  In this paper we consider $\phi^4$ theory in $4-\epsilon$ dimensions at the
Wilson-Fisher fixed point where the theory becomes conformal. We extend the
method in arXiv:1505.00963 for calculating the leading order term in the
anomalous dimensions of some operators with spin. This method involves mostly
symmetry arguments and reduces the process for calculating anomalous dimensions
to some Wick contractions in the corresponding free theory. We apply this
method in the case of operators with two and three fields whose twist is equal
to the number of fields they contain, and we rederive known results for their
anomalous dimensions. We also calculate the leading term in the anomalous
dimensions of operators with spin two and three. In addition, we find
expressions for the primary operators of the free theory, for arbitrary spin
and number of fields, whose twist remains equal to the number of fields.
