A fast algorithm to compute L(1/2,f×χq)

Let f be a fixed (holomorphic or Maass) modular cusp form. Let χq be a Dirichlet character mod q. We describe a fast algorithm that computes the value L(1/2,f×χq) up to any specified precision. In the case when q is smooth or highly composite integer, the time complexity of the algorithm is given by O(1+|q|5/6+o(1)).