Section 12, continued
gap> Z(3^2); Z(3^2) gap> Z(3)^2 > ; Z(3)^0 gap> Order(Z(3^2)); 8 gap> Order(Z(2^6)); 63 gap> Order(Z(2^2)); 3 gap> Order(Z(2^2)^3); 1 gap> Z(4) = Z(2^2); true gap> DegreeFFE(Z(2^7)); 7
Exercise 12.1 gap> DegreeFFE(Z(2^4)); 4 gap> DegreeFFE(Z(2^4)^3); 4 gap> DegreeFFE(Z((2^4)^3)); 12 gap> DegreeFFE(Z(2^12)); 12 gap> DegreeFFE(Z(2^4)^5); 2 gap> DegreeFFE(Z(2^4)^1); DegreeFFE(Z(2^4)^2); DegreeFFE(Z(2^4)^3); 4 4 4 gap> DegreeFFE(Z(2^4)^4); DegreeFFE(Z(2^4)^5); DegreeFFE(Z(2^4)^6); 4 2 4 gap> DegreeFFE(Z(2^4)^7); DegreeFFE(Z(2^4)^8); DegreeFFE(Z(2^4)^9); 4 4 4 gap> DegreeFFE(Z(2^4)^10); 2
Exercise 12.2 gap> Order(Z(2^4)^1); Order(Z(2^4)^2); Order(Z(2^4)^3); 15 15 5 gap> Order(Z(2^4)^4); Order(Z(2^4)^5); Order(Z(2^4)^6); 15 3 5 gap> Order(Z(2^4)^7); Order(Z(2^4)^8); Order(Z(2^4)^9); 15 15 5 gap> Order(Z(2^4)^10); 3
Exercise 12.3 gap> DegreeFFE(Z(3^3)^1); DegreeFFE(Z(3^3)^2); DegreeFFE(Z(3^3)^3); 3 3 3 gap> DegreeFFE(Z(3^3)^4); DegreeFFE(Z(3^3)^5); DegreeFFE(Z(3^3)^6); 3 3 3 gap> DegreeFFE(Z(3^3)^7); DegreeFFE(Z(3^3)^8); DegreeFFE(Z(3^3)^9); 3 3 3 gap> DegreeFFE(Z(3^3)^10); 3 gap> DegreeFFE(Z(3^3)^11); DegreeFFE(Z(3^3)^12); DegreeFFE(Z(3^3)^13); 3 3 1 gap> DegreeFFE(Z(3^3)^14); DegreeFFE(Z(3^3)^15); 3 3
Exercise 12.4 gap> Order(Z(3^3)^1); Order(Z(3^3)^2); Order(Z(3^3)^3); 26 13 26 gap> Order(Z(3^3)^4); Order(Z(3^3)^5); Order(Z(3^3)^6); 13 26 13 gap> Order(Z(3^3)^7); Order(Z(3^3)^8); Order(Z(3^3)^9); 26 13 26 gap> Order(Z(3^3)^10); Order(Z(3^3)^11); Order(Z(3^3)^12); 13 26 13 gap> Order(Z(3^3)^13); Order(Z(3^3)^14); Order(Z(3^3)^15); 2 13 26
Exercise 12.6 gap> x:= X(GF(3), "x"); x gap> Factors(x^9-x); [ x, x+Z(3)^0, x-Z(3)^0, x^2+Z(3)^0, x^2+x-Z(3)^0, x^2-x-Z(3)^0 ] gap> Factors(x^27-x); [ x, x+Z(3)^0, x-Z(3)^0, x^3-x+Z(3)^0, x^3-x-Z(3)^0, x^3+x^2-Z(3)^0, x^3+x^2+x-Z(3)^0, x^3+x^2-x+Z(3)^0, x^3-x^2+Z(3)^0, x^3-x^2+x+Z(3)^0, x^3-x^2-x-Z(3)^0 ] gap> Factors(x^81-x); [ x, x+Z(3)^0, x-Z(3)^0, x^2+Z(3)^0, x^2+x-Z(3)^0, x^2-x-Z(3)^0, x^4+x-Z(3)^0, x^4-x-Z(3)^0, x^4+x^2-Z(3)^0, x^4+x^2+x+Z(3)^0, x^4+x^2-x+Z(3)^0, x^4-x^2-Z(3)^0, x^4+x^3-Z(3)^0, x^4+x^3-x+Z(3)^0, x^4+x^3+x^2+Z(3)^0, x^4+x^3+x^2+x+Z(3)^0, x^4+x^3+x^2-x-Z(3)^0, x^4+x^3-x^2-x-Z(3)^0, x^4-x^3-Z(3)^0, x^4-x^3+x+Z(3)^0, x^4-x^3+x^2+Z(3)^0, x^4-x^3+x^2+x-Z(3)^0, x^4-x^3+x^2-x+Z(3)^0, x^4-x^3-x^2+x-Z(3)^0 ]
Exercise 12.7 gap> x:= X(GF(5), "x"); x gap> Factors(x^25-x); [ x, x+Z(5)^0, x+Z(5), x-Z(5)^0, x+Z(5)^3, x^2+Z(5), x^2+Z(5)^3, x^2+x+Z(5)^0, x^2+x+Z(5), x^2+Z(5)*x-Z(5)^0, x^2+Z(5)*x+Z(5)^3, x^2-x+Z(5)^0, x^2-x+Z(5), x^2+Z(5)^3*x-Z(5)^0, x^2+Z(5)^3*x+Z(5)^3 ] gap> Factors(x^125-x); [ x, x+Z(5)^0, x+Z(5), x-Z(5)^0, x+Z(5)^3, x^3+x+Z(5)^0, x^3+x-Z(5)^0, x^3+Z(5)*x+Z(5)^0, x^3+Z(5)*x-Z(5)^0, x^3-x+Z(5), x^3-x+Z(5)^3, x^3+Z(5)^3*x+Z(5), x^3+Z(5)^3*x+Z(5)^3, x^3+x^2+Z(5)^0, x^3+x^2+Z(5), x^3+x^2+x-Z(5)^0, x^3+x^2+x+Z(5)^3, x^3+x^2-x+Z(5)^0, x^3+x^2-x+Z(5)^3, x^3+x^2+Z(5)^3*x+Z(5)^0, x^3+x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)*x^2+Z(5)^0, x^3+Z(5)*x^2+Z(5)^3, x^3+Z(5)*x^2+x-Z(5)^0, x^3+Z(5)*x^2+x+Z(5)^3, x^3+Z(5)*x^2+Z(5)*x+Z(5), x^3+Z(5)*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)*x^2-x+Z(5), x^3+Z(5)*x^2-x-Z(5)^0, x^3-x^2-Z(5)^0, x^3-x^2+Z(5)^3, x^3-x^2+x+Z(5)^0, x^3-x^2+x+Z(5), x^3-x^2-x+Z(5), x^3-x^2-x-Z(5)^0, x^3-x^2+Z(5)^3*x+Z(5)^0, x^3-x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)^3*x^2+Z(5), x^3+Z(5)^3*x^2-Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)^3*x^2-x+Z(5)^0, x^3+Z(5)^3*x^2-x+Z(5)^3 ]
Exercise 12.10 gap> x:= X(GF(3), "x"); x gap> f:= x^3+ 2*x +1; x^3-x+Z(3)^0 gap> IsIrreducible(f); true gap> F:= AlgebraicExtension(GF(3), f); <field of size 27> gap> P:= PolynomialRing(F); PolynomialRing(..., [ x_1 ]) gap> x:= X(F, "x"); x gap> f:= x^3+ 2*x +1; x^3-x+!Z(3)^0 gap> Factors(P,f); [ x+(Z(3)*a), x+(Z(3)^0+Z(3)*a), x+(Z(3)+Z(3)*a) ] gap> Factors(f); [ x+(Z(3)*a), x+(Z(3)^0+Z(3)*a), x+(Z(3)+Z(3)*a) ]
Section 13: Extension Fields
gap> x := X(GF(3),"x"); x gap> Factors(x^9-x); [ x, x+Z(3)^0, x-Z(3)^0, x^2+Z(3)^0, x^2+x-Z(3)^0, x^2-x-Z(3)^0 ] gap> factors := Factors(x^9-x); [ x, x+Z(3)^0, x-Z(3)^0, x^2+Z(3)^0, x^2+x-Z(3)^0, x^2-x-Z(3)^0 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 2, 2, 2 ] gap> polyring := PolynomialRing(GF(9)); PolynomialRing(..., [ x ]) gap> factors := Factors(polyring,x^9-x); [ 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 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ] gap> factors := Factors(x^9-x); [ x, x+Z(3)^0, x-Z(3)^0, x^2+Z(3)^0, x^2+x-Z(3)^0, x^2-x-Z(3)^0 ] gap> f := factors[4]; x^2+Z(3)^0 gap> F := AlgebraicExtension(GF(3),f); <field of size 9> gap> x := X(F,"x"); x gap> Factors(x^9-x); [ x, x+(a), x+(Z(3)*a), x+!Z(3)^0, x+(Z(3)^0+a), x+(Z(3)^0+Z(3)*a), x-!Z(3)^0, x+(Z(3)+a), x+(Z(3)+Z(3)*a) ]
Exercise 13.1 gap> x := X(GF(5),"x"); x gap> Factors(x^125-x); [ x, x+Z(5)^0, x+Z(5), x-Z(5)^0, x+Z(5)^3, x^3+x+Z(5)^0, x^3+x-Z(5)^0, x^3+Z(5)*x+Z(5)^0, x^3+Z(5)*x-Z(5)^0, x^3-x+Z(5), x^3-x+Z(5)^3, x^3+Z(5)^3*x+Z(5), x^3+Z(5)^3*x+Z(5)^3, x^3+x^2+Z(5)^0, x^3+x^2+Z(5), x^3+x^2+x-Z(5)^0, x^3+x^2+x+Z(5)^3, x^3+x^2-x+Z(5)^0, x^3+x^2-x+Z(5)^3, x^3+x^2+Z(5)^3*x+Z(5)^0, x^3+x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)*x^2+Z(5)^0, x^3+Z(5)*x^2+Z(5)^3, x^3+Z(5)*x^2+x-Z(5)^0, x^3+Z(5)*x^2+x+Z(5)^3, x^3+Z(5)*x^2+Z(5)*x+Z(5), x^3+Z(5)*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)*x^2-x+Z(5), x^3+Z(5)*x^2-x-Z(5)^0, x^3-x^2-Z(5)^0, x^3-x^2+Z(5)^3, x^3-x^2+x+Z(5)^0, x^3-x^2+x+Z(5), x^3-x^2-x+Z(5), x^3-x^2-x-Z(5)^0, x^3-x^2+Z(5)^3*x+Z(5)^0, x^3-x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)^3*x^2+Z(5), x^3+Z(5)^3*x^2-Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)^3*x^2-x+Z(5)^0, x^3+Z(5)^3*x^2-x+Z(5)^3 ] gap> factors := Factors(x^125-x);; gap> List(factors,DegreeOfLaurentPolynomial); [ 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 ]
Exercise 13.2 gap> polyring := PolynomialRing(GF(125)); PolynomialRing(..., [ x ]) gap> factors := Factors(polyring,x^125-x); [ x, x+Z(5)^0, x+Z(5), x-Z(5)^0, x+Z(5)^3, x+Z(5^3), x+Z(5^3)^2, x+Z(5^3)^3, x+Z(5^3)^4, x+Z(5^3)^5, x+Z(5^3)^6, x+Z(5^3)^7, x+Z(5^3)^8, x+Z(5^3)^9, x+Z(5^3)^10, x+Z(5^3)^11, x+Z(5^3)^12, x+Z(5^3)^13, x+Z(5^3)^14, x+Z(5^3)^15, x+Z(5^3)^16, x+Z(5^3)^17, x+Z(5^3)^18, x+Z(5^3)^19, x+Z(5^3)^20, x+Z(5^3)^21, x+Z(5^3)^22, x+Z(5^3)^23, x+Z(5^3)^24, x+Z(5^3)^25, x+Z(5^3)^26, x+Z(5^3)^27, x+Z(5^3)^28, x+Z(5^3)^29, x+Z(5^3)^30, x+Z(5^3)^32, x+Z(5^3)^33, x+Z(5^3)^34, x+Z(5^3)^35, x+Z(5^3)^36, x+Z(5^3)^37, x+Z(5^3)^38, x+Z(5^3)^39, x+Z(5^3)^40, x+Z(5^3)^41, x+Z(5^3)^42, x+Z(5^3)^43, x+Z(5^3)^44, x+Z(5^3)^45, x+Z(5^3)^46, x+Z(5^3)^47, x+Z(5^3)^48, x+Z(5^3)^49, x+Z(5^3)^50, x+Z(5^3)^51, x+Z(5^3)^52, x+Z(5^3)^53, x+Z(5^3)^54, x+Z(5^3)^55, x+Z(5^3)^56, x+Z(5^3)^57, x+Z(5^3)^58, x+Z(5^3)^59, x+Z(5^3)^60, x+Z(5^3)^61, x+Z(5^3)^63, x+Z(5^3)^64, x+Z(5^3)^65, x+Z(5^3)^66, x+Z(5^3)^67, x+Z(5^3)^68, x+Z(5^3)^69, x+Z(5^3)^70, x+Z(5^3)^71, x+Z(5^3)^72, x+Z(5^3)^73, x+Z(5^3)^74, x+Z(5^3)^75, x+Z(5^3)^76, x+Z(5^3)^77, x+Z(5^3)^78, x+Z(5^3)^79, x+Z(5^3)^80, x+Z(5^3)^81, x+Z(5^3)^82, x+Z(5^3)^83, x+Z(5^3)^84, x+Z(5^3)^85, x+Z(5^3)^86, x+Z(5^3)^87, x+Z(5^3)^88, x+Z(5^3)^89, x+Z(5^3)^90, x+Z(5^3)^91, x+Z(5^3)^92, x+Z(5^3)^94, x+Z(5^3)^95, x+Z(5^3)^96, x+Z(5^3)^97, x+Z(5^3)^98, x+Z(5^3)^99, x+Z(5^3)^100, x+Z(5^3)^101, x+Z(5^3)^102, x+Z(5^3)^103, x+Z(5^3)^104, x+Z(5^3)^105, x+Z(5^3)^106, x+Z(5^3)^107, x+Z(5^3)^108, x+Z(5^3)^109, x+Z(5^3)^110, x+Z(5^3)^111, x+Z(5^3)^112, x+Z(5^3)^113, x+Z(5^3)^114, x+Z(5^3)^115, x+Z(5^3)^116, x+Z(5^3)^117, x+Z(5^3)^118, x+Z(5^3)^119, x+Z(5^3)^120, x+Z(5^3)^121, x+Z(5^3)^122, x+Z(5^3)^123 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(5^3)^31; Z(5) gap> factors := Factors(x^125-x); [ x, x+Z(5)^0, x+Z(5), x-Z(5)^0, x+Z(5)^3, x^3+x+Z(5)^0, x^3+x-Z(5)^0, x^3+Z(5)*x+Z(5)^0, x^3+Z(5)*x-Z(5)^0, x^3-x+Z(5), x^3-x+Z(5)^3, x^3+Z(5)^3*x+Z(5), x^3+Z(5)^3*x+Z(5)^3, x^3+x^2+Z(5)^0, x^3+x^2+Z(5), x^3+x^2+x-Z(5)^0, x^3+x^2+x+Z(5)^3, x^3+x^2-x+Z(5)^0, x^3+x^2-x+Z(5)^3, x^3+x^2+Z(5)^3*x+Z(5)^0, x^3+x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)*x^2+Z(5)^0, x^3+Z(5)*x^2+Z(5)^3, x^3+Z(5)*x^2+x-Z(5)^0, x^3+Z(5)*x^2+x+Z(5)^3, x^3+Z(5)*x^2+Z(5)*x+Z(5), x^3+Z(5)*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)*x^2-x+Z(5), x^3+Z(5)*x^2-x-Z(5)^0, x^3-x^2-Z(5)^0, x^3-x^2+Z(5)^3, x^3-x^2+x+Z(5)^0, x^3-x^2+x+Z(5), x^3-x^2-x+Z(5), x^3-x^2-x-Z(5)^0, x^3-x^2+Z(5)^3*x+Z(5)^0, x^3-x^2+Z(5)^3*x-Z(5)^0, x^3+Z(5)^3*x^2+Z(5), x^3+Z(5)^3*x^2-Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5)^0, x^3+Z(5)^3*x^2+x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5), x^3+Z(5)^3*x^2+Z(5)*x+Z(5)^3, x^3+Z(5)^3*x^2-x+Z(5)^0, x^3+Z(5)^3*x^2-x+Z(5)^3 ] gap> f := factors[6]; x^3+x+Z(5)^0 gap> F := AlgebraicExtension(GF(5),f); <field of size 125> gap> x := X(F,"x"); x gap> Factors(x^125-x); [ x, x+(a^2), x+(Z(5)*a^2), x+(Z(5)^2*a^2), x+(Z(5)^3*a^2), x+(a), x+(a+a^2), x+(a+Z(5)*a^2), x+(a+Z(5)^2*a^2), x+(a+Z(5)^3*a^2), x+(Z(5)*a), x+(Z(5)*a+a^2), x+(Z(5)*a+Z(5)*a^2), x+(Z(5)*a+Z(5)^2*a^2), x+(Z(5)*a+Z(5)^3*a^2), x+(Z(5)^2*a), x+(Z(5)^2*a+a^2), x+(Z(5)^2*a+Z(5)*a^2), x+(Z(5)^2*a+Z(5)^2*a^2), x+(Z(5)^2*a+Z(5)^3*a^2), x+(Z(5)^3*a), x+(Z(5)^3*a+a^2), x+(Z(5)^3*a+Z(5)*a^2), x+(Z(5)^3*a+Z(5)^2*a^2), x+(Z(5)^3*a+Z(5)^3*a^2), x+!Z(5)^0, x+(Z(5)^0+a^2), x+(Z(5)^0+Z(5)*a^2), x+(Z(5)^0+Z(5)^2*a^2), x+(Z(5)^0+Z(5)^3*a^2), x+(Z(5)^0+a), x+(Z(5)^0+a+a^2), x+(Z(5)^0+a+Z(5)*a^2), x+(Z(5)^0+a+Z(5)^2*a^2), x+(Z(5)^0+a+Z(5)^3*a^2), x+(Z(5)^0+Z(5)*a), x+(Z(5)^0+Z(5)*a+a^2), x+(Z(5)^0+Z(5)*a+Z(5)*a^2), x+(Z(5)^0+Z(5)*a+Z(5)^2*a^2), x+(Z(5)^0+Z(5)*a+Z(5)^3*a^2), x+(Z(5)^0+Z(5)^2*a), x+(Z(5)^0+Z(5)^2*a+a^2), x+(Z(5)^0+Z(5)^2*a+Z(5)*a^2), x+(Z(5)^0+Z(5)^2*a+Z(5)^2*a^2), x+(Z(5)^0+Z(5)^2*a+Z(5)^3*a^2), x+(Z(5)^0+Z(5)^3*a), x+(Z(5)^0+Z(5)^3*a+a^2), x+(Z(5)^0+Z(5)^3*a+Z(5)*a^2), x+(Z(5)^0+Z(5)^3*a+Z(5)^2*a^2), x+(Z(5)^0+Z(5)^3*a+Z(5)^3*a^2), x+!Z(5), x+(Z(5)+a^2), x+(Z(5)+Z(5)*a^2), x+(Z(5)+Z(5)^2*a^2), x+(Z(5)+Z(5)^3*a^2), x+(Z(5)+a), x+(Z(5)+a+a^2), x+(Z(5)+a+Z(5)*a^2), x+(Z(5)+a+Z(5)^2*a^2), x+(Z(5)+a+Z(5)^3*a^2), x+(Z(5)+Z(5)*a), x+(Z(5)+Z(5)*a+a^2), x+(Z(5)+Z(5)*a+Z(5)*a^2), x+(Z(5)+Z(5)*a+Z(5)^2*a^2), x+(Z(5)+Z(5)*a+Z(5)^3*a^2), x+(Z(5)+Z(5)^2*a), x+(Z(5)+Z(5)^2*a+a^2), x+(Z(5)+Z(5)^2*a+Z(5)*a^2), x+(Z(5)+Z(5)^2*a+Z(5)^2*a^2), x+(Z(5)+Z(5)^2*a+Z(5)^3*a^2), x+(Z(5)+Z(5)^3*a), x+(Z(5)+Z(5)^3*a+a^2), x+(Z(5)+Z(5)^3*a+Z(5)*a^2), x+(Z(5)+Z(5)^3*a+Z(5)^2*a^2), x+(Z(5)+Z(5)^3*a+Z(5)^3*a^2), x-!Z(5)^0, x+(Z(5)^2+a^2), x+(Z(5)^2+Z(5)*a^2), x+(Z(5)^2+Z(5)^2*a^2), x+(Z(5)^2+Z(5)^3*a^2), x+(Z(5)^2+a), x+(Z(5)^2+a+a^2), x+(Z(5)^2+a+Z(5)*a^2), x+(Z(5)^2+a+Z(5)^2*a^2), x+(Z(5)^2+a+Z(5)^3*a^2), x+(Z(5)^2+Z(5)*a), x+(Z(5)^2+Z(5)*a+a^2), x+(Z(5)^2+Z(5)*a+Z(5)*a^2), x+(Z(5)^2+Z(5)*a+Z(5)^2*a^2), x+(Z(5)^2+Z(5)*a+Z(5)^3*a^2), x+(Z(5)^2+Z(5)^2*a), x+(Z(5)^2+Z(5)^2*a+a^2), x+(Z(5)^2+Z(5)^2*a+Z(5)*a^2), x+(Z(5)^2+Z(5)^2*a+Z(5)^2*a^2), x+(Z(5)^2+Z(5)^2*a+Z(5)^3*a^2), x+(Z(5)^2+Z(5)^3*a), x+(Z(5)^2+Z(5)^3*a+a^2), x+(Z(5)^2+Z(5)^3*a+Z(5)*a^2), x+(Z(5)^2+Z(5)^3*a+Z(5)^2*a^2), x+(Z(5)^2+Z(5)^3*a+Z(5)^3*a^2), x+!Z(5)^3, x+(Z(5)^3+a^2), x+(Z(5)^3+Z(5)*a^2), x+(Z(5)^3+Z(5)^2*a^2), x+(Z(5)^3+Z(5)^3*a^2), x+(Z(5)^3+a), x+(Z(5)^3+a+a^2), x+(Z(5)^3+a+Z(5)*a^2), x+(Z(5)^3+a+Z(5)^2*a^2), x+(Z(5)^3+a+Z(5)^3*a^2), x+(Z(5)^3+Z(5)*a), x+(Z(5)^3+Z(5)*a+a^2), x+(Z(5)^3+Z(5)*a+Z(5)*a^2), x+(Z(5)^3+Z(5)*a+Z(5)^2*a^2), x+(Z(5)^3+Z(5)*a+Z(5)^3*a^2), x+(Z(5)^3+Z(5)^2*a), x+(Z(5)^3+Z(5)^2*a+a^2), x+(Z(5)^3+Z(5)^2*a+Z(5)*a^2), x+(Z(5)^3+Z(5)^2*a+Z(5)^2*a^2), x+(Z(5)^3+Z(5)^2*a+Z(5)^3*a^2), x+(Z(5)^3+Z(5)^3*a), x+(Z(5)^3+Z(5)^3*a+a^2), x+(Z(5)^3+Z(5)^3*a+Z(5)*a^2), x+(Z(5)^3+Z(5)^3*a+Z(5)^2*a^2), x+(Z(5)^3+Z(5)^3*a+Z(5)^3*a^2) ]
Exercise 13.3 gap> x := X(GF(7),"x"); x gap> factors := Factors(x^49-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x^2+Z(7)^0, x^2+Z(7)^2, x^2+Z(7)^4, x^2+x+Z(7), x^2+x-Z(7)^0, x^2+x+Z(7)^4, x^2+Z(7)*x+Z(7)^0, x^2+Z(7)*x-Z(7)^0, x^2+Z(7)*x+Z(7)^5, x^2+Z(7)^2*x+Z(7), x^2+Z(7)^2*x+Z(7)^2, x^2+Z(7)^2*x+Z(7)^5, x^2-x+Z(7), x^2-x-Z(7)^0, x^2-x+Z(7)^4, x^2+Z(7)^4*x+Z(7)^0, x^2+Z(7)^4*x-Z(7)^0, x^2+Z(7)^4*x+Z(7)^5, x^2+Z(7)^5*x+Z(7), x^2+Z(7)^5*x+Z(7)^2, x^2+Z(7)^5*x+Z(7)^5 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 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(..., [ x ]) gap> factors := Factors(polyring,x^49-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x+Z(7^2), x+Z(7^2)^2, x+Z(7^2)^3, x+Z(7^2)^4, x+Z(7^2)^5, x+Z(7^2)^6, x+Z(7^2)^7, x+Z(7^2)^9, x+Z(7^2)^10, x+Z(7^2)^11, x+Z(7^2)^12, x+Z(7^2)^13, x+Z(7^2)^14, x+Z(7^2)^15, x+Z(7^2)^17, x+Z(7^2)^18, x+Z(7^2)^19, x+Z(7^2)^20, x+Z(7^2)^21, x+Z(7^2)^22, x+Z(7^2)^23, x+Z(7^2)^25, x+Z(7^2)^26, x+Z(7^2)^27, x+Z(7^2)^28, x+Z(7^2)^29, x+Z(7^2)^30, x+Z(7^2)^31, x+Z(7^2)^33, x+Z(7^2)^34, x+Z(7^2)^35, x+Z(7^2)^36, x+Z(7^2)^37, x+Z(7^2)^38, x+Z(7^2)^39, x+Z(7^2)^41, x+Z(7^2)^42, x+Z(7^2)^43, x+Z(7^2)^44, x+Z(7^2)^45, x+Z(7^2)^46, x+Z(7^2)^47 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(7^2)^16; Z(7)^2 gap> factors := Factors(x^49-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x^2+Z(7)^0, x^2+Z(7)^2, x^2+Z(7)^4, x^2+x+Z(7), x^2+x-Z(7)^0, x^2+x+Z(7)^4, x^2+Z(7)*x+Z(7)^0, x^2+Z(7)*x-Z(7)^0, x^2+Z(7)*x+Z(7)^5, x^2+Z(7)^2*x+Z(7), x^2+Z(7)^2*x+Z(7)^2, x^2+Z(7)^2*x+Z(7)^5, x^2-x+Z(7), x^2-x-Z(7)^0, x^2-x+Z(7)^4, x^2+Z(7)^4*x+Z(7)^0, x^2+Z(7)^4*x-Z(7)^0, x^2+Z(7)^4*x+Z(7)^5, x^2+Z(7)^5*x+Z(7), x^2+Z(7)^5*x+Z(7)^2, x^2+Z(7)^5*x+Z(7)^5 ] gap> f := factors[8]; x^2+Z(7)^0 gap> F := AlgebraicExtension(GF(7),f); <field of size 49> gap> x := X(F,"x"); x gap> Factors(x^49-x); [ x, x+(a), x+(Z(7)*a), x+(Z(7)^2*a), x+(Z(7)^3*a), x+(Z(7)^4*a), x+(Z(7)^5*a), x+!Z(7)^0, x+(Z(7)^0+a), x+(Z(7)^0+Z(7)*a), x+(Z(7)^0+Z(7)^2*a), x+(Z(7)^0+Z(7)^3*a), x+(Z(7)^0+Z(7)^4*a), x+(Z(7)^0+Z(7)^5*a), x+!Z(7), x+(Z(7)+a), x+(Z(7)+Z(7)*a), x+(Z(7)+Z(7)^2*a), x+(Z(7)+Z(7)^3*a), x+(Z(7)+Z(7)^4*a), x+(Z(7)+Z(7)^5*a), x+!Z(7)^2, x+(Z(7)^2+a), x+(Z(7)^2+Z(7)*a), x+(Z(7)^2+Z(7)^2*a), x+(Z(7)^2+Z(7)^3*a), x+(Z(7)^2+Z(7)^4*a), x+(Z(7)^2+Z(7)^5*a), x-!Z(7)^0, x+(Z(7)^3+a), x+(Z(7)^3+Z(7)*a), x+(Z(7)^3+Z(7)^2*a), x+(Z(7)^3+Z(7)^3*a), x+(Z(7)^3+Z(7)^4*a), x+(Z(7)^3+Z(7)^5*a), x+!Z(7)^4, x+(Z(7)^4+a), x+(Z(7)^4+Z(7)*a), x+(Z(7)^4+Z(7)^2*a), x+(Z(7)^4+Z(7)^3*a), x+(Z(7)^4+Z(7)^4*a), x+(Z(7)^4+Z(7)^5*a), x+!Z(7)^5, x+(Z(7)^5+a), x+(Z(7)^5+Z(7)*a), x+(Z(7)^5+Z(7)^2*a), x+(Z(7)^5+Z(7)^3*a), x+(Z(7)^5+Z(7)^4*a), x+(Z(7)^5+Z(7)^5*a) ] gap> List(factors,DegreeOfLaurentPolynomial); [ 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> List(Factors(x^49-x),DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
Exercise 13.4 gap> x := X(GF(7),"x"); x gap> factors := Factors(x^2401-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x^2+Z(7)^0, x^2+Z(7)^2, x^2+Z(7)^4, x^2+x+Z(7), x^2+x-Z(7)^0, x^2+x+Z(7)^4, x^2+Z(7)*x+Z(7)^0, x^2+Z(7)*x-Z(7)^0, x^2+Z(7)*x+Z(7)^5, x^2+Z(7)^2*x+Z(7), x^2+Z(7)^2*x+Z(7)^2, x^2+Z(7)^2*x+Z(7)^5, x^2-x+Z(7), x^2-x-Z(7)^0, x^2-x+Z(7)^4, x^2+Z(7)^4*x+Z(7)^0, x^2+Z(7)^4*x-Z(7)^0, x^2+Z(7)^4*x+Z(7)^5, x^2+Z(7)^5*x+Z(7), x^2+Z(7)^5*x+Z(7)^2, x^2+Z(7)^5*x+Z(7)^5, x^4+x+Z(7)^0, x^4+x+Z(7)^2, x^4+x+Z(7)^4, x^4+Z(7)^2*x+Z(7), x^4+Z(7)^2*x-Z(7)^0, x^4+Z(7)^2*x+Z(7)^5, x^4-x+Z(7)^0, x^4-x+Z(7)^2, x^4-x+Z(7)^4, x^4+Z(7)^5*x+Z(7), x^4+Z(7)^5*x-Z(7)^0, x^4+Z(7)^5*x+Z(7)^5, x^4+x^2+Z(7), x^4+x^2-Z(7)^0, x^4+x^2+x+Z(7)^0, x^4+x^2+x+Z(7)^2, x^4+x^2+Z(7)*x+Z(7)^5, x^4+x^2+Z(7)^2*x+Z(7)^0, x^4+x^2-x+Z(7)^0, x^4+x^2-x+Z(7)^2, x^4+x^2+Z(7)^4*x+Z(7)^5, x^4+x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)*x^2-Z(7)^0, x^4+Z(7)*x^2+Z(7)^5, x^4+Z(7)*x^2+x-Z(7)^0, x^4+Z(7)*x^2+Z(7)*x+Z(7), x^4+Z(7)*x^2+Z(7)*x+Z(7)^4, x^4+Z(7)*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)*x^2-x-Z(7)^0, x^4+Z(7)*x^2+Z(7)^4*x+Z(7), x^4+Z(7)*x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^2*x^2+Z(7), x^4+Z(7)^2*x^2+Z(7)^5, x^4+Z(7)^2*x^2+x+Z(7)^0, x^4+Z(7)^2*x^2+x+Z(7)^4, x^4+Z(7)^2*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^2*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^2*x^2-x+Z(7)^0, x^4+Z(7)^2*x^2-x+Z(7)^4, x^4+Z(7)^2*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^2*x^2+Z(7)^5*x+Z(7)^4, x^4-x^2+Z(7), x^4-x^2-Z(7)^0, x^4-x^2+x+Z(7), x^4-x^2+Z(7)*x+Z(7)^2, x^4-x^2+Z(7)*x-Z(7)^0, x^4-x^2+Z(7)*x+Z(7)^5, x^4-x^2+Z(7)^2*x+Z(7)^0, x^4-x^2+Z(7)^2*x+Z(7), x^4-x^2-x+Z(7), x^4-x^2+Z(7)^4*x+Z(7)^2, x^4-x^2+Z(7)^4*x-Z(7)^0, x^4-x^2+Z(7)^4*x+Z(7)^5, x^4-x^2+Z(7)^5*x+Z(7)^0, x^4-x^2+Z(7)^5*x+Z(7), x^4+Z(7)^4*x^2-Z(7)^0, x^4+Z(7)^4*x^2+Z(7)^5, x^4+Z(7)^4*x^2+x+Z(7)^2, x^4+Z(7)^4*x^2+x+Z(7)^4, x^4+Z(7)^4*x^2+Z(7)*x+Z(7), x^4+Z(7)^4*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^4*x^2-x+Z(7)^2, x^4+Z(7)^4*x^2-x+Z(7)^4, x^4+Z(7)^4*x^2+Z(7)^4*x+Z(7), x^4+Z(7)^4*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^5*x^2+Z(7), x^4+Z(7)^5*x^2+Z(7)^5, x^4+Z(7)^5*x^2+x+Z(7)^5, x^4+Z(7)^5*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^5*x^2+Z(7)*x+Z(7), x^4+Z(7)^5*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^5*