  It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special
property: if a scalar operator with conformal dimension $\Delta$ exists in the
operator spectrum, then the conformal bootstrap demands that large spin primary
operators have to exist in the operator spectrum of the CFT with a conformal
twist close to $2\Delta+2N$ for any integer $N$. In this paper the conformal
bootstrap methods that were used to find the anomalous dimension of the $N=0$
operators have been generalized to find the anomalous dimension of all large
spin operators of this class. In AdS these operators can be interpreted as the
excited states of the product states of objects that were found in other works.
