  We study the electronic structure of the nodal line semimetal ZrSiTe both
experimentally and theoretically. We find two different surface states in
ZrSiTe - topological drumhead surface states and trivial floating band surface
states. Using the spectra of Wilson loops, we show that a non-trivial Berry
phase that exists in a confined region within the Brillouin Zone gives rise to
the topological drumhead-type surface states. The $\mathbb{Z}_2$ structure of
the Berry phase induces a $\mathbb{Z}_2$ 'modular arithmetic' of the surface
states, allowing surface states deriving from different nodal lines to
hybridize and gap out, which can be probed by a set of Wilson loops. Our
findings are confirmed by \textit{ab-initio} calculations and angle-resolved
photoemission experiments, which are in excellent agreement with each other and
the topological analysis. This is the first complete characterization of
topological surface states in the family of square-net based nodal line
semimetals and thus fundamentally increases the understanding of the
topological nature of this growing class of topological semimetals.
