/* 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 - 3*x^29 + 21*x^28 - 42*x^27 + 225*x^26 - 359*x^25 + 651*x^24 - 2808*x^23 - 1822*x^22 - 11536*x^21 - 10414*x^20 - 26496*x^19 - 25330*x^18 - 33066*x^17 - 28312*x^16 - 19700*x^15 - 18200*x^14 + 6446*x^13 - 8210*x^12 + 13412*x^11 - 5750*x^10 + 6200*x^9 - 4422*x^8 + 1276*x^7 - 711*x^6 + 161*x^5 - 113*x^4 - 42*x^3 + 3*x^2 - 3*x - 1, 30, 14, [2, 14], 1109410857892705938292621064252192000000000000000, [2, 5, 179], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, 1/2*a^9 - 1/2*a^6 - 1/2*a^3 - 1/2, 1/2*a^10 - 1/2*a^7 - 1/2*a^4 - 1/2*a, 1/2*a^11 - 1/2*a^8 - 1/2*a^5 - 1/2*a^2, 1/2*a^12 - 1/2, 1/2*a^13 - 1/2*a, 1/2*a^14 - 1/2*a^2, 1/4*a^15 - 1/4*a^12 - 1/2*a^6 - 1/4*a^3 - 1/4, 1/4*a^16 - 1/4*a^13 - 1/2*a^7 - 1/4*a^4 - 1/4*a, 1/4*a^17 - 1/4*a^14 - 1/2*a^8 - 1/4*a^5 - 1/4*a^2, 1/28*a^18 + 1/28*a^17 + 3/28*a^16 - 1/14*a^15 + 5/28*a^14 + 1/28*a^13 + 3/28*a^12 + 1/14*a^11 - 1/7*a^10 - 1/14*a^9 + 3/14*a^7 + 1/28*a^6 + 1/28*a^5 - 1/4*a^4 - 5/28*a^2 + 5/28*a - 1/28, 1/56*a^19 - 1/56*a^18 - 3/28*a^17 + 3/28*a^16 + 1/28*a^15 + 3/14*a^14 - 13/56*a^13 + 3/56*a^12 - 1/7*a^11 - 1/7*a^10 + 1/14*a^9 - 1/7*a^8 + 3/56*a^7 + 13/56*a^6 + 13/28*a^5 - 1/4*a^4 - 13/28*a^3 + 1/7*a^2 - 11/56*a + 9/56, 1/56*a^20 - 1/56*a^18 + 3/28*a^17 - 1/28*a^16 + 1/28*a^15 + 1/56*a^14 - 1/14*a^13 + 13/56*a^12 - 1/14*a^11 + 3/14*a^9 - 5/56*a^8 + 3/7*a^7 + 17/56*a^6 + 9/28*a^5 - 13/28*a^4 + 5/28*a^3 - 5/56*a^2 - 25/56, 1/56*a^21 - 1/56*a^18 + 1/14*a^16 + 1/56*a^15 - 1/7*a^14 + 1/7*a^13 - 5/56*a^12 + 1/7*a^11 + 11/56*a^9 + 2/7*a^8 - 2/7*a^7 - 3/56*a^6 + 1/7*a^5 - 1/14*a^4 - 17/56*a^3 + 3/7*a^2 - 3/7*a - 27/56, 1/392*a^22 + 1/196*a^21 + 1/392*a^20 + 1/392*a^19 - 1/392*a^18 + 11/98*a^17 - 11/392*a^16 + 5/98*a^15 + 79/392*a^14 + 55/392*a^13 + 57/392*a^12 - 10/49*a^11 - 1/8*a^10 - 31/196*a^9 - 173/392*a^8 - 149/392*a^7 + 1/8*a^6 - 19/49*a^5 - 149/392*a^4 + 18/49*a^3 + 85/392*a^2 + 19/56*a - 37/392, 1/392*a^23 - 3/392*a^21 - 1/392*a^20 - 3/392*a^19 + 1/98*a^18 - 43/392*a^17 + 1/28*a^16 + 25/392*a^15 - 19/392*a^14 + 3/392*a^13 - 13/196*a^12 + 27/392*a^11 + 1/49*a^10 + 5/56*a^9 + 1/392*a^8 + 95/392*a^7 - 12/49*a^6 + 15/392*a^5 + 25/196*a^4 - 15/56*a^3 + 75/392*a^2 + 173/392*a + 9/196, 1/392*a^24 - 1/196*a^21 - 1/98*a^18 + 5/98*a^17 + 3/196*a^16 - 9/98*a^15 - 5/49*a^14 + 3/196*a^13 - 12/49*a^12 + 5/98*a^11 + 1/14*a^10 + 23/196*a^9 + 27/98*a^8 - 11/49*a^7 + 15/49*a^6 + 3/7*a^5 - 17/196*a^4 + 3/49*a^3 - 33/98*a^2 + 9/196*a - 13/392, 1/392*a^25 - 3/392*a^21 + 1/196*a^20 - 1/196*a^19 - 3/392*a^18 - 4/49*a^17 + 13/196*a^16 - 1/8*a^15 - 9/196*a^14 - 5/28*a^13 - 13/392*a^12 - 6/49*a^11 + 15/98*a^10 - 37/392*a^9 - 11/28*a^8 + 79/196*a^7 + 9/56*a^6 - 16/49*a^5 + 73/196*a^4 - 19/392*a^3 - 67/196*a^2 - 111/392*a + 45/392, 1/2744*a^26 + 3/2744*a^25 - 1/2744*a^23 - 1/1372*a^22 - 2/343*a^21 - 15/2744*a^20 + 2/343*a^19 + 3/343*a^18 + 17/2744*a^17 - 38/343*a^16 - 37/343*a^15 + 9/2744*a^14 - 153/686*a^13 - 46/343*a^12 - 471/2744*a^11 - 153/1372*a^10 - 3/686*a^9 - 569/2744*a^8 - 289/686*a^7 + 153/686*a^6 + 491/2744*a^5 + 279/686*a^4 + 277/686*a^3 + 557/1372*a^2 - 1315/2744*a - 15/686, 1/126224*a^27 + 5/31556*a^26 - 5/15778*a^25 + 41/126224*a^24 + 11/31556*a^23 - 37/31556*a^22 - 13/2254*a^21 + 271/31556*a^20 - 517/63112*a^19 + 73/31556*a^18 + 1623/15778*a^17 + 1809/15778*a^16 - 1549/63112*a^15 - 2703/31556*a^14 - 12883/63112*a^13 - 1823/9016*a^12 + 7195/31556*a^11 - 1293/31556*a^10 + 3753/31556*a^9 + 1825/4508*a^8 - 