We report on the analysis of 34 years of photometric observations of the pulsating helium atmosphere white dwarf GD358. The complete data set includes archival data from 1982-2006, and 1195.2 hours of new observations from 2007- 2016. From this data set, we extract 15 frequencies representing g-mode pulsation modes, adding 4 modes to the 11 modes known previously. We present evidence that these 15 modes are ell = 1 modes, 13 of which belong to a consecutive sequence in radial overtone k. We perform a detailed asteroseismic analysis using models that include parameterized, complex carbon and oxygen core composition profiles to fit the periods. Recent spectroscopic analyses place GD358 near the red edge of the DBV instability strip, at 24,000 plus or minus 500 K and a log g of 7.8 plus or minus 0.08 dex. The surface gravity translates to a mass range of 0.455 to 0.540 solar masses. Our best fit model has a temperature of 23,650 K and a mass of 0.5706 solar masses. That is slightly more massive than suggested by most the recent spectroscopy. We find a pure helium layer mass of 10^-5.50, consistent with the result of previous studies and the outward diffusion of helium over time.
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