Evaluating L-functions with few known coefficients.
LMS Journal of Computation and Mathematics
We address the problem of evaluating an L-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that is possible to evaluate the L-function more precisely than one would expect from the standard approach. The method, however, requires considerably more computational effort to achieve a given accuracy than would be needed if more Dirichlet coefficients were available.
Ryan, Nathan C. and Farmer, David W.. "Evaluating L-functions with few known coefficients.." LMS Journal of Computation and Mathematics 17, no. 1 (2014) : 245-258.