Zeros of the Ramanujan sum for finite fields

Question

Let $\mathbb{F}_q$ be a finite field with $q$ elements, let $N$ be a positive divisor of $q-1$, and let $\xi_N$ be an element of $\mathbb{F}_q^*$ of order $N$. One can similarly define the Ramanujan sum for $\mathbb{F}_q$ as $$ c_N(k) = \sum_{\substack{i=1 \\ (i,N) = 1}}^N \xi_N^{ik}. $$ That is, $c_N(k)$ is the sum of $k$-th powers of the primitive $N$-th roots of unity in $\mathbb{F}_q$. I'm wondering how many zeros does the sum have? What are its values? How about a lower bound for this? Thanks!