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Abstract We employ supersymmetric localization to determine the exact partition function of 3d N $$ \mathcal{N} $$ = 2 gauge theories on a background given by a round S 2 fibered over a circle and certain complexified background fields. The Coulomb branch localization locus includes monopole configurations, and the partition function reduces to a matrix model. We consider the partition function of the ABJM theory on this background as an explicit case. We verify that the large-N limit of the ABJM theory partition function produces, in the Cardy limit, the entropy function of the dual rotating, electrically charged asymptotically AdS4 supersymmetric black holes and thus provides a microscopic explanation for the Bekenstein-Hawking entropy.