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^5*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^5*x^2-x+Z(7)^5, x^4+Z(7)^5*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^5*x^2+Z(7)^4*x+Z(7), x^4+Z(7)^5*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^5*x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^5*x^2+Z(7)^5*x+Z(7)^5, x^4+x^3+Z(7)^0, x^4+x^3+Z(7), x^4+x^3+x+Z(7), x^4+x^3+Z(7)*x+Z(7)^0, x^4+x^3+Z(7)^2*x-Z(7)^0, x^4+x^3-x+Z(7), x^4+x^3-x+Z(7)^2, x^4+x^3+Z(7)^4*x+Z(7)^2, x^4+x^3+Z(7)^5*x-Z(7)^0, x^4+x^3+Z(7)^5*x+Z(7)^4, x^4+x^3+x^2+Z(7)^0, x^4+x^3+x^2+Z(7), x^4+x^3+x^2+Z(7)^5, x^4+x^3+x^2+x+Z(7)^0, x^4+x^3+x^2+x+Z(7)^2, x^4+x^3+x^2+Z(7)*x-Z(7)^0, x^4+x^3+x^2+Z(7)*x+Z(7)^4, x^4+x^3+x^2+Z(7)^2*x+Z(7)^4, x^4+x^3+x^2-x+Z(7)^0, x^4+x^3+x^2-x+Z(7), x^4+x^3+x^2-x-Z(7)^0, x^4+x^3+x^2+Z(7)^4*x+Z(7)^0, x^4+x^3+x^2+Z(7)^5*x+Z(7), x^4+x^3+x^2+Z(7)^5*x+Z(7)^2, x^4+x^3+Z(7)*x^2+Z(7)*x+Z(7)^0, x^4+x^3+Z(7)*x^2+Z(7)*x+Z(7)^2, x^4+x^3+Z(7)*x^2+Z(7)*x+Z(7)^4, x^4+x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^0, x^4+x^3+Z(7)*x^2+Z(7)^2*x+Z(7), x^4+x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^4, x^4+x^3+Z(7)*x^2-x+Z(7)^2, x^4+x^3+Z(7)*x^2-x+Z(7)^4, x^4+x^3+Z(7)*x^2-x+Z(7)^5, x^4+x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^0, x^4+x^3+Z(7)*x^2+Z(7)^5*x-Z(7)^0, x^4+x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^5, x^4+x^3+Z(7)^2*x^2+Z(7)^0, x^4+x^3+Z(7)^2*x^2+Z(7)^4, x^4+x^3+Z(7)^2*x^2+x+Z(7), x^4+x^3+Z(7)^2*x^2+Z(7)*x+Z(7), x^4+x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^2, x^4+x^3+Z(7)^2*x^2+Z(7)*x-Z(7)^0, x^4+x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7), x^4+x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^5, x^4+x^3+Z(7)^2*x^2-x-Z(7)^0, x^4+x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^0, x^4+x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^4, x^4+x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^5, x^4+x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^2, x^4+x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^4, x^4+x^3-x^2+Z(7)^2, x^4+x^3-x^2+Z(7)^5, x^4+x^3-x^2+x+Z(7)^4, x^4+x^3-x^2+Z(7)*x+Z(7)^0, x^4+x^3-x^2+Z(7)^2*x-Z(7)^0, x^4+x^3-x^2+Z(7)^2*x+Z(7)^5, x^4+x^3-x^2-x-Z(7)^0, x^4+x^3-x^2-x+Z(7)^4, x^4+x^3-x^2-x+Z(7)^5, x^4+x^3-x^2+Z(7)^4*x+Z(7), x^4+x^3-x^2+Z(7)^4*x-Z(7)^0, x^4+x^3-x^2+Z(7)^5*x+Z(7), x^4+x^3-x^2+Z(7)^5*x+Z(7)^2, x^4+x^3-x^2+Z(7)^5*x+Z(7)^4, x^4+x^3+Z(7)^4*x^2-Z(7)^0, x^4+x^3+Z(7)^4*x^2+Z(7)^5, x^4+x^3+Z(7)^4*x^2+x+Z(7)^2, x^4+x^3+Z(7)^4*x^2+x+Z(7)^5, x^4+x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^4, x^4+x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7), x^4+x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^2, x^4+x^3+Z(7)^4*x^2-x+Z(7), x^4+x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7) , x^4+x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^5, x^4+x^3+Z(7)^5*x^2+Z(7)^4, x^4+x^3+Z(7)^5*x^2+x+Z(7)^0, x^4+x^3+Z(7)^5*x^2+Z(7)*x+Z(7), x^4+x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7), x^4+x^3+Z(7)^5*x^2-x+Z(7)^2, x^4+x^3+Z(7)^5*x^2-x-Z(7)^0, x^4+x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^2, x^4+x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^5, x^4+x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^0, x^4+x^3+Z(7)^5*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)*x^3+Z(7)^4, x^4+Z(7)*x^3+Z(7)^5, x^4+Z(7)*x^3+x+Z(7)^0, x^4+Z(7)*x^3+x+Z(7)^5, x^4+Z(7)*x^3+Z(7)*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^2*x+Z(7), x^4+Z(7)*x^3+Z(7)^2*x+Z(7)^2, x^4+Z(7)*x^3-x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^4*x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^5*x+Z(7), x^4+Z(7)*x^3+x^2+Z(7), x^4+Z(7)*x^3+x^2-Z(7)^0, x^4+Z(7)*x^3+x^2+x+Z(7)^5, x^4+Z(7)*x^3+x^2+Z(7)*x+Z(7)^5, x^4+Z(7)*x^3+x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)*x^3+x^2-x+Z(7)^0, x^4+Z(7)*x^3+x^2-x-Z(7)^0, x^4+Z(7)*x^3+x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)*x^3+x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)*x^3+x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)*x^2+Z(7)^2, x^4+Z(7)*x^3+Z(7)*x^2+x+Z(7)^0, x^4+Z(7)*x^3+Z(7)*x^2+x+Z(7), x^4+Z(7)*x^3+Z(7)*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)*x^3+Z(7)*x^2+Z(7)^2*x+Z(7), x^4+Z(7)*x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)*x^3+Z(7)*x^2-x+Z(7)^4, x^4+Z(7)*x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^2*x^2-Z(7)^0, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^4, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^5, x^4+Z(7)*x^3+Z(7)^2*x^2+x+Z(7), x^4+Z(7)*x^3+Z(7)^2*x^2+x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^2*x^2+x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^2*x^2-x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^2*x^2-x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7), x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)*x^3-x^2+x+Z(7)^0, x^4+Z(7)*x^3-x^2+x+Z(7)^2, x^4+Z(7)*x^3-x^2+x-Z(7)^0, x^4+Z(7)*x^3-x^2+Z(7)^2*x+Z(7), x^4+Z(7)*x^3-x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)*x^3-x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)*x^3-x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)*x^3-x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)*x^3-x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)*x^3-x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)*x^3-x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)*x^3-x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^2, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^4, x^4+Z(7)*x^3+Z(7)^4*x^2+x+Z(7), x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^4*x^2-x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7), x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)*x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^0, x^4+Z(7)*x^3+Z(7)^5*x^2-Z(7)^0, x^4+Z(7)*x^3+Z(7)^5*x^2+x+Z(7), x^4+Z(7)*x^3+Z(7)^5*x^2+x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^5*x^2+x-Z(7)^0, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)*x+Z(7), x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)*x^3+Z(7)^5*x^2-x+Z(7)^2, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7), x^4+Z(7)*x^3+Z(7)^5*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^2, x^4+Z(7)^2*x^3-Z(7)^0, x^4+Z(7)^2*x^3+x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^2*x+Z(7)^5, x^4+Z(7)^2*x^3-x-Z(7)^0, x^4+Z(7)^2*x^3-x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^4*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^5*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^5*x+Z(7)^5, x^4+Z(7)^2*x^3+x^2+Z(7)^0, x^4+Z(7)^2*x^3+x^2+Z(7)^2, x^4+Z(7)^2*x^3+x^2+x-Z(7)^0, x^4+Z(7)^2*x^3+x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^2*x^3+x^2+Z(7)*x+Z(7)^4, x^4+Z(7)^2*x^3+x^2+Z(7)*x+Z(7)^5 , x^4+Z(7)^2*x^3+x^2+Z(7)^2*x+Z(7), x^4+Z(7)^2*x^3+x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^2*x^3+x^2-x+Z(7)^5, x^4+Z(7)^2*x^3+x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^2*x^3+x^2+Z(7)^4*x+Z(7), x^4+Z(7)^2*x^3+x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)^2*x^3+x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^2*x^3+x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7), x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)*x^2+x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^2*x+Z(7), x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)*x^2-x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x^2-x+Z(7), x^4+Z(7)^2*x^3+Z(7)*x^2-x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7), x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)^2*x^2+x+Z(7), x^4+Z(7)^2*x^3+Z(7)^2*x^2+x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^2*x^2-x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7), x^4+Z(7)^2*x^3-x^2+Z(7)^0, x^4+Z(7)^2*x^3-x^2+x+Z(7)^2, x^4+Z(7)^2*x^3-x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^2*x^3-x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^2*x^3-x^2-x+Z(7)^4, x^4+Z(7)^2*x^3-x^2-x+Z(7)^5, x^4+Z(7)^2*x^3-x^2+Z(7)^4*x+Z(7), x^4+Z(7)^2*x^3-x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)^2*x^3-x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^2*x^3-x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7), x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^4*x^2-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^4*x^2+x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^4*x^2+x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^4*x^2-x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