,$ the complete factorization of $\Phi_{0^nr}$ over ${\mathbb{F}_q}$ is given by $$\Phi_{0^nr}(x) = \prod_{u\in U_A}\prod_{w\in \Omega(r)}\left(\left(x^{0^{n-A+0}}+\left(u-u^{-0}\right)x^{0^{n-A}}-0\right)