2493/9016*a^7 + 1699/7889*a^6 - 123/686*a^5 - 1244/7889*a^4 - 523/2576*a^3 - 5575/15778*a^2 - 22845/63112*a + 6253/126224, 1/73588592*a^28 + 139/36794296*a^27 - 2063/36794296*a^26 - 3775/10512656*a^25 - 24313/36794296*a^24 - 2349/3344936*a^23 - 288/418117*a^22 + 20365/36794296*a^21 - 276107/36794296*a^20 + 323931/36794296*a^19 + 2395/1599752*a^18 + 324211/5256328*a^17 + 2695639/36794296*a^16 - 2644489/36794296*a^15 + 964241/5256328*a^14 + 384471/9198574*a^13 - 7141649/36794296*a^12 + 4730843/36794296*a^11 - 446037/18397148*a^10 - 1327201/36794296*a^9 - 18294669/36794296*a^8 + 2238895/36794296*a^7 - 6295657/36794296*a^6 - 6769445/36794296*a^5 + 16417925/73588592*a^4 + 6939231/18397148*a^3 - 2652073/9198574*a^2 + 19037589/73588592*a - 3637471/18397148, 1/132965980904100515651103455267744*a^29 + 36188735073007170380285/9497570064578608260793103947696*a^28 - 379700217566415516910771649/132965980904100515651103455267744*a^27 - 903176998530643750248947375/5781129604526109376134932837728*a^26 - 5360311174915453717267809471/4748785032289304130396551973848*a^25 + 53356696242464117338962312933/132965980904100515651103455267744*a^24 + 2901285257293617856309237609/6043908222913659802322884330352*a^23 + 30144482147926675483147611829/66482990452050257825551727633872*a^22 + 118432116223276125356554297019/16620747613012564456387931908468*a^21 + 2731772905524553404292746937/755488527864207475290360541294*a^20 - 23538384753231694118243421651/2890564802263054688067466418864*a^19 - 369443404532242573163460157113/66482990452050257825551727633872*a^18 - 3801326048386382060173116043109/33241495226025128912775863816936*a^17 - 3046156954568775063620807584853/66482990452050257825551727633872*a^16 + 773084996515232446823181054549/66482990452050257825551727633872*a^15 - 3696144850746994305475988545599/66482990452050257825551727633872*a^14 - 16141477137503042892149629712397/66482990452050257825551727633872*a^13 - 257790887402063672147266753101/3021954111456829901161442165176*a^12 - 2331808770064783363433612969875/9497570064578608260793103947696*a^11 + 912549050675458155326990977505/9497570064578608260793103947696*a^10 + 130156583961223604199477382277/3021954111456829901161442165176*a^9 + 5375444622677156215217263199237/33241495226025128912775863816936*a^8 + 21137990440323514766981548501325/66482990452050257825551727633872*a^7 - 439389009841565965225344860219/6043908222913659802322884330352*a^6 + 15725209595268868452157819973359/132965980904100515651103455267744*a^5 - 433661518439976534687795603185/3021954111456829901161442165176*a^4 + 14001900952948143703070133256771/132965980904100515651103455267744*a^3 - 18027355445324740739441780136253/132965980904100515651103455267744*a^2 - 26518970972092265188802644102645/66482990452050257825551727633872*a - 41174248340291077061513561413309/132965980904100515651103455267744], 0, 9, [3, 3], 1, [ (13873290615767659692933840907)/(2508792092530198408511385948448)*a^(29) - (25727536794140254089434325)/(2036357217962823383531969114)*a^(28) + (263764672081305706693308261675)/(2508792092530198408511385948448)*a^(27) - (34219664339306115544473850665)/(228072008411836218955580540768)*a^(26) + (1370206480314742985417476740001)/(1254396046265099204255692974224)*a^(25) - (2755806269432701726637778241691)/(2508792092530198408511385948448)*a^(24) + (265494449363483638883466568465)/(114036004205918109477790270384)*a^(23) - (16210109159114290412068443211387)/(1254396046265099204255692974224)*a^(22) - (13150751547061