221/4096*a^13 - 109/1024*a^12 + 71/512*a^11 + 19/256*a^10 + 407/2048*a^9 + 3/16*a^8 - 219/512*a^7 + 3/64*a^6 - 137/1024*a^5 + 17/256*a^4 + 41/128*a^3 - 3/8*a^2 - 9/64*a - 5/16, 1/16384*a^26 - 1/2048*a^20 + 1/1024*a^19 - 29/8192*a^18 - 1/256*a^17 - 9/1024*a^16 - 3/256*a^15 - 99/4096*a^14 - 5/128*a^13 - 31/1024*a^12 + 15/256*a^11 - 25/2048*a^10 - 5/32*a^9 + 9/128*a^8 - 7/16*a^7 - 425/1024*a^6 + 51/256*a^4 - 11/32*a^3 + 1/64*a^2 - 1/8*a - 3/16, 1/11911375680725909619104130974318592*a^27 - 660938508600746332625960805/992614640060492468258677581193216*a^26 - 17341778069350708095595511663/992614640060492468258677581193216*a^25 + 763013919606777726403791507/1985229280120984936517355162386432*a^24 + 48845696023355698533768872607/496307320030246234129338790596608*a^23 + 5697826569477111676522380507/124076830007561558532334697649152*a^22 - 82676154758915881004436950201/496307320030246234129338790596608*a^21 + 52990517505645109088461593963/124076830007561558532334697649152*a^20 + 2493320574496907217549781720249/1985229280120984936517355162386432*a^19 - 91406589913937647158300089319/496307320030246234129338790596608*a^18 - 2512926179909965873326545518235/496307320030246234129338790596608*a^17 - 7601030316924532167221539905999/992614640060492468258677581193216*a^16 - 11551217444477203661673707317669/992614640060492468258677581193216*a^15 + 1318176207177350259650169631223/248153660015123117064669395298304*a^14 - 3016586252414187659026762254459/124076830007561558532334697649152*a^13 - 25656764856107294188958638490085/496307320030246234129338790596608*a^12 - 79322165328864885135313525399371/496307320030246234129338790596608*a^11 - 10577739151786781758443641502081/124076830007561558532334697649152*a^10 + 9651819395028384545117936464503/124076830007561558532334697649152*a^9 + 33188927653504075001337095300229/248153660015123117064669395298304*a^8 + 97996970921839774725895875139905/248153660015123117064669395298304*a^7 + 10386748812332340940150145436677/62038415003780779266167348824576*a^6 - 15097676434875629840804221243349/31019207501890389633083674412288*a^5 - 3268247053530687380165528713351/124076830007561558532334697649152*a^4 + 2709512480546795830335376258541/7754801875472597408270918603072*a^3 + 1713321153601774424369937426619/15509603750945194816541837206144*a^2 + 1593782194292438241379228635813/3877400937736298704135459301536*a - 783740006509691677218540274669/23264405626417792224812755809216], 0, 1, [], 1, [ (48697601743888322575871258844431)/(11911375680725909619104130974318592)*a^(27) - (8418306149727272463021708685263)/(248153660015123117064669395298304)*a^(26) + (107620124251058643448912446527393)/(992614640060492468258677581193216)*a^(25) - (228721765268433075805147990579139)/(992614640060492468258677581193216)*a^(24) + (37082172341592384720394236534227)/(248153660015123117064669395298304)*a^(23) - (128157013435731941745534671197921)/(496307320030246234129338790596608)*a^(22) + (633273230912136081957026253312981)/(496307320030246234129338790596608)*a^(21) - (172021952089267144401318174021923)/(124076830007561558532334697649152)*a^(20) - (9085728778232801738813140651625889)/(1985229280120984936517355162386432)*a^(19) + (838444440327907293751255390642631)/(248153660015123117064669395298304)*a^(18) + (6538062695662226435004842947683341)/(496307320030246234129338790596608)*a^(17) - (603935156390517701521143353223285)/(496307320030246234129338790596608)*a^(16) - (36873337733836419482583691814594455)/(992614640060492468258677581193216)*a^(15) + (1255460700985894520581200066790687)/(248153660015123117064669395298304)*a^(14) + (4023009632155279246136092329796537)/(62038415003780779266167348824576)*a^(13) + (5257226946745924354105098189042871)/(248153660015123117064669395298304)*a^(12) - (52632879511024889516980939382905949)/(496307320030246234129338790596608)*a^(11) - (1046114608341088541125195521029