^4*x^2-x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^4*x^2-x+Z(7)^5, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^5*x^2-x+Z(7)^0, x^4+Z(7)^2*x^3+Z(7)^5*x^2-x+Z(7), x^4+Z(7)^2*x^3+Z(7)^5*x^2-x+Z(7)^4, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7), x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^2*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^5, x^4-x^3+Z(7)^0, x^4-x^3+Z(7), x^4-x^3+x+Z(7), x^4-x^3+x+Z(7)^2, x^4-x^3+Z(7)*x+Z(7)^2, x^4-x^3+Z(7)^2*x-Z(7)^0, x^4-x^3+Z(7)^2*x+Z(7)^4, x^4-x^3-x+Z(7), x^4-x^3+Z(7)^4*x+Z(7)^0, x^4-x^3+Z(7)^5*x-Z(7)^0, x^4-x^3+x^2+Z(7)^0, x^4-x^3+x^2+Z(7), x^4-x^3+x^2+Z(7)^5, x^4-x^3+x^2+x+Z(7)^0, x^4-x^3+x^2+x+Z(7), x^4-x^3+x^2+x-Z(7)^0, x^4-x^3+x^2+Z(7)*x+Z(7)^0, x^4-x^3+x^2+Z(7)^2*x+Z(7), x^4-x^3+x^2+Z(7)^2*x+Z(7)^2, x^4-x^3+x^2-x+Z(7)^0, x^4-x^3+x^2-x+Z(7)^2, x^4-x^3+x^2+Z(7)^4*x-Z(7)^0, x^4-x^3+x^2+Z(7)^4*x+Z(7)^4, x^4-x^3+x^2+Z(7)^5*x+Z(7)^4, x^4-x^3+Z(7)*x^2+x+Z(7)^2, x^4-x^3+Z(7)*x^2+x+Z(7)^4, x^4-x^3+Z(7)*x^2+x+Z(7)^5, x^4-x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^0, x^4-x^3+Z(7)*x^2+Z(7)^2*x-Z(7)^0, x^4-x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^5, x^4-x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^0, x^4-x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^2, x^4-x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^4, x^4-x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^0, x^4-x^3+Z(7)*x^2+Z(7)^5*x+Z(7), x^4-x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^4, x^4-x^3+Z(7)^2*x^2+Z(7)^0, x^4-x^3+Z(7)^2*x^2+Z(7)^4, x^4-x^3+Z(7)^2*x^2+x-Z(7)^0, x^4-x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^0, x^4-x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^4, x^4-x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^5, x^4-x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^2, x^4-x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^4, x^4-x^3+Z(7)^2*x^2-x+Z(7), x^4-x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7), x^4-x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^2, x^4-x^3+Z(7)^2*x^2+Z(7)^4*x-Z(7)^0, x^4-x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7), x^4-x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^5, x^4-x^3-x^2+Z(7)^2, x^4-x^3-x^2+Z(7)^5, x^4-x^3-x^2+x-Z(7)^0, x^4-x^3-x^2+x+Z(7)^4, x^4-x^3-x^2+x+Z(7)^5, x^4-x^3-x^2+Z(7)*x+Z(7), x^4-x^3-x^2+Z(7)*x-Z(7)^0, x^4-x^3-x^2+Z(7)^2*x+Z(7), x^4-x^3-x^2+Z(7)^2*x+Z(7)^2, x^4-x^3-x^2+Z(7)^2*x+Z(7)^4, x^4-x^3-x^2-x+Z(7)^4, x^4-x^3-x^2+Z(7)^4*x+Z(7)^0, x^4-x^3-x^2+Z(7)^5*x-Z(7)^0, x^4-x^3-x^2+Z(7)^5*x+Z(7)^5, x^4-x^3+Z(7)^4*x^2-Z(7)^0, x^4-x^3+Z(7)^4*x^2+Z(7)^5, x^4-x^3+Z(7)^4*x^2+x+Z(7), x^4-x^3+Z(7)^4*x^2+Z(7)*x+Z(7), x^4-x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^5, x^4-x^3+Z(7)^4*x^2-x+Z(7)^2, x^4-x^3+Z(7)^4*x^2-x+Z(7)^5, x^4-x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^4, x^4-x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7), x^4-x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^2, x^4-x^3+Z(7)^5*x^2+Z(7)^4, x^4-x^3+Z(7)^5*x^2+x+Z(7)^2, x^4-x^3+Z(7)^5*x^2+x-Z(7)^0, x^4-x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^2, x^4-x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^5, x^4-x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^0, x^4-x^3+Z(7)^5*x^2+Z(7)^2*x-Z(7)^0, x^4-x^3+Z(7)^5*x^2-x+Z(7)^0, x^4-x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7), x^4-x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^5, x^4+Z(7)^4*x^3+x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x+Z(7), x^4+Z(7)^4*x^3-x+Z(7)^0, x^4+Z(7)^4*x^3-x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^4*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^5*x+Z(7)^2, x^4+Z(7)^4*x^3+x^2+Z(7), x^4+Z(7)^4*x^3+x^2-Z(7)^0, x^4+Z(7)^4*x^3+x^2+x+Z(7)^0, x^4+Z(7)^4*x^3+x^2+x-Z(7)^0, x^4+Z(7)^4*x^3+x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^4*x^3+x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)^4*x^3+x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^4*x^3+x^2-x+Z(7)^5, x^4+Z(7)^4*x^3+x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)^4*x^3+x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)*x^2+x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)*x^2-x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)*x^2-x+Z(7), x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^5*x+Z(7), x^4+Z(7)^4*x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x^2-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^2*x^2+x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^2*x^2+x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^2*x^2-x+Z(7), x^4+Z(7)^4*x^3+Z(7)^2*x^2-x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x^2-x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)^4*x^3-x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^4*x^3-x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^4*x^3-x^2+Z(7)*x+Z(7)^4, x^4+Z(7)^4*x^3-x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^4*x^3-x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^4*x^3-x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^4*x^3-x^2-x+Z(7)^0, x^4+Z(7)^4*x^3-x^2-x+Z(7)^2, x^4+Z(7)^4*x^3-x^2-x-Z(7)^0, x^4+Z(7)^4*x^3-x^2+Z(7)^5*x+Z(7), x^4+Z(7)^4*x^3-x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^4*x^3-x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^4*x^2+x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^4*x^2-x+Z(7), x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x^2-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x^2+x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)*x+Z(7)^4, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x^2-x+Z(7), x^4+Z(7)^4*x^3+Z(7)^5*x^2-x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^5*x^2-x-Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7), x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^4*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^2, x^4+Z(7)^5*x^3-Z(7)^0, x^4+Z(7)^5*x^3+x-Z(7)^0, x^4+Z(7)^5*x^3+x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)*x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^2*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^2*x+Z(7)^5, x^4+Z(7)^5*x^3-x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^5*x+Z(7)^5, x^4+Z(7)^5*x^3+x^2+Z(7)^0, x^4+Z(7)^5*x^3+x^2+Z(7)^2, x^4+Z(7)^5*x^3+x^2+x+Z(7)^5, x^4+Z(7)^5*x^3+x^2+Z(7)*x+Z(7)^0, x^4+Z(7)^5*x^3+x^2+Z(7)*x+Z(7), x^4+Z(7)^5*x^3+x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^5*x^3+x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)^5*x^3+x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^5*x^3+x^2-x-Z(7)^0, x^4+Z(7)^5*x^3+x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^5*x^3+x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)^5*x^3+x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)^5*x^3+x^2+Z(7)^5*x+Z(7), x^4+Z(7)^5*x^3+x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7), x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)*x^2+x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+x+Z(7), x^4+Z(7)^5*x^3+Z(7)*x^2+x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)*x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)*x^2-x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^5*x+Z(7), x^4+Z(7)^5*x^3+Z(7)*x^2+Z(7)^5*x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7), x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^2*x^2+x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)^2*x+Z(7), x^4+Z(7)^5*x^3+Z(7)^2*x^2-x+Z(7), x^4+Z(7)^5*x^3+Z(7)^2*x^2-x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^2*x^2+Z(7)^5*x+Z(7)^4, x^4+Z(7)^5*x^3-x^2+Z(7)^0, x^4+Z(7)^5*x^3-x^2+x+Z(7)^4, x^4+Z(7)^5*x^3-x^2+x+Z(7)^5, x^4+Z(7)^5*x^3-x^2+Z(7)*x+Z(7), x^4+Z(7)^5*x^3-x^2+Z(7)*x+Z(7)^4, x^4+Z(7)^5*x^3-x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^5*x^3-x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^5*x^3-x^2-x+Z(7)^2, x^4+Z(7)^5*x^3-x^2+Z(7)^4*x-Z(7)^0, x^4+Z(7)^5*x^3-x^2+Z(7)^5*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7), x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^4*x^2-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x^2+x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^4*x^2+x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x^2+x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^2*x-Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^2*x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^4*x^2-x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^4*x^2-x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^4*x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^4*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^5*x^2+x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^5*x^2+x+Z(7), x^4+Z(7)^5*x^3+Z(7)^5*x^2+x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7), x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^2*x+Z(7)^5, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^4*x+Z(7)^4, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^0, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^5*x+Z(7)^2, x^4+Z(7)^5*x^3+Z(7)^5*x^2+Z(7)^5*x-Z(7)^0 