Let $Γ=q_1\mathbb{Z}\oplus q_2 \mathbb{Z}\oplus\cdots\oplus q_d\mathbb{Z}$, with $q_j\in (\mathbb{Z}^+)^d$ for each $j\in \{1,\ldots,d\}$, and denote by $Δ$ the discrete Laplacian on $\ell^2\left( \mathbb{Z}^d\right)$. Using Macaulay2, we first numerically find complex-valued $Γ$-periodic potentials $V:\mathbb{Z}^d\to \mathbb{C}$ such that the operators $Δ+V$ and $Δ$ are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions.