  We give a formula for the modular operator and modular conjugation in terms
of matrix coefficients of corepresentations of a quantum group in the sense of
Kustermans and Vaes. As a consequence, the modular autmorphism group of a
unimodular quantum group can be expressed in terms of matrix coefficients. As
an application, we determine the Duflo-Moore operators for the quantum group
analogue of the normaliser of SU(1,1) in $SL(2,\mathbb{C}$).
