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We consider the semi-classical Dirac operator coupled to a magnetic potentialon a large class of manifolds including all metric contact manifolds. We provea sharp local Weyl law and a bound on its eta invariant. In the absence of aFourier integral parametrix, the method relies on the use of almost analyticcontinuations combined with the Birkhoff normal form and local index theory.

Koszul complexes, Birkhoff normal form and the magnetic Dirac operator