/* 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^21 - 7*x^20 - 45*x^19 + 362*x^18 + 799*x^17 - 7508*x^16 - 7656*x^15 + 79875*x^14 + 49998*x^13 - 459906*x^12 - 252543*x^11 + 1367403*x^10 + 782753*x^9 - 1809622*x^8 - 897807*x^7 + 1116746*x^6 + 430780*x^5 - 303555*x^4 - 87913*x^3 + 25235*x^2 + 7546*x + 343, 21, 2, [21, 0], 988509426193021817935320621873627136, [2, 7, 11], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/7*a^9 - 3/7*a^8 - 1/7*a^7 - 1/7*a^5 - 3/7*a^4 + 1/7*a^3, 1/7*a^10 - 3/7*a^8 - 3/7*a^7 - 1/7*a^6 + 1/7*a^5 - 1/7*a^4 + 3/7*a^3, 1/7*a^11 + 2/7*a^8 + 3/7*a^7 + 1/7*a^6 + 3/7*a^5 + 1/7*a^4 + 3/7*a^3, 1/7*a^12 + 2/7*a^8 + 3/7*a^7 + 3/7*a^6 + 3/7*a^5 + 2/7*a^4 - 2/7*a^3, 1/7*a^13 + 2/7*a^8 - 2/7*a^7 + 3/7*a^6 - 3/7*a^5 - 3/7*a^4 - 2/7*a^3, 1/7*a^14 - 3/7*a^8 - 2/7*a^7 - 3/7*a^6 - 1/7*a^5 - 3/7*a^4 - 2/7*a^3, 1/21*a^15 - 1/21*a^13 + 1/21*a^12 + 1/21*a^11 - 1/21*a^10 + 1/21*a^9 + 5/21*a^8 - 10/21*a^7 + 1/21*a^6 - 2/7*a^5 + 1/3*a^4 - 10/21*a^3 - 1/3*a^2 - 1/3, 1/147*a^16 - 1/49*a^15 + 5/147*a^14 + 1/21*a^13 - 8/147*a^12 - 10/147*a^11 - 8/147*a^10 - 10/147*a^9 - 31/147*a^8 + 46/147*a^7 + 4/49*a^6 + 16/147*a^5 + 2/21*a^4 + 2/21*a^3 - 3/7*a^2 - 1/3*a, 1/147*a^17 + 1/49*a^15 + 1/147*a^14 + 2/49*a^13 - 2/49*a^12 - 10/147*a^11 + 1/147*a^10 + 3/49*a^9 - 11/49*a^8 + 59/147*a^7 + 17/147*a^6 - 1/147*a^5 + 2/21*a^3 + 1/21*a^2 - 1/3, 1/441*a^18 + 1/441*a^17 - 1/441*a^15 - 8/441*a^14 - 1/63*a^13 + 5/147*a^12 + 4/63*a^11 + 2/147*a^10 - 29/441*a^9 - 17/63*a^8 + 19/147*a^7 + 92/441*a^6 - 1/63*a^5 - 5/21*a^4 - 1/63*a^3 - 1/3*a^2 - 4/9*a - 2/9, 1/441*a^19 - 1/441*a^17 - 1/441*a^16 - 1/63*a^15 + 1/441*a^14 + 22/441*a^13 + 13/441*a^12 - 22/441*a^11 + 4/63*a^10 - 3/49*a^9 - 202/441*a^8 - 31/63*a^7 - 18/49*a^6 - 2/9*a^5 - 22/63*a^4 + 16/63*a^3 - 1/9*a^2 + 2/9*a + 2/9, 1/590523477729356804013609217885539*a^20 - 15580673018953633150907211140/196841159243118934671203072628513*a^19 - 13780634575107435841500192721/590523477729356804013609217885539*a^18 - 1559500242777709531716498639058/590523477729356804013609217885539*a^17 - 625263754986037887374975386330/590523477729356804013609217885539*a^16 - 557711655858078678300592169636/590523477729356804013609217885539*a^15 + 41989417577716417386469668259984/590523477729356804013609217885539*a^14 + 5918048931144486895663204365769/590523477729356804013609217885539*a^13 - 27887833030465555099261965641101/590523477729356804013609217885539*a^12 - 17077468048444302778323917678699/590523477729356804013609217885539*a^11 + 1874165308671192312420139577603/65613719747706311557067690876171*a^10 + 38822102298613999316498071730006/590523477729356804013609217885539*a^9 - 138673252636319152482221610917947/590523477729356804013609217885539*a^8 + 3457160069884002335554001968/1178689576306101405216784866039*a^7 + 208813614850772895906729233329243/590523477729356804013609217885539*a^6 - 29960392567768469780987114271202/84360496818479543430515602555077*a^5 + 37908762146873603516871159874903/84360496818479543430515602555077*a^4 - 5738128959484003122783029981929/84360496818479543430515602555077*a^3 + 4827173179899624984350987427329/12051499545497077632930800365011*a^2 + 274201318550225810027950911275/1721642792213868233275828623573*a - 132552699098950905978273602581/573880930737956077758609541191], 0, 1, [], 1, [ (29242582734798367871579816)/(88974457997492361611211272847)*a^(20) - (216355157580782950878197108)/(88974457997492361611211272847)*a^(19) - (1255459412116530432678599392)/(88974457997492361611211272847)*a^(18) + (11261506125470580969886914088)/(88974457997492361611211272847)*a^(17) + (2229168115188219873266659758)/(9886050888610262401245696983)*a^(16) - (78855369446274585631798706708)/(29658152665830787203737090949)*a^(15) - (151641183832185207816490769936)/(88974457997492361611211272847)*a^(14) + (2581347481253078745827434112360)/(88974457997492361611211272847)*a^(13) + (662609303561838024701700345158)/(88974457997492361611211272847)*a^(12) - (15644262344017125814635850629682)/(88974457997492361611211272847)*a^(11) - (2791512375434982003398321097662)/(88974457997492361611211272847)*a^(10) + (51762260533970817549437204121446)/(88974457997492361611211272847)*a^(9) + (10719751726206445444082850986029)/(88974457997492361611211272847)*a^(8) - (514133510592363827522242264160)/(532781185613726716234798041)*a^(7) - (16572690813510855500785204016030)/(88974457997492361611211272847)*a^(6) + (9610305045725229534094341467194)/(12710636856784623087315896121)*a^(5) + (1259234503506305482996909562902)/(12710636856784623087315896121)*a^(4) - (3109565707636757929675209732728)/(12710636856784623087315896121)*a^(3) - (9291624320756211119395048928)/(605268421751648718443614101)*a^(2) + (5433844707319507206217983290)/(259400752179278022190120329)*a + (58987267262360072305880413)/(86466917393092674063373443) , (53596009731201373981916776)/(88974457997492361611211272847)*a^(20) - (363598126948050434728987984)/(88974457997492361611211272847)*a^(19) - (831509142237611394950604244)/(29658152665830787203737090949)*a^(18) + (18904898376329341549930830784)/(88974457997492361611211272847)*a^(17) + (15667335081943451130038157991)/(29658152665830787203737090949)*a^(16) - (394282817129306405563909036628)/(88974457997492361611211272847)*a^(15) - (494160329819596725365363313104)/(88974457997492361611211272847)*a^(14) + (4213423540752180085760165270348)/(88974457997492361611211272847)*a^(13) + (3527673883408289315196025147468)/(88974457997492361611211272847)*a^(12) - (8090432510486098743831936139144)/(29658152665830787203737090949)*a^(11) - (18022067047024352092576546379908)/(88974457997492361611211272847)*a^(10) + (23821088100000024560945362396288)/(29658152665830787203737090949)*a^(9) + (53142483863899135603096633264756)/(88974457997492361611211272847)*a^(8) - (548687265145248789562582189420)/(532781185613726716234798041)*a^(7) - (18802793965148775770175347868136)/(29658152665830787203737090949)*a^(6) + (2698788302947856611188560030428)/(4236878952261541029105298707)*a^(5) + (3133809073442929239644901342656)/(12710636856784623087315896121)*a^(4) - (756954085739325633380674294136)/(4236878952261541029105298707)*a^(3) - (17773507066501979000530441816)/(605268421751648718443614101)*a^(2) + (3382533530872576838606339396)/(259400752179278022190120329)*a + (423697661161344101268928937)/(259400752179278022190120329) , (230592953363564283121831691515)/(590523477729356804013609217885539)*a^(20) - (2313006336465825878360796315269)/(590523477729356804013609217885539)*a^(19) - (644903913667216615233333133683)/(65613719747706311557067690876171)*a^(18) + (117034160187762642973565072925953)/(590523477729356804013609217885539)*a^(17) - (53571390259671837272138702546717)/(590523477729356804013609217885539)*a^(16) - (2399189083277270649295906219705045)/(590523477729356804013609217885539)*a^(15) + (1061639918951014304496376061412968)/(196841159243118934671203072628513)*a^(14) + (26042000723439926485944788898780709)/(590523477729356804013609217885539)*a^(13) - (13661160941657763151165748708842897)/(196841159243118934671203072628513)*a^(12) - (165030138122331828135398456954836505)/(590523477729356804013609217885539)*a^(11) + (238066480163526324785999512352766