Let m,n be the roots of the equation (x^2)+x+1=0. The equation whose roots are m^19, n^7 is ?

the given equation is x^2 + x+ 1 =0. this has w and w^2 as the roots which are cubeth roots of unity. (imaginary roots) w = (-1 + i*root(5))/2 and w^2 = (-1-i*root(5))/2. we also have w^3 =1. let m = w and n = w^2 without loss of generality. m^19 = w^18 * w = (w^3)^6 * w= w n^7 = w^14 = w^12 *w^2 = w^2. so the equation whose roots are m^19 and n^7 is also x^2 + x+ 1=0