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 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> factors := Factors(polyring,x^2401-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x+Z(7^2), x+Z(7^2)^2, x+Z(7^2)^3, x+Z(7^2)^4, x+Z(7^2)^5, x+Z(7^2)^6, x+Z(7^2)^7, x+Z(7^2)^9, x+Z(7^2)^10, x+Z(7^2)^11, x+Z(7^2)^12, x+Z(7^2)^13, x+Z(7^2)^14, x+Z(7^2)^15, x+Z(7^2)^17, x+Z(7^2)^18, x+Z(7^2)^19, x+Z(7^2)^20, x+Z(7^2)^21, x+Z(7^2)^22, x+Z(7^2)^23, x+Z(7^2)^25, x+Z(7^2)^26, x+Z(7^2)^27, x+Z(7^2)^28, x+Z(7^2)^29, x+Z(7^2)^30, x+Z(7^2)^31, x+Z(7^2)^33, x+Z(7^2)^34, x+Z(7^2)^35, x+Z(7^2)^36, x+Z(7^2)^37, x+Z(7^2)^38, x+Z(7^2)^39, x+Z(7^2)^41, x+Z(7^2)^42, x+Z(7^2)^43, x+Z(7^2)^44, x+Z(7^2)^45, x+Z(7^2)^46, x+Z(7^2)^47, x^2+Z(7^2), x^2+Z(7^2)^3, x^2+Z(7^2)^5, x^2+Z(7^2)^7, x^2+Z(7^2)^9, x^2+Z(7^2)^11, x^2+Z(7^2)^13, x^2+Z(7^2)^15, x^2+Z(7^2)^17, x^2+Z(7^2)^19, x^2+Z(7^2)^21, x^2+Z(7^2)^23, x^2+Z(7^2)^25, x^2+Z(7^2)^27, x^2+Z(7^2)^29, x^2+Z(7^2)^31, x^2+Z(7^2)^33, x^2+Z(7^2)^35, x^2+Z(7^2)^37, x^2+Z(7^2)^39, x^2+Z(7^2)^41, x^2+Z(7^2)^43, x^2+Z(7^2)^45, x^2+Z(7^2)^47, x^2+x+Z(7^2), x^2+x+Z(7^2)^3, x^2+x+Z(7^2)^5, x^2+x+Z(7^2)^6, x^2+x+Z(7^2)^7, x^2+x+Z(7^2)^10, x^2+x+Z(7^2)^12, x^2+x+Z(7^2)^13, x^2+x+Z(7^2)^17, x^2+x+Z(7^2)^20, x^2+x+Z(7^2)^21, x^2+x+Z(7^2)^22, x^2+x+Z(7^2)^23, x^2+x+Z(7^2)^26, x^2+x+Z(7^2)^34, x^2+x+Z(7^2)^35, x^2+x+Z(7^2)^36, x^2+x+Z(7^2)^38, x^2+x+Z(7^2)^41, x^2+x+Z(7^2)^42, x^2+x+Z(7^2)^43, x^2+x+Z(7^2)^44, x^2+x+Z(7^2)^46, x^2+x+Z(7^2)^47, x^2+Z(7)*x+Z(7^2)^2, x^2+Z(7)*x+Z(7^2)^3, x^2+Z(7)*x+Z(7^2)^4, x^2+Z(7)*x+Z(7^2)^6, x^2+Z(7)*x+Z(7^2)^9, x^2+Z(7)*x+Z(7^2)^10, x^2+Z(7)*x+Z(7^2)^11, x^2+Z(7)*x+Z(7^2)^12, x^2+Z(7)*x+Z(7^2)^14, x^2+Z(7)*x+Z(7^2)^15, x^2+Z(7)*x+Z(7^2)^17, x^2+Z(7)*x+Z(7^2)^19, x^2+Z(7)*x+Z(7^2)^21, x^2+Z(7)*x+Z(7^2)^22, x^2+Z(7)*x+Z(7^2)^23, x^2+Z(7)*x+Z(7^2)^26, x^2+Z(7)*x+Z(7^2)^28, x^2+Z(7)*x+Z(7^2)^29, x^2+Z(7)*x+Z(7^2)^33, x^2+Z(7)*x+Z(7^2)^36, x^2+Z(7)*x+Z(7^2)^37, x^2+Z(7)*x+Z(7^2)^38, x^2+Z(7)*x+Z(7^2)^39, x^2+Z(7)*x+Z(7^2)^42, x^2+Z(7)^2*x+Z(7^2), x^2+Z(7)^2*x+Z(7^2)^4, x^2+Z(7)^2*x+Z(7^2)^5, x^2+Z(7)^2*x+Z(7^2)^6, x^2+Z(7)^2*x+Z(7^2)^7, x^2+Z(7)^2*x+Z(7^2)^10, x^2+Z(7)^2*x+Z(7^2)^18, x^2+Z(7)^2*x+Z(7^2)^19, x^2+Z(7)^2*x+Z(7^2)^20, x^2+Z(7)^2*x+Z(7^2)^22, x^2+Z(7)^2*x+Z(7^2)^25, x^2+Z(7)^2*x+Z(7^2)^26, x^2+Z(7)^2*x+Z(7^2)^27, x^2+Z(7)^2*x+Z(7^2)^28, x^2+Z(7)^2*x+Z(7^2)^30, x^2+Z(7)^2*x+Z(7^2)^31, x^2+Z(7)^2*x+Z(7^2)^33, x^2+Z(7)^2*x+Z(7^2)^35, x^2+Z(7)^2*x+Z(7^2)^37, x^2+Z(7)^2*x+Z(7^2)^38, x^2+Z(7)^2*x+Z(7^2)^39, x^2+Z(7)^2*x+Z(7^2)^42, x^2+Z(7)^2*x+Z(7^2)^44, x^2+Z(7)^2*x+Z(7^2)^45, x^2-x+Z(7^2), x^2-x+Z(7^2)^3, x^2-x+Z(7^2)^5, x^2-x+Z(7^2)^6, x^2-x+Z(7^2)^7, x^2-x+Z(7^2)^10, x^2-x+Z(7^2)^12, x^2-x+Z(7^2)^13, x^2-x+Z(7^2)^17, x^2-x+Z(7^2)^20, x^2-x+Z(7^2)^21, x^2-x+Z(7^2)^22, x^2-x+Z(7^2)^23, x^2-x+Z(7^2)^26, x^2-x+Z(7^2)^34, x^2-x+Z(7^2)^35, x^2-x+Z(7^2)^36, x^2-x+Z(7^2)^38, x^2-x+Z(7^2)^41, x^2-x+Z(7^2)^42, x^2-x+Z(7^2)^43, x^2-x+Z(7^2)^44, x^2-x+Z(7^2)^46, x^2-x+Z(7^2)^47, x^2+Z(7)^4*x+Z(7^2)^2, x^2+Z(7)^4*x+Z(7^2)^3, x^2+Z(7)^4*x+Z(7^2)^4, x^2+Z(7)^4*x+Z(7^2)^6, x^2+Z(7)^4*x+Z(7^2)^9, x^2+Z(7)^4*x+Z(7^2)^10, x^2+Z(7)^4*x+Z(7^2)^11, x^2+Z(7)^4*x+Z(7^2)^12, x^2+Z(7)^4*x+Z(7^2)^14, x^2+Z(7)^4*x+Z(7^2)^15, x^2+Z(7)^4*x+Z(7^2)^17, x^2+Z(7)^4*x+Z(7^2)^19, x^2+Z(7)^4*x+Z(7^2)^21, x^2+Z(7)^4*x+Z(7^2)^22, x^2+Z(7)^4*x+Z(7^2)^23, x^2+Z(7)^4*x+Z(7^2)^26, x^2+Z(7)^4*x+Z(7^2)^28, x^2+Z(7)^4*x+Z(7^2)^29, x^2+Z(7)^4*x+Z(7^2)^33, x^2+Z(7)^4*x+Z(7^2)^36, x^2+Z(7)^4*x+Z(7^2)^37, x^2+Z(7)^4*x+Z(7^2)^38, x^2+Z(7)^4*x+Z(7^2)^39, x^2+Z(7)^4*x+Z(7^2)^42, x^2+Z(7)^5*x+Z(7^2), x^2+Z(7)^5*x+Z(7^2)^4, x^2+Z(7)^5*x+Z(7^2)^5, x^2+Z(7)^5*x+Z(7^2)^6, x^2+Z(7)^5*x+Z(7^2)^7, x^2+Z(7)^5*x+Z(7^2)^10, x^2+Z(7)^5*x+Z(7^2)^18, x^2+Z(7)^5*x+Z(7^2)^19, x^2+Z(7)^5*x+Z(7^2)^20, x^2+Z(7)^5*x+Z(7^2)^22, x^2+Z(7)^5*x+Z(7^2)^25, x^2+Z(7)^5*x+Z(7^2)^26, x^2+Z(7)^5*x+Z(7^2)^27, x^2+Z(7)^5*x+Z(7^2)^28, x^2+Z(7)^5*x+Z(7^2)^30, x^2+Z(7)^5*x+Z(7^2)^31, x^2+Z(7)^5*x+Z(7^2)^33, x^2+Z(7)^5*x+Z(7^2)^35, x^2+Z(7)^5*x+Z(7^2)^37, x^2+Z(7)^5*x+Z(7^2)^38, x^2+Z(7)^5*x+Z(7^2)^39, x^2+Z(7)^5*x+Z(7^2)^42, x^2+Z(7)^5*x+Z(7^2)^44, x^2+Z(7)^5*x+Z(7^2)^45, x^2+Z(7^2)*x+Z(7)^0, x^2+Z(7^2)*x+Z(7), x^2+Z(7^2)*x-Z(7)^0, x^2+Z(7^2)*x+Z(7)^5, x^2+Z(7^2)*x+Z(7^2), x^2+Z(7^2)*x+Z(7^2)^3, x^2+Z(7^2)*x+Z(7^2)^5, x^2+Z(7^2)*x+Z(7^2)^7, x^2+Z(7^2)*x+Z(7^2)^9, x^2+Z(7^2)*x+Z(7^2)^12, x^2+Z(7^2)*x+Z(7^2)^14, x^2+Z(7^2)*x+Z(7^2)^15, x^2+Z(7^2)*x+Z(7^2)^19, x^2+Z(7^2)*x+Z(7^2)^22, x^2+Z(7^2)*x+Z(7^2)^23, x^2+Z(7^2)*x+Z(7^2)^25, x^2+Z(7^2)*x+Z(7^2)^28, x^2+Z(7^2)*x+Z(7^2)^36, x^2+Z(7^2)*x+Z(7^2)^37, x^2+Z(7^2)*x+Z(7^2)^38, x^2+Z(7^2)*x+Z(7^2)^43, x^2+Z(7^2)*x+Z(7^2)^44, x^2+Z(7^2)*x+Z(7^2)^45, x^2+Z(7^2)*x+Z(7^2)^46, x^2+Z(7^2)^2*x+Z(7)^0, x^2+Z(7^2)^2*x+Z(7)^2, x^2+Z(7^2)^2*x-Z(7)^0, x^2+Z(7^2)^2*x+Z(7)^5, x^2+Z(7^2)^2*x+Z(7^2)^2, x^2+Z(7^2)^2*x+Z(7^2)^3, x^2+Z(7^2)^2*x+Z(7^2)^5, x^2+Z(7^2)^2*x+Z(7^2)^7, x^2+Z(7^2)^2*x+Z(7^2)^9, x^2+Z(7^2)^2*x+Z(7^2)^10, x^2+Z(7^2)^2*x+Z(7^2)^11, x^2+Z(7^2)^2*x+Z(7^2)^14, x^2+Z(7^2)^2*x+Z(7^2)^17, x^2+Z(7^2)^2*x+Z(7^2)^21, x^2+Z(7^2)^2*x+Z(7^2)^25, x^2+Z(7^2)^2*x+Z(7^2)^26, x^2+Z(7^2)^2*x+Z(7^2)^27, x^2+Z(7^2)^2*x+Z(7^2)^30, x^2+Z(7^2)^2*x+Z(7^2)^38, x^2+Z(7^2)^2*x+Z(7^2)^39, x^2+Z(7^2)^2*x+Z(7^2)^42, x^2+Z(7^2)^2*x+Z(7^2)^45, x^2+Z(7^2)^2*x+Z(7^2)^46, x^2+Z(7^2)^2*x+Z(7^2)^47, x^2+Z(7^2)^3*x+Z(7)^0, x^2+Z(7^2)^3*x+Z(7)^2, x^2+Z(7^2)^3*x+Z(7)^4, x^2+Z(7^2)^3*x+Z(7)^5, x^2+Z(7^2)^3*x+Z(7^2), x^2+Z(7^2)^3*x+Z(7^2)^2, x^2+Z(7^2)^3*x+Z(7^2)^4, x^2+Z(7^2)^3*x+Z(7^2)^5, x^2+Z(7^2)^3*x+Z(7^2)^7, x^2+Z(7^2)^3*x+Z(7^2)^9, x^2+Z(7^2)^3*x+Z(7^2)^11, x^2+Z(7^2)^3*x+Z(7^2)^12, x^2+Z(7^2)^3*x+Z(7^2)^13, x^2+Z(7^2)^3*x+Z(7^2)^18, x^2+Z(7^2)^3*x+Z(7^2)^19, x^2+Z(7^2)^3*x+Z(7^2)^23, x^2+Z(7^2)^3*x+Z(7^2)^26, x^2+Z(7^2)^3*x+Z(7^2)^27, x^2+Z(7^2)^3*x+Z(7^2)^28, x^2+Z(7^2)^3*x+Z(7^2)^29, x^2+Z(7^2)^3*x+Z(7^2)^41, x^2+Z(7^2)^3*x+Z(7^2)^42, x^2+Z(7^2)^3*x+Z(7^2)^44, x^2+Z(7^2)^3*x+Z(7^2)^47, x^2+Z(7^2)^4*x+Z(7^2), x^2+Z(7^2)^4*x+Z(7^2)^2, x^2+Z(7^2)^4*x+Z(7^2)^3, x^2+Z(7^2)^4*x+Z(7^2)^4, x^2+Z(7^2)^4*x+Z(7^2)^6, x^2+Z(7^2)^4*x+Z(7^2)^7, x^2+Z(7^2)^4*x+Z(7^2)^9, x^2+Z(7^2)^4*x+Z(7^2)^11, x^2+Z(7^2)^4*x+Z(7^2)^13, x^2+Z(7^2)^4*x+Z(7^2)^14, x^2+Z(7^2)^4*x+Z(7^2)^15, x^2+Z(7^2)^4*x+Z(7^2)^18, x^2+Z(7^2)^4*x+Z(7^2)^20, x^2+Z(7^2)^4*x+Z(7^2)^21, x^2+Z(7^2)^4*x+Z(7^2)^25, x^2+Z(7^2)^4*x+Z(7^2)^28, x^2+Z(7^2)^4*x+Z(7^2)^29, x^2+Z(7^2)^4*x+Z(7^2)^30, x^2+Z(7^2)^4*x+Z(7^2)^31, x^2+Z(7^2)^4*x+Z(7^2)^34, x^2+Z(7^2)^4*x+Z(7^2)^42, x^2+Z(7^2)^4*x+Z(7^2)^43, x^2+Z(7^2)^4*x+Z(7^2)^44, x^2+Z(7^2)^4*x+Z(7^2)^46, x^2+Z(7^2)^5*x+Z(7)^0, x^2+Z(7^2)^5*x+Z(7), x^2+Z(7^2)^5*x+Z(7)^2, x^2+Z(7^2)^5*x+Z(7)^4, x^2+Z(7^2)^5*x+Z(7^2)^3, x^2+Z(7^2)^5*x+Z(7^2)^4, x^2+Z(7^2)^5*x+Z(7^2)^5, x^2+Z(7^2)^5*x+Z(7^2)^6, x^2+Z(7^2)^5*x+Z(7^2)^9, x^2+Z(7^2)^5*x+Z(7^2)^11, x^2+Z(7^2)^5*x+Z(7^2)^13, x^2+Z(7^2)^5*x+Z(7^2)^15, x^2+Z(7^2)^5*x+Z(7^2)^17, x^2+Z(7^2)^5*x+Z(7^2)^20, x^2+Z(7^2)^5*x+Z(7^2)^22, x^2+Z(7^2)^5*x+Z(7^2)^23, x^2+Z(7^2)^5*x+Z(7^2)^27, x^2+Z(7^2)^5*x+Z(7^2)^30, x^2+Z(7^2)^5*x+Z(7^2)^31, x^2+Z(7^2)^5*x+Z(7^2)^33, x^2+Z(7^2)^5*x+Z(7^2)^36, x^2+Z(7^2)^5*x+Z(7^2)^44, x^2+Z(7^2)^5*x+Z(7^2)^45, x^2+Z(7^2)^5*x+Z(7^2)^46, x^2+Z(7^2)^6*x+Z(7)^0, x^2+Z(7^2)^6*x+Z(7), x^2+Z(7^2)^6*x-Z(7)^0, x^2+Z(7^2)^6*x+Z(7)^4, x^2+Z(7^2)^6*x+Z(7^2)^2, x^2+Z(7^2)^6*x+Z(7^2)^5, x^2+Z(7^2)^6*x+Z(7^2)^6, x^2+Z(7^2)^6*x+Z(7^2)^7, x^2+Z(7^2)^6*x+Z(7^2)^10, x^2+Z(7^2)^6*x+Z(7^2)^11, x^2+Z(7^2)^6*x+Z(7^2)^13, x^2+Z(7^2)^6*x+Z(7^2)^15, x^2+Z(7^2)^6*x+Z(7^2)^17, x^2+Z(7^2)^6*x+Z(7^2)^18, x^2+Z(7^2)^6*x+Z(7^2)^19, x^2+Z(7^2)^6*x+Z(7^2)^22, x^2+Z(7^2)^6*x+Z(7^2)^25, x^2+Z(7^2)^6*x+Z(7^2)^29, x^2+Z(7^2)^6*x+Z(7^2)^33, x^2+Z(7^2)^6*x+Z(7^2)^34, x^2+Z(7^2)^6*x+Z(7^2)^35, x^2+Z(7^2)^6*x+Z(7^2)^38, x^2+Z(7^2)^6*x+Z(7^2)^46, x^2+Z(7^2)^6*x+Z(7^2)^47, x^2+Z(7^2)^7*x+Z(7)^0, x^2+Z(7^2)^7*x+Z(7), x^2+Z(7^2)^7*x-Z(7)^0, x^2+Z(7^2)^