  Kjuchukova's $\Xi_p$ invariant gives a ribbon obstruction for Fox $p$-colored
knots. The invariant is derived from dihedral branched covers of 4-manifolds,
and is needed to calculate the signatures of these covers, when singularities
on the branching sets are present. In this note, we give an algorithm for
evaluating $\Xi_p$ from a colored knot diagram, and compute a couple of
examples.
