DegreesAndMultiplicitiesF4_9mod12 := [ [1, 1], [(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [1/2*q*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1), 2], [1/2*q*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1], [q^2*(q^4-q^2+1)*(q^2+q+1)^2*(q^2-q+1)^2, 1], [(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [1/2*q*(q^2-q+1)*(q^2+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [1/2*q*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2, 1], [1/2*q*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [(q-1)*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), q-1], [q^3*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2, 2], [q*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [(q+1)*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), q-3], [(q+1)*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [1/2*q^2*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^2*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [1/2*q^2*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^2*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2, 1], [(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1/4*q-1/4], [(q-1)*(q+1)*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2, 1/4*q-1/4], [q*(q+1)*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [(q-1)*(q+1)*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2, 1/4*q-1/4], [(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1/4*q-5/4], [1/2*q*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [1/2*q*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 1], [(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [q^3*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1)*(q^2+1)^2, 1], [(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-3/2], [1/24*q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q-1)^4, 1], [1/24*q^4*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2*(q+1)^4, 1], [1/12*q^4*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1], [1/8*q^4*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2*(q-1)^4, 1], [1/8*q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 2], [1/8*q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q+1)^4, 1], [1/8*q^4*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 2], [1/4*q^4*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4, 1], [1/4*q^4*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4*(q+1)^4, 2], [1/4*q^4*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 2], [1/4*q^4*(q^4+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1], [1/4*q^4*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 2], [1/4*q^4*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1], [1/3*q^4*(q^4+1)*(q^2+1)^2*(q-1)^4*(q+1)^4, 2], [1/3*q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1], [1/2*q*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2*(q-1)^3, q-1], [1/2*q*(q-1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, q-1], [1/2*q^2*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^2*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [1/2*q^4*(q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1], [1/2*q*(q+1)*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, q-3], [1/2*q*(q-1)*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, q-1], [1/2*q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2, 2], [1/2*q*(q-1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, q-1], [1/2*q*(q+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, q-3], [1/2*q^4*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1], [1/2*q^2*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^2*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 1], [1/2*q*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q+1)^3, q-3], [1/2*q*(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, q-3], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/8*(q-1)*(q-3)], [(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1], [q*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/4*(q-1)*(q+1)], [(q-1)*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*(q-1)*(q-2)], [q^4*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1], [q^2*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1], [q*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, q-4], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/8*(q-3)*(q-5)], [(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/12*(q-1)*(2*q-9)], [q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*q*(q+1)], [(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1], [q^2*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, q-1], [(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, 1/4*(q-1)*(2*q-3)], [q^9*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2, 2], [q*(q-1)*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [(q-1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, 1/4*(q-1)*(2*q-3)], [q^5*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1)*(q^2+1)^2, 1], [q^3*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 2], [q^2*(q+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/3*q*(q-1)], [(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^2*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, q-2], [q*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, q-4], [(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-5/4], [q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-5/4], [(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/12*(2*q-9)*(q-5)], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/2*q-1/2], [1/2*q^6*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^4*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-3/2], [1/2*q^6*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [1/2*q*(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, q-1], [1/2*q^4*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [1/2*q^6*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [1/2*q^4*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^6*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2, 1], [1/2*q^4*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 1], [1/2*q*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, q-3], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/2*q-3/2], [(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/16*(q-1)^2], [q*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, q-1], [(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*(q-1)*(q-5)], [q*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^2*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^3*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, q-1], [q^2*(q-1)*(q+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1/4*q-1/4], [q*(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-3/4], [(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3*(q+1)^3, 1/8*(q-1)*(q+1)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/8*(3*q-1)*(q-1)], [q^10*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1], [(q-1)*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*(q-1)*(q-3)], [q^4*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1], [q^3*(q+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [q*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^2*(q-1)*(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^3*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, q-2], [q^2*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, 1/4*q-5/4], [q*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-15/4], [(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/16*(q-1)*(q-5)], [q*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, q-4], [(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*(q-5)^2], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4, 1/8*(q-1)*(q-3)], [1/2*q^2*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/2*q-1/2], [1/2*q*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q-1)^4, 1/4*(q-1)*(q+1)], [1/2*q^4*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2*(q-1)^3, q-1], [1/2*q*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/2*(q-1)*(q-2)], [1/2*q*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/4*(q-1)*(q-3)], [1/2*q^4*(q-1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, q-1], [1/2*q^9*(q^2-q+1)*(q^2+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^5*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^2*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-3/2], [1/2*q^9*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2, 1], [1/2*q^2*(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, q-1], [1/2*q^5*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, 