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Using the JVLA, we explored the Galactic center (GC) with a resolution of 0.05" at 33.0 and 44.6 GHz. We detected 64 hyper-compact radio sources (HCRs) in the central parsec. The dense group of HCRs can be divided into three spectral types: 38 steep-spectrum ($α\le-0.5$) sources; 10 flat-spectrum ($-0.5<α\le0.2$) sources; and 17 inverted-spectrum sources having $α>0.2$, assuming $S\proptoν^α$. The steep-spectrum HCRs are likely represent a population of massive stellar remnants associated with nonthermal compact radio sources powered by neutron stars and stellar black holes. The surface-density distribution of the HCRs as function of radial distance ($R$) from Sgr~A* can be described as a steep power-law $Σ(R) \propto R^{-Γ}$, with $Γ=1.6\pm0.2$, along with presence of a localized order-of-magnitude enhancement in the range 0.1-0.3 pc. The steeper profile of the HCRs relative to that of the central cluster might result from the concentration massive stellar remnants by mass segregation at the GC. The GC magnetar SGR~J1745-2900 belongs to the inverted-spectrum sub-sample. We find that two spectral components present in the averaged radio spectrum of SGR~J1745-2900, separated at $ν\sim30$ GHz. The centimeter-component is fitted to a power-law with $α_{cm}=-1.5\pm0.6$. The enhanced millimeter-component shows a rising spectrum $α_{mm}=1.1\pm0.2$. Based on the ALMA observations at 225 GHz, we find that the GC magnetar is highly variable on a day-to-day time scale, showing variations up to a factor of 6. Further JVLA and ALMA observations of the variability, spectrum, and polarization of the HCRs are critical for determining whether they are associated with stellar remnants.