How can we find all the monic polynomials P(X) ∈ C [X], with simple roots such that P(X^{n}) = ±P(X) P(ζX) P (ζ^{2}X) …P (ζ^{n-1}X), where ζ is a primitive n-th root of unity?

How can we find all the monic polynomials P(X) ∈ C [X], with simple roots such that P(X^{n}) = ±P(X) P(ζX) P (ζ^{2}X) …P (ζ^{n-1}X), where ζ is a primitive n-th root of unity?