Since we have
$\Gamma(1/2+it)=\sqrt{\pi/\cosh(\pi t)}\exp[i(2 \vartheta(t)+t \log(2\pi)+\arctan(\tanh(\pi t/2)))]$
where $\vartheta(t)$ is the Riemann Siegel function. The zeros on the critical line have ordinates the zeros of
the cosine or sine of the real function
$2 \vartheta(t)+t \log(2\pi)+\arctan(\tanh(\pi t/2))$
But there are real zeros, for example there is one at $s = 4.0260426340124070065475\dots$
X-ray:
