  We study the superconformal index of $\mathcal N=1$ quiver theories at
large-$N$ for general values of electric charges and angular momenta, using
both the Bethe Ansatz formulation and the more recent elliptic extension
method. We are particularly interested in the case of unequal angular momenta,
$J_1\ne J_2$, which has only been partially considered in the literature. We
revisit the previous computation with the Bethe Ansatz formulation with generic
angular momenta and extend it to encompass a large class of competing
exponential terms. In the process, we also provide a simplified derivation of
the original result. We consider the newly-developed elliptic extension method
as well; we apply it to the $J_1\ne J_2$ case, finding a good match with the
Bethe Ansatz results. We also investigate the relation between the two
different approaches, finding in particular that for every saddle of the
elliptic action there are corresponding terms in the Bethe Ansatz formula that
match it at large-$N$.
