The eigenvalue problem for the matrix representation of the diffusion operator appearing in the diffusion equation previously derived for the coarse-grained helical wormlike (HW) chain model is considered. Following the procedure already established in the study of the original diffusion equation for the discrete HW:chain, the problem is solved in the subspace and block-diagonal approximations in the subspace L(1), where L is the "total angular momentum quantum number" and (1) indicates the one-body excitation basis set. The 1(1) eigenvalues lambda(1,k)(j) thus obtained form three branches of the eigenvalue spectrum specified by the index j as before, and it is shown that lambda(1,k)(0) in the j=0 (lowest) branch at small wave number k is approximately proportional to the corresponding Rouse-Zimm eigenvalue in the Hearst version. The behavior of the eigenvalue spectra is also numerically examined taking atactic polystyrene with the fraction of racemic diads f(r)=0.59 and atactic poly(methyl methacrylate) with f(r)=0.79 as typical examples of flexible polymers. It is found that the ratio lambda(1,k)(0)/lambda(1,1)(0), at small k depends somewhat (appreciably for large k) on chain stiffness and local chain conformation.