Conjecture on simultaneous nonvanishing of real and imaginary amplitudes

Let $x$ and $t$ be integers satisfying

$$t \ge 1, \qquad -t+2 < x < t, \qquad x+t \mathrel{\vdots} 2.$$

Let $a(x,t)$ be the complex amplitude under consideration. Simultaneous nonvanishing conjecture. Then

$$\operatorname{Re} a(x,t) \neq 0 \quad\text{and}\quad \operatorname{Im} a(x,t) \neq 0$$

unless $(x,t)\in\{(-3,11),(5,11)\}$ or $x\in\{0,2\}$. The conjecture concerns the exceptional zeros of the real and imaginary parts of the Feynman checker amplitude and remains open in the source.