I usually work in number theory so I am not familiar with Fourier transforms, I have read up on them and know the basics but it never seems to be in number theory language.
I am trying to find the transform of a primitive Dirichlet character $\chi(n) \bmod q$. I know this is a periodic function and $\chi(n)=\exp\left(\frac{Kv(n)}{\phi(p^\alpha)}\right)$ but I have no idea have to find its transform or the transform of $f(n)\chi(n)$
Yes you are right, say how would you calculate $\sum_(n\epsilon Z) f(n)\chi(n)$