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We present the first targeted measurement of the power spectrum of anisotropies of the radio synchrotron background, at 140 MHz, where it is the overwhelmingly dominant photon background. This measurement is important for understanding the background level of radio sky brightness, which is dominated by steep-spectrum synchrotron radiation at frequencies below ν ∼ 0.5 GHz and has been measured to be significantly higher than that produced by known classes of extragalactic sources and most models of Galactic halo emission. We determine the anisotropy power spectrum on scales ranging from 2° to 0.2 arcmin with Low-Frequency Array observations of two 18-deg2 fields – one centred on the Northern hemisphere's coldest patch of radio sky where the Galactic contribution is smallest and the other offset from that location by 15°. We find that the anisotropy power is higher than that attributable to the distribution of point sources above 100  |$\mu$| Jy in flux. This level of radio anisotropy power indicates that if it results from point sources, those sources are likely at low fluxes and incredibly numerous, and likely clustered in a specific manner. [ABSTRACT FROM AUTHOR]