/* 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^28 - 29*x^26 + 319*x^24 - 928*x^22 - 2494*x^20 - 21982*x^18 + 156890*x^16 - 105676*x^14 - 41383*x^12 - 3321805*x^10 + 13163303*x^8 - 22596220*x^6 + 20965492*x^4 - 8196560*x^2 - 1114064, 28, 10, [2, 13], -3356956934459190134013901917828042334392800598032384, [2, 29], [1, a, a^2, a^3, a^4, a^5, a^6, a^7, 1/6*a^8 - 1/2*a^2 + 1/3, 1/6*a^9 - 1/2*a^3 + 1/3*a, 1/6*a^10 - 1/2*a^4 + 1/3*a^2, 1/6*a^11 - 1/2*a^5 + 1/3*a^3, 1/12*a^12 - 1/12*a^10 - 1/4*a^6 + 5/12*a^4 - 1/6*a^2, 1/12*a^13 - 1/12*a^11 - 1/4*a^7 + 5/12*a^5 - 1/6*a^3, 1/24*a^14 - 1/12*a^11 - 1/24*a^10 - 1/12*a^9 + 1/24*a^8 - 5/12*a^6 + 1/4*a^5 + 1/8*a^4 + 1/12*a^3 + 5/12*a^2 - 1/6*a - 1/6, 1/168*a^15 + 1/84*a^13 - 1/56*a^11 - 11/168*a^9 - 2/21*a^7 - 5/24*a^5 - 13/28*a^3 + 5/42*a, 1/504*a^16 + 1/56*a^14 - 1/168*a^12 - 1/12*a^11 - 1/28*a^10 - 1/12*a^9 + 19/504*a^8 + 1/8*a^6 + 1/4*a^5 + 37/168*a^4 + 1/12*a^3 - 9/28*a^2 - 1/6*a + 7/18, 1/1008*a^17 - 1/1008*a^16 + 1/84*a^14 - 1/48*a^13 - 13/336*a^12 + 1/112*a^11 + 13/336*a^10 - 25/504*a^9 - 41/504*a^8 + 23/112*a^7 + 17/48*a^6 + 71/168*a^5 - 43/168*a^4 - 13/28*a^3 - 25/84*a^2 + 23/126*a - 4/9, 1/1008*a^18 - 1/1008*a^16 - 1/112*a^14 - 5/168*a^12 - 11/1008*a^10 - 43/1008*a^8 - 1/2*a^7 - 25/112*a^6 + 47/168*a^4 + 97/252*a^2 - 1/2*a + 2/9, 1/7056*a^19 + 1/7056*a^17 + 1/2352*a^15 + 2/49*a^13 + 139/7056*a^11 + 565/7056*a^9 + 1007/2352*a^7 - 25/56*a^5 + 85/252*a^3 + 94/441*a, 1/14112*a^20 + 1/14112*a^18 - 11/14112*a^16 - 11/1176*a^14 + 181/14112*a^12 - 1/12*a^11 + 1111/14112*a^10 - 1/12*a^9 - 1067/14112*a^8 - 13/168*a^6 + 1/4*a^5 - 1/252*a^4 + 1/12*a^3 + 545/1764*a^2 - 1/6*a - 1/9, 1/28224*a^21 - 1/28224*a^20 + 1/28224*a^19 - 1/28224*a^18 - 11/28224*a^17 + 11/28224*a^16 - 1/588*a^15 - 19/1176*a^14 - 827/28224*a^13 - 181/28224*a^12 + 2035/28224*a^11 - 523/28224*a^10 - 1991/28224*a^9 - 1873/28224*a^8 + 13/336*a^7 + 83/336*a^6 - 317/1008*a^5 - 61/1008*a^4 + 5/882*a^3 + 683/1764*a^2 + 1/252*a - 1/36, 1/592704*a^22 - 1/296352*a^20 + 17/42336*a^18 - 155/592704*a^16 - 9335/592704*a^14 + 3691/148176*a^12 - 1/12*a^11 - 3557/148176*a^10 - 1/12*a^9 - 9707/592704*a^8 - 1/2*a^7 - 7559/21168*a^6 + 1/4*a^5 - 14765/148176*a^4 + 1/12*a^3 - 3938/9261*a^2 + 1/3*a + 37/108, 1/1185408*a^23 - 1/1185408*a^22 - 1/592704*a^21 + 1/592704*a^20 - 1/84672*a^19 + 25/84672*a^18 - 407/1185408*a^17 + 743/1185408*a^16 + 493/1185408*a^15 + 14627/1185408*a^14 + 3187/296352*a^13 + 3365/296352*a^12 - 247/9261*a^11 + 2249/74088*a^10 - 70943/1185408*a^9 + 6767/1185408*a^8 + 311/756*a^7 - 5245/10584*a^6 - 69449/296352*a^5 - 71671/296352*a^4 + 1559/9261*a^3 - 6383/37044*a^2 + 3847/10584*a + 29/216, 1/2709842688*a^24 + 263/387120384*a^22 + 9439/338730336*a^20 + 1190699/2709842688*a^18 + 16193/677460672*a^16 + 3709877/387120384*a^14 - 1495537/169365168*a^12 - 119871835/2709842688*a^10 - 34864273/2709842688*a^8 + 132964487/677460672*a^6 - 54108283/677460672*a^4 + 32894249/169365168*a^2 + 144913/493776, 1/5419685376*a^25 - 1/5419685376*a^24 + 263/774240768*a^23 - 263/774240768*a^22 + 9439/677460672*a^21 - 9439/677460672*a^20 - 345493/5419685376*a^19 - 1190699/5419685376*a^18 - 367855/1354921344*a^17 - 16193/1354921344*a^16 - 1557067/774240768*a^15 - 