About sums similar to gauss sums

Question

It is well known the case for sums like: $$ \sum_{i=0}^{p^n -1}\zeta^{-ai}, $$ where zeta is a primitive $p^n$-rooth of $1$. But, is there a standard formula for sums like: $$ \sum_{i=0}^{p^n -1}i^N\zeta^{-ai} $$ where $N$ is a fixed integer? Do you know references? Thanks for suggestions!