PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

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We show that at least the quasi-exactly solvable eigenvalues of the Schrödinger equation with the potential V(x) = -(ζ 2x -iM)² as well as the periodic potential V(x) = (ζ 2θ-iM)² are real for the PT-invariant non-Hermitian potentials in case the parameter M is any odd integer. We further show that the norm as well as the weight functions for the corresponding weak orthogonal polynomials are also real.