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Eigenchannel R-matrix calculation results are presented for the photodetachment partial cross sections of Na- for energies up to the Na(5p) threshold. The photoelectron angular distribution asymmetry parameter for the process Na-+γ→Na(3p)+e- is also presented over the same energy range. Detailed analyses and identifications of 1P0 resonance structures are presented and compared with corresponding ones in H- and Li-. Our results are compared with works of others, including the four-state close-coupling results of Moores and Norcross [Phys. Rev. A 10, 1646 (1974)], the resonances observed by Johnston and Burrow [Phys. Rev. A 51, 406 (1995)] in studies of temporary negative ion formation in electron scattering by Na atoms, and the recent relative Na(4s) partial cross-section measurements of G. Haeffler et al. [following paper, Phys. Rev. A 59, 3655 (1999)].