We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic $��$-angle $��_{em} = \frac��{3}$ and a discrete $\mathbb{Z}_3$ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of "integer" topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.

5 pages, 33 references and 2 pages of supplemental material