gap> HELP("!");
Help: Showing `Tutorial: Help'
gap> x:=X(GF(3),"x");
x
gap> Factors(x^9-x);
[ x, Z(3)^0+x, -Z(3)^0+x, Z(3)^0+x^2, -Z(3)^0+x+x^2, -Z(3)^0-x+x^2 ]
gap> factors:=Factors(x^9-x);;
gap> List(factors,DegreeOfUnivariateLaurentPolynomial);
[ 1, 1, 1, 2, 2, 2 ]
gap> polyring:=PolynomialRing(GF(9));
PolynomialRing(..., [ x ])
gap> factors:=Factors(polyring,x^9-x);
[ x, Z(3)^0+x, -Z(3)^0+x, Z(3^2)+x, Z(3^2)^2+x, Z(3^2)^3+x, Z(3^2)^5+x, Z(3^2)^6+x, Z(3^2)^7+x ]
gap> Z(3^2)^4;
Z(3)
gap> Z(3^2)^8;
Z(3)^0
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
gap> y:=(GF(5),"y");
Permutation: <expr> must be a positive integer (not a list (string))
gap> y:=X(GF(5),"y");
y
gap> factors:=Factors(x^125-x);
[ x, Z(3)^0+x, -Z(3)^0+x, Z(3)^0+x^2, Z(3)^0+x-x^3+x^4-x^5-x^6+x^7-x^8+x^9+x^10-x^11+x^12+x^13-x^14+x^15-x^16+x^17+x^
18-x^19+x^20+x^21-x^22+x^23-x^24-x^25+x^26-x^27+x^29+x^30, Z(3)^0+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^
12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30,
Z(3)^0-x+x^3+x^4+x^5-x^6-x^7-x^8-x^9+x^10+x^11+x^12-x^13-x^14-x^15-x^16-x^17+x^18+x^19+x^20-x^21-x^22-x^23-x^24+x^
25+x^26+x^27-x^29+x^30, Z(3)^0-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10-x^11+x^12-x^13+x^14-x^15+x^16-x^17+x^18-x^
19+x^20-x^21+x^22-x^23+x^24-x^25+x^26-x^27+x^28-x^29+x^30 ]
gap> factors:=Factors(y^125-y);
[ y, Z(5)^0+y, Z(5)+y, -Z(5)^0+y, Z(5)^3+y, Z(5)^0+y+y^3, -Z(5)^0+y+y^3, Z(5)^0+Z(5)*y+y^3, -Z(5)^0+Z(5)*y+y^3,
Z(5)-y+y^3, Z(5)^3-y+y^3, Z(5)+Z(5)^3*y+y^3, Z(5)^3+Z(5)^3*y+y^3, Z(5)^0+y^2+y^3, Z(5)+y^2+y^3, -Z(5)^0+y+y^2+y^3,
Z(5)^3+y+y^2+y^3, Z(5)^0-y+y^2+y^3, Z(5)^3-y+y^2+y^3, Z(5)^0+Z(5)^3*y+y^2+y^3, -Z(5)^0+Z(5)^3*y+y^2+y^3,
Z(5)^0+Z(5)*y^2+y^3, Z(5)^3+Z(5)*y^2+y^3, -Z(5)^0+y+Z(5)*y^2+y^3, Z(5)^3+y+Z(5)*y^2+y^3, Z(5)+Z(5)*y+Z(5)*y^2+y^3,
Z(5)^3+Z(5)*y+Z(5)*y^2+y^3, Z(5)-y+Z(5)*y^2+y^3, -Z(5)^0-y+Z(5)*y^2+y^3, -Z(5)^0-y^2+y^3, Z(5)^3-y^2+y^3,
Z(5)^0+y-y^2+y^3, Z(5)+y-y^2+y^3, Z(5)-y-y^2+y^3, -Z(5)^0-y-y^2+y^3, Z(5)^0+Z(5)^3*y-y^2+y^3,
-Z(5)^0+Z(5)^3*y-y^2+y^3, Z(5)+Z(5)^3*y^2+y^3, -Z(5)^0+Z(5)^3*y^2+y^3, Z(5)^0+y+Z(5)^3*y^2+y^3,
Z(5)+y+Z(5)^3*y^2+y^3, Z(5)+Z(5)*y+Z(5)^3*y^2+y^3, Z(5)^3+Z(5)*y+Z(5)^3*y^2+y^3, Z(5)^0-y+Z(5)^3*y^2+y^3,
Z(5)^3-y+Z(5)^3*y^2+y^3 ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3 ]
gap> polyring:=PolynomialRing(GF(125));
PolynomialRing(..., [ y ])
gap> factors:=Factors(polyring,x^125-x);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `Factors' on 2 arguments called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> factors:=Factors(polyring,y^125-y);
[ y, Z(5)^0+y, Z(5)+y, -Z(5)^0+y, Z(5)^3+y, Z(5^3)+y, Z(5^3)^2+y, Z(5^3)^3+y, Z(5^3)^4+y, Z(5^3)^5+y, Z(5^3)^6+y,
Z(5^3)^7+y, Z(5^3)^8+y, Z(5^3)^9+y, Z(5^3)^10+y, Z(5^3)^11+y, Z(5^3)^12+y, Z(5^3)^13+y, Z(5^3)^14+y, Z(5^3)^15+y,
Z(5^3)^16+y, Z(5^3)^17+y, Z(5^3)^18+y, Z(5^3)^19+y, Z(5^3)^20+y, Z(5^3)^21+y, Z(5^3)^22+y, Z(5^3)^23+y,
Z(5^3)^24+y, Z(5^3)^25+y, Z(5^3)^26+y, Z(5^3)^27+y, Z(5^3)^28+y, Z(5^3)^29+y, Z(5^3)^30+y, Z(5^3)^32+y,
Z(5^3)^33+y, Z(5^3)^34+y, Z(5^3)^35+y, Z(5^3)^36+y, Z(5^3)^37+y, Z(5^3)^38+y, Z(5^3)^39+y, Z(5^3)^40+y,
Z(5^3)^41+y, Z(5^3)^42+y, Z(5^3)^43+y, Z(5^3)^44+y, Z(5^3)^45+y, Z(5^3)^46+y, Z(5^3)^47+y, Z(5^3)^48+y,
Z(5^3)^49+y, Z(5^3)^50+y, Z(5^3)^51+y, Z(5^3)^52+y, Z(5^3)^53+y, Z(5^3)^54+y, Z(5^3)^55+y, Z(5^3)^56+y,
Z(5^3)^57+y, Z(5^3)^58+y, Z(5^3)^59+y, Z(5^3)^60+y, Z(5^3)^61+y, Z(5^3)^63+y, Z(5^3)^64+y, Z(5^3)^65+y,
Z(5^3)^66+y, Z(5^3)^67+y, Z(5^3)^68+y, Z(5^3)^69+y, Z(5^3)^70+y, Z(5^3)^71+y, Z(5^3)^72+y, Z(5^3)^73+y,
Z(5^3)^74+y, Z(5^3)^75+y, Z(5^3)^76+y, Z(5^3)^77+y, Z(5^3)^78+y, Z(5^3)^79+y, Z(5^3)^80+y, Z(5^3)^81+y,
Z(5^3)^82+y, Z(5^3)^83+y, Z(5^3)^84+y, Z(5^3)^85+y, Z(5^3)^86+y, Z(5^3)^87+y, Z(5^3)^88+y, Z(5^3)^89+y,
Z(5^3)^90+y, Z(5^3)^91+y, Z(5^3)^92+y, Z(5^3)^94+y, Z(5^3)^95+y, Z(5^3)^96+y, Z(5^3)^97+y, Z(5^3)^98+y,
Z(5^3)^99+y, Z(5^3)^100+y, Z(5^3)^101+y, Z(5^3)^102+y, Z(5^3)^103+y, Z(5^3)^104+y, Z(5^3)^105+y, Z(5^3)^106+y,
Z(5^3)^107+y, Z(5^3)^108+y, Z(5^3)^109+y, Z(5^3)^110+y, Z(5^3)^111+y, Z(5^3)^112+y, Z(5^3)^113+y, Z(5^3)^114+y,
Z(5^3)^115+y, Z(5^3)^116+y, Z(5^3)^117+y, Z(5^3)^118+y, Z(5^3)^119+y, Z(5^3)^120+y, Z(5^3)^121+y, Z(5^3)^122+y,
Z(5^3)^123+y ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
gap> z:=X(GF(7),"z");
z
gap> factors:=Factors(z^49-z);
[ z, Z(7)^0+z, Z(7)+z, Z(7)^2+z, -Z(7)^0+z, Z(7)^4+z, Z(7)^5+z, Z(7)^0+z^2, Z(7)^2+z^2, Z(7)^4+z^2, Z(7)+z+z^2,
-Z(7)^0+z+z^2, Z(7)^4+z+z^2, Z(7)^0+Z(7)*z+z^2, -Z(7)^0+Z(7)*z+z^2, Z(7)^5+Z(7)*z+z^2, Z(7)+Z(7)^2*z+z^2,
Z(7)^2+Z(7)^2*z+z^2, Z(7)^5+Z(7)^2*z+z^2, Z(7)-z+z^2, -Z(7)^0-z+z^2, Z(7)^4-z+z^2, Z(7)^0+Z(7)^4*z+z^2,
-Z(7)^0+Z(7)^4*z+z^2, Z(7)^5+Z(7)^4*z+z^2, Z(7)+Z(7)^5*z+z^2, Z(7)^2+Z(7)^5*z+z^2, Z(7)^5+Z(7)^5*z+z^2 ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
gap> polyring:=PolynomialRing(GF(49));
PolynomialRing(..., [ z ])
gap> factors:=Factors(polyring,z^49-z);
[ z, Z(7)^0+z, Z(7)+z, Z(7)^2+z, -Z(7)^0+z, Z(7)^4+z, Z(7)^5+z, Z(7^2)+z, Z(7^2)^2+z, Z(7^2)^3+z, Z(7^2)^4+z,
Z(7^2)^5+z, Z(7^2)^6+z, Z(7^2)^7+z, Z(7^2)^9+z, Z(7^2)^10+z, Z(7^2)^11+z, Z(7^2)^12+z, Z(7^2)^13+z, Z(7^2)^14+z,
Z(7^2)^15+z, Z(7^2)^17+z, Z(7^2)^18+z, Z(7^2)^19+z, Z(7^2)^20+z, Z(7^2)^21+z, Z(7^2)^22+z, Z(7^2)^23+z,
Z(7^2)^25+z, Z(7^2)^26+z, Z(7^2)^27+z, Z(7^2)^28+z, Z(7^2)^29+z, Z(7^2)^30+z, Z(7^2)^31+z, Z(7^2)^33+z,
Z(7^2)^34+z, Z(7^2)^35+z, Z(7^2)^36+z, Z(7^2)^37+z, Z(7^2)^38+z, Z(7^2)^39+z, Z(7^2)^41+z, Z(7^2)^42+z,
Z(7^2)^43+z, Z(7^2)^44+z, Z(7^2)^45+z, Z(7^2)^46+z, Z(7^2)^47+z ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
gap> factors:=Factors(z^(7^4)-z);
[ z, Z(7)^0+z, Z(7)+z, Z(7)^2+z, -Z(7)^0+z, Z(7)^4+z, Z(7)^5+z, Z(7)^0+z^2, Z(7)^2+z^2, Z(7)^4+z^2, Z(7)+z+z^2,
-Z(7)^0+z+z^2, Z(7)^4+z+z^2, Z(7)^0+Z(7)*z+z^2, -Z(7)^0+Z(7)*z+z^2, Z(7)^5+Z(7)*z+z^2, Z(7)+Z(7)^2*z+z^2,
Z(7)^2+Z(7)^2*z+z^2, Z(7)^5+Z(7)^2*z+z^2, Z(7)-z+z^2, -Z(7)^0-z+z^2, Z(7)^4-z+z^2, Z(7)^0+Z(7)^4*z+z^2,
-Z(7)^0+Z(7)^4*z+z^2, Z(7)^5+Z(7)^4*z+z^2, Z(7)+Z(7)^5*z+z^2, Z(7)^2+Z(7)^5*z+z^2, Z(7)^5+Z(7)^5*z+z^2,
Z(7)^0+z+z^4, Z(7)^2+z+z^4, Z(7)^4+z+z^4, Z(7)+Z(7)^2*z+z^4, -Z(7)^0+Z(7)^2*z+z^4, Z(7)^5+Z(7)^2*z+z^4,
Z(7)^0-z+z^4, Z(7)^2-z+z^4, Z(7)^4-z+z^4, Z(7)+Z(7)^5*z+z^4, -Z(7)^0+Z(7)^5*z+z^4, Z(7)^5+Z(7)^5*z+z^4,
Z(7)+z^2+z^4, -Z(7)^0+z^2+z^4, Z(7)^0+z+z^2+z^4, Z(7)^2+z+z^2+z^4, Z(7)^5+Z(7)*z+z^2+z^4, Z(7)^0+Z(7)^2*z+z^2+z^4,
Z(7)^0-z+z^2+z^4, Z(7)^2-z+z^2+z^4, Z(7)^5+Z(7)^4*z+z^2+z^4, Z(7)^0+Z(7)^5*z+z^2+z^4, -Z(7)^0+Z(7)*z^2+z^4,
Z(7)^5+Z(7)*z^2+z^4, -Z(7)^0+z+Z(7)*z^2+z^4, Z(7)+Z(7)*z+Z(7)*z^2+z^4, Z(7)^4+Z(7)*z+Z(7)*z^2+z^4,
Z(7)^5+Z(7)*z+Z(7)*z^2+z^4, Z(7)^2+Z(7)^2*z+Z(7)*z^2+z^4, -Z(7)^0+Z(7)^2*z+Z(7)*z^2+z^4, -Z(7)^0-z+Z(7)*z^2+z^4,
Z(7)+Z(7)^4*z+Z(7)*z^2+z^4, Z(7)^4+Z(7)^4*z+Z(7)*z^2+z^4, Z(7)^5+Z(7)^4*z+Z(7)*z^2+z^4,
Z(7)^2+Z(7)^5*z+Z(7)*z^2+z^4, -Z(7)^0+Z(7)^5*z+Z(7)*z^2+z^4, Z(7)+Z(7)^2*z^2+z^4, Z(7)^5+Z(7)^2*z^2+z^4,
Z(7)^0+z+Z(7)^2*z^2+z^4, Z(7)^4+z+Z(7)^2*z^2+z^4, -Z(7)^0+Z(7)*z+Z(7)^2*z^2+z^4, Z(7)^4+Z(7)^2*z+Z(7)^2*z^2+z^4,
Z(7)^0-z+Z(7)^2*z^2+z^4, Z(7)^4-z+Z(7)^2*z^2+z^4, -Z(7)^0+Z(7)^4*z+Z(7)^2*z^2+z^4, Z(7)^4+Z(7)^5*z+Z(7)^2*z^2+z^4,
Z(7)-z^2+z^4, -Z(7)^0-z^2+z^4, Z(7)+z-z^2+z^4, Z(7)^2+Z(7)*z-z^2+z^4, -Z(7)^0+Z(7)*z-z^2+z^4,
Z(7)^5+Z(7)*z-z^2+z^4, Z(7)^0+Z(7)^2*z-z^2+z^4, Z(7)+Z(7)^2*z-z^2+z^4, Z(7)-z-z^2+z^4, Z(7)^2+Z(7)^4*z-z^2+z^4,
-Z(7)^0+Z(7)^4*z-z^2+z^4, Z(7)^5+Z(7)^4*z-z^2+z^4, Z(7)^0+Z(7)^5*z-z^2+z^4, Z(7)+Z(7)^5*z-z^2+z^4,
-Z(7)^0+Z(7)^4*z^2+z^4, Z(7)^5+Z(7)^4*z^2+z^4, Z(7)^2+z+Z(7)^4*z^2+z^4, Z(7)^4+z+Z(7)^4*z^2+z^4,
Z(7)+Z(7)*z+Z(7)^4*z^2+z^4, Z(7)^2+Z(7)^2*z+Z(7)^4*z^2+z^4, Z(7)^2-z+Z(7)^4*z^2+z^4, Z(7)^4-z+Z(7)^4*z^2+z^4,
Z(7)+Z(7)^4*z+Z(7)^4*z^2+z^4, Z(7)^2+Z(7)^5*z+Z(7)^4*z^2+z^4, Z(7)+Z(7)^5*z^2+z^4, Z(7)^5+Z(7)^5*z^2+z^4,
Z(7)^5+z+Z(7)^5*z^2+z^4, Z(7)^0+Z(7)*z+Z(7)^5*z^2+z^4, Z(7)+Z(7)*z+Z(7)^5*z^2+z^4, -Z(7)^0+Z(7)*z+Z(7)^5*z^2+z^4,
Z(7)^4+Z(7)^2*z+Z(7)^5*z^2+z^4, Z(7)^5+Z(7)^2*z+Z(7)^5*z^2+z^4, Z(7)^5-z+Z(7)^5*z^2+z^4,
Z(7)^0+Z(7)^4*z+Z(7)^5*z^2+z^4, Z(7)+Z(7)^4*z+Z(7)^5*z^2+z^4, -Z(7)^0+Z(7)^4*z+Z(7)^5*z^2+z^4,
Z(7)^4+Z(7)^5*z+Z(7)^5*z^2+z^4, Z(7)^5+Z(7)^5*z+Z(7)^5*z^2+z^4, Z(7)^0+z^3+z^4, Z(7)+z^3+z^4, Z(7)+z+z^3+z^4,
Z(7)^0+Z(7)*z+z^3+z^4, -Z(7)^0+Z(7)^2*z+z^3+z^4, Z(7)-z+z^3+z^4, Z(7)^2-z+z^3+z^4, Z(7)^2+Z(7)^4*z+z^3+z^4,
-Z(7)^0+Z(7)^5*z+z^3+z^4, Z(7)^4+Z(7)^5*z+z^3+z^4, Z(7)^0+z^2+z^3+z^4, Z(7)+z^2+z^3+z^4, Z(7)^5+z^2+z^3+z^4,
