MSG 51.296

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2^3\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_4}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{i_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{i_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{l_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{l_2}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccccccccccccc} a_1 & a_2 & b_1 & b_2 & d_1 & d_2 & e_1 & e_2 & f_1 & f_2 & h_1 & h_2 & i_1 & i_2 & l_1 & l_2 \\ 1 & -1 & 0 & 2 & 1 & -1 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & -1 & -1 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & -1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & -1 & 1 & 1 & -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & -1 & -1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & -1 & 1 & 1 & 0 \\ 0 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & -1 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 \\ 0 & -1 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & -1 & 0 & -1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & -1 & -3 & -1 & 0 & -1 & -1 & 0 \\ 0 & -2 & 0 & 0 & 1 & 1 & 0 & 3 & 0 & -1 & -5 & -3 & 0 & -2 & -1 & -1 \\ 0 & -2 & 0 & 0 & 1 & 1 & 0 & 3 & 1 & -1 & -6 & -2 & 0 & -2 & -1 & -1 \\ 0 & -2 & 0 & 0 & 1 & 1 & 0 & 2 & 0 & -2 & -5 & -3 & 0 & -2 & -1 & -1 \\ 0 & -1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & -2 & -3 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -2 & -1 & 0 & 0 & 0 & -1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccccccccccccc} \text{A}_1 & \text{A}_2 & \text{A}_3 & \text{A}_4 & \text{D}_1 & \text{D}_2 & \text{D}_3 & \text{D}_4 & \text{E}_1 & \text{E}_2 & \text{E}_3 & \text{E}_4 & \text{H}_1 & \text{H}_2 & \text{H}_3 & \text{H}_4 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & -2 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & -2 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 2 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & -2 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & -2 & 0 & 0 & -2 & 0 & 0 & 0 & 1 & 1 & 1 & 2 & 3 & 2 \\ 0 & 0 & 0 & -4 & 0 & 0 & -2 & -2 & 1 & 0 & 1 & 4 & 2 & 4 & 5 & 5 \\ 0 & 0 & 0 & -4 & 0 & 0 & -2 & -2 & 0 & 1 & 1 & 4 & 2 & 4 & 6 & 4 \\ 0 & 0 & 0 & -2 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & 1 & 1 & 2 & 2 & 3 \\ 0 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccccccccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cccccccccccccccc} a_1 & a_2 & b_1 & b_2 & d_1 & d_2 & e_1 & e_2 & f_1 & f_2 & h_1 & h_2 & i_1 & i_2 & l_1 & l_2 \\ 1 & -1 & 0 & 2 & 1 & -1 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & -1 & -1 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & -1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & -1 & 1 & 1 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{cccccccccccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]