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Understanding the origin of the flaring activity from the Galactic centersupermassive black hole, Sagittarius A*, is a major scientific goal of theNuSTAR Galactic plane survey campaign. We report on the data obtained betweenJuly 2012 and April 2015, including 27 observations on Sgr A* with a totalexposure of ~ 1 Ms. We found a total of ten X-ray flares detected in the NuSTARobservation window, with luminosities in the range of $L_{3-79~keV}$~$(0.2-4.0)\times 10^{35}~erg~s^{-1}$. With this largest hard X-ray Sgr A* flare datasetto date, we studied the flare spectral properties. Seven flares are detectedabove 5{\sigma} significance, showing a range of photon indices ({\Gamma} ~2.0-2.8) with typical uncertainties of +/-0.5 (90% confidence level). We foundno significant spectral hardening for brighter flares as indicated by a smallersample. The accumulation of all the flare spectra in 1-79 keV can be well fitwith an absorbed power-law model with {\Gamma}=2.2+/-0.1, and does not requirethe existence of a spectral break. The lack of variation in X-ray spectralindex with luminosity would point to a single mechanism for the flares and isconsistent with the synchrotron scenario. Lastly, we present the quiescentstate spectrum of Sgr A*, and derived an upper limit on the quiescentluminosity of Sgr A* above 10 keV to be $L_{Xq, 10-79 keV}$ < $(2.9{\pm}0.2)\times 10^{34}~erg~s^{-1}$.

Sagittarius A* High Energy X-ray Flare Properties During NuSTAR Monitoring of the Galactic Center from 2012 to 2015