The Andromeda galaxy ( M 31 ) hosts one of the nearest and most quiescent super-massive black holes , which provides a rare , but promising opportunity for studying the physics of black hole accretion at the lowest state . We have conducted a multi-frequency , multi-epoch observing campaign , using the Karl G. Jansky Very Large Array ( VLA ) in its extended configurations in 2011-2012 , to advance our knowledge of the still poorly known radio properties of M 31* . For the first time , we detect M 31* at 10 , 15 and 20 GHz , and measure its spectral index , \alpha \approx - 0.45 \pm 0.08 ( S _ { \nu } \varpropto \nu ^ { \alpha } ) , over the frequency range of 5-20 GHz . The relatively steep spectrum suggests that the observed radio flux is dominated by the optically-thin part of a putative jet , which is located at no more than a few thousand Schwarzschild radii from the black hole . On the other hand , our sensitive radio images show little evidence for an extended component , perhaps except for several parsec-scale “ plumes ” , the nature of which remains unclear . Our data also reveal significant ( a few tens of percent ) flux variation of M 31* at 6 GHz , on timescales of hours to days . Furthermore , a curious decrease of the mean flux density , by \sim 50 % , is found between VLA observations taken during 2002-2005 and our new observations , which might be associated with a substantial increase in the mean X-ray flux of M 31* starting in 2006 .