  We give a concrete method to explicitly compute the rational cohomology of
the unordered configuration spaces of connected, oriented, closed,
even-dimensional manifolds of finite type which we have implemented in Sage
[S+09]. As an application, we give acomplete computation of the stable and
unstable rational cohomology of unordered configuration spaces in some cases,
including that of $\mathbb{CP}^3$ and a genus 1 Riemann surface, which is
equivalently the homology of the elliptic braid group. In an appendix, we also
give large tables of unstable and stable Betti numbers of unordered
configuration spaces. From these, we empirically observe stability phenomenon
in the unstable cohomology of unordered configuration spaces of some manifolds,
some of which we prove and some of which we state as conjecture.
