/* 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^29 - 12*x^28 + 55*x^27 - 97*x^26 + 34*x^25 + 11*x^24 + 138*x^23 - 214*x^22 + 43*x^21 + 224*x^20 - 104*x^19 - 50*x^18 + 748*x^17 - 1490*x^16 + 1965*x^15 - 460*x^14 - 575*x^13 + 2189*x^12 - 1286*x^11 - 53*x^10 + 3178*x^9 - 2804*x^8 + 3117*x^7 - 748*x^6 + 585*x^5 + 965*x^4 + 480*x^3 + 353*x^2 + 369*x - 1, 29, 2, [1, 14], 107084423880431831080183695981363790438987742689, [2287], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/3*a^8 - 1/3, 1/3*a^9 - 1/3*a, 1/3*a^10 - 1/3*a^2, 1/3*a^11 - 1/3*a^3, 1/3*a^12 - 1/3*a^4, 1/9*a^13 - 1/9*a^12 + 1/9*a^11 + 1/9*a^10 - 1/9*a^8 - 1/3*a^6 - 4/9*a^5 + 4/9*a^4 - 1/9*a^3 + 2/9*a^2 + 1/3*a - 2/9, 1/9*a^14 - 1/9*a^11 + 1/9*a^10 - 1/9*a^9 - 1/9*a^8 - 1/3*a^7 + 2/9*a^6 + 1/3*a^4 + 4/9*a^3 - 4/9*a^2 + 1/9*a - 2/9, 1/9*a^15 - 1/9*a^12 + 1/9*a^11 - 1/9*a^10 - 1/9*a^9 + 2/9*a^7 + 1/3*a^5 + 4/9*a^4 - 4/9*a^3 + 1/9*a^2 - 2/9*a - 1/3, 1/9*a^16 + 1/9*a^8 - 2/9, 1/9*a^17 + 1/9*a^9 - 2/9*a, 1/45*a^18 - 1/45*a^17 + 2/45*a^15 - 2/45*a^13 - 1/15*a^12 - 1/15*a^10 + 2/15*a^9 + 2/45*a^8 + 13/45*a^7 - 7/15*a^6 + 14/45*a^5 + 7/15*a^4 - 1/3*a^3 - 4/45*a^2 - 8/45*a + 16/45, 1/135*a^19 - 1/135*a^18 + 2/135*a^16 + 1/45*a^14 - 1/45*a^13 - 1/9*a^12 + 22/135*a^11 - 19/135*a^10 - 1/45*a^9 - 7/135*a^8 + 2/5*a^7 + 8/45*a^6 + 7/45*a^5 - 2/9*a^4 - 14/135*a^3 + 47/135*a^2 - 8/45*a + 10/27, 1/405*a^20 - 1/405*a^18 + 2/405*a^17 + 17/405*a^16 + 2/45*a^15 + 1/27*a^14 + 4/135*a^13 + 7/405*a^12 + 11/135*a^11 + 53/405*a^10 + 10/81*a^9 - 28/405*a^8 - 8/45*a^7 - 1/27*a^6 + 62/135*a^5 + 136/405*a^4 - 44/135*a^3 - 7/405*a^2 + 146/405*a + 13/81, 1/405*a^21 - 1/405*a^19 + 2/405*a^18 + 17/405*a^17 + 2/45*a^16 + 1/27*a^15 + 4/135*a^14 + 7/405*a^13 + 11/135*a^12 + 53/405*a^11 + 10/81*a^10 - 28/405*a^9 + 7/45*a^8 - 1/27*a^7 + 62/135*a^6 + 136/405*a^5 - 44/135*a^4 - 7/405*a^3 + 146/405*a^2 + 13/81*a - 1/3, 1/405*a^22 - 1/405*a^19 + 1/405*a^18 - 7/405*a^17 - 19/405*a^16 - 2/135*a^15 + 13/405*a^14 - 7/135*a^12 + 62/405*a^11 + 46/405*a^10 - 31/405*a^9 - 13/405*a^8 + 41/135*a^7 - 113/405*a^6 + 11/45*a^5 + 52/135*a^4 - 124/405*a^3 - 191/405*a^2 + 47/405*a - 103/405, 1/1215*a^23 + 4/1215*a^19 - 11/1215*a^18 - 17/1215*a^17 + 62/1215*a^16 + 31/1215*a^15 - 22/405*a^14 - 7/135*a^13 - 22/405*a^12 - 16/243*a^11 - 34/243*a^10 - 152/1215*a^9 + 119/1215*a^8 + 247/1215*a^7 - 98/405*a^6 + 13/27*a^5 + 139/405*a^4 - 1/243*a^3 - 359/1215*a^2 + 16/1215*a + 106/243, 1/3645*a^24 + 1/3645*a^23 - 1/1215*a^21 + 1/3645*a^20 - 4/3645*a^19 - 4/3645*a^18 - 58/1215*a^17 - 4/1215*a^16 + 11/729*a^15 + 4/243*a^14 + 2/243*a^13 - 347/3645*a^12 + 32/3645*a^11 + 98/3645*a^10 - 53/405*a^9 - 5/81*a^8 - 238/729*a^7 + 52/1215*a^6 - 29/405*a^5 - 653/3645*a^4 - 1702/3645*a^3 - 463/3645*a^2 + 259/1215*a - 1528/3645, 1/3645*a^25 - 1/3645*a^23 - 1/1215*a^22 + 4/3645*a^21 + 4/3645*a^20 - 17/3645*a^18 + 2/405*a^17 - 37/729*a^16 + 86/3645*a^15 + 7/243*a^14 - 188/3645*a^13 - 44/3645*a^12 + 121/1215*a^11 + 226/3645*a^10 - 13/135*a^9 - 488/3645*a^8 - 1651/3645*a^7 - 508/1215*a^6 + 143/729*a^5 - 68/3645*a^4 - 388/1215*a^3 + 934/3645*a^2 - 1477/3645*a + 212/729, 1/3645*a^26 + 1/3645*a^23 + 4/3645*a^22 + 1/3645*a^21 + 1/3645*a^20 - 1/405*a^19 - 19/3645*a^18 - 1/729*a^17 - 29/729*a^16 - 152/3645*a^15 + 79/3645*a^14 + 202/3645*a^13 - 182/3645*a^12 - 43/405*a^11 + 452/3645*a^10 + 199/3645*a^9 - 304/3645*a^8 - 353/3645*a^7 - 416/3645*a^6 - 1409/3645*a^5 + 649/3645*a^4 - 59/135*a^3 - 587/3645*a^2 - 271/729*a + 1682/3645, 1/346275*a^27 - 14/115425*a^26 + 37/346275*a^25 + 29/346275*a^24 + 43/346275*a^23 - 341/346275*a^22 - 31/346275*a^21 + 179/346275*a^20 - 194/346275*a^19 - 47/18225*a^18 + 9188/346275*a^17 - 874/18225*a^16 - 3791/346275*a^15 - 13787/346275*a^14 - 913/18225*a^13 + 31121/346275*a^12 + 52921/346275*a^11 - 56/18225*a^10 - 12469/346275*a^9 + 13169/346275*a^8 + 2275/13851*a^7 + 141289/346275*a^6 + 151982/346275*a^5 + 6722/13851*a^4 + 12283/115425*a^3 - 30193/69255*a^2 + 68323/346275*a + 10436/115425, 1/1626427001721958364925*a^28 - 846713975122591/1626427001721958364925*a^27 + 26323939276662373/325285400344391672985*a^26 + 50364120216921737/542142333907319454975*a^25 + 139088161850022817/1626427001721958364925*a^24 + 530343898760202652/1626427001721958364925*a^23 + 389108011330849808/1626427001721958364925*a^22 + 53923149680633822/180714111302439818325*a^21 - 14568380555586946/325285400344391672985*a^20 - 14865433777381211/24275029876447139775*a^19 - 274307689210619288/108428466781463890995*a^18 + 88952611739078633722/1626427001721958364925*a^17 - 24153092934563326904/542142333907319454975*a^16 - 71384271753318450188/1626427001721958364925*a^15 - 86881272790218735979/1626427001721958364925*a^14 - 6351971612269213304/180714111302439818325*a^13 + 2822017130522643016/24275029876447139775*a^12 - 219467508305968619168/1626427001721958364925*a^11 + 56939101438483511299/542142333907319454975*a^10 + 173268049379867956/3424056845730438663*a^9 - 48475091872806068282/542142333907319454975*a^8 - 66758935340761069361/1626427001721958364925*a^7 - 605149746088217014144/1626427001721958364925*a^6 + 34981907385533104108/180714111302439818325*a^5 - 206119433252652407972/542142333907319454975*a^4 - 48276760410957487501/1626427001721958364925*a^3 - 618527947870122193232/1626427001721958364925*a^2 - 684969437184629005874/1626427001721958364925*a - 410629689511917775132/1626427001721958364925], 0, 1, [], 1, [ (160136910885135644)/(542142333907319454975)*a^(28) - (737186131261032431)/(20079345700271090925)*a^(27) + (73317982927804360507)/(180714111302439818325)*a^(26) - (312864053260332177479)/(180714111302439818325)*a^(25) + (458661301061348993942)/(180714111302439818325)*a^(24) + (341864296621843036274)/(542142333907319454975)*a^(23) - (199399772941054273487)/(108428466781463890995)*a^(22) - (592668733205291386819)/(108428466781463890995)*a^(21) + (1266436398834570019231)/(180714111302439818325)*a^(20) + (31153750809463285882)/(8091676625482379925)*a^(19) - (6069418214753194350491)/(542142333907319454975)*a^(18) - (928305044183817532036)/(542142333907319454975)*a^(17) + (63696465100017733339)/(7228564452097592733)*a^(16) - (12155161525