Group GAP4(112,19)

x^112+x^111-111*x^110-111*x^109+5994*x^108+5993*x^107-209828*x^106-209721*x^\
105+5353636*x^104+5348071*x^103-106126565*x^102-105939104*x^101+1701488622*x\
^100+1696890395*x^99-22677598680*x^98-22590052484*x^97+256312104511*x^96+254\
965398900*x^95-2493774188540*x^94-2476570958500*x^93+21130712727639*x^92+209\
44560248899*x^91-157379295978645*x^90-155647334935105*x^89+1037977185307140*\
x^88+1023960469232401*x^87-6099158500176854*x^86-5999578029540705*x^85+32089\
381186449735*x^84+31463742599761929*x^83-151793618740735297*x^82-14829659505\
7945729*x^81+647782908087920626*x^80+630307260219313315*x^79-250100520508672\
6264*x^78-2422611201503111092*x^77+8756187576700714754*x^76+8439456330813935\
947*x^75-27851437968918607525*x^74-26695751750933662585*x^73+806051138242235\
97814*x^72+76788402365000861395*x^71-212501355510560486744*x^70-201072449593\
063090750*x^69+510754238397624013270*x^68+479681459673882050296*x^67-1119841\
120051173682000*x^66-1043059785149671737721*x^65+2240381535798903959150*x^64\
+2067825414491569605640*x^63-4090020692120405153344*x^62-3737185385643979352\
128*x^61+6812044921281211571644*x^60+6155560702391633452484*x^59-10346285125\
311741802636*x^58-9235036492184185143356*x^57+14320208677156908189696*x^56+1\
2609642066636248332572*x^55-18045582753391858877064*x^54-1565281130711667991\
3220*x^53+20679551277730323783676*x^52+17640991073143526050532*x^51-21519948\
991464960601108*x^50-18021368711550717158140*x^49+20301880457807887163386*x^\
48+16655188777755357994094*x^47-17328754560664235909710*x^46-138941096879434\
17881438*x^45+13351872823357794550860*x^44+10435188270063117870414*x^43-9262\
385869820369356924*x^42-7034896988125181062790*x^41+5767807102492737224608*x\
^40+4242411795768173421450*x^39-3213123779630608576474*x^38-2279608568963049\
851751*x^37+1595113587287681354565*x^36+1086546300140379132082*x^35-70256937\
8518864828580*x^34-457023114879761283994*x^33+273172321718491048903*x^32+168\
637359092073535111*x^31-93225301537146941449*x^30-54214430199772659250*x^29+\
27739782970616349059*x^28+15064339643762155600*x^27-7141852740438937171*x^26\
-3584094948333740196*x^25+1576750759058209701*x^24+722025950034712740*x^23-2\
95367916702956933*x^22-121511912847504480*x^21+46357244337353767*x^20+168029\
37582732124*x^19-6002794965302915*x^18-1869781244178188*x^17+629219603649069\
*x^16+162944166919044*x^15-52112683103813*x^14-10716528274299*x^13+330304169\
1340*x^12+503989059004*x^11-153306704483*x^10-15531376154*x^9+4883027847*x^8\
+263921985*x^7-96216260*x^6-1366771*x^5+978712*x^4-12768*x^3-3808*x^2+112*x+\
1

1

x^112-x^111+x^107-x^106+x^102-x^101+x^97-x^96+x^92-x^91+x^87-x^86+x^83-x^81+\
x^78-x^76+x^73-x^71+x^68-x^66+x^63-x^61+x^58-x^56+x^54-x^51+x^49-x^46+x^44-x\
^41+x^39-x^36+x^34-x^31+x^29-x^26+x^25-x^21+x^20-x^16+x^15-x^11+x^10-x^6+x^5\
-x+1

1