Z(7)^0+z+z^2+z^3+z^4, Z(7)^2+z+z^2+z^3+z^4, -Z(7)^0+Z(7)*z+z^2+z^3+z^4, Z(7)^4+Z(7)*z+z^2+z^3+z^4,
Z(7)^4+Z(7)^2*z+z^2+z^3+z^4, Z(7)^0-z+z^2+z^3+z^4, Z(7)-z+z^2+z^3+z^4, -Z(7)^0-z+z^2+z^3+z^4,
Z(7)^0+Z(7)^4*z+z^2+z^3+z^4, Z(7)+Z(7)^5*z+z^2+z^3+z^4, Z(7)^2+Z(7)^5*z+z^2+z^3+z^4,
Z(7)^0+Z(7)*z+Z(7)*z^2+z^3+z^4, Z(7)^2+Z(7)*z+Z(7)*z^2+z^3+z^4, Z(7)^4+Z(7)*z+Z(7)*z^2+z^3+z^4,
Z(7)^0+Z(7)^2*z+Z(7)*z^2+z^3+z^4, Z(7)+Z(7)^2*z+Z(7)*z^2+z^3+z^4, Z(7)^4+Z(7)^2*z+Z(7)*z^2+z^3+z^4,
Z(7)^2-z+Z(7)*z^2+z^3+z^4, Z(7)^4-z+Z(7)*z^2+z^3+z^4, Z(7)^5-z+Z(7)*z^2+z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)*z^2+z^3+z^4,
-Z(7)^0+Z(7)^5*z+Z(7)*z^2+z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)*z^2+z^3+z^4, Z(7)^0+Z(7)^2*z^2+z^3+z^4,
Z(7)^4+Z(7)^2*z^2+z^3+z^4, Z(7)+z+Z(7)^2*z^2+z^3+z^4, Z(7)+Z(7)*z+Z(7)^2*z^2+z^3+z^4,
Z(7)^2+Z(7)*z+Z(7)^2*z^2+z^3+z^4, -Z(7)^0+Z(7)*z+Z(7)^2*z^2+z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^2*z^2+z^3+z^4,
Z(7)^5+Z(7)^2*z+Z(7)^2*z^2+z^3+z^4, -Z(7)^0-z+Z(7)^2*z^2+z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)^2*z^2+z^3+z^4,
Z(7)^4+Z(7)^4*z+Z(7)^2*z^2+z^3+z^4, Z(7)^5+Z(7)^4*z+Z(7)^2*z^2+z^3+z^4, Z(7)^2+Z(7)^5*z+Z(7)^2*z^2+z^3+z^4,
Z(7)^4+Z(7)^5*z+Z(7)^2*z^2+z^3+z^4, Z(7)^2-z^2+z^3+z^4, Z(7)^5-z^2+z^3+z^4, Z(7)^4+z-z^2+z^3+z^4,
Z(7)^0+Z(7)*z-z^2+z^3+z^4, -Z(7)^0+Z(7)^2*z-z^2+z^3+z^4, Z(7)^5+Z(7)^2*z-z^2+z^3+z^4, -Z(7)^0-z-z^2+z^3+z^4,
Z(7)^4-z-z^2+z^3+z^4, Z(7)^5-z-z^2+z^3+z^4, Z(7)+Z(7)^4*z-z^2+z^3+z^4, -Z(7)^0+Z(7)^4*z-z^2+z^3+z^4,
Z(7)+Z(7)^5*z-z^2+z^3+z^4, Z(7)^2+Z(7)^5*z-z^2+z^3+z^4, Z(7)^4+Z(7)^5*z-z^2+z^3+z^4, -Z(7)^0+Z(7)^4*z^2+z^3+z^4,
Z(7)^5+Z(7)^4*z^2+z^3+z^4, Z(7)^2+z+Z(7)^4*z^2+z^3+z^4, Z(7)^5+z+Z(7)^4*z^2+z^3+z^4,
Z(7)^4+Z(7)*z+Z(7)^4*z^2+z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^4*z^2+z^3+z^4, Z(7)^2+Z(7)^2*z+Z(7)^4*z^2+z^3+z^4,
Z(7)-z+Z(7)^4*z^2+z^3+z^4, Z(7)+Z(7)^4*z+Z(7)^4*z^2+z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^4*z^2+z^3+z^4,
Z(7)^4+Z(7)^5*z^2+z^3+z^4, Z(7)^0+z+Z(7)^5*z^2+z^3+z^4, Z(7)+Z(7)*z+Z(7)^5*z^2+z^3+z^4,
Z(7)+Z(7)^2*z+Z(7)^5*z^2+z^3+z^4, Z(7)^2-z+Z(7)^5*z^2+z^3+z^4, -Z(7)^0-z+Z(7)^5*z^2+z^3+z^4,
Z(7)^2+Z(7)^4*z+Z(7)^5*z^2+z^3+z^4, Z(7)^5+Z(7)^4*z+Z(7)^5*z^2+z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+z^3+z^4,
-Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+z^3+z^4, Z(7)^4+Z(7)*z^3+z^4, Z(7)^5+Z(7)*z^3+z^4, Z(7)^0+z+Z(7)*z^3+z^4,
Z(7)^5+z+Z(7)*z^3+z^4, Z(7)^0+Z(7)*z+Z(7)*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)*z^3+z^4, Z(7)^2+Z(7)^2*z+Z(7)*z^3+z^4,
Z(7)^5-z+Z(7)*z^3+z^4, Z(7)^4+Z(7)^4*z+Z(7)*z^3+z^4, Z(7)+Z(7)^5*z+Z(7)*z^3+z^4, Z(7)+z^2+Z(7)*z^3+z^4,
-Z(7)^0+z^2+Z(7)*z^3+z^4, Z(7)^5+z+z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)*z+z^2+Z(7)*z^3+z^4,
-Z(7)^0+Z(7)^2*z+z^2+Z(7)*z^3+z^4, Z(7)^0-z+z^2+Z(7)*z^3+z^4, -Z(7)^0-z+z^2+Z(7)*z^3+z^4,
Z(7)^2+Z(7)^4*z+z^2+Z(7)*z^3+z^4, Z(7)^0+Z(7)^5*z+z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)^5*z+z^2+Z(7)*z^3+z^4,
Z(7)^2+Z(7)*z^2+Z(7)*z^3+z^4, Z(7)^0+z+Z(7)*z^2+Z(7)*z^3+z^4, Z(7)+z+Z(7)*z^2+Z(7)*z^3+z^4,
Z(7)^0+Z(7)*z+Z(7)*z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)*z+Z(7)*z^2+Z(7)*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)*z^2+Z(7)*z^3+z^4,
Z(7)^4+Z(7)^2*z+Z(7)*z^2+Z(7)*z^3+z^4, Z(7)^4-z+Z(7)*z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)^4*z+Z(7)*z^2+Z(7)*z^3+z^4,
Z(7)^5+Z(7)^5*z+Z(7)*z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^2*z^2+Z(7)*z^3+z^4,
Z(7)^5+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)+z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^4+z+Z(7)^2*z^2+Z(7)*z^3+z^4,
Z(7)^5+z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^0+Z(7)^2*z+Z(7)^2*z^2+Z(7)*z^3+z^4,
Z(7)^5+Z(7)^2*z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^0-z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^4-z+Z(7)^2*z^2+Z(7)*z^3+z^4,
Z(7)+Z(7)^4*z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)^2*z^2+Z(7)*z^3+z^4, Z(7)^2+Z(7)^5*z+Z(7)^2*z^2+Z(7)*z^
3+z^4, Z(7)^0+z-z^2+Z(7)*z^3+z^4, Z(7)^2+z-z^2+Z(7)*z^3+z^4, -Z(7)^0+z-z^2+Z(7)*z^3+z^4,
Z(7)+Z(7)^2*z-z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)^2*z-z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^2*z-z^2+Z(7)*z^3+z^4,
Z(7)^0+Z(7)^4*z-z^2+Z(7)*z^3+z^4, Z(7)^2+Z(7)^4*z-z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^4*z-z^2+Z(7)*z^3+z^4,
Z(7)^2+Z(7)^5*z-z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^5*z-z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)^5*z-z^2+Z(7)*z^3+z^4,
Z(7)^2+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)+z+Z(7)^4*z^2+Z(7)*z^3+z^4,
Z(7)^2+Z(7)*z+Z(7)^4*z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)*z+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^4*z^2+Z(7)*z^3+z^
4, Z(7)^0+Z(7)^2*z+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)^2+Z(7)^2*z+Z(7)^4*z^2+Z(7)*z^3+z^4,
Z(7)^5-z+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)+Z(7)^4*z+Z(7)^4*z^2+Z(7)*z^3+z^4,
Z(7)^5+Z(7)^4*z+Z(7)^4*z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)^5*z+Z(7)^4*z^2+Z(7)*z^3+z^4,
Z(7)^5+Z(7)^5*z+Z(7)^4*z^2+Z(7)*z^3+z^4, Z(7)^0+Z(7)^5*z^2+Z(7)*z^3+z^4, -Z(7)^0+Z(7)^5*z^2+Z(7)*z^3+z^4,
Z(7)+z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^2+z+Z(7)^5*z^2+Z(7)*z^3+z^4, -Z(7)^0+z+Z(7)^5*z^2+Z(7)*z^3+z^4,
Z(7)+Z(7)*z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)*z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^0+Z(7)^2*z+Z(7)^5*z^2+Z(7)*z^3+z^4
, Z(7)^2+Z(7)^2*z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^5*z^2+Z(7)*z^3+z^4,
Z(7)^2-z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^4+Z(7)^4*z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^5*z^2+Z(7)*z^3+z^4,
-Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+Z(7)*z^3+z^4, Z(7)^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^2*z^3+z^4, -Z(7)^0+z+Z(7)^2*z^3+z^4,
Z(7)^2+Z(7)*z+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^2*z^3+z^4, -Z(7)^0-z+Z(7)^2*z^3+z^4, Z(7)^4-z+Z(7)^2*z^3+z^4,
Z(7)^4+Z(7)^4*z+Z(7)^2*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^2*z^3+z^4,
Z(7)^0+z^2+Z(7)^2*z^3+z^4, Z(7)^2+z^2+Z(7)^2*z^3+z^4, -Z(7)^0+z+z^2+Z(7)^2*z^3+z^4,
-Z(7)^0+Z(7)*z+z^2+Z(7)^2*z^3+z^4, Z(7)^4+Z(7)*z+z^2+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)*z+z^2+Z(7)^2*z^3+z^4,
Z(7)+Z(7)^2*z+z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^2*z+z^2+Z(7)^2*z^3+z^4, Z(7)^5-z+z^2+Z(7)^2*z^3+z^4,
Z(7)^0+Z(7)^4*z+z^2+Z(7)^2*z^3+z^4, Z(7)+Z(7)^4*z+z^2+Z(7)^2*z^3+z^4, Z(7)^2+Z(7)^4*z+z^2+Z(7)^2*z^3+z^4,
Z(7)^0+Z(7)^5*z+z^2+Z(7)^2*z^3+z^4, Z(7)^4+Z(7)^5*z+z^2+Z(7)^2*z^3+z^4, Z(7)+Z(7)*z^2+Z(7)^2*z^3+z^4,
Z(7)^4+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^0+z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^2+Z(7)*z+Z(7)*z^2+Z(7)^2*z^3+z^4,
Z(7)+Z(7)^2*z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^0-z+Z(7)*z^2+Z(7)^2*z^3+z^4,
Z(7)-z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^5-z+Z(7)*z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^4*z+Z(7)*z^2+Z(7)^2*z^3+z^4,
Z(7)^5+Z(7)^4*z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)*z^2+Z(7)^2*z^3+z^4,
-Z(7)^0+Z(7)^5*z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)^4+Z(7)^5*z+Z(7)*z^2+Z(7)^2*z^3+z^4, Z(7)+Z(7)^2*z^2+Z(7)^2*z^3+z^4,
Z(7)^5+Z(7)^2*z^2+Z(7)^2*z^3+z^4, Z(7)+z+Z(7)^2*z^2+Z(7)^2*z^3+z^4, Z(7)^4+z+Z(7)^2*z^2+Z(7)^2*z^3+z^4,
Z(7)^0+Z(7)*z+Z(7)^2*z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)^2*z^2+Z(7)^2*z^3+z^4,
Z(7)^4+Z(7)^2*z+Z(7)^2*z^2+Z(7)^2*z^3+z^4, -Z(7)^0-z+Z(7)^2*z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^4*z+Z(7)^2*z^2+Z(7)^
2*z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^2*z^2+Z(7)^2*z^3+z^4, Z(7)^0-z^2+Z(7)^2*z^3+z^4, Z(7)^2+z-z^2+Z(7)^2*z^3+z^4,
-Z(7)^0+Z(7)*z-z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^2*z-z^2+Z(7)^2*z^3+z^4, Z(7)^4-z-z^2+Z(7)^2*z^3+z^4,
Z(7)^5-z-z^2+Z(7)^2*z^3+z^4, Z(7)+Z(7)^4*z-z^2+Z(7)^2*z^3+z^4, Z(7)^4+Z(7)^4*z-z^2+Z(7)^2*z^3+z^4,
Z(7)^2+Z(7)^5*z-z^2+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)^5*z-z^2+Z(7)^2*z^3+z^4, Z(7)+Z(7)^4*z^2+Z(7)^2*z^3+z^4,
Z(7)^2+Z(7)^4*z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^2+z+Z(7)^4*z^2+Z(7)^2*z^3+z^4,
Z(7)^4+z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^0+Z(7)*z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^5+Z(7)*z+Z(7)^4*z^2+Z(7)^2*z^3+z^
