DegreesAndMultiplicitiesF4_1mod12 := [
[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+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2, 1],
[(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2, 1/4*q-1/4],
[(q-1)*(q+1)*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+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^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, 1],
[(q-1)*(q+1)*(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(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+1)^2*(q^2-q+1)^2, 1/4*q-5/4],
[1/2*q*(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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+1)^2*(q^2-q+1)^2, 1],
[1/2*q*(q^2+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+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*(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-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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q-1)^4, 1],
[1/24*q^4*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q-1)^4, 1],
[1/8*q^4*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2, 2],
[1/8*q^4*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q+1)^4, 1],
[1/8*q^4*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+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],
[1/4*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+1)^2*(q^2-q+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2-q+1)^2, 1],
[1/2*q*(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q-1)^3, q-1],
[1/2*q*(q-1)*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2, q-1],
[1/2*q^2*(q^2+1)*(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^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+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+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+q+1)^2, q-3],
[1/2*q*(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-1],
[1/2*q^4*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2-q+1)^2, 2],
[1/2*q*(q-1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2, q-1],
[1/2*q*(q+1)*(q^2+q+1)*(q^4-q^2+1)*(q^4+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+q+1)*(q^2+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^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2, 1],
[1/2*q*(q^2+1)*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q+1)^3, q-3],
[1/2*q*(q+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+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-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-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-q^2+1)*(q^4+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^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 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, 1/2*q-1/2],
[(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, q-6],
[(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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*(q+2)*(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-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, 1/4*(q-1)*(2*q-3)],
[q^3*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, 2],
[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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2, 1],
[(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, q-6],
[(q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/6*q^2-19/12*q+53/12],
[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+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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+1)*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1],
[1/2*q*(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],
[1/2*q^4*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2, 1],
[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*(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+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1],
[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^4*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2, 1],
[1/2*q*(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-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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, q-1],
[(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2, 1/4*q-1/4],
[q*(q-1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-3/4],
[(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-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-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, 1/4*q-5/4],
[q*(q+1)*(q^4-q^2+1)*(q^4+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^2*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1],
[q*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, q-6],
[(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*q^2-25/8*q+141/16],
[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-q^2+1)*(q^4+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+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+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+1)*(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+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-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1],
[1/2*q^2*(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],
[1/2*q^5*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+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+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2, q-1],
[1/2*q*(q-1)*(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)*(q-2)],
[1/2*q^4*(q+1)*(q^2+q+1)*(q^4-q^2+1)*(q^4+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+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1],
[1/2*q^5*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2, 1],
[1/2*q^2*(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-3],
[1/2*q*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2*(q+1)^4, 1/4*(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+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q+1)^3, q-3],
[1/2*q^4*(q+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+1)^2, q-3],
[1/2*q*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+1)^2*(q-1)^4, 1/12*(q-1)*(2*q-9)],
[(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)*(2*q^2-21*q+63)],
[q^2*(q^2-q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+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-q^2+1)*(q^4+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1],
[(q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 3/4*q-3/4],
[q*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q-1)^4, 1/3*q*(q-1)],
[q*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1/3*(q+2)*(q-1)],
[(q^2-q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*(q-1)*(q^2-2)],
[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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/4*(q-1)*(2*q-3)],
[q^4*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 2],
[(q-1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, q-6],
[q^2*(q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, q-6],
[q*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/8*q^2-25/4*q+141/8],
[q*(q^2+q+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^4, 1/6*q^2-19/12*q+53/12],
[(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, 1/24*q^3-35/48*q^2+25/6*q-407/48],
[(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-1)*(q-9)*(q^2-10*q+33)],
[q*(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)*(2*q^2-21*q+63)],
[(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q-1)^4*(q+1)^4, 1/72*(q+2)*(q-1)*(q^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*(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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2+q+1)^2*(q-1)^3, 1/12*(q-1)*(2*q-9)],
[(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^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-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*(q+2)*(q-1)],
[q^6*(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q^2-q+1)^2, 1/4*q-1/4],
[q^4*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, q-1],
[q*(q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+1)^2*(q^2-q+1)^2*(q^2+q+1)^2, 1/4*q-1/4],
[(q^4-q^2+1)*(q^4+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-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-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-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*(q^2-q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q-1)^2*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/3*(q-1)*(q^2-2)],
[q^3*(q+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+1)*(q-1)^2*(q^2+1)^2*(q^2+q+1)^2, 1/4*(q-1)*(2*q-3)],
[(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+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^6*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, 1],
[q^2*(q-1)*(q+1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q^2+q+1)^2*(q^2+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^2-2*q-4)*(q-1)^2],
[q^6*(q-1)*(q+1)*(q^2+1)*(q^2-q+1)*(q^4-q^2+1)*(q^4+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+q+1)*(q^2+1)*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2-q+1)^2, 1/4*q-5/4],
[q*(q-1)*(q^4-q^2+1)*(q^4+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-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2-q+1)^2, q-6],
[q^3*(q+1)*(q^4-q^2+1)*(q^4+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+q+1)^2*(q^2+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-q^2+1)*(q^4+1)*(q^2-q+1)^2*(q^2+1)^2*(q+1)^3, 1/6*q^2-19/12*q+53/12],
[q^2*(q^4-q^2+1)*(q^4+1)*(q+1)^2*(q^2+1)^2*(q^2+q+1)^2*(q^2-q+1)^2, 5/16*q^2-25/8*q+141/16],
[q*(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, 1/24*q^3-35/48*q^2+25/6*q-407/48],
[(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^4-7/288*q^3+143/576*q^2-35/32*q+2153/1152]
];