  We give numerical estimates of various unstable stationary solutions of the
Gross--Pitaevskii equation in an axially symmetric set up with a linear
trapping potential along the symmetry axis, and a quadratic trapping along the
radial direction. These represent topological coherent modes of Bose--Einstein
condensates in a gravito optical surface trap (GOST). Despite their
instability, we find that many of these solutions decay sufficiently slow, so
that they could be realized experimentally.
