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In this article, we state the Bohr-Sommerfeld conditions around a singularvalue of hyperbolic type of the principal symbol of a self-adjointsemiclassical Toeplitz operator on a compact connected K\"{a}hler surface.These conditions allow the description of the spectrum of the operator in afixed size neighbourhood of the singularity. We provide numerical computationsfor three examples, each associated to a different topology.

Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case