  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.