4, Z(7)^0+Z(7)^2*z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^2-z+Z(7)^4*z^2+Z(7)^2*z^3+z^4,
-Z(7)^0-z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^5-z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)^4*z^2+Z(7)^2*z^3+z^4,
-Z(7)^0+Z(7)^5*z+Z(7)^4*z^2+Z(7)^2*z^3+z^4, Z(7)^4+Z(7)^5*z+Z(7)^4*z^2+Z(7)^2*z^3+z^4,
Z(7)^0+Z(7)*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)^2+Z(7)*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4,
Z(7)^4+Z(7)*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)^0+Z(7)^2*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4,
Z(7)^2+Z(7)^2*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4,
Z(7)^0-z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)-z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)^4-z+Z(7)^5*z^2+Z(7)^2*z^3+z^4,
Z(7)+Z(7)^5*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)^2+Z(7)^5*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4,
Z(7)^5+Z(7)^5*z+Z(7)^5*z^2+Z(7)^2*z^3+z^4, Z(7)^0-z^3+z^4, Z(7)-z^3+z^4, Z(7)+z-z^3+z^4, Z(7)^2+z-z^3+z^4,
Z(7)^2+Z(7)*z-z^3+z^4, -Z(7)^0+Z(7)^2*z-z^3+z^4, Z(7)^4+Z(7)^2*z-z^3+z^4, Z(7)-z-z^3+z^4, Z(7)^0+Z(7)^4*z-z^3+z^4,
-Z(7)^0+Z(7)^5*z-z^3+z^4, Z(7)^0+z^2-z^3+z^4, Z(7)+z^2-z^3+z^4, Z(7)^5+z^2-z^3+z^4, Z(7)^0+z+z^2-z^3+z^4,
Z(7)+z+z^2-z^3+z^4, -Z(7)^0+z+z^2-z^3+z^4, Z(7)^0+Z(7)*z+z^2-z^3+z^4, Z(7)+Z(7)^2*z+z^2-z^3+z^4,
Z(7)^2+Z(7)^2*z+z^2-z^3+z^4, Z(7)^0-z+z^2-z^3+z^4, Z(7)^2-z+z^2-z^3+z^4, -Z(7)^0+Z(7)^4*z+z^2-z^3+z^4,
Z(7)^4+Z(7)^4*z+z^2-z^3+z^4, Z(7)^4+Z(7)^5*z+z^2-z^3+z^4, Z(7)^2+z+Z(7)*z^2-z^3+z^4, Z(7)^4+z+Z(7)*z^2-z^3+z^4,
Z(7)^5+z+Z(7)*z^2-z^3+z^4, Z(7)^0+Z(7)^2*z+Z(7)*z^2-z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)*z^2-z^3+z^4,
Z(7)^5+Z(7)^2*z+Z(7)*z^2-z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)*z^2-z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)*z^2-z^3+z^4,
Z(7)^4+Z(7)^4*z+Z(7)*z^2-z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)*z^2-z^3+z^4, Z(7)+Z(7)^5*z+Z(7)*z^2-z^3+z^4,
Z(7)^4+Z(7)^5*z+Z(7)*z^2-z^3+z^4, Z(7)^0+Z(7)^2*z^2-z^3+z^4, Z(7)^4+Z(7)^2*z^2-z^3+z^4,
-Z(7)^0+z+Z(7)^2*z^2-z^3+z^4, Z(7)^0+Z(7)*z+Z(7)^2*z^2-z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^2*z^2-z^3+z^4,
Z(7)^5+Z(7)*z+Z(7)^2*z^2-z^3+z^4, Z(7)^2+Z(7)^2*z+Z(7)^2*z^2-z^3+z^4, Z(7)^4+Z(7)^2*z+Z(7)^2*z^2-z^3+z^4,
Z(7)-z+Z(7)^2*z^2-z^3+z^4, Z(7)+Z(7)^4*z+Z(7)^2*z^2-z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)^2*z^2-z^3+z^4,
-Z(7)^0+Z(7)^4*z+Z(7)^2*z^2-z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^2*z^2-z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^2*z^2-z^3+z^4,
Z(7)^2-z^2-z^3+z^4, Z(7)^5-z^2-z^3+z^4, -Z(7)^0+z-z^2-z^3+z^4, Z(7)^4+z-z^2-z^3+z^4, Z(7)^5+z-z^2-z^3+z^4,
Z(7)+Z(7)*z-z^2-z^3+z^4, -Z(7)^0+Z(7)*z-z^2-z^3+z^4, Z(7)+Z(7)^2*z-z^2-z^3+z^4, Z(7)^2+Z(7)^2*z-z^2-z^3+z^4,
Z(7)^4+Z(7)^2*z-z^2-z^3+z^4, Z(7)^4-z-z^2-z^3+z^4, Z(7)^0+Z(7)^4*z-z^2-z^3+z^4, -Z(7)^0+Z(7)^5*z-z^2-z^3+z^4,
Z(7)^5+Z(7)^5*z-z^2-z^3+z^4, -Z(7)^0+Z(7)^4*z^2-z^3+z^4, Z(7)^5+Z(7)^4*z^2-z^3+z^4, Z(7)+z+Z(7)^4*z^2-z^3+z^4,
Z(7)+Z(7)*z+Z(7)^4*z^2-z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^4*z^2-z^3+z^4, Z(7)^2-z+Z(7)^4*z^2-z^3+z^4,
Z(7)^5-z+Z(7)^4*z^2-z^3+z^4, Z(7)^4+Z(7)^4*z+Z(7)^4*z^2-z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^4*z^2-z^3+z^4,
Z(7)^2+Z(7)^5*z+Z(7)^4*z^2-z^3+z^4, Z(7)^4+Z(7)^5*z^2-z^3+z^4, Z(7)^2+z+Z(7)^5*z^2-z^3+z^4,
-Z(7)^0+z+Z(7)^5*z^2-z^3+z^4, Z(7)^2+Z(7)*z+Z(7)^5*z^2-z^3+z^4, Z(7)^5+Z(7)*z+Z(7)^5*z^2-z^3+z^4,
Z(7)^0+Z(7)^2*z+Z(7)^5*z^2-z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)^5*z^2-z^3+z^4, Z(7)^0-z+Z(7)^5*z^2-z^3+z^4,
Z(7)+Z(7)^4*z+Z(7)^5*z^2-z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^5*z^2-z^3+z^4, Z(7)^4+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^4*z^3+z^4,
Z(7)^5+z+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^4*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^4*z^3+z^4, Z(7)^0-z+Z(7)^4*z^3+z^4,
Z(7)^5-z+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)^4*z^3+z^4, Z(7)+Z(7)^5*z+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)^5*z+Z(7)^4*z^3+z^4, Z(7)+z^2+Z(7)^4*z^3+z^4, -Z(7)^0+z^2+Z(7)^4*z^3+z^4, Z(7)^0+z+z^2+Z(7)^4*z^3+z^4,
-Z(7)^0+z+z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)*z+z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^2*z+z^2+Z(7)^4*z^3+z^4,
Z(7)^5+Z(7)^2*z+z^2+Z(7)^4*z^3+z^4, Z(7)^5-z+z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^4*z+z^2+Z(7)^4*z^3+z^4,
-Z(7)^0+Z(7)^5*z+z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)*z^2+Z(7)^4*z^3+z^4, Z(7)^4+z+Z(7)*z^2+Z(7)^4*z^3+z^4,
Z(7)^5+Z(7)*z+Z(7)*z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)*z^2+Z(7)^4*z^3+z^4, Z(7)^0-z+Z(7)*z^2+Z(7)^4*z^3+z^4,
Z(7)-z+Z(7)*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)*z^2+Z(7)^4*z^3+z^4, -Z(7)^0+Z(7)^4*z+Z(7)*z^2+Z(7)^4*z^3+z^4,
Z(7)+Z(7)^5*z+Z(7)*z^2+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)^5*z+Z(7)*z^2+Z(7)^4*z^3+z^4, -Z(7)^0+Z(7)^2*z^2+Z(7)^4*z^3+z^4,
Z(7)^4+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^0+z+Z(7)^2*z^2+Z(7)^4*z^3+z^4,
Z(7)^4+z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)+Z(7)*z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)*z+Z(7)^2*z^2+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)^2*z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)-z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^4-z+Z(7)^2*z^2+Z(7)^4*z^3+z^4,
Z(7)^5-z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)^4*z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^2*z^2+Z(7)^4*z^
3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^2*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)*z-z^2+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)*z-z^2+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)*z-z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)^2*z-z^2+Z(7)^4*z^3+z^4,
Z(7)^4+Z(7)^2*z-z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^2*z-z^2+Z(7)^4*z^3+z^4, Z(7)^0-z-z^2+Z(7)^4*z^3+z^4,
Z(7)^2-z-z^2+Z(7)^4*z^3+z^4, -Z(7)^0-z-z^2+Z(7)^4*z^3+z^4, Z(7)+Z(7)^5*z-z^2+Z(7)^4*z^3+z^4,
-Z(7)^0+Z(7)^5*z-z^2+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)^5*z-z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)^4*z^2+Z(7)^4*z^3+z^4,
Z(7)^4+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)^5+z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4,
Z(7)+Z(7)*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)^4*z^2+Z(7)^
4*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)-z+Z(7)^4*z^2+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)^4*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, -Z(7)^0+Z(7)^4*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4,
Z(7)^4+Z(7)^4*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)^5*z+Z(7)^4*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^5*z^2+Z(7)^4*z^3+z^4, -Z(7)^0+Z(7)^5*z^2+Z(7)^4*z^3+z^4,
Z(7)^2+z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^5*z^2+Z(7)^4*z^3+z^
4, -Z(7)^0+Z(7)^2*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)-z+Z(7)^5*z^2+Z(7)^4*z^3+z^4,
Z(7)^2-z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, -Z(7)^0-z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)+Z(7)^4*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4,
Z(7)^5+Z(7)^4*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4,
Z(7)^2+Z(7)^5*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^5*z^2+Z(7)^4*z^3+z^4, Z(7)^2+Z(7)^5*z^3+z^4,
-Z(7)^0+Z(7)^5*z^3+z^4, -Z(7)^0+z+Z(7)^5*z^3+z^4, Z(7)^4+z+Z(7)^5*z^3+z^4, Z(7)^4+Z(7)*z+Z(7)^5*z^3+z^4,
Z(7)^0+Z(7)^2*z+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^5*z^3+z^4, -Z(7)^0-z+Z(7)^5*z^3+z^4,
Z(7)^2+Z(7)^4*z+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^5*z+Z(7)^5*z^3+z^4, Z(7)^0+z^2+Z(7)^5*z^3+z^4,
Z(7)^2+z^2+Z(7)^5*z^3+z^4, Z(7)^5+z+z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)*z+z^2+Z(7)^5*z^3+z^4,
Z(7)+Z(7)*z+z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)*z+z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)^2*z+z^2+Z(7)^5*z^3+z^4,
Z(7)^4+Z(7)^2*z+z^2+Z(7)^5*z^3+z^4, -Z(7)^0-z+z^2+Z(7)^5*z^3+z^4, -Z(7)^0+Z(7)^4*z+z^2+Z(7)^5*z^3+z^4,
Z(7)^4+Z(7)^4*z+z^2+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^4*z+z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^5*z+z^2+Z(7)^5*z^3+z^4,
