  We find zero-free regions in the complex plane at large |q| for the
multivariate Tutte polynomial (also known in statistical mechanics as the
Potts-model partition function) Z_G(q,w) of a graph G with general complex edge
weights w = {w_e}. This generalizes a result of Sokal (cond-mat/9904146) that
applies only within the complex antiferromagnetic regime |1+w_e| \le 1. Our
proof uses the polymer-gas representation of the multivariate Tutte polynomial
together with the Penrose identity.
