The octic periodic polynomial

The coefficients and the discriminant of the octic period polynomial ${\psi _8}(z)$ are computed, where, for a prime $p = 8f + 1$, ${\psi _8}(z)$ denotes the minimal polynomial over ${\mathbf{Q}}$ of the period $(1/8)\sum\nolimits_{n = 1}^{p - 1} {\exp (2\pi i{n^8}/p)}$. Also, the finite set of prime octic nonresidues $(\mod p)$ which divide integers represented by ${\psi _8}(z)$ is characterized.