/* 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^44 - x^43 - 23*x^42 + 24*x^41 + 298*x^40 - 322*x^39 - 2644*x^38 + 2966*x^37 + 17733*x^36 - 20699*x^35 - 93680*x^34 + 114379*x^33 + 400546*x^32 - 514925*x^31 - 1402310*x^30 + 1917235*x^29 + 4042594*x^28 - 5959829*x^27 - 9550726*x^26 + 15510555*x^25 + 18239299*x^24 - 33749854*x^23 - 27151731*x^22 + 60965664*x^21 + 28718628*x^20 - 92631926*x^19 - 11478724*x^18 + 118848820*x^17 - 33434940*x^16 - 1406311*x^15 - 22927136*x^14 - 576983889*x^13 + 635212253*x^12 + 643308528*x^11 - 1294716116*x^10 + 1724346364*x^9 - 424183664*x^8 - 3407721010*x^7 + 3830694322*x^6 + 209294181*x^5 - 4039808114*x^4 + 4041269764*x^3 - 1473288*x^2 - 4104644424*x + 4106118241, 44, 2, [0, 22], 116567320065927752512435466812933331534234135648947894549180382317450046539306640625, [3, 5, 23], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12, a^13, a^14, a^15, a^16, a^17, a^18, a^19, a^20, a^21, a^22, a^23, 1/28657*a^24 + 10946/28657*a^23 - 13/28657*a^22 + 5168/28657*a^21 + 101/28657*a^20 - 754/28657*a^19 - 501/28657*a^18 - 7930/28657*a^17 + 1797/28657*a^16 + 11857/28657*a^15 - 4598/28657*a^14 - 3796/28657*a^13 + 8635/28657*a^12 + 9498/28657*a^11 - 11284/28657*a^10 + 14025/28657*a^9 + 10152/28657*a^8 + 12302/28657*a^7 - 5510/28657*a^6 - 6477/28657*a^5 + 1691/28657*a^4 + 6477/28657*a^3 - 193/28657*a^2 + 11556/28657*a + 4/28657, 1/28657*a^25 - 12/28657*a^23 + 4181/28657*a^22 + 91/28657*a^21 + 11323/28657*a^20 - 433/28657*a^19 + 2529/28657*a^18 + 1524/28657*a^17 + 597/28657*a^16 - 3767/28657*a^15 + 4220/28657*a^14 + 7001/28657*a^13 + 1574/28657*a^12 - 8796/28657*a^11 - 11638/28657*a^10 + 8051/28657*a^9 - 8301/28657*a^8 - 3959/28657*a^7 + 11655/28657*a^6 + 1515/28657*a^5 + 9213/28657*a^4 - 17/28657*a^3 + 3516/28657*a^2 + 26/28657*a + 13530/28657, 1/28657*a^26 - 7752/28657*a^23 - 65/28657*a^22 - 12632/28657*a^21 + 779/28657*a^20 - 6519/28657*a^19 - 4488/28657*a^18 - 8592/28657*a^17 - 10860/28657*a^16 + 3219/28657*a^15 + 9139/28657*a^14 + 13336/28657*a^13 + 8853/28657*a^12 - 12290/28657*a^11 - 12729/28657*a^10 - 11943/28657*a^9 + 3237/28657*a^8 - 12663/28657*a^7 - 7291/28657*a^6 - 11197/28657*a^5 - 8382/28657*a^4 - 4731/28657*a^3 - 2290/28657*a^2 + 8917/28657*a + 48/28657, 1/28657*a^27 - 50/28657*a^23 + 1220/28657*a^22 + 629/28657*a^21 + 2694/28657*a^20 - 3468/28657*a^19 + 5008/28657*a^18 + 13702/28657*a^17 + 6261/28657*a^16 - 7053/28657*a^15 - 9709/28657*a^14 + 13000/28657*a^13 + 12135/28657*a^12 - 4066/28657*a^11 + 4310/28657*a^10 + 379/28657*a^9 - 6481/28657*a^8 - 12683/28657*a^7 + 2870/28657*a^6 - 11022/28657*a^5 + 7652/28657*a^4 + 350/28657*a^3 + 2945/28657*a^2 + 378/28657*a + 2351/28657, 1/28657*a^28 + 4037/28657*a^23 - 21/28657*a^22 + 3181/28657*a^21 + 1582/28657*a^20 - 4035/28657*a^19 - 11348/28657*a^18 + 10959/28657*a^17 - 3174/28657*a^16 + 10001/28657*a^15 + 12356/28657*a^14 - 5723/28657*a^13 - 2171/28657*a^12 - 