I'm pretty new to modular arithmetic and not having a good knowledge of algebra, so sorry for perhaps a basic question.
Suppose that I have a Galois field modulo $N$ and a primitive root $\omega$. I understand that $\omega$ is also a primitive $\phi(N)$-th root of unity modulo $N$.
Knowing the value of $\omega$, is there a fast way, for an arbitrary $n<N$, compute one of the primitive $n$-th roots of unity modulo $N$?
I searched the Wikipedia and didn't find anything, but I could have been inattentive.