  We show that for a non-trivial element $c$ in $\widehat{HF}(-Y)$, there
exists a tight contact structure $\xi$ on $Y$ whose contact invariant realizes
$c$ if and only if there exists a non-trivial fibered knot $K$ such that
$-\tau_c(K)=g(K)$. Moreover, when such a fibered knot $K$ does exist, $\xi$ can
be chosen to satisfy the extra condition that $K$ admits a Legendrian
representative with Thurston-Bennequin number tb$(K)$ equal to $0$ in
$(Y,\xi)$.