-Z(7)^0+Z(7)^5*z+z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^4+Z(7)*z^2+Z(7)^5*z^3+z^4,
Z(7)^0+z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)+z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^5+z+Z(7)*z^2+Z(7)^5*z^3+z^4,
-Z(7)^0+Z(7)*z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)*z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)^2*z+Z(7)*z^2+Z(7)^5*z^
3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^4+Z(7)^2*z+Z(7)*z^2+Z(7)^5*z^3+z^4,
Z(7)^0-z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^5*z+Z(7)*z^2+Z(7)^5*z^3+z^4,
Z(7)^5+Z(7)^5*z+Z(7)*z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^2*z^2+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^2*z^2+Z(7)^5*z^3+z^4,
-Z(7)^0+z+Z(7)^2*z^2+Z(7)^5*z^3+z^4, -Z(7)^0+Z(7)*z+Z(7)^2*z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^2*z^2+Z(7)^5*z^
3+z^4, Z(7)-z+Z(7)^2*z^2+Z(7)^5*z^3+z^4, Z(7)^4-z+Z(7)^2*z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)^2*z^2+Z(7)^5*z^
3+z^4, -Z(7)^0+Z(7)^5*z+Z(7)^2*z^2+Z(7)^5*z^3+z^4, Z(7)^4+Z(7)^5*z+Z(7)^2*z^2+Z(7)^5*z^3+z^4,
Z(7)^0-z^2+Z(7)^5*z^3+z^4, Z(7)^4+z-z^2+Z(7)^5*z^3+z^4, Z(7)^5+z-z^2+Z(7)^5*z^3+z^4,
Z(7)+Z(7)*z-z^2+Z(7)^5*z^3+z^4, Z(7)^4+Z(7)*z-z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)^2*z-z^2+Z(7)^5*z^3+z^4,
Z(7)^5+Z(7)^2*z-z^2+Z(7)^5*z^3+z^4, Z(7)^2-z-z^2+Z(7)^5*z^3+z^4, -Z(7)^0+Z(7)^4*z-z^2+Z(7)^5*z^3+z^4,
-Z(7)^0+Z(7)^5*z-z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)^4*z^2+Z(7)^5*z^3+z^4,
-Z(7)^0+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^2+z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, -Z(7)^0+z+Z(7)^4*z^2+Z(7)^5*z^3+z^4,
Z(7)^5+z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)*z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, -Z(7)^0+Z(7)^2*z+Z(7)^4*z^2+Z(7)^5*z^
3+z^4, Z(7)^4+Z(7)^2*z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^2-z+Z(7)^4*z^2+Z(7)^5*z^3+z^4,
Z(7)^4-z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)^4*z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^4*z+Z(7)^4*z^2+Z(7)^5*z^
3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^4*z^2+Z(7)^5*z^3+z^4, Z(7)^0+z+Z(7)^5*z^2+Z(7)^5*z^3+z^4,
Z(7)+z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, Z(7)^4+z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, Z(7)+Z(7)^2*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4,
Z(7)^2+Z(7)^2*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, Z(7)^5+Z(7)^2*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4,
Z(7)^0+Z(7)^4*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, Z(7)^2+Z(7)^4*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4,
Z(7)^4+Z(7)^4*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4,
Z(7)^2+Z(7)^5*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4, -Z(7)^0+Z(7)^5*z+Z(7)^5*z^2+Z(7)^5*z^3+z^4 ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4 ]
gap> polyring:=PolynomialRing(GF(7^4));
PolynomialRing(..., [ z ])
gap> factors:=Factors(polyring,z^(7^4)-z);
[ z, Z(7)^0+z, Z(7)+z, Z(7)^2+z, -Z(7)^0+z, Z(7)^4+z, Z(7)^5+z, Z(7^2)+z, Z(7^2)^2+z, Z(7^2)^3+z, Z(7^2)^4+z,
Z(7^2)^5+z, Z(7^2)^6+z, Z(7^2)^7+z, Z(7^2)^9+z, Z(7^2)^10+z, Z(7^2)^11+z, Z(7^2)^12+z, Z(7^2)^13+z, Z(7^2)^14+z,
Z(7^2)^15+z, Z(7^2)^17+z, Z(7^2)^18+z, Z(7^2)^19+z, Z(7^2)^20+z, Z(7^2)^21+z, Z(7^2)^22+z, Z(7^2)^23+z,
Z(7^2)^25+z, Z(7^2)^26+z, Z(7^2)^27+z, Z(7^2)^28+z, Z(7^2)^29+z, Z(7^2)^30+z, Z(7^2)^31+z, Z(7^2)^33+z,
Z(7^2)^34+z, Z(7^2)^35+z, Z(7^2)^36+z, Z(7^2)^37+z, Z(7^2)^38+z, Z(7^2)^39+z, Z(7^2)^41+z, Z(7^2)^42+z,
Z(7^2)^43+z, Z(7^2)^44+z, Z(7^2)^45+z, Z(7^2)^46+z, Z(7^2)^47+z, Z(7^4)+z, Z(7^4)^2+z, Z(7^4)^3+z, Z(7^4)^4+z,
Z(7^4)^5+z, Z(7^4)^6+z, Z(7^4)^7+z, Z(7^4)^8+z, Z(7^4)^9+z, Z(7^4)^10+z, Z(7^4)^11+z, Z(7^4)^12+z, Z(7^4)^13+z,
Z(7^4)^14+z, Z(7^4)^15+z, Z(7^4)^16+z, Z(7^4)^17+z, Z(7^4)^18+z, Z(7^4)^19+z, Z(7^4)^20+z, Z(7^4)^21+z,
Z(7^4)^22+z, Z(7^4)^23+z, Z(7^4)^24+z, Z(7^4)^25+z, Z(7^4)^26+z, Z(7^4)^27+z, Z(7^4)^28+z, Z(7^4)^29+z,
Z(7^4)^30+z, Z(7^4)^31+z, Z(7^4)^32+z, Z(7^4)^33+z, Z(7^4)^34+z, Z(7^4)^35+z, Z(7^4)^36+z, Z(7^4)^37+z,
Z(7^4)^38+z, Z(7^4)^39+z, Z(7^4)^40+z, Z(7^4)^41+z, Z(7^4)^42+z, Z(7^4)^43+z, Z(7^4)^44+z, Z(7^4)^45+z,
Z(7^4)^46+z, Z(7^4)^47+z, Z(7^4)^48+z, Z(7^4)^49+z, Z(7^4)^51+z, Z(7^4)^52+z, Z(7^4)^53+z, Z(7^4)^54+z,
Z(7^4)^55+z, Z(7^4)^56+z, Z(7^4)^57+z, Z(7^4)^58+z, Z(7^4)^59+z, Z(7^4)^60+z, Z(7^4)^61+z, Z(7^4)^62+z,
Z(7^4)^63+z, Z(7^4)^64+z, Z(7^4)^65+z, Z(7^4)^66+z, Z(7^4)^67+z, Z(7^4)^68+z, Z(7^4)^69+z, Z(7^4)^70+z,
Z(7^4)^71+z, Z(7^4)^72+z, Z(7^4)^73+z, Z(7^4)^74+z, Z(7^4)^75+z, Z(7^4)^76+z, Z(7^4)^77+z, Z(7^4)^78+z,
Z(7^4)^79+z, Z(7^4)^80+z, Z(7^4)^81+z, Z(7^4)^82+z, Z(7^4)^83+z, Z(7^4)^84+z, Z(7^4)^85+z, Z(7^4)^86+z,
Z(7^4)^87+z, Z(7^4)^88+z, Z(7^4)^89+z, Z(7^4)^90+z, Z(7^4)^91+z, Z(7^4)^92+z, Z(7^4)^93+z, Z(7^4)^94+z,
Z(7^4)^95+z, Z(7^4)^96+z, Z(7^4)^97+z, Z(7^4)^98+z, Z(7^4)^99+z, Z(7^4)^101+z, Z(7^4)^102+z, Z(7^4)^103+z,
Z(7^4)^104+z, Z(7^4)^105+z, Z(7^4)^106+z, Z(7^4)^107+z, Z(7^4)^108+z, Z(7^4)^109+z, Z(7^4)^110+z, Z(7^4)^111+z,
Z(7^4)^112+z, Z(7^4)^113+z, Z(7^4)^114+z, Z(7^4)^115+z, Z(7^4)^116+z, Z(7^4)^117+z, Z(7^4)^118+z, Z(7^4)^119+z,
Z(7^4)^120+z, Z(7^4)^121+z, Z(7^4)^122+z, Z(7^4)^123+z, Z(7^4)^124+z, Z(7^4)^125+z, Z(7^4)^126+z, Z(7^4)^127+z,
Z(7^4)^128+z, Z(7^4)^129+z, Z(7^4)^130+z, Z(7^4)^131+z, Z(7^4)^132+z, Z(7^4)^133+z, Z(7^4)^134+z, Z(7^4)^135+z,
Z(7^4)^136+z, Z(7^4)^137+z, Z(7^4)^138+z, Z(7^4)^139+z, Z(7^4)^140+z, Z(7^4)^141+z, Z(7^4)^142+z, Z(7^4)^143+z,
Z(7^4)^144+z, Z(7^4)^145+z, Z(7^4)^146+z, Z(7^4)^147+z, Z(7^4)^148+z, Z(7^4)^149+z, Z(7^4)^151+z, Z(7^4)^152+z,
Z(7^4)^153+z, Z(7^4)^154+z, Z(7^4)^155+z, Z(7^4)^156+z, Z(7^4)^157+z, Z(7^4)^158+z, Z(7^4)^159+z, Z(7^4)^160+z,
Z(7^4)^161+z, Z(7^4)^162+z, Z(7^4)^163+z, Z(7^4)^164+z, Z(7^4)^165+z, Z(7^4)^166+z, Z(7^4)^167+z, Z(7^4)^168+z,
Z(7^4)^169+z, Z(7^4)^170+z, Z(7^4)^171+z, Z(7^4)^172+z, Z(7^4)^173+z, Z(7^4)^174+z, Z(7^4)^175+z, Z(7^4)^176+z,
Z(7^4)^177+z, Z(7^4)^178+z, Z(7^4)^179+z, Z(7^4)^180+z, Z(7^4)^181+z, Z(7^4)^182+z, Z(7^4)^183+z, Z(7^4)^184+z,
Z(7^4)^185+z, Z(7^4)^186+z, Z(7^4)^187+z, Z(7^4)^188+z, Z(7^4)^189+z, Z(7^4)^190+z, Z(7^4)^191+z, Z(7^4)^192+z,
Z(7^4)^193+z, Z(7^4)^194+z, Z(7^4)^195+z, Z(7^4)^196+z, Z(7^4)^197+z, Z(7^4)^198+z, Z(7^4)^199+z, Z(7^4)^201+z,
Z(7^4)^202+z, Z(7^4)^203+z, Z(7^4)^204+z, Z(7^4)^205+z, Z(7^4)^206+z, Z(7^4)^207+z, Z(7^4)^208+z, Z(7^4)^209+z,
Z(7^4)^210+z, Z(7^4)^211+z, Z(7^4)^212+z, Z(7^4)^213+z, Z(7^4)^214+z, Z(7^4)^215+z, Z(7^4)^216+z, Z(7^4)^217+z,
Z(7^4)^218+z, Z(7^4)^219+z, Z(7^4)^220+z, Z(7^4)^221+z, Z(7^4)^222+z, Z(7^4)^223+z, Z(7^4)^224+z, Z(7^4)^225+z,
Z(7^4)^226+z, Z(7^4)^227+z, Z(7^4)^228+z, Z(7^4)^229+z, Z(7^4)^230+z, Z(7^4)^231+z, Z(7^4)^232+z, Z(7^4)^233+z,
Z(7^4)^234+z, Z(7^4)^235+z, Z(7^4)^236+z, Z(7^4)^237+z, Z(7^4)^238+z, Z(7^4)^239+z, Z(7^4)^240+z, Z(7^4)^241+z,
Z(7^4)^242+z, Z(7^4)^243+z, Z(7^4)^244+z, Z(7^4)^245+z, Z(7^4)^246+z, Z(7^4)^247+z, Z(7^4)^248+z, Z(7^4)^249+z,
Z(7^4)^251+z, Z(7^4)^252+z, Z(7^4)^253+z, Z(7^4)^254+z, Z(7^4)^255+z, Z(7^4)^256+z, Z(7^4)^257+z, Z(7^4)^258+z,
Z(7^4)^259+z, Z(7^4)^260+z, Z(7^4)^261+z, Z(7^4)^262+z, Z(7^4)^263+z, Z(7^4)^264+z, Z(7^4)^265+z, Z(7^4)^266+z,
Z(7^4)^267+z, Z(7^4)^268+z, Z(7^4)^269+z, Z(7^4)^270+z, Z(7^4)^271+z, Z(7^4)^272+z, Z(7^4)^273+z, Z(7^4)^274+z,
Z(7^4)^275+z, Z(7^4)^276+z, Z(7^4)^277+z, Z(7^4)^278+z, Z(7^4)^279+z, Z(7^4)^280+z, Z(7^4)^281+z, Z(7^4)^282+z,
Z(7^4)^283+z, Z(7^4)^284+z, Z(7^4)^285+z, Z(7^4)^286+z, Z(7^4)^287+z, Z(7^4)^288+z, Z(7^4)^289+z, Z(7^4)^290+z,
Z(7^4)^291+z, Z(7^4)^292+z, Z(7^4)^293+z, Z(7^4)^294+z, Z(7^4)^295+z, Z(7^4)^296+z, Z(7^4)^297+z, Z(7^4)^298+z,
Z(7^4)^299+z, Z(7^4)^301+z, Z(7^4)^302+z, Z(7^4)^303+z, Z(7^4)^304+z, Z(7^4)^305+z, Z(7^4)^306+z, Z(7^4)^307+z,
Z(7^4)^308+z, Z(7^4)^309+z, Z(7^4)^310+z, Z(7^4)^311+z, Z(7^4)^312+z, Z(7^4)^313+z, Z(7^4)^314+z, Z(7^4)^315+z,
Z(7^4)^316+z, Z(7^4)^317+z, Z(7^4)^318+z, Z(7^4)^319+z, Z(7^4)^320+z, Z(7^4)^321+z, Z(7^4)^322+z, Z(7^4)^323+z,
Z(7^4)^324+z, Z(7^4)^325+z, Z(7^4)^326+z, Z(7^4)^327+z, Z(7^4)^328+z, Z(7^4)^329+z, Z(7^4)^330+z, Z(7^4)^331+z,
Z(7^4)^332+z, Z(7^4)^333+z, Z(7^4)^334+z, Z(7^4)^335+z, Z(7^4)^336+z, Z(7^4)^337+z, Z(7^4)^338+z, Z(7^4)^339+z,
Z(7^4)^340+z, Z(7^4)^341+z, Z(7^4)^342+z, Z(7^4)^343+z, Z(7^4)^344+z, Z(7^4)^345+z, Z(7^4)^346+z, Z(7^4)^347+z,
