Computing Special Values of MotivicL-Functions

We present an algorithm to compute values L(s) and derivatives L (k) (S) of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-serieswhose Γ-factor is of the form AS with d arbitrary and complex λ j , not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).