938679208164)/(542142333907319454975)*a^(15) + (835540617737698180070)/(21685693356292778199)*a^(14) - (22347136854760017459158)/(542142333907319454975)*a^(13) - (3736297233415459651)/(179815036121830665)*a^(12) + (4484515610786412453368)/(108428466781463890995)*a^(11) - (5416139132912007881464)/(108428466781463890995)*a^(10) + (60716333574899027753)/(28533807047753655525)*a^(9) + (2149517158462765117256)/(60238037100813272775)*a^(8) - (54250427441026151338564)/(542142333907319454975)*a^(7) + (23996485050213726396542)/(542142333907319454975)*a^(6) - (15090889851743320426103)/(542142333907319454975)*a^(5) - (7077206353110435436754)/(542142333907319454975)*a^(4) - (3429373599944390521151)/(542142333907319454975)*a^(3) - (13677970210978035883103)/(542142333907319454975)*a^(2) - (2096426757212998352618)/(108428466781463890995)*a - (72252144709259349043)/(60238037100813272775) , (41495898553450253968)/(1626427001721958364925)*a^(28) - (516327938247140269519)/(1626427001721958364925)*a^(27) + (2510092078015046277542)/(1626427001721958364925)*a^(26) - (569672309245750513271)/(180714111302439818325)*a^(25) + (3640326199265249585767)/(1626427001721958364925)*a^(24) - (1095247888500386907332)/(1626427001721958364925)*a^(23) + (247795293375998369516)/(65057080068878334597)*a^(22) - (51163700740887691579)/(7228564452097592733)*a^(21) + (6465691191728263954906)/(1626427001721958364925)*a^(20) + (101506175452875126964)/(24275029876447139775)*a^(19) - (2409468055695032015849)/(542142333907319454975)*a^(18) + (1095789832152775180213)/(1626427001721958364925)*a^(17) + (1980090838264772762927)/(108428466781463890995)*a^(16) - (74368742471428387865558)/(1626427001721958364925)*a^(15) + (22891589937248078577307)/(325285400344391672985)*a^(14) - (862602312196502298551)/(20079345700271090925)*a^(13) + (3397162371832032790)/(971001195057885591)*a^(12) + (17945319480459006977402)/(325285400344391672985)*a^(11) - (716630492224365108437)/(12047607420162654555)*a^(10) + (2363186037994990489921)/(85601421143260966575)*a^(9) + (36212037170107116050521)/(542142333907319454975)*a^(8) - (166302305473801254273158)/(1626427001721958364925)*a^(7) + (206270501662032129928199)/(1626427001721958364925)*a^(6) - (14059557285042973795699)/(180714111302439818325)*a^(5) + (8661157890356012086013)/(180714111302439818325)*a^(4) + (12432419487669634711973)/(1626427001721958364925)*a^(3) + (4070086746170713844284)/(1626427001721958364925)*a^(2) + (3720969178450685470496)/(325285400344391672985)*a + (2762329148860517618906)/(1626427001721958364925) , (5213507109323772379)/(542142333907319454975)*a^(28) - (14595473314662759664)/(108428466781463890995)*a^(27) + (408406221108486955987)/(542142333907319454975)*a^(26) - (343369825636975268146)/(180714111302439818325)*a^(25) + (902614952712428868769)/(542142333907319454975)*a^(24) + (2137039617172816814)/(2409521484032530911)*a^(23) - (7800539060399634346)/(20079345700271090925)*a^(22) - (2762941504809929085287)/(542142333907319454975)*a^(21) + (2759605954004815902586)/(542142333907319454975)*a^(20) + (38