Riemann-Siegel Z

The Riemann-Siegel $Z$ function is defined by $$Z(t)=e^{i\theta(t)}\zeta \left( \dfrac{1}{2}+it \right),$$ where $\theta$ denotes the Riemann-Siegel theta function and $\zeta$ denotes the Riemann zeta function.

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  Graph of $Z(t)$ on $[-20,20]$.

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  Domain coloring of analytic continuation of $Z(t)$.