Z(7^4)^348+z, Z(7^4)^349+z, Z(7^4)^351+z, Z(7^4)^352+z, Z(7^4)^353+z, Z(7^4)^354+z, Z(7^4)^355+z, Z(7^4)^356+z,
Z(7^4)^357+z, Z(7^4)^358+z, Z(7^4)^359+z, Z(7^4)^360+z, Z(7^4)^361+z, Z(7^4)^362+z, Z(7^4)^363+z, Z(7^4)^364+z,
Z(7^4)^365+z, Z(7^4)^366+z, Z(7^4)^367+z, Z(7^4)^368+z, Z(7^4)^369+z, Z(7^4)^370+z, Z(7^4)^371+z, Z(7^4)^372+z,
Z(7^4)^373+z, Z(7^4)^374+z, Z(7^4)^375+z, Z(7^4)^376+z, Z(7^4)^377+z, Z(7^4)^378+z, Z(7^4)^379+z, Z(7^4)^380+z,
Z(7^4)^381+z, Z(7^4)^382+z, Z(7^4)^383+z, Z(7^4)^384+z, Z(7^4)^385+z, Z(7^4)^386+z, Z(7^4)^387+z, Z(7^4)^388+z,
Z(7^4)^389+z, Z(7^4)^390+z, Z(7^4)^391+z, Z(7^4)^392+z, Z(7^4)^393+z, Z(7^4)^394+z, Z(7^4)^395+z, Z(7^4)^396+z,
Z(7^4)^397+z, Z(7^4)^398+z, Z(7^4)^399+z, Z(7^4)^401+z, Z(7^4)^402+z, Z(7^4)^403+z, Z(7^4)^404+z, Z(7^4)^405+z,
Z(7^4)^406+z, Z(7^4)^407+z, Z(7^4)^408+z, Z(7^4)^409+z, Z(7^4)^410+z, Z(7^4)^411+z, Z(7^4)^412+z, Z(7^4)^413+z,
Z(7^4)^414+z, Z(7^4)^415+z, Z(7^4)^416+z, Z(7^4)^417+z, Z(7^4)^418+z, Z(7^4)^419+z, Z(7^4)^420+z, Z(7^4)^421+z,
Z(7^4)^422+z, Z(7^4)^423+z, Z(7^4)^424+z, Z(7^4)^425+z, Z(7^4)^426+z, Z(7^4)^427+z, Z(7^4)^428+z, Z(7^4)^429+z,
Z(7^4)^430+z, Z(7^4)^431+z, Z(7^4)^432+z, Z(7^4)^433+z, Z(7^4)^434+z, Z(7^4)^435+z, Z(7^4)^436+z, Z(7^4)^437+z,
Z(7^4)^438+z, Z(7^4)^439+z, Z(7^4)^440+z, Z(7^4)^441+z, Z(7^4)^442+z, Z(7^4)^443+z, Z(7^4)^444+z, Z(7^4)^445+z,
Z(7^4)^446+z, Z(7^4)^447+z, Z(7^4)^448+z, Z(7^4)^449+z, Z(7^4)^451+z, Z(7^4)^452+z, Z(7^4)^453+z, Z(7^4)^454+z,
Z(7^4)^455+z, Z(7^4)^456+z, Z(7^4)^457+z, Z(7^4)^458+z, Z(7^4)^459+z, Z(7^4)^460+z, Z(7^4)^461+z, Z(7^4)^462+z,
Z(7^4)^463+z, Z(7^4)^464+z, Z(7^4)^465+z, Z(7^4)^466+z, Z(7^4)^467+z, Z(7^4)^468+z, Z(7^4)^469+z, Z(7^4)^470+z,
Z(7^4)^471+z, Z(7^4)^472+z, Z(7^4)^473+z, Z(7^4)^474+z, Z(7^4)^475+z, Z(7^4)^476+z, Z(7^4)^477+z, Z(7^4)^478+z,
Z(7^4)^479+z, Z(7^4)^480+z, Z(7^4)^481+z, Z(7^4)^482+z, Z(7^4)^483+z, Z(7^4)^484+z, Z(7^4)^485+z, Z(7^4)^486+z,
Z(7^4)^487+z, Z(7^4)^488+z, Z(7^4)^489+z, Z(7^4)^490+z, Z(7^4)^491+z, Z(7^4)^492+z, Z(7^4)^493+z, Z(7^4)^494+z,
Z(7^4)^495+z, Z(7^4)^496+z, Z(7^4)^497+z, Z(7^4)^498+z, Z(7^4)^499+z, Z(7^4)^501+z, Z(7^4)^502+z, Z(7^4)^503+z,
Z(7^4)^504+z, Z(7^4)^505+z, Z(7^4)^506+z, Z(7^4)^507+z, Z(7^4)^508+z, Z(7^4)^509+z, Z(7^4)^510+z, Z(7^4)^511+z,
Z(7^4)^512+z, Z(7^4)^513+z, Z(7^4)^514+z, Z(7^4)^515+z, Z(7^4)^516+z, Z(7^4)^517+z, Z(7^4)^518+z, Z(7^4)^519+z,
Z(7^4)^520+z, Z(7^4)^521+z, Z(7^4)^522+z, Z(7^4)^523+z, Z(7^4)^524+z, Z(7^4)^525+z, Z(7^4)^526+z, Z(7^4)^527+z,
Z(7^4)^528+z, Z(7^4)^529+z, Z(7^4)^530+z, Z(7^4)^531+z, Z(7^4)^532+z, Z(7^4)^533+z, Z(7^4)^534+z, Z(7^4)^535+z,
Z(7^4)^536+z, Z(7^4)^537+z, Z(7^4)^538+z, Z(7^4)^539+z, Z(7^4)^540+z, Z(7^4)^541+z, Z(7^4)^542+z, Z(7^4)^543+z,
Z(7^4)^544+z, Z(7^4)^545+z, Z(7^4)^546+z, Z(7^4)^547+z, Z(7^4)^548+z, Z(7^4)^549+z, Z(7^4)^551+z, Z(7^4)^552+z,
Z(7^4)^553+z, Z(7^4)^554+z, Z(7^4)^555+z, Z(7^4)^556+z, Z(7^4)^557+z, Z(7^4)^558+z, Z(7^4)^559+z, Z(7^4)^560+z,
Z(7^4)^561+z, Z(7^4)^562+z, Z(7^4)^563+z, Z(7^4)^564+z, Z(7^4)^565+z, Z(7^4)^566+z, Z(7^4)^567+z, Z(7^4)^568+z,
Z(7^4)^569+z, Z(7^4)^570+z, Z(7^4)^571+z, Z(7^4)^572+z, Z(7^4)^573+z, Z(7^4)^574+z, Z(7^4)^575+z, Z(7^4)^576+z,
Z(7^4)^577+z, Z(7^4)^578+z, Z(7^4)^579+z, Z(7^4)^580+z, Z(7^4)^581+z, Z(7^4)^582+z, Z(7^4)^583+z, Z(7^4)^584+z,
Z(7^4)^585+z, Z(7^4)^586+z, Z(7^4)^587+z, Z(7^4)^588+z, Z(7^4)^589+z, Z(7^4)^590+z, Z(7^4)^591+z, Z(7^4)^592+z,
Z(7^4)^593+z, Z(7^4)^594+z, Z(7^4)^595+z, Z(7^4)^596+z, Z(7^4)^597+z, Z(7^4)^598+z, Z(7^4)^599+z, Z(7^4)^601+z,
Z(7^4)^602+z, Z(7^4)^603+z, Z(7^4)^604+z, Z(7^4)^605+z, Z(7^4)^606+z, Z(7^4)^607+z, Z(7^4)^608+z, Z(7^4)^609+z,
Z(7^4)^610+z, Z(7^4)^611+z, Z(7^4)^612+z, Z(7^4)^613+z, Z(7^4)^614+z, Z(7^4)^615+z, Z(7^4)^616+z, Z(7^4)^617+z,
Z(7^4)^618+z, Z(7^4)^619+z, Z(7^4)^620+z, Z(7^4)^621+z, Z(7^4)^622+z, Z(7^4)^623+z, Z(7^4)^624+z, Z(7^4)^625+z,
Z(7^4)^626+z, Z(7^4)^627+z, Z(7^4)^628+z, Z(7^4)^629+z, Z(7^4)^630+z, Z(7^4)^631+z, Z(7^4)^632+z, Z(7^4)^633+z,
Z(7^4)^634+z, Z(7^4)^635+z, Z(7^4)^636+z, Z(7^4)^637+z, Z(7^4)^638+z, Z(7^4)^639+z, Z(7^4)^640+z, Z(7^4)^641+z,
Z(7^4)^642+z, Z(7^4)^643+z, Z(7^4)^644+z, Z(7^4)^645+z, Z(7^4)^646+z, Z(7^4)^647+z, Z(7^4)^648+z, Z(7^4)^649+z,
Z(7^4)^651+z, Z(7^4)^652+z, Z(7^4)^653+z, Z(7^4)^654+z, Z(7^4)^655+z, Z(7^4)^656+z, Z(7^4)^657+z, Z(7^4)^658+z,
Z(7^4)^659+z, Z(7^4)^660+z, Z(7^4)^661+z, Z(7^4)^662+z, Z(7^4)^663+z, Z(7^4)^664+z, Z(7^4)^665+z, Z(7^4)^666+z,
Z(7^4)^667+z, Z(7^4)^668+z, Z(7^4)^669+z, Z(7^4)^670+z, Z(7^4)^671+z, Z(7^4)^672+z, Z(7^4)^673+z, Z(7^4)^674+z,
Z(7^4)^675+z, Z(7^4)^676+z, Z(7^4)^677+z, Z(7^4)^678+z, Z(7^4)^679+z, Z(7^4)^680+z, Z(7^4)^681+z, Z(7^4)^682+z,
Z(7^4)^683+z, Z(7^4)^684+z, Z(7^4)^685+z, Z(7^4)^686+z, Z(7^4)^687+z, Z(7^4)^688+z, Z(7^4)^689+z, Z(7^4)^690+z,
Z(7^4)^691+z, Z(7^4)^692+z, Z(7^4)^693+z, Z(7^4)^694+z, Z(7^4)^695+z, Z(7^4)^696+z, Z(7^4)^697+z, Z(7^4)^698+z,
Z(7^4)^699+z, Z(7^4)^701+z, Z(7^4)^702+z, Z(7^4)^703+z, Z(7^4)^704+z, Z(7^4)^705+z, Z(7^4)^706+z, Z(7^4)^707+z,
Z(7^4)^708+z, Z(7^4)^709+z, Z(7^4)^710+z, Z(7^4)^711+z, Z(7^4)^712+z, Z(7^4)^713+z, Z(7^4)^714+z, Z(7^4)^715+z,
Z(7^4)^716+z, Z(7^4)^717+z, Z(7^4)^718+z, Z(7^4)^719+z, Z(7^4)^720+z, Z(7^4)^721+z, Z(7^4)^722+z, Z(7^4)^723+z,
Z(7^4)^724+z, Z(7^4)^725+z, Z(7^4)^726+z, Z(7^4)^727+z, Z(7^4)^728+z, Z(7^4)^729+z, Z(7^4)^730+z, Z(7^4)^731+z,
Z(7^4)^732+z, Z(7^4)^733+z, Z(7^4)^734+z, Z(7^4)^735+z, Z(7^4)^736+z, Z(7^4)^737+z, Z(7^4)^738+z, Z(7^4)^739+z,
Z(7^4)^740+z, Z(7^4)^741+z, Z(7^4)^742+z, Z(7^4)^743+z, Z(7^4)^744+z, Z(7^4)^745+z, Z(7^4)^746+z, Z(7^4)^747+z,
Z(7^4)^748+z, Z(7^4)^749+z, Z(7^4)^751+z, Z(7^4)^752+z, Z(7^4)^753+z, Z(7^4)^754+z, Z(7^4)^755+z, Z(7^4)^756+z,
Z(7^4)^757+z, Z(7^4)^758+z, Z(7^4)^759+z, Z(7^4)^760+z, Z(7^4)^761+z, Z(7^4)^762+z, Z(7^4)^763+z, Z(7^4)^764+z,
Z(7^4)^765+z, Z(7^4)^766+z, Z(7^4)^767+z, Z(7^4)^768+z, Z(7^4)^769+z, Z(7^4)^770+z, Z(7^4)^771+z, Z(7^4)^772+z,
Z(7^4)^773+z, Z(7^4)^774+z, Z(7^4)^775+z, Z(7^4)^776+z, Z(7^4)^777+z, Z(7^4)^778+z, Z(7^4)^779+z, Z(7^4)^780+z,
Z(7^4)^781+z, Z(7^4)^782+z, Z(7^4)^783+z, Z(7^4)^784+z, Z(7^4)^785+z, Z(7^4)^786+z, Z(7^4)^787+z, Z(7^4)^788+z,
Z(7^4)^789+z, Z(7^4)^790+z, Z(7^4)^791+z, Z(7^4)^792+z, Z(7^4)^793+z, Z(7^4)^794+z, Z(7^4)^795+z, Z(7^4)^796+z,
Z(7^4)^797+z, Z(7^4)^798+z, Z(7^4)^799+z, Z(7^4)^801+z, Z(7^4)^802+z, Z(7^4)^803+z, Z(7^4)^804+z, Z(7^4)^805+z,
Z(7^4)^806+z, Z(7^4)^807+z, Z(7^4)^808+z, Z(7^4)^809+z, Z(7^4)^810+z, Z(7^4)^811+z, Z(7^4)^812+z, Z(7^4)^813+z,
Z(7^4)^814+z, Z(7^4)^815+z, Z(7^4)^816+z, Z(7^4)^817+z, Z(7^4)^818+z, Z(7^4)^819+z, Z(7^4)^820+z, Z(7^4)^821+z,
Z(7^4)^822+z, Z(7^4)^823+z, Z(7^4)^824+z, Z(7^4)^825+z, Z(7^4)^826+z, Z(7^4)^827+z, Z(7^4)^828+z, Z(7^4)^829+z,
Z(7^4)^830+z, Z(7^4)^831+z, Z(7^4)^832+z, Z(7^4)^833+z, Z(7^4)^834+z, Z(7^4)^835+z, Z(7^4)^836+z, Z(7^4)^837+z,
Z(7^4)^838+z, Z(7^4)^839+z, Z(7^4)^840+z, Z(7^4)^841+z, Z(7^4)^842+z, Z(7^4)^843+z, Z(7^4)^844+z, Z(7^4)^845+z,
Z(7^4)^846+z, Z(7^4)^847+z, Z(7^4)^848+z, Z(7^4)^849+z, Z(7^4)^851+z, Z(7^4)^852+z, Z(7^4)^853+z, Z(7^4)^854+z,
Z(7^4)^855+z, Z(7^4)^856+z, Z(7^4)^857+z, Z(7^4)^858+z, Z(7^4)^859+z, Z(7^4)^860+z, Z(7^4)^861+z, Z(7^4)^862+z,
Z(7^4)^863+z, Z(7^4)^864+z, Z(7^4)^865+z, Z(7^4)^866+z, Z(7^4)^867+z, Z(7^4)^868+z, Z(7^4)^869+z, Z(7^4)^870+z,
Z(7^4)^871+z, Z(7^4)^872+z, Z(7^4)^873+z, Z(7^4)^874+z, Z(7^4)^875+z, Z(7^4)^876+z, Z(7^4)^877+z, Z(7^4)^878+z,
Z(7^4)^879+z, Z(7^4)^880+z, Z(7^4)^881+z, Z(7^4)^882+z, Z(7^4)^883+z, Z(7^4)^884+z, Z(7^4)^885+z, Z(7^4)^886+z,
Z(7^4)^887+z, Z(7^4)^888+z, Z(7^4)^889+z, Z(7^4)^890+z, Z(7^4)^891+z, Z(7^4)^892+z, Z(7^4)^893+z, Z(7^4)^894+z,
Z(7^4)^895+z, Z(7^4)^896+z, Z(7^4)^897+z, Z(7^4)^898+z, Z(7^4)^899+z, Z(7^4)^901+z, Z(7^4)^902+z, Z(7^4)^903+z,
Z(7^4)^904+z, Z(7^4)^905+z, Z(7^4)^906+z, Z(7^4)^907+z, Z(7^4)^908+z, Z(7^4)^909+z, Z(7^4)^910+z, Z(7^4)^911+z,
Z(7^4)^912+z, Z(7^4)^913+z, Z(7^4)^914+z, Z(7^4)^915+z, Z(7^4)^916+z, Z(7^4)^917+z, Z(7^4)^918+z, Z(7^4)^919+z,
Z(7^4)^920+z, Z(7^4)^921+z, Z(7^4)^922+z, Z(7^4)^923+z, Z(7^4)^924+z, Z(7^4)^925+z, Z(7^4)^926+z, Z(7^4)^927+z,
Z(7^4)^928+z, Z(7^4)^929+z, Z(7^4)^930+z, Z(7^4)^931+z, Z(7^4)^932+z, Z(7^4)^933+z, Z(7^4)^934+z, Z(7^4)^935+z,
Z(7^4)^936+z, Z(7^4)^937+z, Z(7^4)^938+z, Z(7^4)^939+z, Z(7^4)^940+z, Z(7^4)^941+z, Z(7^4)^942+z, Z(7^4)^943+z,
Z(7^4)^944+z, Z(7^4)^945+z, Z(7^4)^946+z, Z(7^4)^947+z, Z(7^4)^948+z, Z(7^4)^949+z, Z(7^4)^951+z, Z(7^4)^952+z,
