  We engineer a large new set of four-dimensional N=1 superconformal field
theories by wrapping M5-branes on complex curves. We present new supersymmetric
AdS_5 M-theory backgrounds which describe these fixed points at large N, and
then directly construct the dual four-dimensional CFTs for a certain subset of
these solutions. Additionally, we provide a direct check of the central charges
of these theories by using the M5-brane anomaly polynomial. This is a companion
paper which elaborates upon results reported in arXiv:1112:5487.
