  We perform further tests of the correspondence between spectral theory and
topological strings, focusing on mirror curves of genus greater than one with
nontrivial mass parameters. In particular, we analyze the geometry relevant to
the SU(3) relativistic Toda lattice, and the resolved C^3/Z_6 orbifold.
Furthermore, we give evidence that the correspondence holds for arbitrary
values of the mass parameters, where the quantization problem leads to resonant
states. We also explore the relation between this correspondence and cluster
integrable systems.
