A generalization of the Gauss sum

For the generalized Gauss sum
$$ S(N;a,q)=\sum\limits_{k=1}^{Nq} e\bigg(\frac1N \Big( k-\frac{a}{q}\Big)^2\bigg), $$
where $N,q$ are natural numbers, $a$ is integer, $0\leq a<q$, $(a,q)=1$, its value is determined.