/* 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 - 6*x^30 - 64*x^29 + 18*x^28 + 120*x^27 + 884*x^26 + 1360*x^25 + 2453*x^24 - 592*x^23 + 11300*x^22 + 12152*x^21 - 15370*x^20 + 39248*x^19 + 6590*x^18 - 25344*x^17 + 75876*x^16 - 25344*x^15 + 6590*x^14 + 39248*x^13 - 15370*x^12 + 12152*x^11 + 11300*x^10 - 592*x^9 + 2453*x^8 + 1360*x^7 + 884*x^6 + 120*x^5 + 18*x^4 - 64*x^3 - 6*x^2 + 1, 32, 273, [0, 16], 845222867573683465013147373404160000000000000000, [2, 3, 5, 17], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, 1/2*a^12 - 1/2, 1/2*a^13 - 1/2*a, 1/2*a^14 - 1/2*a^2, 1/2*a^15 - 1/2*a^3, 1/2*a^16 - 1/2*a^4, 1/2*a^17 - 1/2*a^5, 1/56*a^18 - 3/14*a^17 - 1/7*a^16 + 1/28*a^15 + 3/14*a^13 - 5/56*a^12 - 1/7*a^10 - 3/7*a^9 - 1/7*a^8 + 9/56*a^6 + 3/14*a^5 + 1/28*a^3 - 1/7*a^2 - 3/14*a - 13/56, 1/56*a^19 - 3/14*a^17 - 5/28*a^16 - 1/14*a^15 + 3/14*a^14 - 1/56*a^13 - 1/14*a^12 - 1/7*a^11 - 1/7*a^10 - 2/7*a^9 + 2/7*a^8 + 9/56*a^7 + 1/7*a^6 + 1/14*a^5 - 13/28*a^4 - 3/14*a^3 + 1/14*a^2 - 17/56*a + 3/14, 1/112*a^20 - 1/112*a^18 + 13/56*a^17 - 1/14*a^16 - 11/56*a^15 - 1/112*a^14 - 3/28*a^13 - 1/16*a^12 - 1/14*a^11 - 3/7*a^10 - 3/14*a^9 + 33/112*a^8 - 3/7*a^7 + 47/112*a^6 - 3/56*a^5 - 5/14*a^4 + 13/56*a^3 - 7/16*a^2 + 5/28*a + 25/112, 1/112*a^21 - 1/112*a^19 + 3/14*a^17 + 9/56*a^16 + 3/112*a^15 - 3/28*a^14 + 17/112*a^13 + 5/56*a^12 - 3/7*a^11 - 5/14*a^10 - 15/112*a^9 + 3/7*a^8 + 47/112*a^7 - 1/7*a^6 + 5/14*a^5 - 15/56*a^4 - 45/112*a^3 + 1/28*a^2 + 1/112*a + 1/56, 1/112*a^22 - 1/112*a^18 - 1/28*a^17 + 19/112*a^16 - 13/56*a^15 + 1/7*a^14 - 5/56*a^13 + 9/112*a^12 - 3/7*a^11 + 17/112*a^10 + 5/14*a^9 + 3/7*a^8 + 3/7*a^7 - 17/112*a^6 + 3/28*a^5 - 29/112*a^4 + 19/56*a^3 + 2/7*a^2 + 15/56*a - 55/112, 1/112*a^23 - 1/112*a^19 + 27/112*a^17 - 1/56*a^16 + 3/14*a^15 - 5/56*a^14 + 1/112*a^13 - 3/28*a^12 + 17/112*a^11 + 1/14*a^10 - 3/7*a^9 + 1/7*a^8 - 17/112*a^7 + 3/7*a^6 - 37/112*a^5 - 9/56*a^4 + 5/14*a^3 - 1/56*a^2 - 47/112*a + 1/28, 1/112*a^24 - 1/4*a^15 - 1/4*a^12 - 1/2*a^9 + 1/4*a^3 - 29/112, 1/112*a^25 - 1/4*a^16 - 1/4*a^13 - 1/2*a^10 + 1/4*a^4 - 29/112*a, 1/224*a^26 - 1/224*a^24 - 1/8*a^17 - 1/8*a^15 + 1/8*a^14 - 1/4*a^13 - 1/8*a^12 - 1/4*a^11 - 1/4*a^9 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 + 1/8*a^5 + 1/8*a^3 + 27/224*a^2 + 1/4*a - 27/224, 1/5152*a^27 - 3/2576*a^26 + 19/5152*a^25 - 1/644*a^24 - 1/368*a^23 - 5/1288*a^22 - 3/1288*a^21 + 9/2576*a^20 + 3/2576*a^19 + 19/2576*a^18 + 321/2576*a^17 + 297/1288*a^16 - 171/1288*a^15 - 37/368*a^14 + 431/2576*a^13 + 3/2576*a^12 - 855/2576*a^11 - 311/1288*a^10 + 3/184*a^9 - 1055/2576*a^8 - 773/2576*a^7 + 799/2576*a^6 + 15/368*a^5 + 31/1288*a^4 - 813/5152*a^3 - 7/23*a^2 - 2421/5152*a + 5/368, 1/81091593856*a^28 - 1111753/20272898464*a^27 - 338535/20272898464*a^26 - 3747431/881430368*a^25 - 80899163/81091593856*a^24 + 4339765/1448064176*a^23 - 178418691/40545796928*a^22 + 29115297/10136449232*a^21 - 10236391/2534112308*a^20 + 1454717/194931716*a^19 + 