what do I do!?

$\boxed{ζ(s)=\sum_{k=1}^{∞}\frac{1}{k^s}}$
Applying the analytic continuation of $ζ(s)$ over all complex numbers, define $n$ as all values of $ζ(s)$ that equal $0$. 

All values of $n$ that exhibit the property $Im(n)≠0$ are such that $Re(n)=\frac{1}{2}$. Is this claim true? If so, prove it, and if not, present a counter-example.