Q:

Are there known zeros of the Zeta function off the line 1/2?

I've been doing research in information theory that had some superficial connections to the Zeta function, since I was making use of logarithms of complex numbers.
In short, we'd be looking at the Zeta function using values of s produced by powers of the logarithm function:
$\zeta(\log^n (-1)/x).$
I noticed several zeros for n = 6:
https://www.wolframalpha.com/input/?i=plot+zeta(log%5E6(-1)%2Fx),+x+from+1+to+500
But, I don't know enough about this topic to be sure that this is actually interesting, since I know that at least some of the zeros of this function are considered "trivial". Nonetheless, I thought I'd share this in case some of you found it interesting and had insights.

A:

The only known zeroes of the zeta function off of the ${1 \over 2} + a\times i$ line are the negative even integers, each of which is a zero.  These are called trivial zeroes.  The Riemann Hypothesis states that all other zeroes lie on that magic line.  It is known that at least 40% of them lie there, and none off of it have ever been found.

