Monotonic-zero conjecture for truncated Riemann Xi-functions

Let $Q$ denote the first quadrant of the complex plane, and for $N\in\mathbb N$ let $\Xi_N(z)$ be the truncation of Riemann's uniformly convergent series for the Riemann $\Xi$-function after $N$ terms. A function has monotonic zeros in $Q$ when its zeros there, listed by increasing real part, have monotone nondecreasing imaginary parts. Monotonic-zero conjecture. For $N\in\mathbb N$, $\Xi_N(z)$ has monotonic zeros in $Q$. This conjecture is supported by the paper's computations and concerns approximations whose limiting zero property would imply the Riemann Hypothesis.