High overtones of Dirac perturbations of a Schwarzschild black hole

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of ${\omega }_n$ is equidistant and equals to $\mathrm{\Im }{\omega }_{n+1}-\mathrm{\Im }{\omega }_n=i\mathrm{/}8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of ${\omega }_n$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.