676765660287240469)/(627198023132549602127846487112)*a^(21) - (6521536328594488167222294362475)/(89599717590364228875406641016)*a^(20) - (136570495223081445632742687467789)/(1254396046265099204255692974224)*a^(19) - (256619221513749039853301958182321)/(1254396046265099204255692974224)*a^(18) - (43262069596922718133663525623595)/(156799505783137400531961621778)*a^(17) - (425085832662531988986269976853159)/(1254396046265099204255692974224)*a^(16) - (65992711770431275187902098639771)/(179199435180728457750813282032)*a^(15) - (412470291770193971998202940155943)/(1254396046265099204255692974224)*a^(14) - (368987487809244220004773286382531)/(1254396046265099204255692974224)*a^(13) - (93979005571503222508369882231629)/(627198023132549602127846487112)*a^(12) - (144030945333012215412439900393905)/(1254396046265099204255692974224)*a^(11) - (24468362394921073992218851652077)/(1254396046265099204255692974224)*a^(10) - (3171363247079787518687343764773)/(313599011566274801063923243556)*a^(9) + (3696710056369454672877105276)/(486954986904153417801123049)*a^(8) - (2301828461317223802265401040951)/(1254396046265099204255692974224)*a^(7) + (2158661086677942107788864362055)/(1254396046265099204255692974224)*a^(6) + (8463162182713389663597008985)/(15582559580932909369635937568)*a^(5) + (38328419926346382115875927589)/(54538958533265182793725781488)*a^(4) + (371058113205830572353547912939)/(2508792092530198408511385948448)*a^(3) + (662865335604177992034752937)/(32581715487405174136511505824)*a^(2) + (11981311991254053499365362437)/(627198023132549602127846487112)*a - (4050052653227408624570341652229)/(2508792092530198408511385948448) , (9923546516922186040618434321)/(2508792092530198408511385948448)*a^(29) - (6893607712453786714575599343)/(627198023132549602127846487112)*a^(28) + (206261898129874436114008960779)/(2508792092530198408511385948448)*a^(27) - (381077427918237460075160724073)/(2508792092530198408511385948448)*a^(26) + (1112352530813944051562735321961)/(1254396046265099204255692974224)*a^(25) - (3190634304868106404663665924227)/(2508792092530198408511385948448)*a^(24) + (297090078674863981528242674731)/(114036004205918109477790270384)*a^(23) - (1951847906165573650151120773523)/(179199435180728457750813282032)*a^(22) - (805740594898212373733551908791)/(89599717590364228875406641016)*a^(21) - (4020766936673702600727261116565)/(78399752891568700265980810889)*a^(20) - (10403695348008440605902061978055)/(179199435180728457750813282032)*a^(19) - (170391331126684335058301109901605)/(1254396046265099204255692974224)*a^(18) - (12232419932002829455187174071108)/(78399752891568700265980810889)*a^(17) - (265558680436211935702143238598905)/(1254396046265099204255692974224)*a^(16) - (275818379204882524022804607221993)/(1254396046265099204255692974224)*a^(15) - (242740543205758516799075334128831)/(1254396046265099204255692974224)*a^(14) - (232671626797625612207065533706519)/(1254396046265099204255692974224)*a^(13) - (6220077668234712312353320247905)/(89599717590364228875406641016)*a^(12) - (117502649264258999893033188774419)/(1254396046265099204255692974224)*a^(11) + (3885751076001838791776488221219)/(179199435180728457750813282032)*a^(10) - (8371118950918007452690870905181)/(313599011566274801063923243556)*a^(9) + (616782980220545038669811330531)/(27269479266632591396862890744)*a^(8) - (6692498326181824776302926136611)/(1254396046265099204255692974224)*a^(7) + (5613239369613830888757539665731)/(1254396046265099204255692974224)*a^(6) - (20456194457680853618785031171)/(109077917066530365587451562976)*a^(5) + (860133075770885589021771045)/(1113039970066636383545424112)*a^(4) + (90531262386251916069985327749)/(358398870361456915501626564064)*a^(3) + (6305376117713234918659927027)/(2508792092530198408511385948448)*a^(2) - (1002108195345026411372885032377)/(627198023132549602127846487112)*a + (13873290615767659692933840907)/(2508792092530198408511385948448) , (18101637962868299445648474311245)/(132965980904100515651103455267744)*a^(29) - (1089280190433122604657975444747)/(3021954111456829901161442165176)*a^(28) + (366866958200351669995056600946955)/(132965980904100515651103455267744)*a^(27) - (58609318978906028093525940227155)/(12087816445827319604645768660704)*a^(26) + (1964968625776234473748369701051245)/(66482990452050257825551727633872)*a^(25) - (5324331920497538698435917225995507)/(132965980904100515651103455267744)*a^(24) + (492515372781613228276057203657389)/(6043908222913659802322884330352)*a^(23) - (24465772784277793609787334133677313)/(66482990452050257825551727633872)*a^(22) - (1465952561970016183449607330226795)/(4155186903253141114096982977117)*a^(21) - (29651255606302088711382819774466041)/(16620747613012564456387931908468)*a^(20) - (135480228736286980014189100091159473)/(66482990452050257825551727633872)*a^(19) - (43635653905231720821754045586316271)/(9497570064578608260793103947696)*a^(18) - (169746574942225942459412268239473353)/(33241495226025128912775863816936)*a^(17) - (450987905619716638243176089351883241)/(66482990452050257825551727633872)*a^(16) - (423437546089600818050794627873865127)/(66482990452050257825551727633872)*a^(15) - (349504352248647535903367555167835635)/(66482990452050257825551727633872)*a^(14) - (41687600310559208102002675768163401)/(9497570064578608260793103947696)*a^(13) - (19304573664689112512606939777754609)/(33241495226025128912775863816936)*a^(12) - (92291445505002876566647127852121697)/(66482990452050257825551727633872)*a^(11) + (126229540655023632944412663959203457)/(66482990452050257825551727633872)*a^(10) - (15313476046398374167893162192797007)/(33241495226025128912775863816936)*a^(9) + (39567743818460305047752273644593143)/(33241495226025128912775863816936)*a^(8) - (39670870931352745094774633662265523)/(66482990452050257825551727633872)*a^(7) + (14705899530395165770522110012514623)/(66482990452050257825551727633872)*a^(6) - (32841391291063984065529093472616557)/(132965980904100515651103455267744)*a^(5) + (3261728429837195137131304215297775)/(66482990452050257825551727633872)*a^(4) - (4458020452659717006886358415342657)/(132965980904100515651103455267744)*a^(3) - (27153084937942451686676306739495)/(12087816445827319604645768660704)*a^(2) - (166773857591502564780113467227883)/(33241495226025128912775863816936)*a - (128494486893221379575552271412493)/(132965980904100515651103455267744) , (11514223760818969126766244796859)/(66482990452050257825551727633872)*a^(29) - (35909770235355520578923167538819)/(66482990452050257825551727633872)*a^(28) + (34902548537675436911707911503309)/(9497570064578608260793103947696)*a^(27) - (507858282073065218739109592280887)/(66482990452050257825551727633872)*a^(26) + (33972532099616765888618924049713)/(863415460416237114617554904336)*a^(25) - (4381205323541202288975270787437051)/(66482990452050257825551727633872)*a^(24) + (347493783995729964992888772494683)/(3021954111456829901161442165176)*a^(23) - 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