Monotonicity of the imaginary part of the Riemann $\xi$ function in the region $S$

This paper proves that the imaginary part of the Riemann $\xi$ function is strictly monotonic with $b$ in the region $S=\{t\mathrm{\mid }t=a+bi,0\le a\le 9.508,-1\mathrm{/}2<b<1\mathrm{/}2\}$. That leads to Im($\xi$)=0 being true only when $b=0$ in $S$.