/* 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^32 - 2*x^31 - 14*x^30 + 32*x^29 + 110*x^28 - 256*x^27 - 822*x^26 + 1761*x^25 + 5076*x^24 - 6234*x^23 - 33617*x^22 + 7049*x^21 + 145847*x^20 + 80587*x^19 - 200297*x^18 - 1040496*x^17 + 909785*x^16 - 126545*x^15 + 4807173*x^14 - 6468687*x^13 + 4092091*x^12 - 12326083*x^11 + 15573178*x^10 - 9966741*x^9 + 15430857*x^8 - 15762104*x^7 + 7858456*x^6 - 7358464*x^5 + 5444944*x^4 - 823424*x^3 + 88384*x^2 - 5760*x + 256, 32, 262, [0, 16], 42655280577413385127292283461599409580230712890625, [3, 5, 7, 29], [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, 1/2*a^15 - 1/2*a^14 - 1/2*a^13 - 1/2*a^12 - 1/2*a^11 - 1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a, 1/2*a^16 - 1/2*a, 1/2*a^17 - 1/2*a^2, 1/2*a^18 - 1/2*a^3, 1/2*a^19 - 1/2*a^4, 1/10*a^20 + 1/5*a^19 + 1/10*a^17 + 1/5*a^16 - 1/5*a^15 + 2/5*a^14 - 2/5*a^13 - 1/5*a^12 - 2/5*a^11 + 2/5*a^10 + 1/5*a^9 + 2/5*a^8 - 2/5*a^7 - 1/5*a^6 - 3/10*a^5 - 2/5*a^4 + 1/5*a^3 - 1/2*a^2 - 1/5*a - 2/5, 1/10*a^21 + 1/10*a^19 + 1/10*a^18 - 1/10*a^16 - 1/5*a^15 - 1/5*a^14 - 2/5*a^13 + 1/5*a^11 + 2/5*a^10 - 1/5*a^8 - 2/5*a^7 + 1/10*a^6 + 1/5*a^5 - 1/2*a^4 + 1/10*a^3 - 1/5*a^2 - 1/2*a - 1/5, 1/20*a^22 - 1/20*a^20 + 1/10*a^19 + 1/10*a^17 - 1/20*a^16 - 3/20*a^15 - 7/20*a^14 - 7/20*a^13 + 1/20*a^12 - 3/20*a^11 + 7/20*a^10 - 1/20*a^9 - 7/20*a^8 - 3/10*a^7 + 1/20*a^6 + 3/10*a^5 - 1/20*a^4 + 9/20*a^3 + 1/4*a^2 - 2/5*a + 2/5, 1/20*a^23 - 1/20*a^21 - 1/5*a^19 + 1/10*a^18 - 3/20*a^17 + 3/20*a^16 - 3/20*a^15 + 1/4*a^14 + 9/20*a^13 + 1/20*a^12 - 1/4*a^11 - 9/20*a^10 + 9/20*a^9 + 3/10*a^8 + 9/20*a^7 - 1/2*a^6 + 1/4*a^5 - 3/20*a^4 + 1/20*a^3 + 1/10*a^2 + 1/10*a + 2/5, 1/20*a^24 - 1/20*a^20 + 1/10*a^19 - 3/20*a^18 - 1/20*a^17 + 1/5*a^16 + 1/5*a^15 + 2/5*a^14 + 2/5*a^13 - 1/10*a^12 + 1/10*a^11 + 1/10*a^10 + 3/20*a^9 + 2/5*a^8 - 1/10*a^7 + 2/5*a^6 + 1/20*a^5 + 1/5*a^4 + 9/20*a^3 + 7/20*a^2 + 1/10*a - 2/5, 1/40*a^25 - 1/40*a^24 - 1/40*a^22 - 1/40*a^21 + 1/8*a^19 - 1/5*a^18 - 1/40*a^17 + 3/40*a^16 - 1/8*a^15 + 11/40*a^14 - 7/40*a^13 + 11/40*a^12 + 19/40*a^11 - 1/20*a^10 - 1/20*a^9 + 1/40*a^8 + 3/10*a^7 - 11/40*a^5 + 1/20*a^4 - 9/40*a^3 - 1/4*a^2 - 1/10*a + 2/5, 1/440*a^26 + 1/220*a^25 - 3/440*a^24 - 3/440*a^23 - 1/44*a^22 - 21/440*a^21 - 21/440*a^20 - 1/440*a^19 + 31/440*a^18 + 1/220*a^17 - 2/11*a^16 + 1/10*a^15 + 9/44*a^14 - 109/220*a^13 - 23/110*a^12 + 131/440*a^11 - 4/11*a^10 - 41/440*a^9 - 163/440*a^8 + 71/220*a^7 - 153/440*a^6 - 21/440*a^5 - 163/440*a^4 - 137/440*a^3 - 47/110*a^2 + 13/110*a + 14/55, 1/440*a^27 + 1/110*a^25 - 1/55*a^24 - 1/110*a^23 + 1/44*a^22 + 1/44*a^21 + 19/440*a^20 - 1/5*a^19 + 9/55*a^18 - 51/440*a^17 - 1/88*a^16 + 101/440*a^15 - 211/440*a^14 - 107/440*a^13 - 101/220*a^12 - 59/440*a^11 + 191/440*a^10 + 19/88*a^9 + 21/88*a^8 - 217/440*a^7 + 87/440*a^6 + 1/4*a^5 + 189/440*a^4 + 37/88*a^3 + 26/55*a^2 - 53/110*a + 16/55, 1/880*a^28 + 3/440*a^25 - 7/440*a^24 - 1/40*a^23 - 1/55*a^22 - 7/880*a^21 - 1/220*a^20 - 83/440*a^19 + 89/880*a^18 + 37/176*a^17 - 217/880*a^16 + 119/880*a^15 + 391/880*a^14 - 47/220*a^13 - 329/880*a^12 - 91/880*a^11 + 15/176*a^10 + 45/176*a^9 + 149/880*a^8 - 17/176*a^7 + 97/440*a^6 + 59/176*a^5 - 87/880*a^4 - 161/440*a^3 - 41/220*a^2 + 23/110*a + 1/11, 1/1760*a^29 - 1/880*a^27 + 1/176*a^25 + 3/440*a^24 - 17/880*a^23 + 3/160*a^22 + 7/880*a^21 - 39/880*a^20 + 51/1760*a^19 - 73/352*a^18 + 93/1760*a^17 - 63/352*a^16 - 119/1760*a^15 - 35/176*a^14 - 347/1760*a^13 - 135/352*a^12 + 771/1760*a^11 - 23/160*a^10 + 173/352*a^9 - 145/352*a^8 - 111/440*a^7 + 731/1760*a^6 - 137/1760*a^5 - 81/880*a^4 + 9/55*a^3 - 31/220*a^2 + 23/110*a + 4/55, 1/788329307332495206080*a^30 - 273647326495943/9613772040640185440*a^29 + 2039916433878847/35833150333295236640*a^28 - 76118053460467967/98541163416561900760*a^27 - 188096218806253209/394164653666247603040*a^26 - 1004532165772086261/98541163416561900760*a^25 + 786067483935272425/78832930733249520608*a^24 + 2255536336218377941/157665861466499041216*a^23 + 2230243329975676297/98541163416561900760*a^22 + 12468895811385734187/394164653666247603040*a^21 - 14883716100705914329/788329307332495206080*a^20 - 168852905661253897/1747958552843670080*a^19 + 158686810906565794859/788329307332495206080*a^18 - 21787505725541715561/788329307332495206080*a^17 - 169817880117851536397/788329307332495206080*a^16 + 17957623019501153303/197082326833123801520*a^15 + 148188667037518430921/788329307332495206080*a^14 + 31496076079829491367/157665861466499041216*a^13 + 178555436550903161521/788329307332495206080*a^12 + 1798125515017844659/14333260133318094656*a^11 - 5864877093093421449/19227544081280370880*a^10 - 309177294374850626007/788329307332495206080*a^9 - 48212931678796372929/394164653666247603040*a^8 - 167162946317890604973/788329307332495206080*a^7 - 183105746058106056059/788329307332495206080*a^6 + 88070177429046161951/197082326833123801520*a^5 + 36528014430284199709/98541163416561900760*a^4 - 11690413197754584429/24635290854140475190*a^3 - 19881883107465415079/49270581708280950380*a^2 - 429344957526095494/12317645427070237595*a + 5279795271823257642/12317645427070237595, 1/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^31 - 20889925525748514290042805533672996475748342894658607470761/72113934258971928828609192663042564274628717554498514938448924200567102717310560*a^30 + 3088672774147775049511954201368211068485113729953924884460604901368307223161/13111624410722168877928944120553193504477948646272457261536168036466745948601920*a^29 - 17756273659347998463249243334761481153531952727910409177013513589579148912851/72113934258971928828609192663042564274628717554498514938448924200567102717310560*a^28 + 131845665850486877869498045571811334317793481460109352165014016496678927151783/144227868517943857657218385326085128549257435108997029876897848401134205434621120*a^27 - 49724992952038930985432971698292585659140495332266680755322355765239526674167/72113934258971928828609192663042564274628717554498514938448924200567102717310560*a^26 - 144126195050597204058445332843057108627859263238036317760230965847501410161209/13111624410722168877928944120553193504477948646272457261536168036466745948601920*a^25 + 5960314693012913034673771651892887841414898855475336984639833216182842830517309/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^24 - 207756391561954845273550372424884045352066416721536405919013638544379298804051/28845573703588771531443677065217025709851487021799405975379569680226841086924224*a^23 + 60984093617327819022202825678590855000205147842912088416762208028501708314727/144227868517943857657218385326085128549257435108997029876897848401134205434621120*a^22 + 1024186446197686093572325241212738706385005765168811980776040808513382748320543/57691147407177543062887354130434051419702974043598811950759139360453682173848448*a^21 + 9831042507618616027385144016903158327843023448559645241574140768170282938769579/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^20 + 36941243170342065365282645942015057089059538944322032325915769937612449078621413/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^19 - 24395308491564165579193667494171621620518431077619764138314649152808164940615/1407101156272623001533837905620342717553731074234117364652661935620821516435328*a^18 - 1267264392801332914042714759181298858546115496662351935390614126876815032467231/7035505781363115007669189528101713587768655371170586823263309678104107582176640*a^17 - 17251460453225419532445921090521100684514074184649428115996885548218958739901299/144227868517943857657218385326085128549257435108997029876897848401134205434621120*a^16 + 10725817611827609261664585017885278079043844423286202792399306676999346585646289/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^15 + 22864808203041327921020023035694648115748819663818046594345878219221148571246753/57691147407177543062887354130434051419702974043598811950759139360453682173848448*a^14 - 60625644037309444498960802201814666103985504464686599571527749466015652084493001/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^13 - 36646045520553523588319418058038254443420380187596401135895827646678438346617441/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^12 + 10281603340531812198380572742680961135125059348478133975241500885002534974358849/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^11 - 83029105081459595800697279191414515222659507651418277405637446053070992174566561/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^10 - 11699787871173739989526990738939861953508225249184242724002166841686699741289403/36056967129485964414304596331521282137314358777249257469224462100283551358655280*a^9 - 125745480692280213823497352011627512242641632106295126112583206277039550953223297/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^8 - 133551343301505639906055217392227209293363396158164686846228377816980331760800453/288455737035887715314436770652170257098514870217994059753795696802268410869242240*a^7 + 3399062661061449389750201068041464829979883463543931269165695810597979114163019/144227868517943857657218385326085128549257435108997029876897848401134205434621120*a^6 - 3034959994759567152566312187662941858361597202084590017553308950094371276544307/9014241782371491103576149082880320534328589694312314367306115525070887839663820*a^5 + 1068440590703473895857464023748608889677815118482354737478075804007806673189049/7211393425897192882860919266304256427462871755449851493844892420056710271731056*a^4 - 4131298301815072323612228344225588362907184802166146299461174998687034468904889/9014241782371491103576149082880320534328589694312314367306115525070887839663820*a^3 - 461678264904253273056718599379533103954605283210223099397210015209516688448469/9014241782371491103576149082880320534328589694312314367306115525070887839663820*a^2 + 377281144831000144994964273914202687611090811711442589308049308712410194860453/2253560445592872775894037270720080133582147423578078591826528881267721959915955*a - 902499289029543860064023555750542287594322284588310982843126081405894084785838/2253560445592872775894037270720080133582147423578078591826528881267721959915955], 1, 0,0,0,0,0, [[x^2 - x - 26, 1], [x^2 - x + 1, 1], [x^2 - x - 1, 1], [x^2 - x + 2, 1], [x^2 - x + 9, 1], [x^2 - x - 5, 1], [x^2 - x + 4, 1], [x^4 - x^3 + x^2 - x + 1, 1], [x^4 - x^3 - 19*x^2 + 4*x + 76, 1], [x^4 - x^3 + 131*x^2 - 26*x + 4036, 1], [x^4 - x^3 - 9*x^2 + 9*x + 11, 1], [x^4 - x^3 - 44*x^2 + 9*x + 431, 1], [x^4 - x^3 + 26*x^2 - 26*x + 151, 1], [x^4 - x^3 - 4*x^2 + 4*x + 1, 1], [x^4 - x^3 + 6*x^2 - x + 11, 1], [x^4 - x^3 + 4*x^2 - 15*x + 15, 1], [x^4 - x^3 + 19*x^2 - 5*x + 95, 1], [x^4 - x^3 - 8*x^2 - 9*x + 81, 1], [x^4 - x^3 + 5*x^2 + 2*x + 4, 1], [x^4 - x^3 - 58*x^2 + 16*x + 781, 1], [x^4 - 13*x^2 + 16, 1], [x^4 - x^3 - x^2 - 2*x + 4, 1], [x^4 - x^3 + 8*x^2 - 2*x + 19, 1], [x^4 - x^3 + 2*x^2 + x + 1, 1], [x^4 + 11*x^2 + 4, 1], [x^4 - x^3 - 3*x^2 + x + 1, 1], [x^8 - 2*x^7 + 24*x^6 - 38*x^5 + 167*x^4 - 166*x^3 + 139*x^2 - 135*x + 109, 1], [x^8 - x^7 + 6*x^6 - 27*x^5 + 39*x^4 - 91*x^3 + 14*x^2 + 305*x + 295, 1], [x^8 - x^7 - 18*x^6 - 9*x^5 + 261*x^4 + 95*x^3 - 1780*x^2 - 475*x + 9025, 1], [x^8 - x^7 + 11*x^6 + x^5 + 43*x^4 - 2*x^3 + 44*x^2 + 8*x + 16, 1], [x^8 - x^7 - 4*x^6 - 9*x^5 + 23*x^4 + 18*x^3 - 16*x^2 + 8*x + 16, 1], [x^8 - 28*x^6 + 218*x^4 - 413*x^2 + 121, 1], [x^8 - x^7 + 4*x^6 + x^5 + 9*x^4 - x^3 + 4*x^2 + x + 1, 1], [x^8 - 2*x^7 - 11*x^6 - 8*x^5 + 141*x^4 - 140*x^3 - 165*x^2 - 1900*x + 9025, 1], [x^8 - 3*x^7 + 24*x^6 + 43*x^5 - 29*x^4 + 285*x^3 + 1090*x^2 + 1145*x + 505, 1], [x^8 + 31*x^6 + 476*x^4 + 3851*x^2 + 17161, 1], [x^8 - x^7 + 11*x^6 + 9*x^5 + 26*x^4 + 65*x^3 - 15*x^2 + 150*x + 295, 1], [x^8 - 2*x^7 - 30*x^6 + 58*x^5 + 434*x^4 - 718*x^3 - 2675*x^2 + 1812*x + 12496, 1], [x^8 - x^7 - x^6 + 3*x^5 - x^4 + 6*x^3 - 4*x^2 - 8*x + 16, 1], [x^8 - 2*x^7 - 2*x^5 + 29*x^4 + 2*x^3 + 55*x^2 + 27*x + 151, 1], [x^8 - 2*x^7 + 20*x^6 - 32*x^5 + 114*x^4 - 108*x^3 + 35*x^2 - 48*x + 36, 1], [x^8 - 3*x^7 + 20*x^6 + 7*x^5 + 939*x^4 + 1363*x^3 + 34620*x^2 + 57013*x + 609961, 1], [x^8 - x^7 - 50*x^6 - 9*x^5 + 709*x^4 + 631*x^3 - 2790*x^2 - 4851*x - 2099, 1], [x^8 - 2*x^7 - 65*x^6 + 178*x^5 + 1104*x^4 - 3928*x^3 - 1370*x^2 + 10892*x - 1769, 1], [x^8 - x^7 - 10*x^6 - 54*x^5 + 299*x^4 + 786*x^3 - 2710*x^2 - 4141*x + 11761, 1], [x^8 - x^7 + 6*x^6 - 11*x^5 + 41*x^4 + 55*x^3 + 150*x^2 + 125*x + 625, 1], [x^8 - x^7 - 39*x^6 + 74*x^5 + 326*x^4 - 650*x^3 - 695*x^2 + 1095*x + 205, 1], [x^8 - x^7 - 14*x^6 + 9*x^5 + 61*x^4 - 5*x^3 - 90*x^2 - 45*x - 5, 1], [x^8 - 2*x^7 - 8*x^6 + 10*x^5 + 156*x^4 - 220*x^3 - 287*x^2 + 554*x + 4516, 1], [x^8 - 2*x^7 - 3*x^6 - 5*x^5 + 36*x^4 - 35*x^3 + 23*x^2 - 171*x + 361, 1], [x^8 - x^6 + 116*x^4 + 139*x^2 + 5041, 1], [x^8 - 3*x^7 + 2*x^6 + 90*x^5 - 44*x^4 - 525*x^3 + 1308*x^2 + 4806*x + 3501, 1], [x^8 - x^7 + 8*x^6 + 11*x^4 + 2*x^2 - 7*x + 31, 1], [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1, 1], [x^8 - x^7 + 45*x^6 + 26*x^5 + 1514*x^4 + 466*x^3 + 19045*x^2 + 3879*x + 185761, 1], [x^8 - x^7 + 10*x^6 - 9*x^5 + 79*x^4 - 59*x^3 + 180*x^2 + 99*x + 121, 1], [x^8 - x^7 - 5*x^6 - 4*x^5 + 24*x^4 + 16*x^3 - 65*x^2 - 11*x + 121, 1], [x^8 - 13*x^6 + 44*x^4 - 17*x^2 + 1, 1], [x^8 + 47*x^6 + 884*x^4 + 7363*x^2 + 32041, 1], [x^8 - 23*x^6 + 149*x^4 - 232*x^2 + 16, 1], [x^8 - 3*x^7 + 5*x^6 - 3*x^5 + 4*x^4 + 3*x^3 + 5*x^2 + 3*x + 1, 1], [x^16 - x^15 - 10*x^14 - 13*x^13 + 79*x^12 + 95*x^11 - 386*x^10 + 51*x^9 + 1335*x^8 - 102*x^7 - 1544*x^6 - 760*x^5 + 1264*x^4 + 416*x^3 - 640*x^2 + 128*x + 256, 1], [x^16 - 2*x^15 - 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