202137853/40545796928*a^18 - 2297265381/10136449232*a^17 + 4877298729/40545796928*a^16 - 284774923/1267056154*a^15 + 28668265/266748664*a^14 + 61062193/5068224616*a^13 + 10039962313/40545796928*a^12 - 4996645883/10136449232*a^11 + 1778246291/5792256704*a^10 + 5721727/97465858*a^9 + 540657589/2534112308*a^8 + 2484528465/10136449232*a^7 + 4323172117/40545796928*a^6 + 704762111/1448064176*a^5 + 29368319025/81091593856*a^4 - 8270901473/20272898464*a^3 + 3186976635/20272898464*a^2 - 8894114573/20272898464*a - 37791327027/81091593856, 1/81091593856*a^29 - 460923/10136449232*a^27 - 1321595/1066994656*a^26 + 287359505/81091593856*a^25 + 5382685/2896128352*a^24 + 1839051/445558208*a^23 - 167829/724032088*a^22 - 1709339/5068224616*a^21 + 1793945/5068224616*a^20 + 8418663/1762860736*a^19 - 4700739/633528077*a^18 - 6877769571/40545796928*a^17 + 1166494529/10136449232*a^16 + 251010219/5068224616*a^15 - 426674951/5068224616*a^14 - 700302207/3118907456*a^13 - 15585905/110178796*a^12 + 14764061969/40545796928*a^11 + 4548494245/10136449232*a^10 + 84710701/266748664*a^9 - 4670451529/10136449232*a^8 + 14845826313/40545796928*a^7 + 1915780785/5068224616*a^6 - 2616019239/81091593856*a^5 + 8127778/27544699*a^4 + 3079714913/10136449232*a^3 + 626917365/2896128352*a^2 - 16544892471/81091593856*a + 7335871601/20272898464, 1/2857622031826505216*a^30 + 7557813/1428811015913252608*a^29 - 10877665/2857622031826505216*a^28 - 30063986275/408698803178848*a^27 + 147726305923767/408231718832357888*a^26 - 3753261647483415/1428811015913252608*a^25 + 10552949579894697/2857622031826505216*a^24 - 1746753062829013/714405507956626304*a^23 + 333003251230917/204115859416178944*a^22 + 37445089707585/51028964854044736*a^21 + 309169187703741/1428811015913252608*a^20 + 95300854747025/54954269842817408*a^19 + 2243703231320651/357202753978313152*a^18 - 154562974572713771/714405507956626304*a^17 + 5199026856205393/46090677932685568*a^16 + 1808830912262347/89300688494578288*a^15 - 3124694560078001/46090677932685568*a^14 + 309905414443333/8027028179287936*a^13 - 56506682964527247/357202753978313152*a^12 - 247235924789838483/714405507956626304*a^11 - 4171579863897565/8874602583312128*a^10 - 138908262911127279/357202753978313152*a^9 + 42970402637792811/204115859416178944*a^8 - 186209450362627121/714405507956626304*a^7 - 25106462550943229/219817079371269632*a^6 + 360351479244494121/1428811015913252608*a^5 + 1049766112180212751/2857622031826505216*a^4 - 1663409196355825/7765277260398112*a^3 + 294246258922823537/2857622031826505216*a^2 - 143153873608074723/1428811015913252608*a + 837251644659234383/2857622031826505216, 1/134308235495845745152*a^31 + 1/134308235495845745152*a^30 - 213940715/134308235495845745152*a^29 + 220682697/134308235495845745152*a^28 + 2576441744470865/134308235495845745152*a^27 - 38584408073228855/134308235495845745152*a^26 - 594076212624305/618931960810349056*a^25 - 33901823380287689/10331402730449672704*a^24 + 57676022324789437/67154117747922872576*a^23 + 170706917901480641/67154117747922872576*a^22 + 1760963526035657/919919421204422912*a^21 - 5184893738845981/2919744249909690112*a^20 - 13120292747606999/1975121110233025664*a^19 + 9141844003432157/1767213624945338752*a^18 + 54728212052014767/737957337889262336*a^17 + 10147613037298776873/67154117747922872576*a^16 + 652457099918357207/2919744249909690112*a^15 + 1050533910678523079/9593445392560410368*a^14 - 26886492109286451/459959710602211456*a^13 + 2075000263966150659/33577058873961436288*a^12 + 25560203727769855033/67154117747922872576*a^11 - 1718300521073974547/5165701365224836352*a^10 - 27720020322200391527/67154117747922872576*a^9 + 7150490362531648537/67154117747922872576*a^8 + 5332445055830891965/19186890785120820736*a^7 - 55498703234344568141/134308235495845745152*a^6 - 53125331466494798531/134308235495845745152*a^5 + 62384158746191320889/134308235495845745152*a^4 - 51947126542941615903/134308235495845745152*a^3 + 222781091810137447/1128640634418871808*a^2 - 28093785124115018507/134308235495845745152*a - 2868581203943125971/10331402730449672704], 1, 16, [4, 4], 1, [ (10115630303613468499)/(67154117747922872576)*a^(31) + (10955286308811139)/(254854336804261376)*a^(30) - (7097749494871534319)/(8394264718490359072)*a^(29) - (189859000779308695351)/(19186890785120820736)*a^(28) - (44122616656843393)/(114013782254537984)*a^(27) + (156037864474214279425)/(10331402730449672704)*a^(26) + (4672209749539424081601)/(33577058873961436288)*a^(25) + (33544856023756934694337)/(134308235495845745152)*a^(24) + (1150818225322384177535)/(2398361348140102592)*a^(23) + (6621236039032137512651)/(67154117747922872576)*a^(22) + (4716290987554550034369)/(2582850682612418176)*a^(21) + (6695799013182615228735)/(2919744249909690112)*a^(20) - (37943758766504169928313)/(33577058873961436288)*a^(19) + (50329182181694230630891)/(8394264718490359072)*a^(18) + (596661939155444835725)/(322856335326552272)*a^(17) - (84721314070516893525281)/(67154117747922872576)*a^(16) + (363373349492095772564275)/(33577058873961436288)*a^(15) - (129879119369970803980387)/(67154117747922872576)*a^(14) + (1616890361916249496991)/(377270324426532992)*a^(13) + (20575865915639761862665)/(4197132359245179536)*a^(12) - (1407226887684003917927)/(8394264718490359072)*a^(11) + (33304517895382376400829)/(9593445392560410368)*a^(10) + (48320843743809771335025)/(33577058873961436288)*a^(9) + (359862580911360355913)/(309465980405174528)*a^(8) + (2981751610244084671081)/(2919744249909690112)*a^(7) + (43549926250140913226115)/(134308235495845745152)*a^(6) + (274887587197085005469)/(729936062477422528)*a^(5) + (18603632892036024803183)/(134308235495845745152)*a^(4) + (4709058258287294615043)/(67154117747922872576)*a^(3) + (1098570249339500988333)/(134308235495845745152)*a^(2) - (11197323945355880947)/(8394264718490359072)*a - (313571325731510717985)/(134308235495845745152) , (5289040508646213225)/(134308235495845745152)*a^(31) - (5184028121007995275)/(67154117747922872576)*a^(30) - (29608291856446849865)/(134308235495845745152)*a^(29) - (34524333423473657535)/(16788529436980718144)*a^(28) + (746331462436254908025)/(134308235495845745152)*a^(27) + (22257495712946207575)/(9593445392560410368)*a^(26) + (3461579496477284585569)/(134308235495845745152)*a^(25) - (434406713485320432875)/(33577058873961436288)*a^(24) + (379158327078868167435)/(67154117747922872576)*a^(23) - (187858571321701236155)/(987560555116512832)*a^(22) + (35783566374276444619605)/(67154117747922872576)*a^(21) - (13324142850688464372315)/(33577058873961436288)*a^(20) - (1752159811812428112345)/(1291425341306209088)*a^(19) + (98527890391582227947145)/(33577058873961436288)*a^(18) - (199984012735313370658825)/(67154117747922872576)*a^(17) - (7166045948004864024295)/(8394264718490359072)*a^(16) + (26136437166822905566925)/(5165701365224836352)*a^(15) - (240990016671253937175275)/(33577058873961436288)*a^(14) + (57943933713980521506905)/(16788529436980718144)*a^(13) + (1696466819275000178005)/(2582850682612418176)*a^(12) - (229141615055489306070165)/(67154117747922872576)*a^(11) + (38751438711071189091055)/(16788529436980718144)*a^(10) - (6584385913864142107725)/(9593445392560410368)*a^(9) - (1689913370901992272125)/(2582850682612418176)*a^(8) + (46692322923547328940415)/(134308235495845745152)*a^(7) - (7876035856620144643855)/(67154117747922872576)*a^(6) - (1719787267924375377465)/(134308235495845745152)*a^(5) - (16274301085059084365)/(883606812472669376)*a^(4) + (164387193633763397135)/(19186890785120820736)*a^(3) + (331050921936085745)/(504918178555811072)*a^(2) + (164709094198095896305)/(19186890785120820736)*a - (283753110958393645)/(2398361348140102592) , (288238083237700137)/(750325337965618688)*a^(31) + (17165872914916923)/(750325337965618688)*a^(30) - (75177516394226205)/(32622840781113856)*a^(29) - (806352095723903667)/(32622840781113856)*a^(28) + (4088148794234273337)/(750325337965618688)*a^(27) + (34850837883152367795)/(750325337965618688)*a^(26) + (2883147434496201087)/(8430621774894592)*a^(25) + (407257685522114990529)/(750325337965618688)*a^(24) + (365597588161859032341)/(375162668982809344)*a^(23) - (4780718961918018489)/(28858666844831488)*a^(22) + (1626951261990868045569)/(375162668982809344)*a^(21) + (11513825424843719047)/(2330202912936704)*a^(20) - (1054753726467472043451)/(187581334491404672)*a^(19) + (2774819358466894545585)/(187581334491404672)*a^(18) + (6043531852527938445)/(1728860225727232)*a^(17) - (3616277985399391157253)/(375162668982809344)*a^(16) + (348187329245612848839)/(12102021580090624)*a^(15) - (426585571862482813875)/(53594666997544192)*a^(14) + (351465309724525814553)/(187581334491404672)*a^(13) + (2924179471495014093213)/(187581334491404672)*a^(12) - (1912397840230883131527)/(375162668982809344)*a^(11) + (1646763791478593488755)/(375162668982809344)*a^(10) + (1790488802178872935977)/(375162668982809344)*a^(9) + (51976377827982093)/(16311420390556928)*a^(8) + (743722943082955046307)/(750325337965618688)*a^(7) + (467184610483769993985)/(750325337965618688)*a^(6) + (292493670009148025181)/(750325337965618688)*a^(5) + (7880245111345835949)/(107189333995088384)*a^(4) + (813908145523602573)/(57717333689662976)*a^(3) - (1868371024344726051)/(107189333995088384)*a^(2) - (2439021803597151387)/(750325337965618688)*a + (10053034696177)/(10705016877568) , (396174417884787)/(299795168517512824)*a^(31) + (104991461683874841)/(1475914675778524672)*a^(30) - (356435736524437317)/(67154117747922872576)*a^(29) - (277583099220326541)/(543758038444719616)*a^(28) - (4770710994233592539)/(1049283089811294884)*a^(27) + (170050099308894967731)/(134308235495845745152)*a^(26) + (651773081722619453327)/(67154117747922872576)*a^(25) + (8748393582392862390595)/(134308235495845745152)*a^(24) + (3436981282579041274317)/(33577058873961436288)*a^(23) + (11943365221452192927073)/(67154117747922872576)*a^(22) - (356400170825804470207)/(16788529436980718144)*a^(21) + (54940969133652966881527)/(67154117747922872576)*a^(20) + (29170546777341024078651)/(33577058873961436288)*a^(19) - (16747777129109341801417)/(16788529436980718144)*a^(18) + (92308679056856716651627)/(33577058873961436288)*a^(17) + (33825897789284579329061)/(67154117747922872576)*a^(16) - 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(64167063026280304721)/(10331402730449672704)*a^(28) - (358450353686920349)/(2166261862836221696)*a^(27) + (184328352581454914327)/(19186890785120820736)*a^(26) + (2931211616707672522773)/(33577058873961436288)*a^(25) + (909512895436983853627)/(5839488499819380224)*a^(24) + (5004676138123278302887)/(16788529436980718144)*a^(23) + (197978147933582499253)/(3534427249890677504)*a^(22) + (38332062883394622359415)/(33577058873961436288)*a^(21) + (95960571085486815812397)/(67154117747922872576)*a^(20) - (25019799537767897470171)/(33577058873961436288)*a^(19) + (7873171884364309817867)/(2098566179622589768)*a^(18) + (9591986466016159907111)/(8394264718490359072)*a^(17) - (58302796582796004379213)/(67154117747922872576)*a^(16) + (228230991851672157531437)/(33577058873961436288)*a^(15) - (84386281522831430315183)/(67154117747922872576)*a^(14) + (51480665181075124135)/(19856332864554368)*a^(13) + (25929410402634575849611)/(8394264718490359072)*a^(12) - (687140233606996465535)/(4197132359245179536)*a^(11) + (144119884386409530689439)/(67154117747922872576)*a^(10) + (29983730279738552447691)/(33577058873961436288)*a^(9) + (1533273557280963884443)/(2166261862836221696)*a^(8) + (41728667673928739359585)/(67154117747922872576)*a^(7) + (26355099694230828203583)/(134308235495845745152)*a^(6) + (8693884154831908913)/(37474396064689103)*a^(5) + (11529628400543256082771)/(134308235495845745152)*a^(4) + (2927879008104696653517)/(67154117747922872576)*a^(3) + (682220892631119564033)/(134308235495845745152)*a^(2) - 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