3709877/774240768*a^14 - 4951969/338730336*a^13 + 1495537/338730336*a^12 + 215018021/5419685376*a^11 - 331768613/5419685376*a^10 - 96311953/5419685376*a^9 + 34864273/5419685376*a^8 - 559474057/1354921344*a^7 + 544496185/1354921344*a^6 - 29913259/1354921344*a^5 + 392838619/1354921344*a^4 + 102790985/338730336*a^3 + 80015863/338730336*a^2 - 11223839/48390048*a - 144913/987552, 1/2284351445439844188097536*a^26 - 5124095733929/47590655113330087252032*a^24 + 1363382683578602263/2284351445439844188097536*a^22 - 64842891516076821773/2284351445439844188097536*a^20 + 850268112250719935161/2284351445439844188097536*a^18 - 8779020968014583971/207668313221804017099776*a^16 + 1913104556387043516923/99319628062601921221632*a^14 + 6634133868292048118083/326335920777120598299648*a^12 - 1/12*a^11 - 75458226950711250595099/1142175722719922094048768*a^10 - 1/12*a^9 - 73264997973685096090595/2284351445439844188097536*a^8 - 1/2*a^7 + 98499428667056812542263/285543930679980523512192*a^6 + 1/4*a^5 + 216312965896651049804671/571087861359961047024384*a^4 + 1/12*a^3 - 1112504923048812373855/23795327556665043626016*a^2 + 1/3*a - 565101812347605383/59463542415656085696, 1/2284351445439844188097536*a^27 + 29255821360699/380725240906640698016256*a^25 - 1/5419685376*a^24 + 212289333192903697/2284351445439844188097536*a^23 + 2731/5419685376*a^22 - 29161105111737130157/2284351445439844188097536*a^21 - 5291/338730336*a^20 + 84132664484690857039/2284351445439844188097536*a^19 + 2585773/5419685376*a^18 - 52721734691563140979/207668313221804017099776*a^17 + 239363/677460672*a^16 - 185962392169269475411/99319628062601921221632*a^15 - 44453735/5419685376*a^14 - 12745950036388619525117/326335920777120598299648*a^13 + 6889679/169365168*a^12 + 8253079932589187685145/571087861359961047024384*a^11 - 297350597/5419685376*a^10 - 84631962196405284443789/2284351445439844188097536*a^9 - 22957811/5419685376*a^8 + 28565790733108454842459/142771965339990261756096*a^7 - 610784207/1354921344*a^6 + 157372495364721533090641/571087861359961047024384*a^5 - 69852353/1354921344*a^4 + 112274626017172175101/1982943963055420302168*a^3 - 122386577/338730336*a^2 - 160356432824379480401/2913713578367148199104*a + 326003/987552], 0, 7, [7], 1, [ (893987411232422461)/(761450481813281396032512)*a^(26) - (5890651603801740619)/(190362620453320349008128)*a^(24) + (222388004625032538623)/(761450481813281396032512)*a^(22) - (228989287251949291993)/(761450481813281396032512)*a^(20) - (2943339938116710657247)/(761450481813281396032512)*a^(18) - (2499162309614097148487)/(69222771073934672366592)*a^(16) + (3027361796899635122659)/(33106542687533973740544)*a^(14) + (15341663797160463272663)/(108778640259040199433216)*a^(12) + (112671059871714646474219)/(380725240906640698016256)*a^(10) - (2507120216904998437276027)/(761450481813281396032512)*a^(8) + (626771082363430765823809)/(95181310226660174504064)*a^(6) - (1354406873338314055752649)/(190362620453320349008128)*a^(4) + (115654167157623278526185)/(23795327556665043626016)*a^(2) - (6702938323227765829)/(6607060268406231744) , (3543517613634037073)/(571087861359961047024384)*a^(26) - (4073172073883241013)/(23795327556665043626016)*a^(24) + (991751389797708962867)/(571087861359961047024384