  We study the point spectrum of the linearisation of Euler's equation for the
ideal fluid on the torus about a shear flow. By separation of variables the
problem is reduced to the spectral theory of a complex Hill's equation. Using
Hill's determinant an Evans function of the original Euler equation is
constructed. The Evans function allows us to completely characterise the point
spectrum of the linearisation, and to count the isolated eigenvalues with
non-zero real part. In particular this approach also works in the case where
complex eigenvalues appear.