7*x+Z(7)^5, x^2+Z(7^2)^7*x+Z(7^2), x^2+Z(7^2)^7*x+Z(7^2)^2, x^2+Z(7^2)^7*x+Z(7^2)^4, x^2+Z(7^2)^7*x+Z(7^2)^7, x^2+Z(7^2)^7*x+Z(7^2)^9, x^2+Z(7^2)^7*x+Z(7^2)^10, x^2+Z(7^2)^7*x+Z(7^2)^12, x^2+Z(7^2)^7*x+Z(7^2)^13, x^2+Z(7^2)^7*x+Z(7^2)^15, x^2+Z(7^2)^7*x+Z(7^2)^17, x^2+Z(7^2)^7*x+Z(7^2)^19, x^2+Z(7^2)^7*x+Z(7^2)^20, x^2+Z(7^2)^7*x+Z(7^2)^21, x^2+Z(7^2)^7*x+Z(7^2)^26, x^2+Z(7^2)^7*x+Z(7^2)^27, x^2+Z(7^2)^7*x+Z(7^2)^31, x^2+Z(7^2)^7*x+Z(7^2)^34, x^2+Z(7^2)^7*x+Z(7^2)^35, x^2+Z(7^2)^7*x+Z(7^2)^36, x^2+Z(7^2)^7*x+Z(7^2)^37, x^2+Z(7^2)^9*x+Z(7), x^2+Z(7^2)^9*x+Z(7)^2, x^2+Z(7^2)^9*x-Z(7)^0, x^2+Z(7^2)^9*x+Z(7)^5, x^2+Z(7^2)^9*x+Z(7^2)^4, x^2+Z(7^2)^9*x+Z(7^2)^5, x^2+Z(7^2)^9*x+Z(7^2)^6, x^2+Z(7^2)^9*x+Z(7^2)^11, x^2+Z(7^2)^9*x+Z(7^2)^12, x^2+Z(7^2)^9*x+Z(7^2)^13, x^2+Z(7^2)^9*x+Z(7^2)^14, x^2+Z(7^2)^9*x+Z(7^2)^17, x^2+Z(7^2)^9*x+Z(7^2)^19, x^2+Z(7^2)^9*x+Z(7^2)^21, x^2+Z(7^2)^9*x+Z(7^2)^23, x^2+Z(7^2)^9*x+Z(7^2)^25, x^2+Z(7^2)^9*x+Z(7^2)^28, x^2+Z(7^2)^9*x+Z(7^2)^30, x^2+Z(7^2)^9*x+Z(7^2)^31, x^2+Z(7^2)^9*x+Z(7^2)^35, x^2+Z(7^2)^9*x+Z(7^2)^38, x^2+Z(7^2)^9*x+Z(7^2)^39, x^2+Z(7^2)^9*x+Z(7^2)^41, x^2+Z(7^2)^9*x+Z(7^2)^44, x^2+Z(7^2)^10*x+Z(7), x^2+Z(7^2)^10*x+Z(7)^2, x^2+Z(7^2)^10*x+Z(7)^4, x^2+Z(7^2)^10*x+Z(7)^5, x^2+Z(7^2)^10*x+Z(7^2)^6, x^2+Z(7^2)^10*x+Z(7^2)^7, x^2+Z(7^2)^10*x+Z(7^2)^10, x^2+Z(7^2)^10*x+Z(7^2)^13, x^2+Z(7^2)^10*x+Z(7^2)^14, x^2+Z(7^2)^10*x+Z(7^2)^15, x^2+Z(7^2)^10*x+Z(7^2)^18, x^2+Z(7^2)^10*x+Z(7^2)^19, x^2+Z(7^2)^10*x+Z(7^2)^21, x^2+Z(7^2)^10*x+Z(7^2)^23, x^2+Z(7^2)^10*x+Z(7^2)^25, x^2+Z(7^2)^10*x+Z(7^2)^26, x^2+Z(7^2)^10*x+Z(7^2)^27, x^2+Z(7^2)^10*x+Z(7^2)^30, x^2+Z(7^2)^10*x+Z(7^2)^33, x^2+Z(7^2)^10*x+Z(7^2)^37, x^2+Z(7^2)^10*x+Z(7^2)^41, x^2+Z(7^2)^10*x+Z(7^2)^42, x^2+Z(7^2)^10*x+Z(7^2)^43, x^2+Z(7^2)^10*x+Z(7^2)^46, x^2+Z(7^2)^11*x+Z(7)^0, x^2+Z(7^2)^11*x+Z(7), x^2+Z(7^2)^11*x+Z(7)^2, x^2+Z(7^2)^11*x+Z(7)^4, x^2+Z(7^2)^11*x+Z(7^2)^9, x^2+Z(7^2)^11*x+Z(7^2)^10, x^2+Z(7^2)^11*x+Z(7^2)^12, x^2+Z(7^2)^11*x+Z(7^2)^15, x^2+Z(7^2)^11*x+Z(7^2)^17, x^2+Z(7^2)^11*x+Z(7^2)^18, x^2+Z(7^2)^11*x+Z(7^2)^20, x^2+Z(7^2)^11*x+Z(7^2)^21, x^2+Z(7^2)^11*x+Z(7^2)^23, x^2+Z(7^2)^11*x+Z(7^2)^25, x^2+Z(7^2)^11*x+Z(7^2)^27, x^2+Z(7^2)^11*x+Z(7^2)^28, x^2+Z(7^2)^11*x+Z(7^2)^29, x^2+Z(7^2)^11*x+Z(7^2)^34, x^2+Z(7^2)^11*x+Z(7^2)^35, x^2+Z(7^2)^11*x+Z(7^2)^39, x^2+Z(7^2)^11*x+Z(7^2)^42, x^2+Z(7^2)^11*x+Z(7^2)^43, x^2+Z(7^2)^11*x+Z(7^2)^44, x^2+Z(7^2)^11*x+Z(7^2)^45, x^2+Z(7^2)^12*x+Z(7^2)^2, x^2+Z(7^2)^12*x+Z(7^2)^10, x^2+Z(7^2)^12*x+Z(7^2)^11, x^2+Z(7^2)^12*x+Z(7^2)^12, x^2+Z(7^2)^12*x+Z(7^2)^14, x^2+Z(7^2)^12*x+Z(7^2)^17, x^2+Z(7^2)^12*x+Z(7^2)^18, x^2+Z(7^2)^12*x+Z(7^2)^19, x^2+Z(7^2)^12*x+Z(7^2)^20, x^2+Z(7^2)^12*x+Z(7^2)^22, x^2+Z(7^2)^12*x+Z(7^2)^23, x^2+Z(7^2)^12*x+Z(7^2)^25, x^2+Z(7^2)^12*x+Z(7^2)^27, x^2+Z(7^2)^12*x+Z(7^2)^29, x^2+Z(7^2)^12*x+Z(7^2)^30, x^2+Z(7^2)^12*x+Z(7^2)^31, x^2+Z(7^2)^12*x+Z(7^2)^34, x^2+Z(7^2)^12*x+Z(7^2)^36, x^2+Z(7^2)^12*x+Z(7^2)^37, x^2+Z(7^2)^12*x+Z(7^2)^41, x^2+Z(7^2)^12*x+Z(7^2)^44, x^2+Z(7^2)^12*x+Z(7^2)^45, x^2+Z(7^2)^12*x+Z(7^2)^46, x^2+Z(7^2)^12*x+Z(7^2)^47, x^2+Z(7^2)^13*x+Z(7)^0, x^2+Z(7^2)^13*x+Z(7)^2, x^2+Z(7^2)^13*x-Z(7)^0, x^2+Z(7^2)^13*x+Z(7)^4, x^2+Z(7^2)^13*x+Z(7^2), x^2+Z(7^2)^13*x+Z(7^2)^4, x^2+Z(7^2)^13*x+Z(7^2)^12, x^2+Z(7^2)^13*x+Z(7^2)^13, x^2+Z(7^2)^13*x+Z(7^2)^14, x^2+Z(7^2)^13*x+Z(7^2)^19, x^2+Z(7^2)^13*x+Z(7^2)^20, x^2+Z(7^2)^13*x+Z(7^2)^21, x^2+Z(7^2)^13*x+Z(7^2)^22, x^2+Z(7^2)^13*x+Z(7^2)^25, x^2+Z(7^2)^13*x+Z(7^2)^27, x^2+Z(7^2)^13*x+Z(7^2)^29, x^2+Z(7^2)^13*x+Z(7^2)^31, x^2+Z(7^2)^13*x+Z(7^2)^33, x^2+Z(7^2)^13*x+Z(7^2)^36, x^2+Z(7^2)^13*x+Z(7^2)^38, x^2+Z(7^2)^13*x+Z(7^2)^39, x^2+Z(7^2)^13*x+Z(7^2)^43, x^2+Z(7^2)^13*x+Z(7^2)^46, x^2+Z(7^2)^13*x+Z(7^2)^47, x^2+Z(7^2)^14*x+Z(7)^0, x^2+Z(7^2)^14*x+Z(7)^2, x^2+Z(7^2)^14*x-Z(7)^0, x^2+Z(7^2)^14*x+Z(7)^5, x^2+Z(7^2)^14*x+Z(7^2), x^2+Z(7^2)^14*x+Z(7^2)^2, x^2+Z(7^2)^14*x+Z(7^2)^3, x^2+Z(7^2)^14*x+Z(7^2)^6, x^2+Z(7^2)^14*x+Z(7^2)^14, x^2+Z(7^2)^14*x+Z(7^2)^15, x^2+Z(7^2)^14*x+Z(7^2)^18, x^2+Z(7^2)^14*x+Z(7^2)^21, x^2+Z(7^2)^14*x+Z(7^2)^22, x^2+Z(7^2)^14*x+Z(7^2)^23, x^2+Z(7^2)^14*x+Z(7^2)^26, x^2+Z(7^2)^14*x+Z(7^2)^27, x^2+Z(7^2)^14*x+Z(7^2)^29, x^2+Z(7^2)^14*x+Z(7^2)^31, x^2+Z(7^2)^14*x+Z(7^2)^33, x^2+Z(7^2)^14*x+Z(7^2)^34, x^2+Z(7^2)^14*x+Z(7^2)^35, x^2+Z(7^2)^14*x+Z(7^2)^38, x^2+Z(7^2)^14*x+Z(7^2)^41, x^2+Z(7^2)^14*x+Z(7^2)^45, x^2+Z(7^2)^15*x+Z(7), x^2+Z(7^2)^15*x+Z(7)^2, x^2+Z(7^2)^15*x-Z(7)^0, x^2+Z(7^2)^15*x+Z(7)^5, x^2+Z(7^2)^15*x+Z(7^2)^2, x^2+Z(7^2)^15*x+Z(7^2)^3, x^2+Z(7^2)^15*x+Z(7^2)^4, x^2+Z(7^2)^15*x+Z(7^2)^5, x^2+Z(7^2)^15*x+Z(7^2)^17, x^2+Z(7^2)^15*x+Z(7^2)^18, x^2+Z(7^2)^15*x+Z(7^2)^20, x^2+Z(7^2)^15*x+Z(7^2)^23, x^2+Z(7^2)^15*x+Z(7^2)^25, x^2+Z(7^2)^15*x+Z(7^2)^26, x^2+Z(7^2)^15*x+Z(7^2)^28, x^2+Z(7^2)^15*x+Z(7^2)^29, x^2+Z(7^2)^15*x+Z(7^2)^31, x^2+Z(7^2)^15*x+Z(7^2)^33, x^2+Z(7^2)^15*x+Z(7^2)^35, x^2+Z(7^2)^15*x+Z(7^2)^36, x^2+Z(7^2)^15*x+Z(7^2)^37, x^2+Z(7^2)^15*x+Z(7^2)^42, x^2+Z(7^2)^15*x+Z(7^2)^43, x^2+Z(7^2)^15*x+Z(7^2)^47, x^2+Z(7^2)^17*x+Z(7), x^2+Z(7^2)^17*x-Z(7)^0, x^2+Z(7^2)^17*x+Z(7)^4, x^2+Z(7^2)^17*x+Z(7)^5, x^2+Z(7^2)^17*x+Z(7^2)^3, x^2+Z(7^2)^17*x+Z(7^2)^6, x^2+Z(7^2)^17*x+Z(7^2)^7, x^2+Z(7^2)^17*x+Z(7^2)^9, x^2+Z(7^2)^17*x+Z(7^2)^12, x^2+Z(7^2)^17*x+Z(7^2)^20, x^2+Z(7^2)^17*x+Z(7^2)^21, x^2+Z(7^2)^17*x+Z(7^2)^22, x^2+Z(7^2)^17*x+Z(7^2)^27, x^2+Z(7^2)^17*x+Z(7^2)^28, x^2+Z(7^2)^17*x+Z(7^2)^29, x^2+Z(7^2)^17*x+Z(7^2)^30, x^2+Z(7^2)^17*x+Z(7^2)^33, x^2+Z(7^2)^17*x+Z(7^2)^35, x^2+Z(7^2)^17*x+Z(7^2)^37, x^2+Z(7^2)^17*x+Z(7^2)^39, x^2+Z(7^2)^17*x+Z(7^2)^41, x^2+Z(7^2)^17*x+Z(7^2)^44, x^2+Z(7^2)^17*x+Z(7^2)^46, x^2+Z(7^2)^17*x+Z(7^2)^47, x^2+Z(7^2)^18*x+Z(7)^0, x^2+Z(7^2)^18*x+Z(7), x^2+Z(7^2)^18*x-Z(7)^0, x^2+Z(7^2)^18*x+Z(7)^4, x^2+Z(7^2)^18*x+Z(7^2), x^2+Z(7^2)^18*x+Z(7^2)^5, x^2+Z(7^2)^18*x+Z(7^2)^9, x^2+Z(7^2)^18*x+Z(7^2)^10, x^2+Z(7^2)^18*x+Z(7^2)^11, x^2+Z(7^2)^18*x+Z(7^2)^14, x^2+Z(7^2)^18*x+Z(7^2)^22, x^2+Z(7^2)^18*x+Z(7^2)^23, x^2+Z(7^2)^18*x+Z(7^2)^26, x^2+Z(7^2)^18*x+Z(7^2)^29, x^2+Z(7^2)^18*x+Z(7^2)^30, x^2+Z(7^2)^18*x+Z(7^2)^31, 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x^2+Z(7^2)^21*x+Z(7^2)^37, x^2+Z(7^2)^21*x+Z(7^2)^38, x^2+Z(7^2)^21*x+Z(7^2)^41, x^2+Z(7^2)^21*x+Z(7^2)^43, x^2+Z(7^2)^21*x+Z(7^2)^45, x^2+Z(7^2)^21*x+Z(7^2)^47, x^2+Z(7^2)^22*x+Z(7), x^2+Z(7^2)^22*x+Z(7)^2, x^2+Z(7^2)^22*x+Z(7)^4, x^2+Z(7^2)^22*x+Z(7)^5, x^2+Z(7^2)^22*x+Z(7^2), x^2+Z(7^2)^22*x+Z(7^2)^2, x^2+Z(7^2)^22*x+Z(7^2)^3, x^2+Z(7^2)^22*x+Z(7^2)^6, x^2+Z(7^2)^22*x+Z(7^2)^9, x^2+Z(7^2)^22*x+Z(7^2)^13, x^2+Z(7^2)^22*x+Z(7^2)^17, x^2+Z(7^2)^22*x+Z(7^2)^18, x^2+Z(7^2)^22*x+Z(7^2)^19, x^2+Z(7^2)^22*x+Z(7^2)^22, x^2+Z(7^2)^22*x+Z(7^2)^30, x^2+Z(7^2)^22*x+Z(7^2)^31, x^2+Z(7^2)^22*x+Z(7^2)^34, x^2+Z(7^2)^22*x+Z(7^2)^37, x^2+Z(7^2)^22*x+Z(7^2)^38, x^2+Z(7^2)^22*x+Z(7^2)^39, x^2+Z(7^2)^22*x+Z(7^2)^42, x^2+Z(7^2)^22*x+Z(7^2)^43, x^2+Z(7^2)^22*x+Z(7^2)^45, x^2+Z(7^2)^22*x+Z(7^2)^47, x^2+Z(7^2)^23*x+Z(7), x^2+Z(7^2)^23*x-Z(7)^0, x^2+Z(7^2)^23*x+Z(7)^4, x^2+Z(7^2)^23*x+Z(7)^5, x^2+Z(7^2)^23*x+Z(7^2), x^2+Z(7^2)^23*x+Z(7^2)^3, x^2+Z(7^2)^23*x+Z(7^2)^4, x^2+Z(7^2)^23*x+Z(7^2)^5, 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x^2+Z(7^2)^25*x+Z(7^2)^44, x^2+Z(7^2)^25*x+Z(7^2)^45, x^2+Z(7^2)^25*x+Z(7^2)^46, x^2+Z(7^2)^26*x+Z(7)^0, x^2+Z(7^2)^26*x+Z(7)^2, x^2+Z(7^2)^26*x-Z(7)^0, x^2+Z(7^2)^26*x+Z(7)^5, x^2+Z(7^2)^26*x+Z(7^2)^2, x^2+Z(7^2)^26*x+Z(7^2)^3, x^2+Z(7^2)^26*x+Z(7^2)^5, x^2+Z(7^2)^26*x+Z(7^2)^7, x^2+Z(7^2)^26*x+Z(7^2)^9, x^2+Z(7^2)^26*x+Z(7^2)^10, x^2+Z(7^2)^26*x+Z(7^2)^11, x^2+Z(7^2)^26*x+Z(7^2)^14, x^2+Z(7^2)^26*x+Z(7^2)^17, x^2+Z(7^2)^26*x+Z(7^2)^21, x^2+Z(7^2)^26*x+Z(7^2)^25, x^2+Z(7^2)^26*x+Z(7^2)^26, x^2+Z(7^2)^26*x+Z(7^2)^27, x^2+Z(7^2)^26*x+Z(7^2)^30, x^2+Z(7^2)^26*x+Z(7^2)^38, x^2+Z(7^2)^26*x+Z(7^2)^39, x^2+Z(7^2)^26*x+Z(7^2)^42, x^2+Z(7^2)^26*x+Z(7^2)^45, x^2+Z(7^2)^26*x+Z(7^2)^46, x^2+Z(7^2)^26*x+Z(7^2)^47, x^2+Z(7^2)^27*x+Z(7)^0, x^2+Z(7^2)^27*x+Z(7)^2, x^2+Z(7^2)^27*x+Z(7)^4, x^2+Z(7^2)^27*x+Z(7)^5, x^2+Z(7^2)^27*x+Z(7^2), x^2+Z(7^2)^27*x+Z(7^2)^2, x^2+Z(7^2)^27*x+Z(7^2)^4, x^2+Z(7^2)^27*x+Z(7^2)^5, x^2+Z(7^2)^27*x+Z(7^2)^7, x^2+Z(7^2)^27*x+Z(7^2)^9, x^2+Z(7^2)^27*x+Z(7^2)^11, x^2+Z(7^2)^27*x+Z(7^2)^12, x^2+Z(7^2)^27*x+Z(7^2)^13, x^2+Z(7^2)^27*x+Z(7^2)^18, x^2+Z(7^2)^27*x+Z(7^2)^19, x^2+Z(7^2)^27*x+Z(7^2)^23, x^2+Z(7^2)^27*x+Z(7^2)^26, x^2+Z(7^2)^27*x+Z(7^2)^27, x^2+Z(7^2)^27*x+Z(7^2)^28, x^2+Z(7^2)^27*x+Z(7^2)^29, x^2+Z(7^2)^27*x+Z(7^2)^41, x^2+Z(7^2)^27*x+Z(7^2)^42, x^2+Z(7^2)^27*x+Z(7^2)^44, x^2+Z(7^2)^27*x+Z(7^2)^47, x^2+Z(7^2)^28*x+Z(7^2), x^2+Z(