MSG 100.175

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z} \times \mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{D}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{D}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_2}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\varepsilon _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccc} a_1 & c_1 & d_1 & f_1 & h_1 & h_2 \\ 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 0 & -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 1 & 0 & 0 \\ 1 & 0 & -1 & 0 & 1 & 1 \\ 1 & 0 & -1 & 0 & 0 & 2 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccc} \text{A}_1 & \text{A}_2 & \text{B}_1 & \text{D}_1 & \text{D}_2 & \text{E}_1 \\ 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cccccc} a_1 & c_1 & d_1 & f_1 & h_1 & h_2 \\ 1 & 0 & -1 & 0 & 0 & 2 \\ 0 & 1 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right) \end{align*} \]