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DFT calculations of the magnetic resonance fingerprint of a wide variety of native defect models and their complexes are carried out using the GIPAW method in order to determine the origin of the two EPR S=1/2 spectra observed in high-energy particle irradiated β-Ga2O3 single crystals. The first of these (EPR1) can be observed at room temperature and below and is characterized by gb=2.0313, gc=2.0079, ga∗=2.0025 and a quasi isotropic hyperfine interaction with two equivalent Ga neighbors of 14 G. The second center (EPR2) is observed after photoexcitation at low temperature and is characterized by gb=2.0064, gc=2.0464, ga∗=2.0024 and a quasi isotropic hyperfine interaction with two equivalent Ga neighbors of 10 G. A spin S=1 spectrum with a similar g-tensor and a 50\% reduced hyperfine splitting accompanies each of these. Ga-vacancies and their complexes with Ga-interstitials, the split interstitial oxygen and a self-trapped hole are considered in the modeling. The VGa1−Gaib−VGa1 model has the best matching g-tensor principal component directions with EPR1. Given the Fermi level not too far below the conduction band minimum it provides lower energy than the simple VGa1 model in the EPR active S=1/2 and S=1 states than VGa2 or other complexes. The latter are less likely to occur in the EPR active state because of their deeper 2−/3− transition levels. A metastable state of VGa2 is a promising model to explain the EPR2 spectrum as well as its accompanying S=1 state. An oxygen trapped hole on a split-interstitial O-dumbbell is also considered as a relevant candidate for EPR2 but less likely to be in the EPR active state and exhibits hyperfine with 3 Ga. The self-trapped hole, previously suggested, is excluded on the same basis.