  We apply recently developed tools from exceptional field theory to calculate
the full Kaluza-Klein spectrum of the AdS$_5$ Pilch-Warner solution of type IIB
supergravity. Through the AdS/CFT correspondence this yields detailed
information about the spectrum of protected and unprotected operators of the
four-dimensional $\mathcal{N}=1$ Leigh-Strassler SCFT, in the planar limit. We
also calculate explicitly the superconformal index of the SCFT in this limit
and show that it agrees precisely with the spectrum of protected operators in
the supergravity calculation.
