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I will present a formula for a limit of the superconformal index known as Cardy-like limit which is valid for generic 4d N=1 SCFTs with classical gauge group. In this limit, the index captures the entropy of a large-charge black hole, whose microstates are dual under AdS/CFT to 1/4-BPS states in the SCFT. The formula extends previous results beyond the leading (semiclassical) order, and generalizes them to generic SCFTs, beyond the well-understood N=4 and toric cases.