Z(7^4)^953+z, Z(7^4)^954+z, Z(7^4)^955+z, Z(7^4)^956+z, Z(7^4)^957+z, Z(7^4)^958+z, Z(7^4)^959+z, Z(7^4)^960+z,
Z(7^4)^961+z, Z(7^4)^962+z, Z(7^4)^963+z, Z(7^4)^964+z, Z(7^4)^965+z, Z(7^4)^966+z, Z(7^4)^967+z, Z(7^4)^968+z,
Z(7^4)^969+z, Z(7^4)^970+z, Z(7^4)^971+z, Z(7^4)^972+z, Z(7^4)^973+z, Z(7^4)^974+z, Z(7^4)^975+z, Z(7^4)^976+z,
Z(7^4)^977+z, Z(7^4)^978+z, Z(7^4)^979+z, Z(7^4)^980+z, Z(7^4)^981+z, Z(7^4)^982+z, Z(7^4)^983+z, Z(7^4)^984+z,
Z(7^4)^985+z, Z(7^4)^986+z, Z(7^4)^987+z, Z(7^4)^988+z, Z(7^4)^989+z, Z(7^4)^990+z, Z(7^4)^991+z, Z(7^4)^992+z,
Z(7^4)^993+z, Z(7^4)^994+z, Z(7^4)^995+z, Z(7^4)^996+z, Z(7^4)^997+z, Z(7^4)^998+z, Z(7^4)^999+z, Z(7^4)^1001+z,
Z(7^4)^1002+z, Z(7^4)^1003+z, Z(7^4)^1004+z, Z(7^4)^1005+z, Z(7^4)^1006+z, Z(7^4)^1007+z, Z(7^4)^1008+z,
Z(7^4)^1009+z, Z(7^4)^1010+z, Z(7^4)^1011+z, Z(7^4)^1012+z, Z(7^4)^1013+z, Z(7^4)^1014+z, Z(7^4)^1015+z,
Z(7^4)^1016+z, Z(7^4)^1017+z, Z(7^4)^1018+z, Z(7^4)^1019+z, Z(7^4)^1020+z, Z(7^4)^1021+z, Z(7^4)^1022+z,
Z(7^4)^1023+z, Z(7^4)^1024+z, Z(7^4)^1025+z, Z(7^4)^1026+z, Z(7^4)^1027+z, Z(7^4)^1028+z, Z(7^4)^1029+z,
Z(7^4)^1030+z, Z(7^4)^1031+z, Z(7^4)^1032+z, Z(7^4)^1033+z, Z(7^4)^1034+z, Z(7^4)^1035+z, Z(7^4)^1036+z,
Z(7^4)^1037+z, Z(7^4)^1038+z, Z(7^4)^1039+z, Z(7^4)^1040+z, Z(7^4)^1041+z, Z(7^4)^1042+z, Z(7^4)^1043+z,
Z(7^4)^1044+z, Z(7^4)^1045+z, Z(7^4)^1046+z, Z(7^4)^1047+z, Z(7^4)^1048+z, Z(7^4)^1049+z, Z(7^4)^1051+z,
Z(7^4)^1052+z, Z(7^4)^1053+z, Z(7^4)^1054+z, Z(7^4)^1055+z, Z(7^4)^1056+z, Z(7^4)^1057+z, Z(7^4)^1058+z,
Z(7^4)^1059+z, Z(7^4)^1060+z, Z(7^4)^1061+z, Z(7^4)^1062+z, Z(7^4)^1063+z, Z(7^4)^1064+z, Z(7^4)^1065+z,
Z(7^4)^1066+z, Z(7^4)^1067+z, Z(7^4)^1068+z, Z(7^4)^1069+z, Z(7^4)^1070+z, Z(7^4)^1071+z, Z(7^4)^1072+z,
Z(7^4)^1073+z, Z(7^4)^1074+z, Z(7^4)^1075+z, Z(7^4)^1076+z, Z(7^4)^1077+z, Z(7^4)^1078+z, Z(7^4)^1079+z,
Z(7^4)^1080+z, Z(7^4)^1081+z, Z(7^4)^1082+z, Z(7^4)^1083+z, Z(7^4)^1084+z, Z(7^4)^1085+z, Z(7^4)^1086+z,
Z(7^4)^1087+z, Z(7^4)^1088+z, Z(7^4)^1089+z, Z(7^4)^1090+z, Z(7^4)^1091+z, Z(7^4)^1092+z, Z(7^4)^1093+z,
Z(7^4)^1094+z, Z(7^4)^1095+z, Z(7^4)^1096+z, Z(7^4)^1097+z, Z(7^4)^1098+z, Z(7^4)^1099+z, Z(7^4)^1101+z,
Z(7^4)^1102+z, Z(7^4)^1103+z, Z(7^4)^1104+z, Z(7^4)^1105+z, Z(7^4)^1106+z, Z(7^4)^1107+z, Z(7^4)^1108+z,
Z(7^4)^1109+z, Z(7^4)^1110+z, Z(7^4)^1111+z, Z(7^4)^1112+z, Z(7^4)^1113+z, Z(7^4)^1114+z, Z(7^4)^1115+z,
Z(7^4)^1116+z, Z(7^4)^1117+z, Z(7^4)^1118+z, Z(7^4)^1119+z, Z(7^4)^1120+z, Z(7^4)^1121+z, Z(7^4)^1122+z,
Z(7^4)^1123+z, Z(7^4)^1124+z, Z(7^4)^1125+z, Z(7^4)^1126+z, Z(7^4)^1127+z, Z(7^4)^1128+z, Z(7^4)^1129+z,
Z(7^4)^1130+z, Z(7^4)^1131+z, Z(7^4)^1132+z, Z(7^4)^1133+z, Z(7^4)^1134+z, Z(7^4)^1135+z, Z(7^4)^1136+z,
Z(7^4)^1137+z, Z(7^4)^1138+z, Z(7^4)^1139+z, Z(7^4)^1140+z, Z(7^4)^1141+z, Z(7^4)^1142+z, Z(7^4)^1143+z,
Z(7^4)^1144+z, Z(7^4)^1145+z, Z(7^4)^1146+z, Z(7^4)^1147+z, Z(7^4)^1148+z, Z(7^4)^1149+z, Z(7^4)^1151+z,
Z(7^4)^1152+z, Z(7^4)^1153+z, Z(7^4)^1154+z, Z(7^4)^1155+z, Z(7^4)^1156+z, Z(7^4)^1157+z, Z(7^4)^1158+z,
Z(7^4)^1159+z, Z(7^4)^1160+z, Z(7^4)^1161+z, Z(7^4)^1162+z, Z(7^4)^1163+z, Z(7^4)^1164+z, Z(7^4)^1165+z,
Z(7^4)^1166+z, Z(7^4)^1167+z, Z(7^4)^1168+z, Z(7^4)^1169+z, Z(7^4)^1170+z, Z(7^4)^1171+z, Z(7^4)^1172+z,
Z(7^4)^1173+z, Z(7^4)^1174+z, Z(7^4)^1175+z, Z(7^4)^1176+z, Z(7^4)^1177+z, Z(7^4)^1178+z, Z(7^4)^1179+z,
Z(7^4)^1180+z, Z(7^4)^1181+z, Z(7^4)^1182+z, Z(7^4)^1183+z, Z(7^4)^1184+z, Z(7^4)^1185+z, Z(7^4)^1186+z,
Z(7^4)^1187+z, Z(7^4)^1188+z, Z(7^4)^1189+z, Z(7^4)^1190+z, Z(7^4)^1191+z, Z(7^4)^1192+z, Z(7^4)^1193+z,
Z(7^4)^1194+z, Z(7^4)^1195+z, Z(7^4)^1196+z, Z(7^4)^1197+z, Z(7^4)^1198+z, Z(7^4)^1199+z, Z(7^4)^1201+z,
Z(7^4)^1202+z, Z(7^4)^1203+z, Z(7^4)^1204+z, Z(7^4)^1205+z, Z(7^4)^1206+z, Z(7^4)^1207+z, Z(7^4)^1208+z,
Z(7^4)^1209+z, Z(7^4)^1210+z, Z(7^4)^1211+z, Z(7^4)^1212+z, Z(7^4)^1213+z, Z(7^4)^1214+z, Z(7^4)^1215+z,
Z(7^4)^1216+z, Z(7^4)^1217+z, Z(7^4)^1218+z, Z(7^4)^1219+z, Z(7^4)^1220+z, Z(7^4)^1221+z, Z(7^4)^1222+z,
Z(7^4)^1223+z, Z(7^4)^1224+z, Z(7^4)^1225+z, Z(7^4)^1226+z, Z(7^4)^1227+z, Z(7^4)^1228+z, Z(7^4)^1229+z,
Z(7^4)^1230+z, Z(7^4)^1231+z, Z(7^4)^1232+z, Z(7^4)^1233+z, Z(7^4)^1234+z, Z(7^4)^1235+z, Z(7^4)^1236+z,
Z(7^4)^1237+z, Z(7^4)^1238+z, Z(7^4)^1239+z, Z(7^4)^1240+z, Z(7^4)^1241+z, Z(7^4)^1242+z, Z(7^4)^1243+z,
Z(7^4)^1244+z, Z(7^4)^1245+z, Z(7^4)^1246+z, Z(7^4)^1247+z, Z(7^4)^1248+z, Z(7^4)^1249+z, Z(7^4)^1251+z,
Z(7^4)^1252+z, Z(7^4)^1253+z, Z(7^4)^1254+z, Z(7^4)^1255+z, Z(7^4)^1256+z, Z(7^4)^1257+z, Z(7^4)^1258+z,
Z(7^4)^1259+z, Z(7^4)^1260+z, Z(7^4)^1261+z, Z(7^4)^1262+z, Z(7^4)^1263+z, Z(7^4)^1264+z, Z(7^4)^1265+z,
Z(7^4)^1266+z, Z(7^4)^1267+z, Z(7^4)^1268+z, Z(7^4)^1269+z, Z(7^4)^1270+z, Z(7^4)^1271+z, Z(7^4)^1272+z,
Z(7^4)^1273+z, Z(7^4)^1274+z, Z(7^4)^1275+z, Z(7^4)^1276+z, Z(7^4)^1277+z, Z(7^4)^1278+z, Z(7^4)^1279+z,
Z(7^4)^1280+z, Z(7^4)^1281+z, Z(7^4)^1282+z, Z(7^4)^1283+z, Z(7^4)^1284+z, Z(7^4)^1285+z, Z(7^4)^1286+z,
Z(7^4)^1287+z, Z(7^4)^1288+z, Z(7^4)^1289+z, Z(7^4)^1290+z, Z(7^4)^1291+z, Z(7^4)^1292+z, Z(7^4)^1293+z,
Z(7^4)^1294+z, Z(7^4)^1295+z, Z(7^4)^1296+z, Z(7^4)^1297+z, Z(7^4)^1298+z, Z(7^4)^1299+z, Z(7^4)^1301+z,
Z(7^4)^1302+z, Z(7^4)^1303+z, Z(7^4)^1304+z, Z(7^4)^1305+z, Z(7^4)^1306+z, Z(7^4)^1307+z, Z(7^4)^1308+z,
Z(7^4)^1309+z, Z(7^4)^1310+z, Z(7^4)^1311+z, Z(7^4)^1312+z, Z(7^4)^1313+z, Z(7^4)^1314+z, Z(7^4)^1315+z,
Z(7^4)^1316+z, Z(7^4)^1317+z, Z(7^4)^1318+z, Z(7^4)^1319+z, Z(7^4)^1320+z, Z(7^4)^1321+z, Z(7^4)^1322+z,
Z(7^4)^1323+z, Z(7^4)^1324+z, Z(7^4)^1325+z, Z(7^4)^1326+z, Z(7^4)^1327+z, Z(7^4)^1328+z, Z(7^4)^1329+z,
Z(7^4)^1330+z, Z(7^4)^1331+z, Z(7^4)^1332+z, Z(7^4)^1333+z, Z(7^4)^1334+z, Z(7^4)^1335+z, Z(7^4)^1336+z,
Z(7^4)^1337+z, Z(7^4)^1338+z, Z(7^4)^1339+z, Z(7^4)^1340+z, Z(7^4)^1341+z, Z(7^4)^1342+z, Z(7^4)^1343+z,
Z(7^4)^1344+z, Z(7^4)^1345+z, Z(7^4)^1346+z, Z(7^4)^1347+z, Z(7^4)^1348+z, Z(7^4)^1349+z, Z(7^4)^1351+z,
Z(7^4)^1352+z, Z(7^4)^1353+z, Z(7^4)^1354+z, Z(7^4)^1355+z, Z(7^4)^1356+z, Z(7^4)^1357+z, Z(7^4)^1358+z,
Z(7^4)^1359+z, Z(7^4)^1360+z, Z(7^4)^1361+z, Z(7^4)^1362+z, Z(7^4)^1363+z, Z(7^4)^1364+z, Z(7^4)^1365+z,
Z(7^4)^1366+z, Z(7^4)^1367+z, Z(7^4)^1368+z, Z(7^4)^1369+z, Z(7^4)^1370+z, Z(7^4)^1371+z, Z(7^4)^1372+z,
Z(7^4)^1373+z, Z(7^4)^1374+z, Z(7^4)^1375+z, Z(7^4)^1376+z, Z(7^4)^1377+z, Z(7^4)^1378+z, Z(7^4)^1379+z,
Z(7^4)^1380+z, Z(7^4)^1381+z, Z(7^4)^1382+z, Z(7^4)^1383+z, Z(7^4)^1384+z, Z(7^4)^1385+z, Z(7^4)^1386+z,
Z(7^4)^1387+z, Z(7^4)^1388+z, Z(7^4)^1389+z, Z(7^4)^1390+z, Z(7^4)^1391+z, Z(7^4)^1392+z, Z(7^4)^1393+z,
Z(7^4)^1394+z, Z(7^4)^1395+z, Z(7^4)^1396+z, Z(7^4)^1397+z, Z(7^4)^1398+z, Z(7^4)^1399+z, Z(7^4)^1401+z,
Z(7^4)^1402+z, Z(7^4)^1403+z, Z(7^4)^1404+z, Z(7^4)^1405+z, Z(7^4)^1406+z, Z(7^4)^1407+z, Z(7^4)^1408+z,
Z(7^4)^1409+z, Z(7^4)^1410+z, Z(7^4)^1411+z, Z(7^4)^1412+z, Z(7^4)^1413+z, Z(7^4)^1414+z, Z(7^4)^1415+z,
Z(7^4)^1416+z, Z(7^4)^1417+z, Z(7^4)^1418+z, Z(7^4)^1419+z, Z(7^4)^1420+z, Z(7^4)^1421+z, Z(7^4)^1422+z,
Z(7^4)^1423+z, Z(7^4)^1424+z, Z(7^4)^1425+z, Z(7^4)^1426+z, Z(7^4)^1427+z, Z(7^4)^1428+z, Z(7^4)^1429+z,
Z(7^4)^1430+z, Z(7^4)^1431+z, Z(7^4)^1432+z, Z(7^4)^1433+z, Z(7^4)^1434+z, Z(7^4)^1435+z, Z(7^4)^1436+z,
Z(7^4)^1437+z, Z(7^4)^1438+z, Z(7^4)^1439+z, Z(7^4)^1440+z, Z(7^4)^1441+z, Z(7^4)^1442+z, Z(7^4)^1443+z,
Z(7^4)^1444+z, Z(7^4)^1445+z, Z(7^4)^1446+z, Z(7^4)^1447+z, Z(7^4)^1448+z, Z(7^4)^1449+z, Z(7^4)^1451+z,
Z(7^4)^1452+z, Z(7^4)^1453+z, Z(7^4)^1454+z, Z(7^4)^1455+z, Z(7^4)^1456+z, Z(7^4)^1457+z, Z(7^4)^1458+z,
Z(7^4)^1459+z, Z(7^4)^1460+z, Z(7^4)^1461+z, Z(7^4)^1462+z, Z(7^4)^1463+z, Z(7^4)^1464+z, Z(7^4)^1465+z,
Z(7^4)^1466+z, Z(7^4)^1467+z, Z(7^4)^1468+z, Z(7^4)^1469+z, Z(7^4)^1470+z, Z(7^4)^1471+z, Z(7^4)^1472+z,
Z(7^4)^1473+z, Z(7^4)^1474+z, Z(7^4)^1475+z, Z(7^4)^1476+z, Z(7^4)^1477+z, Z(7^4)^1478+z, Z(7^4)^1479+z,
Z(7^4)^1480+z, Z(7^4)^1481+z, Z(7^4)^1482+z, Z(7^4)^1483+z, Z(7^4)^1484+z, Z(7^4)^1485+z, Z(7^4)^1486+z,
Z(7^4)^1487+z, Z(7^4)^1488+z, Z(7^4)^1489+z, Z(7^4)^1490+z, Z(7^4)^1491+z, Z(7^4)^1492+z, Z(7^4)^1493+z,
Z(7^4)^1494+z, Z(7^4)^1495+z, Z(7^4)^1496+z, Z(7^4)^1497+z, Z(7^4)^1498+z, Z(7^4)^1499+z, Z(7^4)^1501+z,
Z(7^4)^1502+z, Z(7^4)^1503+z, Z(7^4)^1504+z, Z(7^4)^1505+z, Z(7^4)^1506+z, Z(7^4)^1507+z, Z(7^4)^1508+z,
Z(7^4)^1509+z, Z(7^4)^1510+z, Z(7^4)^1511+z, Z(7^4)^1512+z, Z(7^4)^1513+z, Z(7^4)^1514+z, Z(7^4)^1515+z,
