MSG 129.420

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_9}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{B}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{B}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_9}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_2}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_2}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_5}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccccccccccc} a_1 & a_2 & b_1 & c_1 & c_3 & d_1 & d_2 & e_1 & g_1 & g_2 & g_5 & h_1 & h_2 & i_5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -\frac{1}{2} & \frac{1}{2} & 1 & 0 & -2 & \frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & 0 & 1 & 0 \\ 0 & 0 & 0 & \frac{1}{2} & -\frac{1}{2} & -1 & 0 & 2 & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} & 0 & -1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & -\frac{1}{2} & -\frac{1}{2} & 1 & 0 & -2 & \frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & 0 & 1 & -1 \\ 0 & -1 & 0 & \frac{1}{2} & \frac{1}{2} & -1 & 0 & 2 & -\frac{1}{2} & \frac{1}{2} & \frac{1}{2} & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & -1 & 0 & 2 & 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -2 & 0 & 3 & 0 & 0 & 1 & 0 & -2 & 0 \\ \frac{1}{2} & -\frac{1}{2} & 0 & 0 & 0 & 1 & 0 & -2 & -\frac{1}{2} & \frac{1}{2} & -\frac{1}{2} & 0 & 1 & 0 \\ 1 & -1 & 0 & 0 & 0 & 4 & 0 & -8 & -1 & 1 & -2 & 0 & 5 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 & 0 & -4 & 0 & 0 & -1 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & -2 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{ccccccccccccccccccccc} \text{A}_1 & \text{A}_2 & \text{A}_3 & \text{A}_4 & \text{A}_9 & \text{B}_1 & \text{B}_2 & \text{C}_1 & \text{C}_3 & \text{C}_4 & \text{D}_9 & \text{E}_1 & \text{E}_2 & a_1 & a_2 & b_1 & c_1 & c_3 & g_1 & g_2 & i_5 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 \\ 0 & 1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 1 & -1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & -1 & -1 & 1 & -1 & -2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 & 1 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ 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 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -1 & 0 & 0 & 0 & -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 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 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 & 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 & 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 & 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 & 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 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{ccccccccccc} 1 & 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 & 1 & 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 & 1 & 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 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cccccccccccccccc} a_1 & a_2 & b_1 & c_1 & c_3 & d_1 & d_2 & e_1 & g_1 & g_2 & g_5 & h_1 & h_2 & i_5 & \alpha _1 & \varepsilon _1 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & 0 & 0 & 0 & 2 & -2 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 1 & 0 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 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 & 0 & 0 & 1 & 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 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 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 & 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}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]