  In this note we give concise formulas, which lead to a simple and fast
computer program that computes a powerful knot invariant. This invariant
$\rho_1$ is not new, yet our formulas are by far the simplest and fastest:
given a knot we write one of the standard matrices $A$ whose determinant is its
Alexander polynomial, yet instead of computing the determinant we consider a
certain quadratic expression in the entries of $A^{-1}$. The proximity of our
formulas to the Alexander polynomial suggest that they should have a
topological explanation. This we don't have yet.
