generality of our approach we also derive these results for the so-called parametric resonances which have been particularly useful in numerical studies [@GG:00]. Finally, we give numerical verifications of our analytic results.

The paper is organized as follows. Although the system and its effective Hamiltonian have been nicely explained earlier in [@GG:00; @KS:06; @KS:08], for the sake of completeness of this paper we will describe these briefly in section II. In the same section we will also describe the exact and the parametric resonances. In Sec. III we will derive result for resonances in an open-clean chain of finite length, in terms of a polynomial equation. For long chains, we will solve this polynomial equation in the leading order of the inverse of the length. In Sec. IV we will use the perturbation theory to obtain the first and the second order corrections in the complex energies for a weak disorder. In Sec. V we will calculate statistics of the scattered complex energies. In the same section we will simplify our results for long chains and obtain compact expressions. In Sec. VI we will briefly discuss about the numerical methods to calculate complex energies of non-Hermitian effective Hamiltonians and numerically 