Group GAP4(126,16)

x^126-126*x^124+7749*x^122-310002*x^120+9071370*x^118-207007164*x^116+383538\
2733*x^114-59312605482*x^112+781116855246*x^110-8894198570180*x^108+88604619\
549138*x^106-x^105-779580565677396*x^104+105*x^103+6104434955801364*x^102-53\
55*x^101-42809999261174712*x^100+176750*x^99+270292724927059725*x^98-4244625\
*x^97-1543184770664642490*x^96+79051896*x^95+7996502902534965630*x^94-118844\
0120*x^93-37725541486217306820*x^92+14822585520*x^91+162468227017804162910*x\
^90-156439401300*x^89-640123216139995742700*x^88+1418094202525*x^87+23116902\
56022550663260*x^86-11168611392939*x^85-7663698762596301745320*x^84+77121745\
982190*x^83+23352844306303066332330*x^82-470332081679915*x^81-65474711643083\
565461940*x^80+2548287532847700*x^79+169036020255019662467100*x^78-123253907\
20100100*x^77-402071420852137858525704*x^76+53428286291870952*x^75+881464268\
791225305229428*x^74-208235245028008275*x^73-1781395428361466179891272*x^72+\
731607251248136025*x^71+3318692940883314545045256*x^70-2321895299299639875*x\
^69-5698288981324710008022960*x^68+6667278301293702750*x^67+9014376596845617\
637691877*x^66-17342767440188678565*x^65-13131299015438947254905994*x^64+408\
99043396363323601*x^63+17601528467503269724661226*x^62-87487219882910811663*\
x^61-21690772454903019256653228*x^60+169779016315722997890*x^59+245477412053\
56997496340290*x^58-298859976251236708931*x^57-25480324152248111058995604*x^\
56+476980522096974216090*x^55+24222036539791414216576068*x^54-68969432844596\
9913066*x^53-21051766953198611444834712*x^52+902562948336734962508*x^51+1669\
5360633936219363547146*x^50-1067502559489394431575*x^49-12055300192497417459\
678900*x^48+1139186034447148772910*x^47+7906034079730864473556860*x^46-10946\
31202882524426602*x^45-4695980070313598123461320*x^44+944799381756009008460*\
x^43+2518365729317836635370979*x^42-730439933039573771700*x^41-1215081475451\
194924659198*x^40+504175711502876246050*x^39+525367821980006674740981*x^38-3\
09522951630484581486*x^37-202652169466087622675198*x^36+16827941759317138998\
0*x^35+69386340632410435946445*x^34-80616952281418821569*x^33-20967270183023\
029191018*x^32+33836051336879082522*x^31+5555430561313791917836*x^30-1235959\
6217756710230*x^29-1281003071386952159976*x^28+3898988487321988116*x^27+2548\
52189991699133176*x^26-1052728260163125966*x^25-43308215292661768176*x^24+24\
0716249485353495*x^23+6212613004482996909*x^22-46033199724083385*x^21-741852\
470319571422*x^20+7252290716891850*x^19+72506156968680505*x^18-9241914867157\
35*x^17-5681660354843634*x^16+93130268214480*x^15+347856702261588*x^14-72119\
35331496*x^13-16097082229592*x^12+413657350848*x^11+538738484361*x^10-167371\
81615*x^9-12264116634*x^8+446949261*x^7+173222105*x^6-7156863*x^5-1296246*x^\
4+58646*x^3+3528*x^2-168*x+1

1

x^126-x^125+3*x^124-4*x^123+9*x^122-14*x^121+28*x^120-47*x^119+89*x^118-155*\
x^117+286*x^116-507*x^115+924*x^114-1652*x^113+2993*x^112-5373*x^111+9707*x^\
110-17460*x^109+31501*x^108-56714*x^107+102256*x^106-184183*x^105+331981*x^1\
04-598091*x^103+1077870*x^102-1942071*x^101+3499720*x^100-6305992*x^99+11363\
361*x^98-20475625*x^97+36896355*x^96-66484244*x^95+119801329*x^94-215873462*\
x^93+388991876*x^92-700937471*x^91+1263047761*x^90-2275930827*x^89+410108887\
8*x^88-7389902771*x^87+13316149700*x^86-23994866364*x^85+43237262993*x^84+21\
357433328*x^83+41122226294*x^82+44829903355*x^81+58771982561*x^80+7201005044\
3*x^79+90363818034*x^78+112428265413*x^77+140309421098*x^76+174910927762*x^7\
5+218136179847*x^74+271995096775*x^73+339188190681*x^72+422938182716*x^71+52\
7433295421*x^70+657631260692*x^69+820173512866*x^68+1022522303939*x^67+12754\
55982485*x^66+1589762138259*x^65+1983672130650*x^64+2471308128353*x^63+30857\
98271206*x^62+3840490116150*x^61+4802414554615*x^60+5964363948891*x^59+74809\
55276489*x^58+9250187175908*x^57+11676087325961*x^56+14305242302344*x^55+182\
97119525486*x^54+21989452405163*x^53+28910028948153*x^52+33365995387659*x^51\
+46443514913810*x^50+49198504809661*x^49+77054520405618*x^48+67786004127514*\
x^47+135521541493383*x^46+77104987167263*x^45+261724099947017*x^44+280074158\
80892*x^43+572545771180405*x^42-254806839471604*x^41+113399711795356*x^40-50\
467619558159*x^39+22460203677267*x^38-9995730998229*x^37+4448518794604*x^36-\
1979777113795*x^35+881083704774*x^34-392119137760*x^33+174509433513*x^32-776\
64004259*x^31+34563733525*x^30-15382308530*x^29+6845771321*x^28-3046654856*x\
^27+1355888968*x^26-603427359*x^25+268550439*x^24-119516189*x^23+53189708*x^\
22-23671647*x^21+10534874*x^20-4688460*x^19+2086561*x^18-928607*x^17+413269*\
x^16-183922*x^15+81853*x^14-36428*x^13+16212*x^12-7215*x^11+3211*x^10-1429*x\
^9+636*x^8-283*x^7+126*x^6-56*x^5+25*x^4-11*x^3+5*x^2-2*x+1

18641256022302832680524309