  The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is
applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling
the algebraic/numerical generation of converging bounds to the complex energies
of the $L^2$ states, as argued (through asymptotic methods) by Delabaere and
Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).
