Trigonometric sum evaluation

Question

Let $q$ a prime number and $1 \leq a<q$ a positive integer. We know from Ramanujan identity that $$\underset{h=1,\left(h,q\right)=1}{\overset{q}{\sum}}e^{2\pi ih\frac{a}{q}}=\underset{h=1}{\overset{q-1}{\sum}}e^{2\pi ih\frac{a}{q}}=\mu\left(q\right)=-1$$because $q$ is prime. Is it possible to obtain a non trivial evaluation of $$\underset{h=1}{\overset{n}{\sum}}e^{2\pi ih\frac{a}{q}}$$with $1<n<q-1$? (Always in the case of $q$ prime number)