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This paper commences a series of investigations into the stellar populations of local elliptical galaxies as determined from their integrated spectra. The goal of the series is to determine the star formation and chemical evolution histories of present-day elliptical galaxies. The primary galaxy sample analyzed is that of González, which consists of 39 elliptical galaxies drawn primarily from the local field and nearby groups, plus the bulge of Messier 31. Single-burst stellar population (SSP)-equivalent ages, metallicities, and abundance ratios are derived from Hβ, Mg b, and <Fe> line strengths using an extension of the Worthey models that incorporates nonsolar line-strength ``response functions'' by Tripicco & Bell. These functions account for changes in the Lick/IDS indices caused by nonsolar abundance ratios, allowing us to correct the Worthey models for the enhancements of Mg and other α-like elements relative to the Fe-peak elements.

SSP-equivalent ages of the González elliptical galaxies are found to vary widely, 1.5 Gyr≲t≲18 Gyr, while metallicities [Z/H] and enhancement ratios [E/Fe] are strongly peaked around <[Z/H]>=+0.26 and <[E/Fe]>=+0.20 (in an aperture of radius r_e/8). The enhancement ratios [E/Fe] are milder than previous estimates because of the application of nonsolar abundance corrections to both Mg b and <Fe> for the first time. While [E/Fe] is usually greater than zero, it is not the ``E'' elements that are actually enhanced but rather the Fe-peak elements that are depressed; this serves not only to weaken <Fe> but also to strengthen Mg b, accounting for the overall generally mild enhancements. Based on index strengths from the Lick/IDS galaxy library (Trager et al.), C is not depressed with Fe but rather seems to be on a par with other elements such as Mg in the E group. Gradients in stellar populations within galaxies are found to be mild, with SSP-equivalent age increasing by 25%, metallicity decreasing by <[Z/H]>=0.20 dex, and [E/Fe] remaining nearly constant out to an aperture of radius r_e/2 for nearly all systems.

Our ages have an overall zero-point uncertainty of at least ∼25% because of uncertainties in the stellar evolution prescription, the oxygen abundance, the effect of [E/Fe]≠0 on the isochrones, and other unknowns. However, the relative age rankings of stellar populations should be largely unaffected by these errors. In particular, the large spread in ages appears to be real and cannot be explained by contamination of Hβ by blue stragglers or hot horizontal-branch stars, or by fill-in of Hβ by emission. Correlations between these derived SSP-equivalent parameters and other galaxy observables will be discussed in future papers.