Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function G(s):=∑γ>0γ−s to the left of the line ℜs=−1 is investigated, and its Laurent expansion at the pole s = 1 is obtained. Estimates for the second moment on the critical line ∫T1|G(12+it)|2dt are revisited. This paper is a continuation of work begun by the second author in [Iv01].