Z(7^4)^1516+z, Z(7^4)^1517+z, Z(7^4)^1518+z, Z(7^4)^1519+z, Z(7^4)^1520+z, Z(7^4)^1521+z, Z(7^4)^1522+z,
Z(7^4)^1523+z, Z(7^4)^1524+z, Z(7^4)^1525+z, Z(7^4)^1526+z, Z(7^4)^1527+z, Z(7^4)^1528+z, Z(7^4)^1529+z,
Z(7^4)^1530+z, Z(7^4)^1531+z, Z(7^4)^1532+z, Z(7^4)^1533+z, Z(7^4)^1534+z, Z(7^4)^1535+z, Z(7^4)^1536+z,
Z(7^4)^1537+z, Z(7^4)^1538+z, Z(7^4)^1539+z, Z(7^4)^1540+z, Z(7^4)^1541+z, Z(7^4)^1542+z, Z(7^4)^1543+z,
Z(7^4)^1544+z, Z(7^4)^1545+z, Z(7^4)^1546+z, Z(7^4)^1547+z, Z(7^4)^1548+z, Z(7^4)^1549+z, Z(7^4)^1551+z,
Z(7^4)^1552+z, Z(7^4)^1553+z, Z(7^4)^1554+z, Z(7^4)^1555+z, Z(7^4)^1556+z, Z(7^4)^1557+z, Z(7^4)^1558+z,
Z(7^4)^1559+z, Z(7^4)^1560+z, Z(7^4)^1561+z, Z(7^4)^1562+z, Z(7^4)^1563+z, Z(7^4)^1564+z, Z(7^4)^1565+z,
Z(7^4)^1566+z, Z(7^4)^1567+z, Z(7^4)^1568+z, Z(7^4)^1569+z, Z(7^4)^1570+z, Z(7^4)^1571+z, Z(7^4)^1572+z,
Z(7^4)^1573+z, Z(7^4)^1574+z, Z(7^4)^1575+z, Z(7^4)^1576+z, Z(7^4)^1577+z, Z(7^4)^1578+z, Z(7^4)^1579+z,
Z(7^4)^1580+z, Z(7^4)^1581+z, Z(7^4)^1582+z, Z(7^4)^1583+z, Z(7^4)^1584+z, Z(7^4)^1585+z, Z(7^4)^1586+z,
Z(7^4)^1587+z, Z(7^4)^1588+z, Z(7^4)^1589+z, Z(7^4)^1590+z, Z(7^4)^1591+z, Z(7^4)^1592+z, Z(7^4)^1593+z,
Z(7^4)^1594+z, Z(7^4)^1595+z, Z(7^4)^1596+z, Z(7^4)^1597+z, Z(7^4)^1598+z, Z(7^4)^1599+z, Z(7^4)^1601+z,
Z(7^4)^1602+z, Z(7^4)^1603+z, Z(7^4)^1604+z, Z(7^4)^1605+z, Z(7^4)^1606+z, Z(7^4)^1607+z, Z(7^4)^1608+z,
Z(7^4)^1609+z, Z(7^4)^1610+z, Z(7^4)^1611+z, Z(7^4)^1612+z, Z(7^4)^1613+z, Z(7^4)^1614+z, Z(7^4)^1615+z,
Z(7^4)^1616+z, Z(7^4)^1617+z, Z(7^4)^1618+z, Z(7^4)^1619+z, Z(7^4)^1620+z, Z(7^4)^1621+z, Z(7^4)^1622+z,
Z(7^4)^1623+z, Z(7^4)^1624+z, Z(7^4)^1625+z, Z(7^4)^1626+z, Z(7^4)^1627+z, Z(7^4)^1628+z, Z(7^4)^1629+z,
Z(7^4)^1630+z, Z(7^4)^1631+z, Z(7^4)^1632+z, Z(7^4)^1633+z, Z(7^4)^1634+z, Z(7^4)^1635+z, Z(7^4)^1636+z,
Z(7^4)^1637+z, Z(7^4)^1638+z, Z(7^4)^1639+z, Z(7^4)^1640+z, Z(7^4)^1641+z, Z(7^4)^1642+z, Z(7^4)^1643+z,
Z(7^4)^1644+z, Z(7^4)^1645+z, Z(7^4)^1646+z, Z(7^4)^1647+z, Z(7^4)^1648+z, Z(7^4)^1649+z, Z(7^4)^1651+z,
Z(7^4)^1652+z, Z(7^4)^1653+z, Z(7^4)^1654+z, Z(7^4)^1655+z, Z(7^4)^1656+z, Z(7^4)^1657+z, Z(7^4)^1658+z,
Z(7^4)^1659+z, Z(7^4)^1660+z, Z(7^4)^1661+z, Z(7^4)^1662+z, Z(7^4)^1663+z, Z(7^4)^1664+z, Z(7^4)^1665+z,
Z(7^4)^1666+z, Z(7^4)^1667+z, Z(7^4)^1668+z, Z(7^4)^1669+z, Z(7^4)^1670+z, Z(7^4)^1671+z, Z(7^4)^1672+z,
Z(7^4)^1673+z, Z(7^4)^1674+z, Z(7^4)^1675+z, Z(7^4)^1676+z, Z(7^4)^1677+z, Z(7^4)^1678+z, Z(7^4)^1679+z,
Z(7^4)^1680+z, Z(7^4)^1681+z, Z(7^4)^1682+z, Z(7^4)^1683+z, Z(7^4)^1684+z, Z(7^4)^1685+z, Z(7^4)^1686+z,
Z(7^4)^1687+z, Z(7^4)^1688+z, Z(7^4)^1689+z, Z(7^4)^1690+z, Z(7^4)^1691+z, Z(7^4)^1692+z, Z(7^4)^1693+z,
Z(7^4)^1694+z, Z(7^4)^1695+z, Z(7^4)^1696+z, Z(7^4)^1697+z, Z(7^4)^1698+z, Z(7^4)^1699+z, Z(7^4)^1701+z,
Z(7^4)^1702+z, Z(7^4)^1703+z, Z(7^4)^1704+z, Z(7^4)^1705+z, Z(7^4)^1706+z, Z(7^4)^1707+z, Z(7^4)^1708+z,
Z(7^4)^1709+z, Z(7^4)^1710+z, Z(7^4)^1711+z, Z(7^4)^1712+z, Z(7^4)^1713+z, Z(7^4)^1714+z, Z(7^4)^1715+z,
Z(7^4)^1716+z, Z(7^4)^1717+z, Z(7^4)^1718+z, Z(7^4)^1719+z, Z(7^4)^1720+z, Z(7^4)^1721+z, Z(7^4)^1722+z,
Z(7^4)^1723+z, Z(7^4)^1724+z, Z(7^4)^1725+z, Z(7^4)^1726+z, Z(7^4)^1727+z, Z(7^4)^1728+z, Z(7^4)^1729+z,
Z(7^4)^1730+z, Z(7^4)^1731+z, Z(7^4)^1732+z, Z(7^4)^1733+z, Z(7^4)^1734+z, Z(7^4)^1735+z, Z(7^4)^1736+z,
Z(7^4)^1737+z, Z(7^4)^1738+z, Z(7^4)^1739+z, Z(7^4)^1740+z, Z(7^4)^1741+z, Z(7^4)^1742+z, Z(7^4)^1743+z,
Z(7^4)^1744+z, Z(7^4)^1745+z, Z(7^4)^1746+z, Z(7^4)^1747+z, Z(7^4)^1748+z, Z(7^4)^1749+z, Z(7^4)^1751+z,
Z(7^4)^1752+z, Z(7^4)^1753+z, Z(7^4)^1754+z, Z(7^4)^1755+z, Z(7^4)^1756+z, Z(7^4)^1757+z, Z(7^4)^1758+z,
Z(7^4)^1759+z, Z(7^4)^1760+z, Z(7^4)^1761+z, Z(7^4)^1762+z, Z(7^4)^1763+z, Z(7^4)^1764+z, Z(7^4)^1765+z,
Z(7^4)^1766+z, Z(7^4)^1767+z, Z(7^4)^1768+z, Z(7^4)^1769+z, Z(7^4)^1770+z, Z(7^4)^1771+z, Z(7^4)^1772+z,
Z(7^4)^1773+z, Z(7^4)^1774+z, Z(7^4)^1775+z, Z(7^4)^1776+z, Z(7^4)^1777+z, Z(7^4)^1778+z, Z(7^4)^1779+z,
Z(7^4)^1780+z, Z(7^4)^1781+z, Z(7^4)^1782+z, Z(7^4)^1783+z, Z(7^4)^1784+z, Z(7^4)^1785+z, Z(7^4)^1786+z,
Z(7^4)^1787+z, Z(7^4)^1788+z, Z(7^4)^1789+z, Z(7^4)^1790+z, Z(7^4)^1791+z, Z(7^4)^1792+z, Z(7^4)^1793+z,
Z(7^4)^1794+z, Z(7^4)^1795+z, Z(7^4)^1796+z, Z(7^4)^1797+z, Z(7^4)^1798+z, Z(7^4)^1799+z, Z(7^4)^1801+z,
Z(7^4)^1802+z, Z(7^4)^1803+z, Z(7^4)^1804+z, Z(7^4)^1805+z, Z(7^4)^1806+z, Z(7^4)^1807+z, Z(7^4)^1808+z,
Z(7^4)^1809+z, Z(7^4)^1810+z, Z(7^4)^1811+z, Z(7^4)^1812+z, Z(7^4)^1813+z, Z(7^4)^1814+z, Z(7^4)^1815+z,
Z(7^4)^1816+z, Z(7^4)^1817+z, Z(7^4)^1818+z, Z(7^4)^1819+z, Z(7^4)^1820+z, Z(7^4)^1821+z, Z(7^4)^1822+z,
Z(7^4)^1823+z, Z(7^4)^1824+z, Z(7^4)^1825+z, Z(7^4)^1826+z, Z(7^4)^1827+z, Z(7^4)^1828+z, Z(7^4)^1829+z,
Z(7^4)^1830+z, Z(7^4)^1831+z, Z(7^4)^1832+z, Z(7^4)^1833+z, Z(7^4)^1834+z, Z(7^4)^1835+z, Z(7^4)^1836+z,
Z(7^4)^1837+z, Z(7^4)^1838+z, Z(7^4)^1839+z, Z(7^4)^1840+z, Z(7^4)^1841+z, Z(7^4)^1842+z, Z(7^4)^1843+z,
Z(7^4)^1844+z, Z(7^4)^1845+z, Z(7^4)^1846+z, Z(7^4)^1847+z, Z(7^4)^1848+z, Z(7^4)^1849+z, Z(7^4)^1851+z,
Z(7^4)^1852+z, Z(7^4)^1853+z, Z(7^4)^1854+z, Z(7^4)^1855+z, Z(7^4)^1856+z, Z(7^4)^1857+z, Z(7^4)^1858+z,
Z(7^4)^1859+z, Z(7^4)^1860+z, Z(7^4)^1861+z, Z(7^4)^1862+z, Z(7^4)^1863+z, Z(7^4)^1864+z, Z(7^4)^1865+z,
Z(7^4)^1866+z, Z(7^4)^1867+z, Z(7^4)^1868+z, Z(7^4)^1869+z, Z(7^4)^1870+z, Z(7^4)^1871+z, Z(7^4)^1872+z,
Z(7^4)^1873+z, Z(7^4)^1874+z, Z(7^4)^1875+z, Z(7^4)^1876+z, Z(7^4)^1877+z, Z(7^4)^1878+z, Z(7^4)^1879+z,
Z(7^4)^1880+z, Z(7^4)^1881+z, Z(7^4)^1882+z, Z(7^4)^1883+z, Z(7^4)^1884+z, Z(7^4)^1885+z, Z(7^4)^1886+z,
Z(7^4)^1887+z, Z(7^4)^1888+z, Z(7^4)^1889+z, Z(7^4)^1890+z, Z(7^4)^1891+z, Z(7^4)^1892+z, Z(7^4)^1893+z,
Z(7^4)^1894+z, Z(7^4)^1895+z, Z(7^4)^1896+z, Z(7^4)^1897+z, Z(7^4)^1898+z, Z(7^4)^1899+z, Z(7^4)^1901+z,
Z(7^4)^1902+z, Z(7^4)^1903+z, Z(7^4)^1904+z, Z(7^4)^1905+z, Z(7^4)^1906+z, Z(7^4)^1907+z, Z(7^4)^1908+z,
Z(7^4)^1909+z, Z(7^4)^1910+z, Z(7^4)^1911+z, Z(7^4)^1912+z, Z(7^4)^1913+z, Z(7^4)^1914+z, Z(7^4)^1915+z,
Z(7^4)^1916+z, Z(7^4)^1917+z, Z(7^4)^1918+z, Z(7^4)^1919+z, Z(7^4)^1920+z, Z(7^4)^1921+z, Z(7^4)^1922+z,
Z(7^4)^1923+z, Z(7^4)^1924+z, Z(7^4)^1925+z, Z(7^4)^1926+z, Z(7^4)^1927+z, Z(7^4)^1928+z, Z(7^4)^1929+z,
Z(7^4)^1930+z, Z(7^4)^1931+z, Z(7^4)^1932+z, Z(7^4)^1933+z, Z(7^4)^1934+z, Z(7^4)^1935+z, Z(7^4)^1936+z,
Z(7^4)^1937+z, Z(7^4)^1938+z, Z(7^4)^1939+z, Z(7^4)^1940+z, Z(7^4)^1941+z, Z(7^4)^1942+z, Z(7^4)^1943+z,
Z(7^4)^1944+z, Z(7^4)^1945+z, Z(7^4)^1946+z, Z(7^4)^1947+z, Z(7^4)^1948+z, Z(7^4)^1949+z, Z(7^4)^1951+z,
Z(7^4)^1952+z, Z(7^4)^1953+z, Z(7^4)^1954+z, Z(7^4)^1955+z, Z(7^4)^1956+z, Z(7^4)^1957+z, Z(7^4)^1958+z,
Z(7^4)^1959+z, Z(7^4)^1960+z, Z(7^4)^1961+z, Z(7^4)^1962+z, Z(7^4)^1963+z, Z(7^4)^1964+z, Z(7^4)^1965+z,
Z(7^4)^1966+z, Z(7^4)^1967+z, Z(7^4)^1968+z, Z(7^4)^1969+z, Z(7^4)^1970+z, Z(7^4)^1971+z, Z(7^4)^1972+z,
Z(7^4)^1973+z, Z(7^4)^1974+z, Z(7^4)^1975+z, Z(7^4)^1976+z, Z(7^4)^1977+z, Z(7^4)^1978+z, Z(7^4)^1979+z,
Z(7^4)^1980+z, Z(7^4)^1981+z, Z(7^4)^1982+z, Z(7^4)^1983+z, Z(7^4)^1984+z, Z(7^4)^1985+z, Z(7^4)^1986+z,
Z(7^4)^1987+z, Z(7^4)^1988+z, Z(7^4)^1989+z, Z(7^4)^1990+z, Z(7^4)^1991+z, Z(7^4)^1992+z, Z(7^4)^1993+z,
Z(7^4)^1994+z, Z(7^4)^1995+z, Z(7^4)^1996+z, Z(7^4)^1997+z, Z(7^4)^1998+z, Z(7^4)^1999+z, Z(7^4)^2001+z,
Z(7^4)^2002+z, Z(7^4)^2003+z, Z(7^4)^2004+z, Z(7^4)^2005+z, Z(7^4)^2006+z, Z(7^4)^2007+z, Z(7^4)^2008+z,
Z(7^4)^2009+z, Z(7^4)^2010+z, Z(7^4)^2011+z, Z(7^4)^2012+z, Z(7^4)^2013+z, Z(7^4)^2014+z, Z(7^4)^2015+z,
Z(7^4)^2016+z, Z(7^4)^2017+z, Z(7^4)^2018+z, Z(7^4)^2019+z, Z(7^4)^2020+z, Z(7^4)^2021+z, Z(7^4)^2022+z,
Z(7^4)^2023+z, Z(7^4)^2024+z, Z(7^4)^2025+z, Z(7^4)^2026+z, Z(7^4)^2027+z, Z(7^4)^2028+z, Z(7^4)^2029+z,
Z(7^4)^2030+z, Z(7^4)^2031+z, Z(7^4)^2032+z, Z(7^4)^2033+z, Z(7^4)^2034+z, Z(7^4)^2035+z, Z(7^4)^2036+z,
Z(7^4)^2037+z, Z(7^4)^2038+z, Z(7^4)^2039+z, Z(7^4)^2040+z, Z(7^4)^2041+z, Z(7^4)^2042+z, Z(7^4)^2043+z,
Z(7^4)^2044+z, Z(7^4)^2045+z, Z(7^4)^2046+z, Z(7^4)^2047+z, Z(7^4)^2048+z, Z(7^4)^2049+z, Z(7^4)^2051+z,
Z(7^4)^2052+z, Z(7^4)^2053+z, Z(7^4)^2054+z, Z(7^4)^2055+z, Z(7^4)^2056+z, Z(7^4)^2057+z, Z(7^4)^2058+z,
Z(7^4)^2059+z, Z(7^4)^2060+z, Z(7^4)^2061+z, Z(7^4)^2062+z, Z(7^4)^2063+z, Z(7^4)^2064+z, Z(7^4)^2065+z,
Z(7^4)^2066+z, Z(7^4)^2067+z, Z(7^4)^2068+z, Z(7^4)^2069+z, Z(7^4)^2070+z, Z(7^4)^2071+z, Z(7^4)^2072+z,
Z(7^4)^2073+z, Z(7^4)^2074+z, Z(7^4)^2075+z, Z(7^4)^2076+z, Z(7^4)^2077+z, Z(7^4)^2078+z, Z(7^4)^2079+z,
