MSG 126.380

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{C}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_5}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{i_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{i_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_3}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _2}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccccccccccccc} a_1 & a_2 & c_1 & e_1 & e_2 & f_1 & f_2 & g_1 & g_2 & g_3 & i_1 & i_2 & i_3 \\ -1 & 0 & \frac{1}{2} & -1 & 0 & 0 & -\frac{1}{2} & -\frac{1}{2} & 0 & \frac{1}{2} & -\frac{1}{2} & 0 & \frac{1}{2} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & \frac{1}{2} & 1 & 0 & 0 & \frac{1}{2} & \frac{3}{2} & 0 & -\frac{1}{2} & \frac{1}{2} & 0 & -\frac{1}{2} \\ 1 & 0 & -\frac{1}{2} & 1 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & \frac{1}{2} & \frac{1}{2} & 0 & -\frac{1}{2} \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 \\ 1 & 0 & \frac{1}{2} & 1 & 0 & 0 & \frac{1}{2} & \frac{3}{2} & 0 & -\frac{1}{2} & \frac{1}{2} & -1 & -\frac{1}{2} \\ 0 & 0 & \frac{1}{2} & 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & -\frac{1}{2} & -\frac{1}{2} & 0 & \frac{1}{2} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & -2 & 0 & 1 & -1 & 0 & 0 & 0 & -1 & 1 & 0 \\ -2 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{ccccccccccccc} \text{A}_1 & \text{A}_3 & \text{A}_5 & \text{C}_5 & \text{D}_5 & \text{F}_1 & \text{F}_2 & \text{F}_3 & \text{F}_4 & \text{F}_5 & c_1 & g_3 & i_3 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 0 & 0 & -1 & 1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 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 & 1 & 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 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{ccccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccccccccccccc} a_1 & a_2 & c_1 & e_1 & e_2 & f_1 & f_2 & g_1 & g_2 & g_3 & i_1 & i_2 & i_3 & \varepsilon _1 & \varepsilon _2 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & -1 & -1 & 1 & 0 & -1 & 1 & 0 & 2 & -2 \\ 0 & 1 & 0 & 0 & -1 & 1 & -1 & -1 & 1 & 0 & -2 & 2 & 0 & 3 & -3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 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 & 1 & 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 & 1 & 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 & 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 & 2 \\ \end{array} \right) \end{align*} \]