Computing special values of motivic L-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-series whose F-factor is of the form A(s) Pi(i=1)(d) Gamma(s+lambda(j)/(2) over bar /2) with d arbitrary and complex lambda(j), not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).