The composite Choi matrix $Z = J(\Phi_2 \circ \Phi_1)$ is nonzero

The Choi matrix $Z = J(\Phi_2 \circ \Phi_1)$ of the composition of the two explicit maps of the dimension-ten pair, a $100 \times 100$ matrix whose $((u_1,u_2),(v_1,v_2))$ entry is $\big(\Phi_2(\Phi_1(E_{u_1 v_1}))\big)_{u_2 v_2}$, is not the zero matrix. Concretely its top-left entry equals $6 \cdot 1296^2 = 10{,}077{,}696$, because $\Phi_1(E_{00}) = 1296\, E E^*$ and $\Phi_2$ then returns $1296\,\operatorname{tr}\big(R(E_{00})\big)$ in that entry.