)*a^(22) - (1873559275117964457517)/(571087861359961047024384)*a^(20) - (11610445793031387516463)/(571087861359961047024384)*a^(18) - (8565253277718647004335)/(51917078305451004274944)*a^(16) + (18462639713852148218335)/(24829907015650480305408)*a^(14) + (34691316140678501544587)/(81583980194280149574912)*a^(12) + (81073194087772235146549)/(285543930679980523512192)*a^(10) - (11635209615422433029959327)/(571087861359961047024384)*a^(8) + (3750196896949057052078059)/(71385982669995130878048)*a^(6) - (9058684583606081689682773)/(142771965339990261756096)*a^(4) + (72912798661381802842919)/(1982943963055420302168)*a^(2) + (70677353903864583773)/(14865885603914021424) , (6090040623165973835)/(761450481813281396032512)*a^(26) - (2329139428138191997)/(10575701136295574944896)*a^(24) + (1697352374214424857557)/(761450481813281396032512)*a^(22) - (3170633443228645559695)/(761450481813281396032512)*a^(20) - (19773844724666567580757)/(761450481813281396032512)*a^(18) - (14833607312178785662577)/(69222771073934672366592)*a^(16) + (31149772348784644322785)/(33106542687533973740544)*a^(14) + (58394361782962129784705)/(108778640259040199433216)*a^(12) + (201449542196242060401739)/(380725240906640698016256)*a^(10) - (19721949713863188986001433)/(761450481813281396032512)*a^(8) + (6376945828703159595489361)/(95181310226660174504064)*a^(6) - (15902574400830487853533075)/(190362620453320349008128)*a^(4) + (405490149591100238235383)/(7931775852221681208672)*a^(2) + (12829693575529240187)/(19821180805218695232) , (1304023813163)/(1332273109801632768)*a^(26) - (1542455434381)/(55511379575068032)*a^(24) + (392564494983125)/(1332273109801632768)*a^(22) - (949174940167471)/(1332273109801632768)*a^(20) - (4033134997618597)/(1332273109801632768)*a^(18) - (2811255185231009)/(121115737254693888)*a^(16) + (189122893423679255)/(1332273109801632768)*a^(14) - (290453041582399)/(190324729971661824)*a^(12) - (68241145892442701)/(666136554900816384)*a^(10) - (4576910387666447641)/(1332273109801632768)*a^(8) + (1807729442689779529)/(166534138725204096)*a^(6) - (4518730143760780627)/(333068277450408192)*a^(4) + (4924358749419709)/(513994255324704)*a^(2) + (33662768146427)/(34680162166848) , (10267358183329459)/(10526965186358728977408)*a^(26) - (11363558882901553)/(438623549431613707392)*a^(24) + (2588160350297963533)/(10526965186358728977408)*a^(22) - (2623253819968721783)/(10526965186358728977408)*a^(20) - (37691076136358326109)/(10526965186358728977408)*a^(18) - (28322707846292177785)/(956996835123520816128)*a^(16) + (40729722048747470873)/(457694138537336042496)*a^(14) + (1858690478422785903439)/(10526965186358728977408)*a^(12) + (951527864409322380731)/(5263482593179364488704)*a^(10) - (37636487156814243161)/(11841355665195420672)*a^(8) + (6447870398196812945345)/(1315870648294841122176)*a^(6) - (7623631864083024258107)/(2631741296589682244352)*a^(4) + (157625349770865767303)/(109655887357903426848)*a^(2) + (345193878074547253)/(1918178787601809216) , (7191534422149373)/(4028838528112599979008)*a^(26) - (1477110879112235387)/(27194660064760049858304)*a^(24) + (69357679539656183981)/(108778640259040199433216)*a^(22) - (251900496620159587843)/(108778640259040199433216)*a^(20) - (388950721