Question on $\xi(\sigma + it)$

Question

I am aware that $\xi(\sigma + it)$ is real for $\sigma = 1/2$. Are there other known values of $\sigma$ for which $\xi(\sigma + it)$ is also real?

Thanks

Answer 1

$\xi(\sigma+it) $ is real for $\sigma \in \mathbb{R}, t=0$.

There are other real values: For the X-rays (lines of pure real or pure imaginary values) of $\xi(s)$ I found https://www.numbertheory.org/pdfs/xrays.pdf. In the picture below you see the imaginary part of $\xi(x + 10i)$ for $x=-10\dots 10.$