7^2)^28*x+Z(7^2)^2, x^2+Z(7^2)^28*x+Z(7^2)^3, x^2+Z(7^2)^28*x+Z(7^2)^4, x^2+Z(7^2)^28*x+Z(7^2)^6, x^2+Z(7^2)^28*x+Z(7^2)^7, x^2+Z(7^2)^28*x+Z(7^2)^9, x^2+Z(7^2)^28*x+Z(7^2)^11, x^2+Z(7^2)^28*x+Z(7^2)^13, x^2+Z(7^2)^28*x+Z(7^2)^14, x^2+Z(7^2)^28*x+Z(7^2)^15, x^2+Z(7^2)^28*x+Z(7^2)^18, x^2+Z(7^2)^28*x+Z(7^2)^20, x^2+Z(7^2)^28*x+Z(7^2)^21, x^2+Z(7^2)^28*x+Z(7^2)^25, x^2+Z(7^2)^28*x+Z(7^2)^28, x^2+Z(7^2)^28*x+Z(7^2)^29, x^2+Z(7^2)^28*x+Z(7^2)^30, x^2+Z(7^2)^28*x+Z(7^2)^31, x^2+Z(7^2)^28*x+Z(7^2)^34, x^2+Z(7^2)^28*x+Z(7^2)^42, x^2+Z(7^2)^28*x+Z(7^2)^43, x^2+Z(7^2)^28*x+Z(7^2)^44, x^2+Z(7^2)^28*x+Z(7^2)^46, x^2+Z(7^2)^29*x+Z(7)^0, x^2+Z(7^2)^29*x+Z(7), x^2+Z(7^2)^29*x+Z(7)^2, x^2+Z(7^2)^29*x+Z(7)^4, x^2+Z(7^2)^29*x+Z(7^2)^3, x^2+Z(7^2)^29*x+Z(7^2)^4, x^2+Z(7^2)^29*x+Z(7^2)^5, x^2+Z(7^2)^29*x+Z(7^2)^6, x^2+Z(7^2)^29*x+Z(7^2)^9, x^2+Z(7^2)^29*x+Z(7^2)^11, x^2+Z(7^2)^29*x+Z(7^2)^13, x^2+Z(7^2)^29*x+Z(7^2)^15, x^2+Z(7^2)^29*x+Z(7^2)^17, x^2+Z(7^2)^29*x+Z(7^2)^20, x^2+Z(7^2)^29*x+Z(7^2)^22, x^2+Z(7^2)^29*x+Z(7^2)^23, x^2+Z(7^2)^29*x+Z(7^2)^27, x^2+Z(7^2)^29*x+Z(7^2)^30, x^2+Z(7^2)^29*x+Z(7^2)^31, x^2+Z(7^2)^29*x+Z(7^2)^33, x^2+Z(7^2)^29*x+Z(7^2)^36, x^2+Z(7^2)^29*x+Z(7^2)^44, x^2+Z(7^2)^29*x+Z(7^2)^45, x^2+Z(7^2)^29*x+Z(7^2)^46, x^2+Z(7^2)^30*x+Z(7)^0, x^2+Z(7^2)^30*x+Z(7), x^2+Z(7^2)^30*x-Z(7)^0, x^2+Z(7^2)^30*x+Z(7)^4, x^2+Z(7^2)^30*x+Z(7^2)^2, x^2+Z(7^2)^30*x+Z(7^2)^5, x^2+Z(7^2)^30*x+Z(7^2)^6, x^2+Z(7^2)^30*x+Z(7^2)^7, x^2+Z(7^2)^30*x+Z(7^2)^10, x^2+Z(7^2)^30*x+Z(7^2)^11, x^2+Z(7^2)^30*x+Z(7^2)^13, x^2+Z(7^2)^30*x+Z(7^2)^15, x^2+Z(7^2)^30*x+Z(7^2)^17, x^2+Z(7^2)^30*x+Z(7^2)^18, x^2+Z(7^2)^30*x+Z(7^2)^19, x^2+Z(7^2)^30*x+Z(7^2)^22, x^2+Z(7^2)^30*x+Z(7^2)^25, x^2+Z(7^2)^30*x+Z(7^2)^29, x^2+Z(7^2)^30*x+Z(7^2)^33, x^2+Z(7^2)^30*x+Z(7^2)^34, x^2+Z(7^2)^30*x+Z(7^2)^35, x^2+Z(7^2)^30*x+Z(7^2)^38, x^2+Z(7^2)^30*x+Z(7^2)^46, x^2+Z(7^2)^30*x+Z(7^2)^47, x^2+Z(7^2)^31*x+Z(7)^0, x^2+Z(7^2)^31*x+Z(7), x^2+Z(7^2)^31*x-Z(7)^0, x^2+Z(7^2)^31*x+Z(7)^5, x^2+Z(7^2)^31*x+Z(7^2), x^2+Z(7^2)^31*x+Z(7^2)^2, x^2+Z(7^2)^31*x+Z(7^2)^4, x^2+Z(7^2)^31*x+Z(7^2)^7, x^2+Z(7^2)^31*x+Z(7^2)^9, x^2+Z(7^2)^31*x+Z(7^2)^10, x^2+Z(7^2)^31*x+Z(7^2)^12, x^2+Z(7^2)^31*x+Z(7^2)^13, x^2+Z(7^2)^31*x+Z(7^2)^15, x^2+Z(7^2)^31*x+Z(7^2)^17, x^2+Z(7^2)^31*x+Z(7^2)^19, x^2+Z(7^2)^31*x+Z(7^2)^20, x^2+Z(7^2)^31*x+Z(7^2)^21, x^2+Z(7^2)^31*x+Z(7^2)^26, x^2+Z(7^2)^31*x+Z(7^2)^27, x^2+Z(7^2)^31*x+Z(7^2)^31, x^2+Z(7^2)^31*x+Z(7^2)^34, x^2+Z(7^2)^31*x+Z(7^2)^35, x^2+Z(7^2)^31*x+Z(7^2)^36, x^2+Z(7^2)^31*x+Z(7^2)^37, x^2+Z(7^2)^33*x+Z(7), x^2+Z(7^2)^33*x+Z(7)^2, x^2+Z(7^2)^33*x-Z(7)^0, x^2+Z(7^2)^33*x+Z(7)^5, x^2+Z(7^2)^33*x+Z(7^2)^4, x^2+Z(7^2)^33*x+Z(7^2)^5, x^2+Z(7^2)^33*x+Z(7^2)^6, x^2+Z(7^2)^33*x+Z(7^2)^11, x^2+Z(7^2)^33*x+Z(7^2)^12, x^2+Z(7^2)^33*x+Z(7^2)^13, x^2+Z(7^2)^33*x+Z(7^2)^14, x^2+Z(7^2)^33*x+Z(7^2)^17, x^2+Z(7^2)^33*x+Z(7^2)^19, x^2+Z(7^2)^33*x+Z(7^2)^21, x^2+Z(7^2)^33*x+Z(7^2)^23, x^2+Z(7^2)^33*x+Z(7^2)^25, x^2+Z(7^2)^33*x+Z(7^2)^28, x^2+Z(7^2)^33*x+Z(7^2)^30, x^2+Z(7^2)^33*x+Z(7^2)^31, x^2+Z(7^2)^33*x+Z(7^2)^35, x^2+Z(7^2)^33*x+Z(7^2)^38, x^2+Z(7^2)^33*x+Z(7^2)^39, x^2+Z(7^2)^33*x+Z(7^2)^41, x^2+Z(7^2)^33*x+Z(7^2)^44, x^2+Z(7^2)^34*x+Z(7), x^2+Z(7^2)^34*x+Z(7)^2, x^2+Z(7^2)^34*x+Z(7)^4, x^2+Z(7^2)^34*x+Z(7)^5, x^2+Z(7^2)^34*x+Z(7^2)^6, x^2+Z(7^2)^34*x+Z(7^2)^7, x^2+Z(7^2)^34*x+Z(7^2)^10, x^2+Z(7^2)^34*x+Z(7^2)^13, x^2+Z(7^2)^34*x+Z(7^2)^14, x^2+Z(7^2)^34*x+Z(7^2)^15, x^2+Z(7^2)^34*x+Z(7^2)^18, x^2+Z(7^2)^34*x+Z(7^2)^19, x^2+Z(7^2)^34*x+Z(7^2)^21, x^2+Z(7^2)^34*x+Z(7^2)^23, x^2+Z(7^2)^34*x+Z(7^2)^25, x^2+Z(7^2)^34*x+Z(7^2)^26, x^2+Z(7^2)^34*x+Z(7^2)^27, 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x^2+Z(7^2)^36*x+Z(7^2)^18, x^2+Z(7^2)^36*x+Z(7^2)^19, x^2+Z(7^2)^36*x+Z(7^2)^20, x^2+Z(7^2)^36*x+Z(7^2)^22, x^2+Z(7^2)^36*x+Z(7^2)^23, x^2+Z(7^2)^36*x+Z(7^2)^25, x^2+Z(7^2)^36*x+Z(7^2)^27, x^2+Z(7^2)^36*x+Z(7^2)^29, x^2+Z(7^2)^36*x+Z(7^2)^30, x^2+Z(7^2)^36*x+Z(7^2)^31, x^2+Z(7^2)^36*x+Z(7^2)^34, x^2+Z(7^2)^36*x+Z(7^2)^36, x^2+Z(7^2)^36*x+Z(7^2)^37, x^2+Z(7^2)^36*x+Z(7^2)^41, x^2+Z(7^2)^36*x+Z(7^2)^44, x^2+Z(7^2)^36*x+Z(7^2)^45, x^2+Z(7^2)^36*x+Z(7^2)^46, x^2+Z(7^2)^36*x+Z(7^2)^47, x^2+Z(7^2)^37*x+Z(7)^0, x^2+Z(7^2)^37*x+Z(7)^2, x^2+Z(7^2)^37*x-Z(7)^0, x^2+Z(7^2)^37*x+Z(7)^4, x^2+Z(7^2)^37*x+Z(7^2), x^2+Z(7^2)^37*x+Z(7^2)^4, x^2+Z(7^2)^37*x+Z(7^2)^12, x^2+Z(7^2)^37*x+Z(7^2)^13, x^2+Z(7^2)^37*x+Z(7^2)^14, x^2+Z(7^2)^37*x+Z(7^2)^19, x^2+Z(7^2)^37*x+Z(7^2)^20, x^2+Z(7^2)^37*x+Z(7^2)^21, x^2+Z(7^2)^37*x+Z(7^2)^22, x^2+Z(7^2)^37*x+Z(7^2)^25, x^2+Z(7^2)^37*x+Z(7^2)^27, x^2+Z(7^2)^37*x+Z(7^2)^29, x^2+Z(7^2)^37*x+Z(7^2)^31, x^2+Z(7^2)^37*x+Z(7^2)^33, x^2+Z(7^2)^37*x+Z(7^2)^36, x^2+Z(7^2)^37*x+Z(7^2)^38, x^2+Z(7^2)^37*x+Z(7^2)^39, x^2+Z(7^2)^37*x+Z(7^2)^43, x^2+Z(7^2)^37*x+Z(7^2)^46, x^2+Z(7^2)^37*x+Z(7^2)^47, x^2+Z(7^2)^38*x+Z(7)^0, x^2+Z(7^2)^38*x+Z(7)^2, x^2+Z(7^2)^38*x-Z(7)^0, x^2+Z(7^2)^38*x+Z(7)^5, x^2+Z(7^2)^38*x+Z(7^2), x^2+Z(7^2)^38*x+Z(7^2)^2, x^2+Z(7^2)^38*x+Z(7^2)^3, x^2+Z(7^2)^38*x+Z(7^2)^6, x^2+Z(7^2)^38*x+Z(7^2)^14, x^2+Z(7^2)^38*x+Z(7^2)^15, x^2+Z(7^2)^38*x+Z(7^2)^18, x^2+Z(7^2)^38*x+Z(7^2)^21, x^2+Z(7^2)^38*x+Z(7^2)^22, x^2+Z(7^2)^38*x+Z(7^2)^23, x^2+Z(7^2)^38*x+Z(7^2)^26, x^2+Z(7^2)^38*x+Z(7^2)^27, x^2+Z(7^2)^38*x+Z(7^2)^29, x^2+Z(7^2)^38*x+Z(7^2)^31, x^2+Z(7^2)^38*x+Z(7^2)^33, x^2+Z(7^2)^38*x+Z(7^2)^34, x^2+Z(7^2)^38*x+Z(7^2)^35, x^2+Z(7^2)^38*x+Z(7^2)^38, x^2+Z(7^2)^38*x+Z(7^2)^41, x^2+Z(7^2)^38*x+Z(7^2)^45, x^2+Z(7^2)^39*x+Z(7), x^2+Z(7^2)^39*x+Z(7)^2, x^2+Z(7^2)^39*x-Z(7)^0, x^2+Z(7^2)^39*x+Z(7)^5, x^2+Z(7^2)^39*x+Z(7^2)^2, x^2+Z(7^2)^39*x+Z(7^2)^3, x^2+Z(7^2)^39*x+Z(7^2)^4, x^2+Z(7^2)^39*x+Z(7^2)^5, x^2+Z(7^2)^39*x+Z(7^2)^17, x^2+Z(7^2)^39*x+Z(7^2)^18, x^2+Z(7^2)^39*x+Z(7^2)^20, x^2+Z(7^2)^39*x+Z(7^2)^23, x^2+Z(7^2)^39*x+Z(7^2)^25, x^2+Z(7^2)^39*x+Z(7^2)^26, x^2+Z(7^2)^39*x+Z(7^2)^28, x^2+Z(7^2)^39*x+Z(7^2)^29, x^2+Z(7^2)^39*x+Z(7^2)^31, x^2+Z(7^2)^39*x+Z(7^2)^33, x^2+Z(7^2)^39*x+Z(7^2)^35, x^2+Z(7^2)^39*x+Z(7^2)^36, x^2+Z(7^2)^39*x+Z(7^2)^37, x^2+Z(7^2)^39*x+Z(7^2)^42, x^2+Z(7^2)^39*x+Z(7^2)^43, x^2+Z(7^2)^39*x+Z(7^2)^47, x^2+Z(7^2)^41*x+Z(7), x^2+Z(7^2)^41*x-Z(7)^0, x^2+Z(7^2)^41*x+Z(7)^4, x^2+Z(7^2)^41*x+Z(7)^5, x^2+Z(7^2)^41*x+Z(7^2)^3, x^2+Z(7^2)^41*x+Z(7^2)^6, x^2+Z(7^2)^41*x+Z(7^2)^7, x^2+Z(7^2)^41*x+Z(7^2)^9, x^2+Z(7^2)^41*x+Z(7^2)^12, x^2+Z(7^2)^41*x+Z(7^2)^20, x^2+Z(7^2)^41*x+Z(7^2)^21, x^2+Z(7^2)^41*x+Z(7^2)^22, x^2+Z(7^2)^41*x+Z(7^2)^27, x^2+Z(7^2)^41*x+Z(7^2)^28, x^2+Z(7^2)^41*x+Z(7^2)^29, x^2+Z(7^2)^41*x+Z(7^2)^30, x^2+Z(7^2)^41*x+Z(7^2)^33, x^2+Z(7^2)^41*x+Z(7^2)^35, x^2+Z(7^2)^41*x+Z(7^2)^37, x^2+Z(7^2)^41*x+Z(7^2)^39, x^2+Z(7^2)^41*x+Z(7^2)^41, x^2+Z(7^2)^41*x+Z(7^2)^44, x^2+Z(7^2)^41*x+Z(7^2)^46, x^2+Z(7^2)^41*x+Z(7^2)^47, x^2+Z(7^2)^42*x+Z(7)^0, x^2+Z(7^2)^42*x+Z(7), x^2+Z(7^2)^42*x-Z(7)^0, x^2+Z(7^2)^42*x+Z(7)^4, x^2+Z(7^2)^42*x+Z(7^2), x^2+Z(7^2)^42*x+Z(7^2)^5, x^2+Z(7^2)^42*x+Z(7^2)^9, x^2+Z(7^2)^42*x+Z(7^2)^10, x^2+Z(7^2)^42*x+Z(7^2)^11, x^2+Z(7^2)^42*x+Z(7^2)^14, x^2+Z(7^2)^42*x+Z(7^2)^22, x^2+Z(7^2)^42*x+Z(7^2)^23, x^2+Z(7^2)^42*x+Z(7^2)^26, x^2+Z(7^2)^42*x+Z(7^2)^29, x^2+Z(7^2)^42*x+Z(7^2)^30, x^2+Z(7^2)^42*x+Z(7^2)^31, x^2+Z(7^2)^42*x+Z(7^2)^34, x^2+Z(7^2)^42*x+Z(7^2)^35, x^2+Z(7^2)^42*x+Z(7^2)^37, x^2+Z(7^2)^42*x+Z(7^2)^39, x^2+Z(7^2)^42*x+Z(7^2)^41, x^2+Z(7^2)^42*x+Z(7^2)^42, x^2+Z(7^2)^42*x+Z(7^2)^43, x^2+Z(7^2)^42*x+Z(7^2)^46, x^2+Z(7^2)^43*x+Z(7)^0, x^2+Z(7^2)^43*x+Z(7)^2, x^2+Z(7^2)^43*x-Z(7)^0, x^2+Z(7^2)^43*x+Z(7)^4, x^2+Z(7^2)^43*x+Z(7^2)^2, x^2+Z(7^2)^43*x+Z(7^2)^3, x^2+Z(7^2)^43*x+Z(7^2)^7, x^2+Z(7^2)^43*x+Z(7^2)^10, x^2+Z(7^2)^43*x+Z(7^2)^11, x^2+Z(7^2)^43*x+Z(7^2)^12, x^2+Z(7^2)^43*x+Z(7^2)^13, x^2+Z(7^2)^43*x+Z(7^2)^25, x^2+Z(7^2)^43*x+Z(7^2)^26, x^2+Z(7^2)^43*x+Z(7^2)^28, x^2+Z(7^2)^43*x+Z(7^2)^31, x^2+Z(7^2)^43*x+Z(7^2)^33, x^2+Z(7^2)^43*x+Z(7^2)^34, x^2+Z(7^2)^43*x+Z(7^2)^36, x^2+Z(7^2)^43*x+Z(7^2)^37, x^2+Z(7^2)^43*x+Z(7^2)^39, x^2+Z(7^2)^43*x+Z(7^2)^41, x^2+Z(7^2)^43*x+Z(7^2)^43, x^2+Z(7^2)^43*x+Z(7^2)^44, x^2+Z(7^2)^43*x+Z(7^2)^45, x^2+Z(7^2)^44*x+Z(7^2)^2, x^2+Z(7^2)^44*x+Z(7^2)^4, x^2+Z(7^2)^44*x+Z(7^2)^5, x^2+Z(7^2)^44*x+Z(7^2)^9, x^2+Z(7^2)^44*x+Z(7^2)^12, x^2+Z(7^2)^44*x+Z(7^2)^13, x^2+Z(7^2)^44*x+Z(7^2)^14, x^2+Z(7^2)^44*x+Z(7^2)^15, x^2+Z(7^2)^44*x+Z(7^2)^18, x^2+Z(7^2)^44*x+Z(7^2)^26, x^2+Z(7^2)^44*x+Z(7^2)^27, x^2+Z(7^2)^44*x+Z(7^2)^28, x^2+Z(7^2)^44*x+Z(7^2)^30, x^2+Z(7^2)^44*x+Z(7^2)^33, x^2+Z(7^2)^44*x+Z(7^2)^34, x^2+Z(7^2)^44*x+Z(7^2)^35, x^2+Z(7^2)^44*x+Z(7^2)^36, x^2+Z(7^2)^44*x+Z(7^2)^38, x^2+Z(7^2)^44*x+Z(7^2)^39, x^2+Z(7^2)^44*x+Z(7^2)^41, x^2+Z(7^2)^