/* 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^30 - 5*x^29 + 2*x^28 + 21*x^27 + 40*x^26 - 46*x^25 + 39*x^24 - 296*x^23 - 1612*x^22 - 2561*x^21 + 962*x^20 + 4669*x^19 + 19325*x^18 + 55780*x^17 + 98099*x^16 + 110152*x^15 + 94739*x^14 + 50734*x^13 + 40862*x^12 + 44242*x^11 + 25838*x^10 + 20656*x^9 + 3131*x^8 + 2527*x^7 + 6736*x^6 + 1305*x^5 + 3768*x^4 - 512*x^3 + 661*x^2 - 25*x - 1, 30, 14, [2, 14], 553999258054841955537532525076904905639678955078125, [5, 751], [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, 1/3*a^13 - 1/3*a^5, 1/3*a^14 - 1/3*a^6, 1/9*a^15 - 1/9*a^14 + 1/9*a^13 - 1/9*a^12 + 1/9*a^11 - 1/9*a^10 + 1/9*a^9 - 1/9*a^8 - 4/9*a^7 + 4/9*a^6 - 4/9*a^5 + 4/9*a^4 - 4/9*a^3 + 4/9*a^2 - 4/9*a + 4/9, 1/9*a^16 + 1/9*a^8 - 2/9, 1/9*a^17 + 1/9*a^9 - 2/9*a, 1/9*a^18 + 1/9*a^10 - 2/9*a^2, 1/9*a^19 + 1/9*a^11 - 2/9*a^3, 1/27*a^20 + 1/27*a^19 - 1/27*a^18 + 1/27*a^17 - 1/27*a^15 - 2/27*a^14 + 2/27*a^13 - 4/27*a^12 + 1/9*a^11 + 1/9*a^10 - 1/9*a^9 + 1/27*a^8 + 4/27*a^7 + 8/27*a^6 + 10/27*a^5 + 1/3*a^4 - 1/27*a^3 + 4/27*a^2 - 13/27*a + 5/27, 1/27*a^21 + 1/27*a^19 - 1/27*a^18 - 1/27*a^17 - 1/27*a^16 - 1/27*a^15 + 4/27*a^14 + 1/9*a^13 - 2/27*a^12 + 1/9*a^11 + 4/27*a^9 + 1/9*a^8 + 4/27*a^7 + 2/27*a^6 - 10/27*a^5 - 1/27*a^4 - 1/27*a^3 + 7/27*a^2 - 1/3*a - 5/27, 1/27*a^22 + 1/27*a^19 + 1/27*a^17 - 1/27*a^16 - 1/27*a^15 + 2/27*a^14 - 1/27*a^13 + 4/27*a^12 + 1/9*a^11 - 2/27*a^10 + 1/9*a^9 - 5/27*a^7 - 2/9*a^6 + 4/27*a^5 + 2/27*a^4 - 10/27*a^3 - 1/27*a^2 - 1/27*a + 7/27, 1/27*a^23 - 1/27*a^19 - 1/27*a^18 + 1/27*a^17 - 1/27*a^16 + 4/27*a^14 - 1/27*a^13 + 1/27*a^12 + 1/27*a^11 + 1/9*a^9 - 1/9*a^8 + 2/27*a^7 + 11/27*a^6 + 4/27*a^5 + 5/27*a^4 + 1/9*a^3 - 11/27*a^2 - 1/27*a + 10/27, 1/5481*a^24 + 34/5481*a^23 - 16/5481*a^22 + 44/5481*a^21 + 2/5481*a^20 - 235/5481*a^19 + 115/5481*a^18 + 17/1827*a^17 - 92/5481*a^16 + 20/609*a^15 - 260/1827*a^14 - 128/783*a^13 + 296/1827*a^12 - 563/5481*a^11 - 76/5481*a^10 - 796/5481*a^9 + 311/5481*a^8 - 2263/5481*a^7 + 19/5481*a^6 - 20/87*a^5 - 1298/5481*a^4 + 215/609*a^3 + 583/1827*a^2 - 449/5481*a - 2140/5481, 1/16443*a^25 - 1/16443*a^24 - 191/16443*a^23 + 22/1827*a^22 + 86/16443*a^21 + 101/16443*a^20 + 47/1827*a^19 + 289/16443*a^18 - 659/16443*a^17 - 17/5481*a^16 - 787/16443*a^15 + 2/2349*a^14 - 26/189*a^13 + 634/16443*a^12 + 1156/16443*a^11 + 18/203*a^10 + 1172/16443*a^9 - 1780/16443*a^8 + 1642/5481*a^7 - 710/2349*a^6 - 5918/16443*a^5 - 1399/5481*a^4 - 2437/16443*a^3 - 2185/16443*a^2 - 3883/16443*a - 175/2349, 1/49329*a^26 - 1/16443*a^24 - 38/7047*a^23 - 913/49329*a^22 + 586/49329*a^21 + 293/49329*a^20 + 5/1701*a^19 + 1877/49329*a^18 - 1424/49329*a^17 + 1871/49329*a^16 + 1579/49329*a^15 - 463/49329*a^14 + 6247/49329*a^13 + 7628/49329*a^12 + 6436/49329*a^11 + 2882/49329*a^10 - 20/49329*a^9 + 4679/49329*a^8 + 14383/49329*a^7 + 13409/49329*a^6 + 2728/7047*a^5 + 170/49329*a^4 + 18835/49329*a^3 + 24256/49329*a^2 - 24197/49329*a + 74/7047, 1/49329*a^27 + 1/49329*a^24 + 386/49329*a^23 + 514/49329*a^22 - 358/49329*a^21 - 839/49329*a^20 + 1814/49329*a^19 - 2393/49329*a^18 - 136/7047*a^17 - 1490/49329*a^16 + 1928/49329*a^15 - 5168/49329*a^14 - 5395/49329*a^13 - 2201/49329*a^12 + 5981/49329*a^11 + 3931/49329*a^10 + 5207/49329*a^9 + 3490/49329*a^8 - 10972/49329*a^7 - 23570/49329*a^6 + 3176/7047*a^5 - 4394/49329*a^4 + 7738/49329*a^3 - 17099/49329*a^2 - 22741/49329*a + 5927/16443, 1/1698525676071*a^28 - 2137156/242646525153*a^27 + 267763/58569850899*a^26 - 367088/54791150841*a^25 + 1186888/242646525153*a^24 + 11888307520/1698525676071*a^23 - 3093067303/1698525676071*a^22 - 4169648075/242646525153*a^21 - 25503223408/1698525676071*a^20 - 3114117326/1698525676071*a^19 + 29428150796/1698525676071*a^18 + 973512686/58569850899*a^17 + 69276765407/1698525676071*a^16 + 26119636432/1698525676071*a^15 - 229960298653/1698525676071*a^14 + 35976612691/1698525676071*a^13 + 152462260997/1698525676071*a^12 + 