401)/(15509603750945194816541837206144)*a^(10) + (11333056107685074884487534820031483)/(124076830007561558532334697649152)*a^(9) + (10951423759488539355852076884879891)/(124076830007561558532334697649152)*a^(8) - (26834619020380626788688653483219813)/(248153660015123117064669395298304)*a^(7) - (11749289453817974293985018327998771)/(62038415003780779266167348824576)*a^(6) - (788515526374794041514449292167775)/(15509603750945194816541837206144)*a^(5) + (4335380894706504470928515712537249)/(62038415003780779266167348824576)*a^(4) + (11842796268162365879027266313113)/(15509603750945194816541837206144)*a^(3) - (535219021817140721082463116171659)/(7754801875472597408270918603072)*a^(2) - (44059373846897482576256885643855)/(969350234434074676033864825384)*a - (103149574910772043104449599768933)/(11632202813208896112406377904608) , (71791879640986774456197658533757)/(11911375680725909619104130974318592)*a^(27) - (90477062384682254994162599418447)/(1985229280120984936517355162386432)*a^(26) + (235503052486723617207990823050375)/(1985229280120984936517355162386432)*a^(25) - (362600426888859641373728543520791)/(1985229280120984936517355162386432)*a^(24) - (42531878719602933647443437573725)/(248153660015123117064669395298304)*a^(23) + (28386868980201704020974451665995)/(248153660015123117064669395298304)*a^(22) + (619756840837203684085338909557411)/(496307320030246234129338790596608)*a^(21) - (13395565818835228427526008413839)/(62038415003780779266167348824576)*a^(20) - (19557218534841210327910857846426355)/(1985229280120984936517355162386432)*a^(19) + (2430291133506977765339386987459843)/(992614640060492468258677581193216)*a^(18) + (26562822283447075492554757477933465)/(992614640060492468258677581193216)*a^(17) + (5969721622661537843547033235447219)/(992614640060492468258677581193216)*a^(16) - (66281127683346543478539805483669989)/(992614640060492468258677581193216)*a^(15) - (11829527978124719209947593819034079)/(496307320030246234129338790596608)*a^(14) + (68163469109142904664269737632304141)/(496307320030246234129338790596608)*a^(13) + (35889367936834730683745811270008681)/(496307320030246234129338790596608)*a^(12) - (94100154768318190802616141205854119)/(496307320030246234129338790596608)*a^(11) - (49077353184769017620452400939869349)/(248153660015123117064669395298304)*a^(10) + (42517244393992678366686725941283377)/(248153660015123117064669395298304)*a^(9) + (57344982219128678522789180206873263)/(248153660015123117064669395298304)*a^(8) - (44066333150614720560447290780622463)/(248153660015123117064669395298304)*a^(7) - (52322737856552900216417843702678685)/(124076830007561558532334697649152)*a^(6) - (17770655445505501435083740437096137)/(124076830007561558532334697649152)*a^(5) + (20043629611360100175274585667049315)/(124076830007561558532334697649152)*a^(4) + (669086187668982128253030921810049)/(15509603750945194816541837206144)*a^(3) - (2541371786499170183304995913185865)/(15509603750945194816541837206144)*a^(2) - (769581966981412407087272271323343)/(7754801875472597408270918603072)*a - (301474910638040489288760355360639)/(23264405626417792224812755809216) , -(718574339928026148842097201829)/(248153660015123117064669395298304)*a^(27) + (53595942566104091596367361325513)/(1985229280120984936517355162386432)*a^(26) - (204989880980703867107551040998463)/(1985229280120984936517355162386432)*a^(25) + (511940572588269707864063466556637)/(1985229280120984936517355162386432)*a^(24) - (81451933984910977714230356281241)/(248153660015123117064669395298304)*a^(23) + (206351617488119508857399648118259)/(496307320030246234129338790596608)*a^(22) - (1165177249238142950598071247029)/(969350234434074676033864825384)*a^(21) + (253621816805911241549545280628893)/(124076830007561558532334697649152)*a^(20) + (12827231820252805592011660217371)/(7754801875472597408270918603072)*a^(19) - (4875089941556024081261577