Group GAP4(128,486)
Name: C4 x (((C4 x C2) : C2) : C2)
Maximal quotients:GAP4(64,58) GAP4(64,90) GAP4(64,91)
Real polynomial:
x^128-320*x^126+49408*x^124-4904576*x^122+351907496*x^120-19454180320*x^118+\
862544250240*x^116-31525212402240*x^114+968899843188660*x^112-25418839774104\
800*x^110+575899367020449024*x^108-11372857538499674560*x^106+19722947588652\
2191312*x^104-3022120607456805555264*x^102+41123247584311047509824*x^100-499\
031764548858626503168*x^98+5419552575034756384098170*x^96-528291233469747634\
94286944*x^94+463370632922170931801317248*x^92-3664540877623780307386571968*\
x^90+26174688107404752891160819000*x^88-169087673236210774875208496160*x^86+\
988976198126905286454092428480*x^84-5241638840412849096145545693760*x^82+251\
89388318161620653782988181360*x^80-109800514001317084885160556361088*x^78+43\
4214855977749085981230559658880*x^76-1557794432527470481437392253394944*x^74\
+5069082271898771363454774874200248*x^72-14955100680213542505897133071327328\
*x^70+39979408556385730832990596597644288*x^68-96768823605157834803039737794\
739520*x^66+211869959119040379198592659110354819*x^64-4191183182531630392114\
85135821867488*x^62+748081270067399887212235753158258048*x^60-12028925273577\
56339492155744544497088*x^58+1739389848331321023340528703687179640*x^56-2257\
278382409708542900683786208396704*x^54+2623077392706751385530026024243406528\
*x^52-2722582065345016572149146643745302848*x^50+251697403130089578199846075\
7830380144*x^48-2066123401775767582719411634842035840*x^46+15007955423504430\
66996337078267641472*x^44-961002566781275151500528705906217984*x^42+54018211\
7961598587057949759108409464*x^40-265306069105633116221134038461318624*x^38+\
113266466050866208510025128937080320*x^36-4179279906620958115851452579267795\
2*x^34+13241711368151393713513974556622714*x^32-3576542317038270391072093719\
393824*x^30+816672854045411342641462734758272*x^28-1561446562208711790883822\
91626560*x^26+24717548126633916024112694992336*x^24-319614050196532147100680\
9652672*x^22+332056859516558888303308245312*x^20-271467449229342394594303905\
28*x^18+1699568197838508205212796980*x^16-78532793814034131600512544*x^14+25\
41722739998091094578048*x^12-53338806384564262207808*x^10+647796851082722071\
016*x^8-3971647775306098720*x^6+9891646520513728*x^4-4752195125056*x^2+44609\
6641
Common denominator of the automorphisms:
6931538134070227963716406582851900279101861702952463687706892056933611030174\
6712406829269080978087491947800167574439542886662764238726032918667938327702\
9290375116779872436834829306292562859377944038530479601911030495690391732858\
8411337157073745404779399483994512453418680110729077208184866909518082578197\
3285221839284593754499937765617900209986430239018507247381528239596748015037\
1367412575648225555463300331363464977724719104000
Complex polynomial:
x^128-16*x^124+296*x^120-7648*x^116+163496*x^112+1330048*x^108+617248*x^104-\
275459200*x^100+290034224*x^96-27200949248*x^92-81942962048*x^88+15073226823\
68*x^84+33608486035712*x^80-100483043290112*x^76+229958851397632*x^72-487264\
090249216*x^68+1022800437105920*x^64-974528180498432*x^60+919835405590528*x^\
56-803864346320896*x^52+537735776571392*x^48+48234325835776*x^44-52443495710\
72*x^40-3481721503744*x^36+74248761344*x^32-141035110400*x^28+632061952*x^24\
+2723938304*x^20+669679616*x^16-62652416*x^12+4849664*x^8-524288*x^4+65536
Common denominator of the automorphisms:
314357769364168004853486985923891952607035392
Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
Copyleft © 2002-2008 the PARI group.