  We present a simple closed form expression for the topologically twisted
index of the ABJM theory as a function of the magnetic fluxes and complex
chemical potentials valid at fixed $k$ and to all orders in the $1/N$
expansion. This in turn leads to analytic expressions for the topologically
twisted index at fixed genus in the 't Hooft limit to all orders in the
$1/\sqrt{\lambda}$ expansion. These results have important implications for
holography and the microscopic entropy counting of supersymmetric static
AdS$_4$ black holes. Generalizations to other SCFTs arising from M2-branes are
also briefly discussed.