061911401)/(992614640060492468258677581193216)*a^(18) - (5023518935963406398846518183707029)/(992614640060492468258677581193216)*a^(17) + (7835102510703957774934815193886455)/(992614640060492468258677581193216)*a^(16) + (2570834454364856521849941561778609)/(124076830007561558532334697649152)*a^(15) - (13683618003804750936223551628342517)/(496307320030246234129338790596608)*a^(14) - (13445948967635711179344640490238547)/(496307320030246234129338790596608)*a^(13) + (11165501354235956754859446228419721)/(496307320030246234129338790596608)*a^(12) + (252656522297898639176134546250671)/(3877400937736298704135459301536)*a^(11) - (6129797856878184878954558322493325)/(248153660015123117064669395298304)*a^(10) - (17201116526427990211541320359995425)/(248153660015123117064669395298304)*a^(9) + (3221225390929840605155366064477515)/(248153660015123117064669395298304)*a^(8) + (2927516751145839792211311118032769)/(31019207501890389633083674412288)*a^(7) + (4932441397885364564819090866138817)/(124076830007561558532334697649152)*a^(6) - (5738382099141270114548274167301113)/(124076830007561558532334697649152)*a^(5) - (3407642857366354654702100736977125)/(124076830007561558532334697649152)*a^(4) + (169997755046218737493930028032029)/(3877400937736298704135459301536)*a^(3) + (273707628023271847190420297773907)/(15509603750945194816541837206144)*a^(2) - (28135304585359982936393953698995)/(7754801875472597408270918603072)*a - (1834895517567753582803935700861)/(7754801875472597408270918603072) , (122574876504144073982069566011)/(248153660015123117064669395298304)*a^(27) - (11678724978952082860032816996593)/(1985229280120984936517355162386432)*a^(26) + (56575110841477358538286628707167)/(1985229280120984936517355162386432)*a^(25) - (9977296700418815525346080754925)/(124076830007561558532334697649152)*a^(24) + (68022557281992890347349951258511)/(496307320030246234129338790596608)*a^(23) - (17145310537861068746994536618445)/(124076830007561558532334697649152)*a^(22) + (37827656596907841274174263166381)/(124076830007561558532334697649152)*a^(21) - (95277179775430955015575550181811)/(124076830007561558532334697649152)*a^(20) + (61600452678176846167155718332489)/(248153660015123117064669395298304)*a^(19) + (2090534978841029091347569656241045)/(992614640060492468258677581193216)*a^(18) - (443101037930565899662969301741939)/(992614640060492468258677581193216)*a^(17) - (309934844053477207564312662261487)/(62038415003780779266167348824576)*a^(16) - (574814714990761458848960460232813)/(248153660015123117064669395298304)*a^(15) + (7608517049713678905216886828445083)/(496307320030246234129338790596608)*a^(14) + (223875768887042358113104014485675)/(496307320030246234129338790596608)*a^(13) - (41721113547769275505796589231127)/(1938700468868149352067729650768)*a^(12) - (805232495087744899478193805428999)/(62038415003780779266167348824576)*a^(11) + (8586630034666530632845512338535793)/(248153660015123117064669395298304)*a^(10) + (5777714977861673683112751323113001)/(248153660015123117064669395298304)*a^(9) - (27156341596766216538327493335061)/(969350234434074676033864825384)*a^(8) - (1977499624967166376309046629113839)/(62038415003780779266167348824576)*a^(7) + (3369763996383780253410911258038193)/(124076830007561558532334697649152)*a^(6) + (6264289910260309650666601206223457)/(124076830007561558532334697649152)*a^(5) + (53305359587906917713501549338799)/(3877400937736298704135459301536)*a^(4) - (312275728704804981928396496037449)/(15509603750945194816541837206144)*a^(3) + (29598534811148525654631905499875)/(7754801875472597408270918603072)*a^(2) + (92617279726597806470823624878689)/(7754801875472597408270918603072)*a + (625114662118577263896113966799)/(242337558608518669008466206346) , (407292717110574682019889273545887)/(11911375680725909619104130974318592)*a^(27) - 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