24182799313/242646525153*a^11 - 125374199056/1698525676071*a^10 - 259367916014/1698525676071*a^9 + 101168133212/1698525676071*a^8 - 322141988129/1698525676071*a^7 - 204137227345/1698525676071*a^6 + 1776112561/242646525153*a^5 - 11353595342/54791150841*a^4 - 602903428150/1698525676071*a^3 + 33877139299/188725075119*a^2 + 8980159702/33304425021*a + 118981838386/1698525676071, 1/4634583293229377106287478276191459511*a^29 + 103794522720642869416004/662083327604196729469639753741637073*a^28 + 19269935420306996845505940747818/4634583293229377106287478276191459511*a^27 + 10720167178107747165913144312096/4634583293229377106287478276191459511*a^26 - 25630557569499600611140075427852/4634583293229377106287478276191459511*a^25 + 5450790303852013395347160031948/149502686878367003428628331490047081*a^24 - 35718617576885291949375400009759198/4634583293229377106287478276191459511*a^23 + 84790019335751630171660777538861532/4634583293229377106287478276191459511*a^22 - 38185647942947650490515623684983368/4634583293229377106287478276191459511*a^21 - 51142856836829079524070843927958835/4634583293229377106287478276191459511*a^20 - 118654380862941898052031305275325272/4634583293229377106287478276191459511*a^19 - 40195456973738356593185026272764861/4634583293229377106287478276191459511*a^18 - 856119732594203484031168103910220/94583332514885247067091393391662439*a^17 + 164078576019005937998052417195651694/4634583293229377106287478276191459511*a^16 - 23982430859315560696257601279172398/662083327604196729469639753741637073*a^15 + 11081897274248611311816981403542229/662083327604196729469639753741637073*a^14 - 2588849376923463702873144072534172/4634583293229377106287478276191459511*a^13 + 255611601803071193772036367713129535/4634583293229377106287478276191459511*a^12 + 547307846818859750206996728950850506/4634583293229377106287478276191459511*a^11 + 454496060944340210956519553573998081/4634583293229377106287478276191459511*a^10 + 598378329756934360300317104324118632/4634583293229377106287478276191459511*a^9 - 608045335128255467065083455694497783/4634583293229377106287478276191459511*a^8 - 18291730736113101157617960990464674/94583332514885247067091393391662439*a^7 + 39237889473688585637586433477142656/662083327604196729469639753741637073*a^6 - 764002448284593116469521898813378881/4634583293229377106287478276191459511*a^5 - 1633650018686413898506570823357740882/4634583293229377106287478276191459511*a^4 - 184280233010641738613290988954404673/1544861097743125702095826092063819837*a^3 - 195379467646771073955678973821125344/514953699247708567365275364021273279*a^2 - 23368459629184273723744433241418820/662083327604196729469639753741637073*a - 659105124440624055827120945664922784/1544861097743125702095826092063819837], 0, 4, [4], 1, [ (115917857870738661729779601288481)/(2931425232909156929973104539020531)*a^(29) - (81751585716874810045187895950546)/(418775033272736704281872077002933)*a^(28) + (21744917285727901669987487581984)/(325713914767684103330344948780059)*a^(27) + (2446400849245958586978134443211981)/(2931425232909156929973104539020531)*a^(26) + (1597165239678119482919207629287470)/(977141744303052309991034846340177)*a^(25) - (20691718196002058534441178887780)/(12063478324729040864086849954817)*a^(24) + (4204131193463711890151233795824217)/(2931425232909156929973104539020531)*a^(23) - (34049713887852417493043777233955077)/(2931425232909156929973104539020531)*a^(22) - (6517584468360574797658423254603763)/(101083628721005411378382915138639)*a^(21) - (308824507335129990426313350648177988)/(2931425232909156929973104539020531)*a^(20) + (91914219166231604008914923169986170)/(2931425232909156929973104539020531)*a^(19) + (546950030362296991883892655911010562)/(2931425232909156929973104539020531)*a^(18) + (46425325682897199243512520377546056)/(59825004753248100611696011000419)*a^(17) + (227928865220331661187485937415936553)/(101083628721005411378382915138639)*a^