7959/28657*a^11 + 9319/28657*a^10 + 7001/28657*a^9 + 7748/28657*a^8 - 12484/28657*a^7 + 48/28657*a^6 - 971/28657*a^5 - 1071/28657*a^4 + 11568/28657*a^3 - 9272/28657*a^2 + 7011/28657*a + 200/28657, 1/28657*a^29 + 71/28657*a^23 - 1652/28657*a^22 + 662/28657*a^21 - 10574/28657*a^20 - 5092/28657*a^19 - 1151/28657*a^18 + 367/28657*a^17 + 5733/28657*a^16 + 2837/28657*a^15 - 13333/28657*a^14 - 9214/28657*a^13 + 8115/28657*a^12 + 8959/28657*a^11 - 4121/28657*a^10 - 13602/28657*a^9 + 12059/28657*a^8 - 545/28657*a^7 + 5067/28657*a^6 + 11394/28657*a^5 + 5367/28657*a^4 + 6920/28657*a^3 + 12413/28657*a^2 + 2224/28657*a + 12509/28657, 1/28657*a^30 - 5079/28657*a^23 + 1585/28657*a^22 - 4961/28657*a^21 - 12263/28657*a^20 - 4931/28657*a^19 + 7281/28657*a^18 - 4377/28657*a^17 - 10122/28657*a^16 + 4530/28657*a^15 + 2017/28657*a^14 - 8939/28657*a^13 - 2329/28657*a^12 + 9289/28657*a^11 + 13823/28657*a^10 - 9378/28657*a^9 - 4912/28657*a^8 - 8665/28657*a^7 + 1406/28657*a^6 + 6722/28657*a^5 + 1487/28657*a^4 + 11058/28657*a^3 - 12730/28657*a^2 - 5571/28657*a - 284/28657, 1/28657*a^31 + 1739/28657*a^23 - 13674/28657*a^22 - 13803/28657*a^21 - 7778/28657*a^20 - 10904/28657*a^19 + 1517/28657*a^18 + 5150/28657*a^17 - 10090/28657*a^16 - 13294/28657*a^15 - 6726/28657*a^14 + 3948/28657*a^13 - 7413/28657*a^12 - 4223/28657*a^11 - 6814/28657*a^10 - 13239/28657*a^9 - 600/28657*a^8 + 11004/28657*a^7 - 9336/28657*a^6 + 3040/28657*a^5 + 2547/28657*a^4 - 14283/28657*a^3 - 11480/28657*a^2 + 3104/28657*a - 8341/28657, 1/28657*a^32 + 8137/28657*a^23 + 8804/28657*a^22 + 3368/28657*a^21 + 14056/28657*a^20 - 5499/28657*a^19 - 11978/28657*a^18 - 3837/28657*a^17 + 13993/28657*a^16 + 6991/28657*a^15 + 4567/28657*a^14 + 2721/28657*a^13 - 4220/28657*a^12 + 11253/28657*a^11 + 8249/28657*a^10 - 2968/28657*a^9 + 9388/28657*a^8 + 4265/28657*a^7 + 13492/28657*a^6 + 3849/28657*a^5 - 3261/28657*a^4 - 12782/28657*a^3 - 5153/28657*a^2 + 12989/28657*a - 6956/28657, 1/28657*a^33 + 7158/28657*a^23 - 5479/28657*a^22 + 1859/28657*a^21 + 3717/28657*a^20 - 9278/28657*a^19 + 3506/28657*a^18 + 4839/28657*a^17 - 128/28657*a^16 + 12277/28657*a^15 - 9395/28657*a^14 - 8414/28657*a^13 - 13435/28657*a^12 + 10952/28657*a^11 - 2088/28657*a^10 + 137/28657*a^9 - 13085/28657*a^8 + 11019/28657*a^7 - 9486/28657*a^6 - 135/28657*a^5 + 11568/28657*a^4 - 8279/28657*a^3 + 7295/28657*a^2 + 14146/28657*a - 3891/28657, 1/28657*a^34 - 8709/28657*a^23 + 8942/28657*a^22 + 7360/28657*a^21 + 12846/28657*a^20 + 13122/28657*a^19 + 8872/28657*a^18 - 6705/28657*a^17 - 12313/28657*a^16 + 233/28657*a^15 + 5834/28657*a^14 - 8503/28657*a^13 - 13886/28657*a^12 + 14289/28657*a^11 - 13074/28657*a^10 + 10093/28657*a^9 - 11502/28657*a^8 - 4241/28657*a^7 + 8413/28657*a^6 + 6908/28657*a^5 + 9454/28657*a^4 + 11955/28657*a^3 - 8553/28657*a^2 + 11020/28657*a + 25/28657, 1/28657*a^35 - 4183/28657*a^23 + 8771/28657*a^22 + 811/28657*a^21 + 4364/28657*a^20 + 4739/28657*a^19 - 14050/28657*a^18 - 11313/28657*a^17 + 3584/28657*a^16 - 11381/28657*a^15 + 10001/28657*a^14 - 3072/28657*a^13 - 8121/28657*a^12 + 906/28657*a^11 + 2590/28657*a^10 - 3911/28657*a^9 + 2682/28657*a^8 - 1992/28657*a^7 - 7864/28657*a^6 - 1763/28657*a^5 + 9176/28657*a^4 + 2664/28657*a^3 - 7711/28657*a^2 - 2155/28657*a + 6179/28657, 1/28657*a^36 + 2003/28657*a^23 + 3746/28657*a^22 - 13927/28657*a^21 - 2633/28657*a^20 + 12895/28657*a^19 + 13622/28657*a^18 - 11457/28657*a^17 - 2664/28657*a^16 + 2565/28657*a^15 - 7659/28657*a^14 - 10811/28657*a^13 + 13291/28657*a^12 + 14122/28657*a^11 - 6804/28657*a^10 + 8378/28657*a^9 - 5850/28657*a^8 + 12087/28657*a^7 - 9865/28657*a^6 - 3250/28657*a^5 - 2162/28657*a^4 + 4715/28657*a^3 - 7078/28657*a^2 + 568/28657*a - 11925/28657, 1/28657*a^37 + 1513/28657*a^23 + 12112/28657*a^22 - 8960/28657*a^21 + 11191/28657*a^20 + 5063/28657*a^19 - 10949/28657*a^18 + 5148/28657*a^17 + 13956/28657*a^16 - 577/28657*a^15 + 86/28657*a^14 - 6083/28657*a^13 - 1612/28657*a^12 - 3050/28657*a^11 - 143/28657*a^10 - 14065/28657*a^9 - 4556/28657*a^8 - 5751/28657*a^7 + 335/28657*a^6 - 10352/28657*a^5 - 832/28657*a^4 + 1112/28657*a^3 - 14051/28657*a^2 - 3737/28657*a - 8012/28657, 1/28657*a^38 - 14097/28657*a^23 + 10709/28657*a^22 - 13289/28657*a^21 - 4465/28657*a^20 + 12230/28657*a^19 - 10578/28657*a^18 + 4763/28657*a^17 + 2977/28657*a^16 - 273/28657*a^15 - 12960/28657*a^14 + 10336/28657*a^13 - 213/28657*a^12 - 13460/28657*a^11 + 7712/28657*a^10 + 10456/28657*a^9 - 5575/28657*a^8 - 14198/28657*a^7 - 12909/28657*a^6 - 1825/28657*a^5 - 6898/28657*a^4 - 13058/28657*a^3 + 1702/28657*a^2 - 11470/28657*a - 6052/28657, 1/28657*a^39 - 1474/28657*a^23 + 4049/28657*a^22 + 2737/28657*a^21 + 3177/28657*a^20 - 7969/28657*a^19 - 8212/28657*a^18 + 4724/28657*a^17 - 752/28657*a^16 + 7545/28657*a^15 - 14193/28657*a^14 - 9806/28657*a^13 + 7856/28657*a^12 - 13143/28657*a^11 - 13742/28657*a^10 + 207/28657*a^9 + 14145/28657*a^8 + 4878/28657*a^7 + 12832/28657*a^6 - 11965/28657*a^5 + 11002/28657*a^4 + 6769/28657*a^3 - 9776/28657*a^2 + 12492/28657*a - 926/28657, 1/3983323*a^40 - 43/3983323*a^39 - 47/3983323*a^38 - 64/3983323*a^37 + 13/3983323*a^36 - 3/3983323*a^35 - 68/3983323*a^34 + 5/3983323*a^33 + 23/3983323*a^32 - 16/3983323*a^31 + 45/3983323*a^30 + 11/3983323*a^29 + 7/3983323*a^28 - 23/3983323*a^27 - 30/3983323*a^26 + 39/3983323*a^25 + 60/3983323*a^24 - 400398/3983323*a^23 - 1528952/3983323*a^22 - 103117/3983323*a^21 - 506271/3983323*a^20 + 273720/3983323*a^19 - 815018/3983323*a^18 + 1343695/3983323*a^17 - 811089/3983323*a^16 - 1679061/3983323*a^15 - 477397/3983323*a^14 + 1538586/3983323*a^13 + 952302/3983323*a^12 - 1877059/3983323*a^11 + 814551/3983323*a^10 + 1702555/3983323*a^9 - 144244/3983323*a^8 + 828752/3983323*a^7 - 1090985/3983323*a^6 - 1526087/3983323*a^5 - 1595416/3983323*a^4 + 269515/3983323*a^3 + 777450/3983323*a^2 - 181133/3983323*a - 5034/28657, 