The plot $\Re\ x^{Zeta\ Zero} + \Im\ x^{Zeta\ Zero}$ for the first $1000$ Zeta Zeros up to $x = 30$ using the following Mathematica code:
a = Sum[Im[n^ZetaZero[i]] + Re[n^ZetaZero[i]], {i, 1000}];
Plot[{If[a >= 0, (a^2)/n, -(a^2)/n]}, {n, 0, 30}]
looks like this:
which seems to peak at the primes and prime powers. Would I be correct in making this assumption? I am fairly new to the study of the zeta function and apologise if I am asking a very straightforward question, but could someone please point me in the direction of more documentation on this subject - with particular reference to the plot in question?
Also, is there any way of refining the plot so that the peaks become clearer?