769)/(590523477729356804013609217885539)*a^(10) + (69674462835220473530406040421927000)/(65613719747706311557067690876171)*a^(9) - (643260191525130083873769412002461638)/(590523477729356804013609217885539)*a^(8) - (8022656805845961851529310675159646)/(3536068728918304215650354598117)*a^(7) + (222764850034671499512207228089712583)/(196841159243118934671203072628513)*a^(6) + (183369570117920084460184491508720715)/(84360496818479543430515602555077)*a^(5) - (4102907548009749717109438677664305)/(9373388535386615936723955839453)*a^(4) - (75338939936271504808594793967073861)/(84360496818479543430515602555077)*a^(3) + (337059671394678738876364514220538)/(12051499545497077632930800365011)*a^(2) + (72194601183111500614799257150649)/(573880930737956077758609541191)*a + (5261015451747809106853510517047)/(573880930737956077758609541191) , (55292852588752334099848513500)/(65613719747706311557067690876171)*a^(20) - (1334305525310649575736568630439)/(196841159243118934671203072628513)*a^(19) - (18644532620642085882725190536597)/(590523477729356804013609217885539)*a^(18) + (202556142221389118281997416777108)/(590523477729356804013609217885539)*a^(17) + (68589756213555646018862798542030)/(196841159243118934671203072628513)*a^(16) - (4103285466993972872289106991213332)/(590523477729356804013609217885539)*a^(15) + (115714374312649324911810639244861)/(590523477729356804013609217885539)*a^(14) + (42773289763992875369405595697675328)/(590523477729356804013609217885539)*a^(13) - (1797271154485434221904318263104726)/(65613719747706311557067690876171)*a^(12) - (245185373432105393376646145112881411)/(590523477729356804013609217885539)*a^(11) + (11730919808678162050339046845096501)/(65613719747706311557067690876171)*a^(10) + (758342148100085601234811572279868984)/(590523477729356804013609217885539)*a^(9) - (276302090441559171926981616719704223)/(590523477729356804013609217885539)*a^(8) - (2296159917387075822811384429632437)/(1178689576306101405216784866039)*a^(7) + (376777925474276974556243640393465416)/(590523477729356804013609217885539)*a^(6) + (114681865610758025666994935721403727)/(84360496818479543430515602555077)*a^(5) - (10484555820979329647014425189259714)/(28120165606159847810171867518359)*a^(4) - (34606289993002109120116204901135275)/(84360496818479543430515602555077)*a^(3) + (299136394455164591383717268487410)/(4017166515165692544310266788337)*a^(2) + (71058921929247653361649318962638)/(1721642792213868233275828623573)*a - (602512130320073577691122941219)/(1721642792213868233275828623573) , (498171598539126377714770764868)/(590523477729356804013609217885539)*a^(20) - (4611443207480525399875802777567)/(590523477729356804013609217885539)*a^(19) - (14069663026070225238719018550862)/(590523477729356804013609217885539)*a^(18) + (227004514213023002800038205076578)/(590523477729356804013609217885539)*a^(17) - (26138398724375367606305191092008)/(590523477729356804013609217885539)*a^(16) - (1480683362759533698149034228854156)/(196841159243118934671203072628513)*a^(15) + (4790524061067761430323118252072080)/(590523477729356804013609217885539)*a^(14) + (44478241973877350563500865111221821)/(590523477729356804013609217885539)*a^(13) - (21383954584436518502107402067401766)/(196841159243118934671203072628513)*a^(12) - (27262720110393155996140583389506156)/(65613719747706311557067690876171)*a^(11) + (369937403360915477457030800806686820)/(590523477729356804013609217885539)*a^(10) + (743988128805778920065600793607022711)/(590523477729356804013609217885539)*a^(9) - (1017977857866753462994254410940978503)/(590523477729356804013609217885539)*a^(8) - (6815651960244552275985425841712334)/(3536068728918304215650354598117)*a^(7) + (1250183686601539864545044407963706353)/(590523477729356804013609217885539)*a^(6) + (11239760570581291379969686349264219)/(9373388535386615936723955839453)*a^(5) - (9405694533855793580301910210644606)/(9373388535386615936723955839453)*a^(4) - (8474283985936882625886471157211315)/(28120165606159847810171867518359)*a^(3) + (222454709424284783264681706028993)/(1721642792213868233275828623573)*a^(2) + (66887342017665319559572673149936)/(1721642792213868233275828623573)*a + (1752753134646595821035786682833)/(1721642792213868233275828623573) , (84310510590867900085355275000)/(196841159243118934671203072628513)*a^(20) - (779499577970599787213753904688)/(590523477729356804013609217885539)*a^(19) - (18245735834487119348801039595098)/(590523477729356804013609217885539)*a^(18) + (47017764762104781858112092340703)/(590523477729356804013609217885539)*a^(17) + (553722506877748380581342920197619)/(590523477729356804013609217885539)*a^(16) - (368752424361453458201737386549757)/(196841159243118934671203072628513)*a^(15) - (1013748058615399760666227593721879)/(65613719747706311557067690876171)*a^(14) + (12524736677893726544379289698826258)/(590523477729356804013609217885539)*a^(13) + (87289323728746249678562412194004266)/(590523477729356804013609217885539)*a^(12) - (65370364637058617113390046656676029)/(590523477729356804013609217885539)*a^(11) - (475281206978684323525142669507291746)/(590523477729356804013609217885539)*a^(10) + (90586938250296097647209970966364648)/(590523477729356804013609217885539)*a^(9) + (1312387693226781028852430278490944175)/(590523477729356804013609217885539)*a^(8) + (1687519881392620696924059854505137)/(3536068728918304215650354598117)*a^(7) - (1365818824066818515854900115672535703)/(590523477729356804013609217885539)*a^(6) - (7403181924797523621794743851174140)/(12051499545497077632930800365011)*a^(5) + (76751470474580944554192263147731000)/(84360496818479543430515602555077)*a^(4) + (16928583615421079087685643002061555)/(84360496818479543430515602555077)*a^(3) - (1217271814650678953179513358949140)/(12051499545497077632930800365011)*a^(2) - (14056314206660983733213652712778)/(573880930737956077758609541191)*a - (1628689672732662292578767963524)/(1721642792213868233275828623573) , (263052564932489356953795722593)/(590523477729356804013609217885539)*a^(20) - (229005484171404263679115263374)/(65613719747706311557067690876171)*a^(19) - (9929753146979194229526789181768)/(590523477729356804013609217885539)*a^(18) + (102376820833899177533174140123367)/(590523477729356804013609217885539)*a^(17) + (115261761637956598274983464867761)/(590523477729356804013609217885539)*a^(16) - (2011841729238511443299205671140463)/(590523477729356804013609217885539)*a^(15) - (131456012379048895995642669406064)/(590523477729356804013609217885539)*a^(14) + (19888291030903461918456433662023767)/(590523477729356804013609217885539)*a^(13) - (5984261425165395891358610396689348)/(590523477729356804013609217885539)*a^(12) - (103091226661154480685105291493357127)/(590523477729356804013609217885539)*a^(11) + (13468994541108408832161699656284247)/(196841159243118934671203072628513)*a^(10) + (256219871741300722416945465569219477)/(590523477729356804013609217885539)*a^(9) - (116728135365135588848120006413009147)/(590523477729356804013609217885539)*a^(8) - (137955740554404606918071438444502)/(392896525435367135072261622013)*a^(7) + (235084320879319628644306513593403159)/(590523477729356804013609217885539)*a^(6) - 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