(16) + (1684275024250878536371983691861026502)/(418775033272736704281872077002933)*a^(15) + (1930873663107564167100471619768397720)/(418775033272736704281872077002933)*a^(14) + (11839596974860338479016944556903742798)/(2931425232909156929973104539020531)*a^(13) + (6631298072316620488951087922297576219)/(2931425232909156929973104539020531)*a^(12) + (5156913857330263628588027631362203219)/(2931425232909156929973104539020531)*a^(11) + (5455448215645887772531313514213106850)/(2931425232909156929973104539020531)*a^(10) + (3340792188423435736973495957685763852)/(2931425232909156929973104539020531)*a^(9) + (2606567875273474842659231942985953075)/(2931425232909156929973104539020531)*a^(8) + (10775427971142703039607864123086735)/(59825004753248100611696011000419)*a^(7) + (46619456459294172065496600251627612)/(418775033272736704281872077002933)*a^(6) + (29688954175171341690246258113321344)/(108571304922561367776781649593353)*a^(5) + (201996735021259577240600439338325928)/(2931425232909156929973104539020531)*a^(4) + (449689043340289779302736557066509963)/(2931425232909156929973104539020531)*a^(3) - (10301637061320269719641862491223109)/(977141744303052309991034846340177)*a^(2) + (10669262777105214025444600032562186)/(418775033272736704281872077002933)*a + (19205021542353105336983593973573)/(2931425232909156929973104539020531) , (7367742084900834019119187421616326)/(1544861097743125702095826092063819837)*a^(29) - (13159502040894206308844082074095169)/(662083327604196729469639753741637073)*a^(28) - (50648453230131751402852129217836369)/(4634583293229377106287478276191459511)*a^(27) + (507181785169498990125328737395206841)/(4634583293229377106287478276191459511)*a^(26) + (1308016738317947033292746953874673973)/(4634583293229377106287478276191459511)*a^(25) - (368410015427044971171130793245635464)/(4634583293229377106287478276191459511)*a^(24) - (279170371630616399048283789517797692)/(4634583293229377106287478276191459511)*a^(23) - (5936226798579538158737723858979528727)/(4634583293229377106287478276191459511)*a^(22) - (40649409401997119023224611162961814097)/(4634583293229377106287478276191459511)*a^(21) - (85821813384748156515139627733743878997)/(4634583293229377106287478276191459511)*a^(20) - (18980177133731215708172944748158010786)/(4634583293229377106287478276191459511)*a^(19) + (140659723610831644983005062159073022821)/(4634583293229377106287478276191459511)*a^(18) + (630771811238301308323218967384858373)/(5563725442052073356887729023038967)*a^(17) + (1556279431671057370806734820493911954176)/(4634583293229377106287478276191459511)*a^(16) + (443124849806273197422981453322355674924)/(662083327604196729469639753741637073)*a^(15) + (563820371052367501977592462832347948772)/(662083327604196729469639753741637073)*a^(14) + (3453206836000874065456035724448073666463)/(4634583293229377106287478276191459511)*a^(13) + (1957310862158681010286055407567317680081)/(4634583293229377106287478276191459511)*a^(12) + (1065623135776436209618253338948473153481)/(4634583293229377106287478276191459511)*a^(11) + (1265174379255593082797596789308039219851)/(4634583293229377106287478276191459511)*a^(10) + (1201542291508861049855137870384424460169)/(4634583293229377106287478276191459511)*a^(9) + (669171330585803645093701887855311892692)/(4634583293229377106287478276191459511)*a^(8) + (2626409252494762047603506486248351336)/(94583332514885247067091393391662439)*a^(7) + (4019749078191081776987770883077988213)/(662083327604196729469639753741637073)*a^(6) + (148577929638338589396205183143034609297)/(4634583293229377106287478276191459511)*a^(5) + (141768185592218600427476531394566620165)/(4634583293229377106287478276191459511)*a^(4) + (3273839871051312703320562969326398408)/(149502686878367003428628331490047081)*a^(3) + (1514184108918288503688985995706489775)/(1544861097743125702095826092063819837)*a^(2) - 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