1], [1/2*q^13*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 1], [1/2*q^4*(q+1)*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, q-3], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 3/4*q^2-3/2*q+7/4], [1/2*q^13*(q^2+1)*(q^4-q^2+1)*(q^4+1), 2], [1/2*q^4*(q-1)*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, q-1], [1/2*q^13*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^4*(q-1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, q-1], [1/2*q*(q-1)*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, (q-1)*(q-2)], [1/2*q^4*(q+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2, q-3], [1/2*q^9*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2, 1], [1/2*q^2*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [1/2*q^9*(q^2+1)*(q^2+q+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^5*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1], [1/2*q^5*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, 1], [1/2*q^2*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, q-3], [1/2*q*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q+1)^4, 1/4*(q-1)*(q+1)], [1/2*q*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/2*(q-1)*(q-2)], [1/2*q^4*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q+1)^3, q-3], [1/2*q^4*(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2, q-3], [1/2*q*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/4*(q-3)*(q-5)], [1/2*q^2*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/2*q-3/2], [1/2*q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^4, 1/8*(q-3)*(q-5)], [q*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4, 1/12*(q-1)*(2*q-9)], [(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/48*(q-1)*(2*q^2-21*q+63)], [q^2*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, q-1], [q^3*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/8*(q-1)*(q-5)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q-1)^3, 1/8*(q-1)*(2*q-1)*(q+1)], [q*(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/4*(q-1)*(2*q-3)], [q^2*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^3*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1], [(q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/16*(q-1)*(6*q^2-23*q+29)], [q^4*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [q^2*(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-3/4], [q*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4, 1/3*q*(q-1)], [q*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1/3*q*(q+1)], [(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/3*q^2*(q-1)], [q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/4*(q-1)*(q+1)], [(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*q*(q+1)*(q-2)], [q^3*(q-1)*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [q^9*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [q^6*(q+1)*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [q*(q-1)*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/2*(q-1)*(q-3)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q+1)^3, 1/8*(2*q-5)*(q-1)*(q+1)], [q^2*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q*(q-1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/4*(q-1)*(2*q-3)], [(q-1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/16*(q-1)*(6*q^2-35*q+45)], [q^4*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [q^3*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, q-4], [q^2*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-15/4], [q^3*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-5/4], [q^2*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, q-4], [q*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/8*(q-5)^2], [q*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1/12*(2*q-9)*(q-5)], [(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/48*(2*q-15)*(q-5)^2], [(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4, 1/1152*(q-1)*(q-9)*(q^2-10*q+33)], [q*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/48*(q-1)*(2*q^2-21*q+63)], [(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q-1)^4*(q+1)^4, 1/72*q*(q-2)*(q+3)*(q+1)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q-1)^4, 1/32*(q+1)*(q-1)^3], [q^2*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/16*(q-1)^2], [q^3*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/12*(q-1)*(2*q-9)], [(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3, 1/48*(q-1)*(q^3-7*q^2+16*q-18)], [q^4*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/8*(q-1)*(q-3)], [q^2*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*(q-1)*(q-5)], [(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4, 1/18*q^2*(q-1)^2], [q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q-1)^3, 1/8*(q-1)*(2*q-1)*(q+1)], [(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q-1)^3*(q+1)^3, 1/6*q^2*(q-1)*(q+1)], [q^3*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*q*(q+1)], [q^6*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^3*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^9*(q-1)*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), q-1], [q^6*(q-1)*(q+1)*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2, 1/4*q-1/4], [q^4*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1], [q*(q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/16*(q-1)*(6*q^2-23*q+29)], [q^5*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-1/2], [q^3*(q-1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4*(q+1)^4, 1/96*(q-1)*(q+3)*(q-3)*(q+1)], [q^2*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3*(q+1)^3, 1/8*(q-1)*(q+1)], [(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4*(q+1)^4, 1/8*(q-1)*(q+1)*(q^2+1)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^3*(q+1)^3, 1/8*q*(q-1)*(q-2)*(q+1)], [q^4*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/4*(q-1)*(q+1)], [q*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/3*q^2*(q-1)], [(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q-1)^4*(q+1)^4, 1/12*q^2*(q-1)*(q+1)], [q^24, 1], [q^2*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 1/8*(3*q-1)*(q-1)], [q^16*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [q*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*q*(q+1)*(q-2)], [q^3*(q+1)*(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, 1/4*(q-1)*(2*q-3)], [(q^4+1)*(q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/64*(q-1)*(q-3)*(5*q^2-4*q+7)], [q^4*(q-1)*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*(q-1)*(q-2)], [q^10*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), 1], [q^3*(q-1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, 1/4*(q-1)*(2*q-3)], [q^7*(q+1)*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1], [q^2*(q-1)*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*(q-1)*(q-3)], [q^3*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/3*q*(q-1)], [(q^2-q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3*(q+1)^3, 1/6*q*(q-1)*(q-2)*(q+1)], [q*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q+1)^3, 1/8*(2*q-5)*(q-1)*(q+1)], [(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1/18*q*(q-2)*(q-3)*(q+1)], [q^6*(q-1)*(q+1)*(q^2-q+1)*(q^2+1)*(q^4+1)*(q^4-q^2+1)*(q^2+q+1)^2, 1/4*q-1/4], [q^3*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4], [q^9*(q+1)*(q^2+1)*(q^4+1)*(q^2+q+1)*(q^2-q+1)*(q^4-q^2+1), q-3], [q^6*(q^2+1)*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, 1/4*q-5/4], [q*(q-1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/16*(q-1)*(6*q^2-35*q+45)], [q^5*(q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2, 1/2*q-3/2], [q^4*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2*(q^2+1)^2, q-4], [q^3*(q+1)*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-5/4], [(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4*(q+1)^4, 1/72*q*(q-1)*(q-3)*(q+2)], [(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2*(q^2-q+1)^2*(q+1)^4, 1/32*(q-1)*(q+1)*(q-3)^2], [q^2*(q-1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/16*(q-1)*(q-5)], [(q-1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/48*(q-1)*(q-5)*(q^2-6*q+6)], [q^4*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/8*(q-3)*(q-5)], [q^3*(q^2+q+1)*(q^4+1)*(q^4-q^2+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/12*(2*q-9)*(q-5)], [q^2*(q^4+1)*(q^4-q^2+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*(q-5)^2], [q*(q^4+1)*(q^4-q^2+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^3, 1/48*(2*q-15)*(q-5)^2], [(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^4, 1/1152*(q-5)^2*(q-9)^2] ];