Z(7^4)^2080+z, Z(7^4)^2081+z, Z(7^4)^2082+z, Z(7^4)^2083+z, Z(7^4)^2084+z, Z(7^4)^2085+z, Z(7^4)^2086+z,
Z(7^4)^2087+z, Z(7^4)^2088+z, Z(7^4)^2089+z, Z(7^4)^2090+z, Z(7^4)^2091+z, Z(7^4)^2092+z, Z(7^4)^2093+z,
Z(7^4)^2094+z, Z(7^4)^2095+z, Z(7^4)^2096+z, Z(7^4)^2097+z, Z(7^4)^2098+z, Z(7^4)^2099+z, Z(7^4)^2101+z,
Z(7^4)^2102+z, Z(7^4)^2103+z, Z(7^4)^2104+z, Z(7^4)^2105+z, Z(7^4)^2106+z, Z(7^4)^2107+z, Z(7^4)^2108+z,
Z(7^4)^2109+z, Z(7^4)^2110+z, Z(7^4)^2111+z, Z(7^4)^2112+z, Z(7^4)^2113+z, Z(7^4)^2114+z, Z(7^4)^2115+z,
Z(7^4)^2116+z, Z(7^4)^2117+z, Z(7^4)^2118+z, Z(7^4)^2119+z, Z(7^4)^2120+z, Z(7^4)^2121+z, Z(7^4)^2122+z,
Z(7^4)^2123+z, Z(7^4)^2124+z, Z(7^4)^2125+z, Z(7^4)^2126+z, Z(7^4)^2127+z, Z(7^4)^2128+z, Z(7^4)^2129+z,
Z(7^4)^2130+z, Z(7^4)^2131+z, Z(7^4)^2132+z, Z(7^4)^2133+z, Z(7^4)^2134+z, Z(7^4)^2135+z, Z(7^4)^2136+z,
Z(7^4)^2137+z, Z(7^4)^2138+z, Z(7^4)^2139+z, Z(7^4)^2140+z, Z(7^4)^2141+z, Z(7^4)^2142+z, Z(7^4)^2143+z,
Z(7^4)^2144+z, Z(7^4)^2145+z, Z(7^4)^2146+z, Z(7^4)^2147+z, Z(7^4)^2148+z, Z(7^4)^2149+z, Z(7^4)^2151+z,
Z(7^4)^2152+z, Z(7^4)^2153+z, Z(7^4)^2154+z, Z(7^4)^2155+z, Z(7^4)^2156+z, Z(7^4)^2157+z, Z(7^4)^2158+z,
Z(7^4)^2159+z, Z(7^4)^2160+z, Z(7^4)^2161+z, Z(7^4)^2162+z, Z(7^4)^2163+z, Z(7^4)^2164+z, Z(7^4)^2165+z,
Z(7^4)^2166+z, Z(7^4)^2167+z, Z(7^4)^2168+z, Z(7^4)^2169+z, Z(7^4)^2170+z, Z(7^4)^2171+z, Z(7^4)^2172+z,
Z(7^4)^2173+z, Z(7^4)^2174+z, Z(7^4)^2175+z, Z(7^4)^2176+z, Z(7^4)^2177+z, Z(7^4)^2178+z, Z(7^4)^2179+z,
Z(7^4)^2180+z, Z(7^4)^2181+z, Z(7^4)^2182+z, Z(7^4)^2183+z, Z(7^4)^2184+z, Z(7^4)^2185+z, Z(7^4)^2186+z,
Z(7^4)^2187+z, Z(7^4)^2188+z, Z(7^4)^2189+z, Z(7^4)^2190+z, Z(7^4)^2191+z, Z(7^4)^2192+z, Z(7^4)^2193+z,
Z(7^4)^2194+z, Z(7^4)^2195+z, Z(7^4)^2196+z, Z(7^4)^2197+z, Z(7^4)^2198+z, Z(7^4)^2199+z, Z(7^4)^2201+z,
Z(7^4)^2202+z, Z(7^4)^2203+z, Z(7^4)^2204+z, Z(7^4)^2205+z, Z(7^4)^2206+z, Z(7^4)^2207+z, Z(7^4)^2208+z,
Z(7^4)^2209+z, Z(7^4)^2210+z, Z(7^4)^2211+z, Z(7^4)^2212+z, Z(7^4)^2213+z, Z(7^4)^2214+z, Z(7^4)^2215+z,
Z(7^4)^2216+z, Z(7^4)^2217+z, Z(7^4)^2218+z, Z(7^4)^2219+z, Z(7^4)^2220+z, Z(7^4)^2221+z, Z(7^4)^2222+z,
Z(7^4)^2223+z, Z(7^4)^2224+z, Z(7^4)^2225+z, Z(7^4)^2226+z, Z(7^4)^2227+z, Z(7^4)^2228+z, Z(7^4)^2229+z,
Z(7^4)^2230+z, Z(7^4)^2231+z, Z(7^4)^2232+z, Z(7^4)^2233+z, Z(7^4)^2234+z, Z(7^4)^2235+z, Z(7^4)^2236+z,
Z(7^4)^2237+z, Z(7^4)^2238+z, Z(7^4)^2239+z, Z(7^4)^2240+z, Z(7^4)^2241+z, Z(7^4)^2242+z, Z(7^4)^2243+z,
Z(7^4)^2244+z, Z(7^4)^2245+z, Z(7^4)^2246+z, Z(7^4)^2247+z, Z(7^4)^2248+z, Z(7^4)^2249+z, Z(7^4)^2251+z,
Z(7^4)^2252+z, Z(7^4)^2253+z, Z(7^4)^2254+z, Z(7^4)^2255+z, Z(7^4)^2256+z, Z(7^4)^2257+z, Z(7^4)^2258+z,
Z(7^4)^2259+z, Z(7^4)^2260+z, Z(7^4)^2261+z, Z(7^4)^2262+z, Z(7^4)^2263+z, Z(7^4)^2264+z, Z(7^4)^2265+z,
Z(7^4)^2266+z, Z(7^4)^2267+z, Z(7^4)^2268+z, Z(7^4)^2269+z, Z(7^4)^2270+z, Z(7^4)^2271+z, Z(7^4)^2272+z,
Z(7^4)^2273+z, Z(7^4)^2274+z, Z(7^4)^2275+z, Z(7^4)^2276+z, Z(7^4)^2277+z, Z(7^4)^2278+z, Z(7^4)^2279+z,
Z(7^4)^2280+z, Z(7^4)^2281+z, Z(7^4)^2282+z, Z(7^4)^2283+z, Z(7^4)^2284+z, Z(7^4)^2285+z, Z(7^4)^2286+z,
Z(7^4)^2287+z, Z(7^4)^2288+z, Z(7^4)^2289+z, Z(7^4)^2290+z, Z(7^4)^2291+z, Z(7^4)^2292+z, Z(7^4)^2293+z,
Z(7^4)^2294+z, Z(7^4)^2295+z, Z(7^4)^2296+z, Z(7^4)^2297+z, Z(7^4)^2298+z, Z(7^4)^2299+z, Z(7^4)^2301+z,
Z(7^4)^2302+z, Z(7^4)^2303+z, Z(7^4)^2304+z, Z(7^4)^2305+z, Z(7^4)^2306+z, Z(7^4)^2307+z, Z(7^4)^2308+z,
Z(7^4)^2309+z, Z(7^4)^2310+z, Z(7^4)^2311+z, Z(7^4)^2312+z, Z(7^4)^2313+z, Z(7^4)^2314+z, Z(7^4)^2315+z,
Z(7^4)^2316+z, Z(7^4)^2317+z, Z(7^4)^2318+z, Z(7^4)^2319+z, Z(7^4)^2320+z, Z(7^4)^2321+z, Z(7^4)^2322+z,
Z(7^4)^2323+z, Z(7^4)^2324+z, Z(7^4)^2325+z, Z(7^4)^2326+z, Z(7^4)^2327+z, Z(7^4)^2328+z, Z(7^4)^2329+z,
Z(7^4)^2330+z, Z(7^4)^2331+z, Z(7^4)^2332+z, Z(7^4)^2333+z, Z(7^4)^2334+z, Z(7^4)^2335+z, Z(7^4)^2336+z,
Z(7^4)^2337+z, Z(7^4)^2338+z, Z(7^4)^2339+z, Z(7^4)^2340+z, Z(7^4)^2341+z, Z(7^4)^2342+z, Z(7^4)^2343+z,
Z(7^4)^2344+z, Z(7^4)^2345+z, Z(7^4)^2346+z, Z(7^4)^2347+z, Z(7^4)^2348+z, Z(7^4)^2349+z, Z(7^4)^2351+z,
Z(7^4)^2352+z, Z(7^4)^2353+z, Z(7^4)^2354+z, Z(7^4)^2355+z, Z(7^4)^2356+z, Z(7^4)^2357+z, Z(7^4)^2358+z,
Z(7^4)^2359+z, Z(7^4)^2360+z, Z(7^4)^2361+z, Z(7^4)^2362+z, Z(7^4)^2363+z, Z(7^4)^2364+z, Z(7^4)^2365+z,
Z(7^4)^2366+z, Z(7^4)^2367+z, Z(7^4)^2368+z, Z(7^4)^2369+z, Z(7^4)^2370+z, Z(7^4)^2371+z, Z(7^4)^2372+z,
Z(7^4)^2373+z, Z(7^4)^2374+z, Z(7^4)^2375+z, Z(7^4)^2376+z, Z(7^4)^2377+z, Z(7^4)^2378+z, Z(7^4)^2379+z,
Z(7^4)^2380+z, Z(7^4)^2381+z, Z(7^4)^2382+z, Z(7^4)^2383+z, Z(7^4)^2384+z, Z(7^4)^2385+z, Z(7^4)^2386+z,
Z(7^4)^2387+z, Z(7^4)^2388+z, Z(7^4)^2389+z, Z(7^4)^2390+z, Z(7^4)^2391+z, Z(7^4)^2392+z, Z(7^4)^2393+z,
Z(7^4)^2394+z, Z(7^4)^2395+z, Z(7^4)^2396+z, Z(7^4)^2397+z, Z(7^4)^2398+z, Z(7^4)^2399+z ]
gap> List(factors,Degree);
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1 ]
gap> R:=Integers mod 2;
GF(2)
gap> x:=X(R,"x");
x
gap> g := 1+x^2+x^3;
Z(2)^0+x^2+x^3
gap> a := x+x^2+x^4;
x+x^2+x^4
gap> b:=a*g;
x+x^2+x^3+x^4+x^5+x^6+x^7
gap> CoefficientsOfLaurentPolynomial(b);
[ <an immutable GF2 vector of length 7>, 1 ]
gap> Elements(CoefficientsOfLaurentPolynomial(b));
[ 1, <an immutable GF2 vector of length 7> ]
gap> em:=CoefficientsOfLaurentPolynomial(b);
[ <an immutable GF2 vector of length 7>, 1 ]
gap> Elements(em[1]);
[ Z(2)^0 ]
gap> Elements(em[2]);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `AsSSortedList' on 1 arguments called from
AsSSortedList( coll ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> CoefficientsOfUnivariatePolynomial(b);
<an immutable GF2 vector of length 8>
gap> Elements(CoefficientsOfUnivariatePolynomial(b));
[ 0*Z(2), Z(2)^0 ]
gap> IntVecFFE(b);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `IntVecFFE' on 1 arguments called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> g*(1+x+x^3);
Z(2)^0+x+x^2+x^3+x^4+x^5+x^6
gap> IntVecFFE( CoefficientsOfUnivariatePolynomial( b ) );
[ 0, 1, 1, 1, 1, 1, 1, 1 ]
gap> IntVecFFE( CoefficientsOfUnivariatePolynomial( g*(1+x+x^3) ) );
[ 1, 1, 1, 1, 1, 1, 1 ]
gap> Factors(g);
[ Z(2)^0+x^2+x^3 ]
gap> polyring:=PolynomialRing(GF(8));
PolynomialRing(..., [ x ])
gap> factors:=Factors(polyring,g);
[ Z(2^3)^3+x, Z(2^3)^5+x, Z(2^3)^6+x ]
gap> a:=Z(2^3)^3;
Z(2^3)^3
gap> a^2;
Z(2^3)^6
gap> a^3;
Z(2^3)^2
gap> a^4;
Z(2^3)^5
gap> a^5;
Z(2^3)
gap> a^6;
Z(2^3)^4
gap> a^7;
Z(2)^0
gap> 1+a;
Z(2^3)
gap> 1+a^2;
Z(2^3)^2
gap> a+a^2;
Z(2^3)^4
gap> 1+a+a^2;
Z(2^3)^5
gap> v:=x+x^2+x^5+x^6;
x+x^2+x^5+x^6
gap> v/g;
(x+x^2+x^5+x^6)/(Z(2)^0+x^2+x^3)
gap> PolynomialReduction(v,[g],MonomialTotalDegreeLess);
[ Z(2)+x, [ Z(2)+x^3 ] ]
gap> w:=v+x+1;
Z(2)^0+x^2+x^5+x^6
gap> w:=v+x^5;
x+x^2+x^6
gap> w/g;
x+x^2+x^3
gap> v:=x+x^4+x^5+x^6;
x+x^4+x^5+x^6
gap> v/g;
x+x^3
gap> v:=1+x+x^2+x^4+x^5+x^6;
Z(2)^0+x+x^2+x^4+x^5+x^6
gap> v/g;
(Z(2)^0+x+x^2+x^4+x^5+x^6)/(Z(2)^0+x^2+x^3)
gap> PolynomialReduction(v,[g],MonomialTotalDegreeLess);
[ Z(2)+x^2, [ x+x^3 ] ]
gap> w:=v+x^3;
Z(2)^0+x+x^2+x^3+x^4+x^5+x^6
gap> w/g;
Z(2)^0+x+x^3
gap> x:= X(Rationals, "x");
x
gap> F:= AlgebraicExtension(Rationals, x^4-10*x^2+1);
<field in characteristic 0>
gap> a:= RootOfDefiningPolynomial(F);
(a)
gap> a^3;
(a^3)
gap> g:= GaloisGroup(AsField(GF(3),GF(81)));
<group with 1 generators>
gap> Size(g);
4
gap> Elements(g);
[ IdentityMapping( GF(3^4) ), FrobeniusAutomorphism( GF(3^4) )^2, FrobeniusAutomorphism( GF(3^4) ),
FrobeniusAutomorphism( GF(3^4) )^3 ]
gap> IsCyclic(g);
true
gap> Subfields(GF(81));
[ GF(3), GF(3^2), GF(3^4) ]
gap> g:= GaloisGroup(AsField(GF(2), GF(2^3));
Syntax error: ) expected
g:= GaloisGroup(AsField(GF(2), GF(2^3));
^
gap> g:= GaloisGroup(AsField(GF(2), GF(2^3)));
<group with 1 generators>
gap> Size(g);
3
gap> g:= GaloisGroup(AsField(GF(2), GF(2^5)));
<group with 1 generators>
gap> Size(g);
5
gap> g:= GaloisGroup(AsField(GF(2), GF(2^9)));
<group with 1 generators>
gap> Size(g);
9
gap> IsAbelian(g);
true
gap> IsCyclic(g);
true
gap> g:= GaloisGroup(AsField(GF(3^2), GF(3^8)));
<group with 1 generators>
gap> Size(g);
4
gap> IsCyclic(g);
true
gap> g:= GaloisGroup(AsField(GF(3^2), GF(3^10)));
<group with 1 generators>
gap>
gap> IsCyclic(g);
true
gap> Factors(x^4-10*x^2+1);
[ 1-10*x^2+x^4 ]
gap> LogTo();
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This PREP workshop is made possible by the NSF grant DUE: 0089005