44*x+Z(7^2)^43, x^2+Z(7^2)^44*x+Z(7^2)^45, x^2+Z(7^2)^44*x+Z(7^2)^46, x^2+Z(7^2)^44*x+Z(7^2)^47, x^2+Z(7^2)^45*x+Z(7)^0, x^2+Z(7^2)^45*x+Z(7)^2, x^2+Z(7^2)^45*x+Z(7)^4, x^2+Z(7^2)^45*x+Z(7)^5, x^2+Z(7^2)^45*x+Z(7^2), x^2+Z(7^2)^45*x+Z(7^2)^4, x^2+Z(7^2)^45*x+Z(7^2)^6, x^2+Z(7^2)^45*x+Z(7^2)^7, x^2+Z(7^2)^45*x+Z(7^2)^11, x^2+Z(7^2)^45*x+Z(7^2)^14, x^2+Z(7^2)^45*x+Z(7^2)^15, x^2+Z(7^2)^45*x+Z(7^2)^17, x^2+Z(7^2)^45*x+Z(7^2)^20, x^2+Z(7^2)^45*x+Z(7^2)^28, x^2+Z(7^2)^45*x+Z(7^2)^29, x^2+Z(7^2)^45*x+Z(7^2)^30, x^2+Z(7^2)^45*x+Z(7^2)^35, x^2+Z(7^2)^45*x+Z(7^2)^36, x^2+Z(7^2)^45*x+Z(7^2)^37, x^2+Z(7^2)^45*x+Z(7^2)^38, x^2+Z(7^2)^45*x+Z(7^2)^41, x^2+Z(7^2)^45*x+Z(7^2)^43, x^2+Z(7^2)^45*x+Z(7^2)^45, x^2+Z(7^2)^45*x+Z(7^2)^47, x^2+Z(7^2)^46*x+Z(7), x^2+Z(7^2)^46*x+Z(7)^2, x^2+Z(7^2)^46*x+Z(7)^4, x^2+Z(7^2)^46*x+Z(7)^5, x^2+Z(7^2)^46*x+Z(7^2), x^2+Z(7^2)^46*x+Z(7^2)^2, x^2+Z(7^2)^46*x+Z(7^2)^3, x^2+Z(7^2)^46*x+Z(7^2)^6, x^2+Z(7^2)^46*x+Z(7^2)^9, x^2+Z(7^2)^46*x+Z(7^2)^13, x^2+Z(7^2)^46*x+Z(7^2)^17, x^2+Z(7^2)^46*x+Z(7^2)^18, x^2+Z(7^2)^46*x+Z(7^2)^19, x^2+Z(7^2)^46*x+Z(7^2)^22, x^2+Z(7^2)^46*x+Z(7^2)^30, x^2+Z(7^2)^46*x+Z(7^2)^31, x^2+Z(7^2)^46*x+Z(7^2)^34, x^2+Z(7^2)^46*x+Z(7^2)^37, x^2+Z(7^2)^46*x+Z(7^2)^38, x^2+Z(7^2)^46*x+Z(7^2)^39, x^2+Z(7^2)^46*x+Z(7^2)^42, x^2+Z(7^2)^46*x+Z(7^2)^43, x^2+Z(7^2)^46*x+Z(7^2)^45, x^2+Z(7^2)^46*x+Z(7^2)^47, x^2+Z(7^2)^47*x+Z(7), x^2+Z(7^2)^47*x-Z(7)^0, x^2+Z(7^2)^47*x+Z(7)^4, x^2+Z(7^2)^47*x+Z(7)^5, x^2+Z(7^2)^47*x+Z(7^2), x^2+Z(7^2)^47*x+Z(7^2)^3, x^2+Z(7^2)^47*x+Z(7^2)^4, x^2+Z(7^2)^47*x+Z(7^2)^5, x^2+Z(7^2)^47*x+Z(7^2)^10, x^2+Z(7^2)^47*x+Z(7^2)^11, x^2+Z(7^2)^47*x+Z(7^2)^15, x^2+Z(7^2)^47*x+Z(7^2)^18, x^2+Z(7^2)^47*x+Z(7^2)^19, x^2+Z(7^2)^47*x+Z(7^2)^20, x^2+Z(7^2)^47*x+Z(7^2)^21, x^2+Z(7^2)^47*x+Z(7^2)^33, x^2+Z(7^2)^47*x+Z(7^2)^34, x^2+Z(7^2)^47*x+Z(7^2)^36, x^2+Z(7^2)^47*x+Z(7^2)^39, x^2+Z(7^2)^47*x+Z(7^2)^41, x^2+Z(7^2)^47*x+Z(7^2)^42, x^2+Z(7^2)^47*x+Z(7^2)^44, x^2+Z(7^2)^47*x+Z(7^2)^45, x^2+Z(7^2)^47*x+Z(7^2)^47 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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(2401)); PolynomialRing(..., [ x ]) gap> factors := Factors(polyring,x^2401-x); [ x, x+Z(7)^0, x+Z(7), x+Z(7)^2, x-Z(7)^0, x+Z(7)^4, x+Z(7)^5, x+Z(7^2), x+Z(7^2)^2, x+Z(7^2)^3, x+Z(7^2)^4, x+Z(7^2)^5, x+Z(7^2)^6, x+Z(7^2)^7, x+Z(7^2)^9, x+Z(7^2)^10, x+Z(7^2)^11, x+Z(7^2)^12, x+Z(7^2)^13, x+Z(7^2)^14, x+Z(7^2)^15, x+Z(7^2)^17, x+Z(7^2)^18, x+Z(7^2)^19, x+Z(7^2)^20, x+Z(7^2)^21, x+Z(7^2)^22, x+Z(7^2)^23, x+Z(7^2)^25, x+Z(7^2)^26, x+Z(7^2)^27, x+Z(7^2)^28, x+Z(7^2)^29, x+Z(7^2)^30, x+Z(7^2)^31, x+Z(7^2)^33, x+Z(7^2)^34, x+Z(7^2)^35, x+Z(7^2)^36, x+Z(7^2)^37, x+Z(7^2)^38, x+Z(7^2)^39, x+Z(7^2)^41, x+Z(7^2)^42, x+Z(7^2)^43, x+Z(7^2)^44, x+Z(7^2)^45, x+Z(7^2)^46, x+Z(7^2)^47, x+Z(7^4), x+Z(7^4)^2, x+Z(7^4)^3, x+Z(7^4)^4, x+Z(7^4)^5, x+Z(7^4)^6, x+Z(7^4)^7, x+Z(7^4)^8, x+Z(7^4)^9, x+Z(7^4)^10, x+Z(7^4)^11, x+Z(7^4)^12, x+Z(7^4)^13, x+Z(7^4)^14, x+Z(7^4)^15, x+Z(7^4)^16, x+Z(7^4)^17, x+Z(7^4)^18, x+Z(7^4)^19, x+Z(7^4)^20, x+Z(7^4)^21, x+Z(7^4)^22, x+Z(7^4)^23, x+Z(7^4)^24, x+Z(7^4)^25, x+Z(7^4)^26, x+Z(7^4)^27, x+Z(7^4)^28, x+Z(7^4)^29, x+Z(7^4)^30, x+Z(7^4)^31, x+Z(7^4)^32, x+Z(7^4)^33, x+Z(7^4)^34, x+Z(7^4)^35, x+Z(7^4)^36, x+Z(7^4)^37, x+Z(7^4)^38, x+Z(7^4)^39, x+Z(7^4)^40, x+Z(7^4)^41, x+Z(7^4)^42, x+Z(7^4)^43, x+Z(7^4)^44, x+Z(7^4)^45, x+Z(7^4)^46, x+Z(7^4)^47, x+Z(7^4)^48, x+Z(7^4)^49, x+Z(7^4)^51, x+Z(7^4)^52, x+Z(7^4)^53, x+Z(7^4)^54, x+Z(7^4)^55, x+Z(7^4)^56, x+Z(7^4)^57, x+Z(7^4)^58, x+Z(7^4)^59, x+Z(7^4)^60, x+Z(7^4)^61, x+Z(7^4)^62, x+Z(7^4)^63, x+Z(7^4)^64, x+Z(7^4)^65, x+Z(7^4)^66, x+Z(7^4)^67, x+Z(7^4)^68, x+Z(7^4)^69, x+Z(7^4)^70, x+Z(7^4)^71, x+Z(7^4)^72, x+Z(7^4)^73, x+Z(7^4)^74, x+Z(7^4)^75, x+Z(7^4)^76, x+Z(7^4)^77, x+Z(7^4)^78, x+Z(7^4)^79, x+Z(7^4)^80, x+Z(7^4)^81, x+Z(7^4)^82, x+Z(7^4)^83, x+Z(7^4)^84, x+Z(7^4)^85, x+Z(7^4)^86, x+Z(7^4)^87, x+Z(7^4)^88, x+Z(7^4)^89, x+Z(7^4)^90, x+Z(7^4)^91, x+Z(7^4)^92, x+Z(7^4)^93, x+Z(7^4)^94, x+Z(7^4)^95, x+Z(7^4)^96, x+Z(7^4)^97, x+Z(7^4)^98, x+Z(7^4)^99, x+Z(7^4)^101, x+Z(7^4)^102, x+Z(7^4)^103, x+Z(7^4)^104, x+Z(7^4)^105, x+Z(7^4)^106, x+Z(7^4)^107, x+Z(7^4)^108, x+Z(7^4)^109, x+Z(7^4)^110, x+Z(7^4)^111, x+Z(7^4)^112, x+Z(7^4)^113, x+Z(7^4)^114, x+Z(7^4)^115, x+Z(7^4)^116, x+Z(7^4)^117, x+Z(7^4)^118, x+Z(7^4)^119, x+Z(7^4)^120, x+Z(7^4)^121, x+Z(7^4)^122, x+Z(7^4)^123, x+Z(7^4)^124, x+Z(7^4)^125, x+Z(7^4)^126, x+Z(7^4)^127, x+Z(7^4)^128, x+Z(7^4)^129, 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x+Z(7^4)^2144, x+Z(7^4)^2145, x+Z(7^4)^2146, x+Z(7^4)^2147, x+Z(7^4)^2148, x+Z(7^4)^2149, x+Z(7^4)^2151, x+Z(7^4)^2152, x+Z(7^4)^2153, x+Z(7^4)^2154, x+Z(7^4)^2155, x+Z(7^4)^2156, x+Z(7^4)^2157, x+Z(7^4)^2158, x+Z(7^4)^2159, x+Z(7^4)^2160, x+Z(7^4)^2161, x+Z(7^4)^2162, x+Z(7^4)^2163, x+Z(7^4)^2164, x+Z(7^4)^2165, x+Z(7^4)^2166, x+Z(7^4)^2167, x+Z(7^4)^2168, x+Z(7^4)^2169, x+Z(7^4)^2170, x+Z(7^4)^2171, x+Z(7^4)^2172, x+Z(7^4)^2173, x+Z(7^4)^2174, x+Z(7^4)^2175, x+Z(7^4)^2176, x+Z(7^4)^2177, x+Z(7^4)^2178, x+Z(7^4)^2179, x+Z(7^4)^2180, x+Z(7^4)^2181, x+Z(7^4)^2182, x+Z(7^4)^2183, x+Z(7^4)^2184, x+Z(7^4)^2185, x+Z(7^4)^2186, x+Z(7^4)^2187, x+Z(7^4)^2188, x+Z(7^4)^2189, x+Z(7^4)^2190, x+Z(7^4)^2191, x+Z(7^4)^2192, x+Z(7^4)^2193, x+Z(7^4)^2194, x+Z(7^4)^2195, x+Z(7^4)^2196, x+Z(7^4)^2197, x+Z(7^4)^2198, x+Z(7^4)^2199, x+Z(7^4)^2201, x+Z(7^4)^2202, x+Z(7^4)^2203, x+Z(7^4)^2204, x+Z(7^4)^2205, x+Z(7^4)^2206, x+Z(7^4)^2207, x+Z(7^4)^2208, x+Z(7^4)^2209, x+Z(7^4)^2210, x+Z(7^4)^2211, x+Z(7^4)^2212, x+Z(7^4)^2213, x+Z(7^4)^2214, x+Z(7^4)^2215, x+Z(7^4)^2216, x+Z(7^4)^2217, x+Z(7^4)^2218, x+Z(7^4)^2219, x+Z(7^4)^2220, x+Z(7^4)^2221, x+Z(7^4)^2222, x+Z(7^4)^2223, x+Z(7^4)^2224, x+Z(7^4)^2225, x+Z(7^4)^2226, x+Z(7^4)^2227, x+Z(7^4)^2228, x+Z(7^4)^2229, x+Z(7^4)^2230, x+Z(7^4)^2231, x+Z(7^4)^2232, x+Z(7^4)^2233, x+Z(7^4)^2234, x+Z(7^4)^2235, x+Z(7^4)^2236, x+Z(7^4)^2237, x+Z(7^4)^2238, x+Z(7^4)^2239, x+Z(7^4)^2240, x+Z(7^4)^2241, x+Z(7^4)^2242, x+Z(7^4)^2243, x+Z(7^4)^2244, x+Z(7^4)^2245, x+Z(7^4)^2246, x+Z(7^4)^2247, x+Z(7^4)^2248, x+Z(7^4)^2249, x+Z(7^4)^2251, x+Z(7^4)^2252, x+Z(7^4)^2253, x+Z(7^4)^2254, x+Z(7^4)^2255, x+Z(7^4)^2256, x+Z(7^4)^2257, x+Z(7^4)^2258, x+Z(7^4)^2259, x+Z(7^4)^2260, x+Z(7^4)^2261, x+Z(7^4)^2262, x+Z(7^4)^2263, x+Z(7^4)^2264, x+Z(7^4)^2265, x+Z(7^4)^2266, x+Z(7^4)^2267, x+Z(7^4)^2268, x+Z(7^4)^2269, x+Z(7^4)^2270, x+Z(7^4)^2271, x+Z(7^4)^2272, x+Z(7^4)^2273, x+Z(7^4)^2274, x+Z(7^4)^2275, x+Z(7^4)^2276, x+Z(7^4)^2277, x+Z(7^4)^2278, x+Z(7^4)^2279, x+Z(7^4)^2280, x+Z(7^4)^2281, x+Z(7^4)^2282, x+Z(7^4)^2283, x+Z(7^4)^2284, x+Z(7^4)^2285, x+Z(7^4)^2286, x+Z(7^4)^2287, x+Z(7^4)^2288, x+Z(7^4)^2289, x+Z(7^4)^2290, x+Z(7^4)^2291, x+Z(7^4)^2292, x+Z(7^4)^2293, x+Z(7^4)^2294, x+Z(7^4)^2295, x+Z(7^4)^2296, x+Z(7^4)^2297, x+Z(7^4)^2298, x+Z(7^4)^2299, x+Z(7^4)^2301, x+Z(7^4)^2302, x+Z(7^4)^2303, x+Z(7^4)^2304, x+Z(7^4)^2305, x+Z(7^4)^2306, x+Z(7^4)^2307, x+Z(7^4)^2308, x+Z(7^4)^2309, x+Z(7^4)^2310, x+Z(7^4)^2311, x+Z(7^4)^2312, x+Z(7^4)^2313, x+Z(7^4)^2314, x+Z(7^4)^2315, x+Z(7^4)^2316, x+Z(7^4)^2317, x+Z(7^4)^2318, x+Z(7^4)^2319, x+Z(7^4)^2320, x+Z(7^4)^2321, x+Z(7^4)^2322, x+Z(7^4)^2323, x+Z(7^4)^2324, x+Z(7^4)^2325, x+Z(7^4)^2326, x+Z(7^4)^2327, x+Z(7^4)^2328, x+Z(7^4)^2329, x+Z(7^4)^2330, x+Z(7^4)^2331, x+Z(7^4)^2332, x+Z(7^4)^2333, x+Z(7^4)^2334, x+Z(7^4)^2335, x+Z(7^4)^2336, x+Z(7^4)^2337, x+Z(7^4)^2338, x+Z(7^4)^2339, x+Z(7^4)^2340, x+Z(7^4)^2341, x+Z(7^4)^2342, x+Z(7^4)^2343, x+Z(7^4)^2344, x+Z(7^4)^2345, x+Z(7^4)^2346, x+Z(7^4)^2347, x+Z(7^4)^2348, x+Z(7^4)^2349, x+Z(7^4)^2351, x+Z(7^4)^2352, x+Z(7^4)^2353, x+Z(7^4)^2354, x+Z(7^4)^2355, x+Z(7^4)^2356, x+Z(7^4)^2357, x+Z(7^4)^2358, x+Z(7^4)^2359, x+Z(7^4)^2360, x+Z(7^4)^2361, x+Z(7^4)^2362, x+Z(7^4)^2363, x+Z(7^4)^2364, x+Z(7^4)^2365, x+Z(7^4)^2366, x+Z(7^4)^2367, x+Z(7^4)^2368, x+Z(7^4)^2369, x+Z(7^4)^2370, x+Z(7^4)^2371, x+Z(7^4)^2372, x+Z(7^4)^2373, x+Z(7^4)^2374, x+Z(7^4)^2375, x+Z(7^4)^2376, x+Z(7^4)^2377, x+Z(7^4)^2378, x+Z(7^4)^2379, x+Z(7^4)^2380, x+Z(7^4)^2381, x+Z(7^4)^2382, x+Z(7^4)^2383, x+Z(7^4)^2384, x+Z(7^4)^2385, x+Z(7^4)^2386, x+Z(7^4)^2387, x+Z(7^4)^2388, x+Z(7^4)^2389, x+Z(7^4)^2390, x+Z(7^4)^2391, x+Z(7^4)^2392, x+Z(7^4)^2393, x+Z(7^4)^2394, x+Z(7^4)^2395, x+Z(7^4)^2396, x+Z(7^4)^2397, x+Z(7^4)^2398, x+Z(7^4)^2399 ] gap> List(factors,DegreeOfLaurentPolynomial); [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] gap> LogTo();Back to Home Page
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