1/3983323*a^41 + 50/3983323*a^39 + 41/3983323*a^37 - 58/3983323*a^35 - 40/3983323*a^33 + 52/3983323*a^31 + 63/3983323*a^29 - 46/3983323*a^27 + 69/3983323*a^25 + 783156/3983323*a^23 + 9062/28657*a^22 + 1219205/3983323*a^21 - 7223/28657*a^20 + 277101/3983323*a^19 + 13744/28657*a^18 - 582513/3983323*a^17 - 1119/28657*a^16 + 1008826/3983323*a^15 - 8359/28657*a^14 + 230260/3983323*a^13 - 9130/28657*a^12 + 445655/3983323*a^11 - 4052/28657*a^10 - 903368/3983323*a^9 - 4140/28657*a^8 + 839797/3983323*a^7 - 11119/28657*a^6 + 151417/3983323*a^5 + 1695/28657*a^4 + 1165558/3983323*a^3 - 9371/28657*a^2 - 1386657/3983323*a - 6107/28657, 1/5500969063*a^42 + 114/5500969063*a^41 - 154/5500969063*a^40 - 31537/5500969063*a^39 - 94482/5500969063*a^38 - 15074/5500969063*a^37 - 68596/5500969063*a^36 + 80319/5500969063*a^35 - 10632/5500969063*a^34 + 5123/5500969063*a^33 + 23716/5500969063*a^32 - 65590/5500969063*a^31 - 43311/5500969063*a^30 + 71936/5500969063*a^29 + 52319/5500969063*a^28 - 55040/5500969063*a^27 - 67064/5500969063*a^26 + 12698/5500969063*a^25 - 95471/5500969063*a^24 + 1669779628/5500969063*a^23 - 1795757706/5500969063*a^22 - 2028011570/5500969063*a^21 + 2411464291/5500969063*a^20 + 142052597/5500969063*a^19 + 1076196489/5500969063*a^18 + 2583475676/5500969063*a^17 - 860725813/5500969063*a^16 - 1504518919/5500969063*a^15 - 2517486720/5500969063*a^14 - 608195519/5500969063*a^13 - 629810102/5500969063*a^12 + 2714969632/5500969063*a^11 + 2004505629/5500969063*a^10 + 2101227756/5500969063*a^9 - 269093028/5500969063*a^8 + 570400744/5500969063*a^7 + 2714670997/5500969063*a^6 + 51523621/5500969063*a^5 - 650493013/5500969063*a^4 - 977972298/5500969063*a^3 + 2742876477/5500969063*a^2 - 910393118/5500969063*a - 9053653/39575317, 1/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^43 + 663322316731053022879876111776901738612861773389558276560243967511013378052051498483205986016465063026605379957748640561848608252/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^42 + 1389695180682739071060223992019585006160419524135136818125101902979227286436400528235317160951219229632906178957535596028914315281834/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^41 - 311297362359138135920615165724564707445434046796533118873167136987759296410213272971701141330244309342584598859570811883961397902591/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^40 + 189165366404028065045856401021773611277148818677694689697651650458058963797944675256611009697789826885378181815132071460048421931047820/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^39 + 103184652463512436541622315768252053487039972021331072492406860887531332413766071114087338990647969543821724442802358072164970580143905/15548871779422679760733924651630165416533823791251887956811700137031266722304982404895289485804787291799575316024861565336925547503186431619*a^38 - 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