972104364477)/(108778640259040199433216)*a^(18) - (305497928581737489197)/(9888967296276381766656)*a^(16) + (1675699216074031307449)/(4729506098219139105792)*a^(14) - (6453066247929702489811)/(15539805751291457061888)*a^(12) - (16675816923931184832107)/(54389320129520099716608)*a^(10) - (697770714534919528639777)/(108778640259040199433216)*a^(8) + (415085066359638364386271)/(13597330032380024929152)*a^(6) - (1567129360447541565712171)/(27194660064760049858304)*a^(4) + (200983172112204872932111)/(3399332508095006232288)*a^(2) - (561477272531117682347)/(19821180805218695232) , (1350093796420055)/(5464955611100105713152)*a^(27) - (69130519673907451)/(69222771073934672366592)*a^(26) - (2934605322979255)/(455412967591675476096)*a^(25) + (1842681307367039)/(67600362376889328483)*a^(24) + (324243907929409541)/(5464955611100105713152)*a^(23) - (6276768439938188959)/(23074257024644890788864)*a^(22) - (207741899316818779)/(5464955611100105713152)*a^(21) + (10657629976416997109)/(23074257024644890788864)*a^(20) - (4930352920647568669)/(5464955611100105713152)*a^(19) + (75527286108349891183)/(23074257024644890788864)*a^(18) - (42813004415142335503)/(5464955611100105713152)*a^(17) + (640170280122695789065)/(23074257024644890788864)*a^(16) + (4275465363445677505)/(237606765700004596224)*a^(15) - (110363042156555257763)/(1003228566288908295168)*a^(14) + (768195463237114613)/(15932815192711678464)*a^(13) - (288819442834963680091)/(3296322432092127255552)*a^(12) + (181968914131347437497)/(2732477805550052856576)*a^(11) - (1345291289257690016021)/(11537128512322445394432)*a^(10) - (3863063382846941586025)/(5464955611100105713152)*a^(9) + (73785011095825855647851)/(23074257024644890788864)*a^(8) + (635449844022460353499)/(683119451387513214144)*a^(7) - (21871477755372625517735)/(2884282128080611348608)*a^(6) - (766131718594729790227)/(1366238902775026428288)*a^(5) + (52365267582380901943577)/(5768564256161222697216)*a^(4) - (40874501628474025055)/(56926620948959434512)*a^(3) - (12266433739426013176249)/(2163211596060458511456)*a^(2) + (10115707624279727291)/(6970606646811359328)*a + (563698540918315213)/(1801925527747154112) , (600040228206165781)/(380725240906640698016256)*a^(26) - (8150937266638801231)/(190362620453320349008128)*a^(24) + (1997444846065557365)/(4700311616131366642176)*a^(22) - (9916568535603134275)/(14100934848394099926528)*a^(20) - (634909458343028503487)/(126908413635546899338752)*a^(18) - (512797583770660987405)/(11537128512322445394432)*a^(16) + (100210154016683903891)/(613084123843221735936)*a^(14) + (245963176602231268861)/(2014419264056299989504)*a^(12) + (1018731467433797940797)/(3525233712098524981632)*a^(10) - (22370690515919292267233)/(4700311616131366642176)*a^(8) + (10233681504594917819543)/(881308428024631245408)*a^(6) - (19984066129015924856779)/(1175077904032841660544)*a^(4) + (19609974492269549540531)/(1487207972291565226626)*a^(2) - (18085869559507580725)/(9910590402609347616) , (410739367813034597)/(253816827271093798677504)*a^(27) + (1142650705481732213)/(285543930679980523512192)*a^(26) - (16849057434043068319)/(380725240906640698016256)*a^(25) - (14047665983060448665)/(126908413635546899338752)*a^(24) + (339142221122641616675)/(761450481813281396032512)*a^(23) + (1284616586695748082167)/(1142175722719922094048768)*a^(22) - (630630500527607171923)/(761450481813281396032512)*a^(21) - (602106387179771882455)/(285543930679980523512192)*a^(20) - (3648781258034454722371)/(761450481813281396032512)*a^(19) - (15748122566824159119271)/(1142175722719922094048768)*a^(18) - (3068383206343136835773)/(69222771073934672366592)*a^(17) - (2722548298647288165995)/(25958539152725502137472)*a^(16) + (5681018348919642018007)/(33106542687533973740544)*a^(15) + (24855691392900187628779)/(49659814031300960610816)*a^(14) + (5254085927786938661501)/(108778640259040199433216)*a^(13) + (14160135517167728821385)/(40791990097140074787456)*a^(12) + (6685253467242013696381)/(23795327556665043626016)*a^(11) - (128642600285349502298581)/(1142175722719922094048768)*a^(10) - (3415085415960213563070871)/(761450481813281396032512)*a^(9) - (15885958062777254066302231)/(1142175722719922094048768)*a^(8) + (163881670017981707106383)/(11897663778332521813008)*a^(7) + (9722096801999086071783281)/(285543930679980523512192)*a^(6) - (4289854145548460228991709)/(190362620453320349008128)*a^(5) - (9255466379650767646343101)/(285543930679980523512192)*a^(4) + (135639038287152005564807)/(11897663778332521813008)*a^(3) + (337848605486691603992269)/(23795327556665043626016)*a^(2) + (4270482358022584373965)/(971237859455716066368)*a + (68902244852071823537)/(29731771207828042848) , (2212103161618258567)/(2284351445439844188097536)*a^(27) + (320837024183752649)/(761450481813281396032512)*a^(26) - (3303029448461162405)/(126908413635546899338752)*a^(25) - (4434304873651805287)/(380725240906640698016256)*a^(24) + (576803201330502608479)/(2284351445439844188097536)*a^(23) + (90272361288998411737)/(761450481813281396032512)*a^(22) - (758284303649828637419)/(2284351445439844188097536)*a^(21) - (173951952790376528261)/(761450481813281396032512)*a^(20) - (7793990712070450832927)/(2284351445439844188097536)*a^(19) - (1056304149848645419817)/(761450481813281396032512)*a^(18) - (5859948234048187552741)/(207668313221804017099776)*a^(17) - (757243454658924461467)/(69222771073934672366592)*a^(16) + (9573801140542305479651)/(99319628062601921221632)*a^(15) + (1678996063542376917269)/(33106542687533973740544)*a^(14) + (43493704418058006963493)/(326335920777120598299648)*a^(13) + (2311909807494998551627)/(108778640259040199433216)*a^(12) + (85049069148829304610793)/(571087861359961047024384)*a^(11) + (5349834793146567046237)/(190362620453320349008128)*a^(10) - (6898105094570783673547379)/(2284351445439844188097536)*a^(9) - (979338498305937141339941)/(761450481813281396032512)*a^(8) + (890627517038920480278643)/(142771965339990261756096)*a^(7) + (172946815790226430506139)/(47590655113330087252032)*a^(6) - (3400496253478353553970321)/(571087861359961047024384)*a^(5) - (1014610912929054767495063)/(190362620453320349008128)*a^(4) + (1290049459817804263001)/(743603986145782613313)*a^(3) + (23086076424046734256531)/(5948831889166260906504)*a^(2) + (3687839601039934656721)/(2913713578367148199104)*a + (120298365776565389)/(6607060268406231744) , (11009784809638010219)/(761450481813281396032512)*a^(27) - 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