There is a picture on wikipedia of Ramanujan tau function. At first I noticed that there are exceptional red point (where the red points are sparse in the lower part), this should be due to Sato-Tate conjecture. But it seems strange since where red points are dense blue points are sparse! Is there any explanation about these?

(Wiki: The blue line picks only the values of n that are multiples of 121.)

By the way, is there any conjecture about the growth （a lower bound） of this function? (Surely stronger than the Lehmer's conjecture.)