  In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes
data" (arxiv:1209.2045) we described all smooth solutions of the two-function
tt*-Toda equations in terms of asymptotic data, holomorphic data, and monodromy
data. In this supplementary article we focus on the holomorphic data and its
interpretation in quantum cohomology, and enumerate those solutions with
integral Stokes data. This leads to a characterization of quantum D-modules for
certain complete intersections of Fano type in weighted projective spaces.
