Detecting fibered strongly quasi-positive links

We prove that an $n$-component fibered link $L$ in $S^3$ is strongly quasi-positive if and only if $\tau(L)=g_3(L)+n-1$, where $g_3(L)$ denotes the Seifert genus and $\tau$ is the Ozsv\'ath-Szab\'o concordance invariant. We also provide a table which contains a list of some fibered prime links with at most 9 crossings; and we explicitly determine the ones that are strongly quasi-positive and their maximal self-linking number.