991359602348566808)/(8091676625482379925)*a^(19) - (5295054697405337174557)/(542142333907319454975)*a^(18) - (22785725233756048160)/(21685693356292778199)*a^(17) + (964403720419458192142)/(60238037100813272775)*a^(16) - (1784464182627931376254)/(60238037100813272775)*a^(15) + (6587938043339790225932)/(180714111302439818325)*a^(14) - (10371477054557576367722)/(542142333907319454975)*a^(13) - (216478090895467258154)/(8091676625482379925)*a^(12) + (28016225060698675486777)/(542142333907319454975)*a^(11) - (20582012611201499396338)/(542142333907319454975)*a^(10) - (464103285828927163184)/(28533807047753655525)*a^(9) + (12143911763448745043314)/(180714111302439818325)*a^(8) - (554981643527637806314)/(6693115233423696975)*a^(7) + (1262183776612921091423)/(36142822260487963665)*a^(6) + (1515560424641118661186)/(542142333907319454975)*a^(5) - (3004596352302306078773)/(180714111302439818325)*a^(4) + (325278014797777826429)/(180714111302439818325)*a^(3) - (45960317182113383618)/(542142333907319454975)*a^(2) - (5398864312514208653564)/(542142333907319454975)*a - (602079630981642998236)/(542142333907319454975) , (46350023955984263027)/(1626427001721958364925)*a^(28) - (569214090480607163111)/(1626427001721958364925)*a^(27) + (2709362457737637881518)/(1626427001721958364925)*a^(26) - (1754564767756314172162)/(542142333907319454975)*a^(25) + (3108241049058459823538)/(1626427001721958364925)*a^(24) - (535748331523606729543)/(1626427001721958364925)*a^(23) + (1331315965989017612876)/(325285400344391672985)*a^(22) - (28167292881488343518)/(4015869140054218185)*a^(21) + (4867590522705125945069)/(1626427001721958364925)*a^(20) + (126839229242084743496)/(24275029876447139775)*a^(19) - (2338880001615506775986)/(542142333907319454975)*a^(18) + (762956974113378464192)/(1626427001721958364925)*a^(17) + (146623555478940294706)/(7228564452097592733)*a^(16) - (78764522335149450711037)/(1626427001721958364925)*a^(15) + (22884448503344688322631)/(325285400344391672985)*a^(14) - (6249921729449114958796)/(180714111302439818325)*a^(13) - (24403185154383726344)/(4855005975289427955)*a^(12) + (4154949143830800024326)/(65057080068878334597)*a^(11) - (6509790532464047213042)/(108428466781463890995)*a^(10) + (1806567466655106643739)/(85601421143260966575)*a^(9) + (14559691753537975818863)/(180714111302439818325)*a^(8) - (170789508246825746038372)/(1626427001721958364925)*a^(7) + (201797014120392533962306)/(1626427001721958364925)*a^(6) - (3851024803389106665112)/(60238037100813272775)*a^(5) + (19074760261619798727851)/(542142333907319454975)*a^(4) + (34913240714453949399877)/(1626427001721958364925)*a^(3) - (1122473740493262394639)/(1626427001721958364925)*a^(2) + (998284343612602414994)/(65057080068878334597)*a + (2745004226117959758229)/(1626427001721958364925) , (518658667076588824)/(85601421143260966575)*a^(28) - (6303221461060990678)/(85601421143260966575)*a^(27) + (29013581843820656333)/(85601421143260966575)*a^(26) - (16421644574545328993)/(28533807047753655525)*a^(25) + (1923515393251708162)/(85601421143260966575)*a^(24) + (37366515945228792121)/(85601421143260966575)*a^(23) + (4043904575606735084)/(4505337954908471925)*a^(22) - (45903283374730415138)/(28533807047753655525)*a^(21) - (34122916602699968921)/(85601421143260966575)*a^(20) + (2881692203528248099)/(1277633151391954725)*a^(19) - (13421448892306753316)/(28533807047753655525)*a^(18) - (147947140367640463769)/(85601421143260966575)*a^(17) + (128912930705750154527)/(28533807047753655525)*a^(16) - (746216823778621136873)/(85601421143260966575)*a^(15) + (837153574719957474242)/(85601421143260966575)*a^(14) + (55710705260089646998)/(28533807047753655525)*a^(13) - (11390411840450925668)/(1277633151391954725)*a^(12) + (1068466387276984626244)/(85601421143260966575)*a^(11) - (34258962096211862324)/(9511269015917885175)*a^(10) - (522736442213760891179)/(85601421143260966575)*a^(9) + (129665115394304196694)/(5706761409550731105)*a^(8) - (1061682269498647071299)/(85601421143260966575)*a^(7) + (872914251203002018733)/(85601421143260966575)*a^(6) + (3203890770532318324)/(1141352281910146221)*a^(5) + (62967665177740171622)/(28533807047753655525)*a^(4) + (28073325932449763504)/(3424056845730438663)*a^(3) + (400676355413157696127)/(85601421143260966575)*a^(2) + (176113613789284308007)/(85601421143260966575)*a + (10974989487442874977)/(17120284228652193315) , (9374904703691398522)/(1626427001721958364925)*a^(28) - (22196930804081490899)/(325285400344391672985)*a^(27) + (494363876145316247201)/(1626427001721958364925)*a^(26) - (29184942221092447352)/(60238037100813272775)*a^(25) - (9633768933886443083)/(1626427001721958364925)*a^(24) + (20104180178637891544)/(65057080068878334597)*a^(23) + (1133024206668293941304)/(1626427001721958364925)*a^(22) - (594143934597817095502)/(542142333907319454975)*a^(21) - (497989259779373642777)/(1626427001721958364925)*a^(20) + (45819332665218175294)/(24275029876447139775)*a^(19) - (297477208313953964377)/(542142333907319454975)*a^(18) - (217505551884139731577)/(325285400344391672985)*a^(17) + (2309250217966055131403)/(542142333907319454975)*a^(16) - (12182142623437303762763)/(1626427001721958364925)*a^(15) + (13811167311737031812063)/(1626427001721958364925)*a^(14) + (1361192695012189341773)/(542142333907319454975)*a^(13) - (204541666686039173702)/(24275029876447139775)*a^(12) + (23387459353675429062451)/(1626427001721958364925)*a^(11) - (2782858114507829417453)/(542142333907319454975)*a^(10) - (385023835314579488672)/(85601421143260966575)*a^(9) + (11519121024621730321787)/(542142333907319454975)*a^(8) - (22263837104336417166422)/(1626427001721958364925)*a^(7) + (3356461857503392329532)/(325285400344391672985)*a^(6) + (2706361455623939723786)/(542142333907319454975)*a^(5) - (2945016890639247550339)/(542142333907319454975)*a^(4) + (19352869397966204291486)/(1626427001721958364925)*a^(3) - (512510346987230346809)/(1626427001721958364925)*a^(2) + (5479898921675762766628)/(1626427001721958364925)*a + (1799598964553014196132)/(1626427001721958364925) , (75958067600686746241)/(1626427001721958364925)*a^(28) - 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