Polylog of primitive root of unity

COnsider $O(k)=\sum_{\omega\in W_k} Li_s(\omega x)$ Where $W_k$ is the set of the kth primitive roots of unity. We easily remember that $\sum_{\omega\in R_k} Li_s (\omega x) = k^{1-s} Li_s(x^k)$ Where $R_k$ is the set of the kth root of unity (this one is easy to prove) Using the fact that every kth root of unity is a dth primitive root of unity for d|k, so we can write $k^{1-s} Li_s(x^k)=\sum_{d|k} O(d)$ Using the möbius inversion we have $O(k)=\sum_{d|k} d^{1-s} \mu(k/d) Li_s(x^d)$ SO the sum of the coefficients will be $\sum_{d|k} d^{1-s} \mu(k/d) = \prod_{p^a|k} \sum_{d|p^a} d^{1-s} \mu(p^a/d)=\prod_{p^a|k} (p^{a(1-s)} -p^{(a-1)(1-s)})$ SO at k=2015 which is $2015=5*13*31$ and s=2 we have $O(2015)= (5^{-1}-1)(13^{-1}-1)(31^{-1}-1)=-\dfrac{288}{403}$ and $288+403=\boxed{691}$