This article presents the first results of the application of quantum mechanics with complex coordinates to the calculation of partial widths for the radiationless decay of an inner-hole excited autoionizing state, the Netls2s22p6 'S. This is succeeded by the reduction of the multi-electron, multichannel problem in the complex energy plane to five, symmetry adapted, two-electron problems, in accordance with a published theory of many-electron resonances. These two-electron problems are solved independently by using rotated analytic Hartree-Fock orbitals (expressed in terms of Slater orbitals) for the localized components, and Slater plus Gamow orbitals for the rotated, asymptotic square-integrable functions carrying the width information. A recently proposed variational principle is employed for the optimization of nonlinear parameters. Within this independent asymptotic pair approximation (IAPA), our results for the partial widths to the five Ne" channels are