  In this paper, we consider the perturbations of the Harmonic Oscillator
Operator by an odd pair of point interactions: $z (\delta(x - b) - \delta(x +
b))$. We study the spectrum by analyzing a convenient formula for the
eigenvalue. We conclude that if $z = ir$, $r$ real, as $r \to \infty$, the
number of non-real eigenvalues tends to infinity.
