| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{100}\right\} & \left\{4^-{}_{100}\right\} & \left\{4_{010}\right\} & \left\{4^-{}_{010}\right\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{110}\right\} & \left\{2_{\text{1-10}}\right\} & \left\{2_{011}\right\} & \left\{2_{\text{01-1}}\right\} & \left\{2_{101}\right\} & \left\{2_{\text{10-1}}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{100}\right\} & \left\{\bar{4}^-{}_{100}\right\} & \left\{\bar{4}_{010}\right\} & \left\{\bar{4}^-{}_{010}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{001}\right\} & \left\{m_{110}\right\} & \left\{m_{\text{1-10}}\right\} & \left\{m_{011}\right\} & \left\{m_{\text{01-1}}\right\} & \left\{m_{101}\right\} & \left\{m_{\text{10-1}}\right\} & \left\{\bar{3}_{111}\right\} & \left\{\bar{3}^-{}_{111}\right\} & \left\{\bar{3}^-{}_{\text{1-1-1}}\right\} & \left\{\bar{3}_{\text{1-1-1}}\right\} & \left\{\bar{3}^-{}_{\text{-11-1}}\right\} & \left\{\bar{3}_{\text{-11-1}}\right\} & \left\{\bar{3}^-{}_{\text{-1-11}}\right\} & \left\{\bar{3}_{\text{-1-11}}\right\} \\ \text{A}_1 & \text{A} & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \text{A}_2 & \text{A} & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{A}_3 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \text{A}_4 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{A}_5 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & -2 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{A}_6 & \text{A} & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \text{A}_7 & \text{A} & 3 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -3 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_8 & \text{A} & 3 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_9 & \text{A} & 3 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -3 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_{10} & \text{A} & 3 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(0,1,0\right)\) | \(\left( \begin{array}{cccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{010}\right\} & \left\{4^-{}_{010}\right\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{2_{101}\right\} & \left\{2_{\text{10-1}}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{010}\right\} & \left\{\bar{4}^-{}_{010}\right\} & \left\{m_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{001}\right\} & \left\{m_{101}\right\} & \left\{m_{\text{10-1}}\right\} \\ \text{B}_1 & \text{A} & 1 & -1 & -1 & -1 & 1 & -1 & 1 & 1 & -1 & 1 & 1 & 1 & -1 & 1 & -1 & -1 \\ \text{B}_2 & \text{A} & 1 & -1 & -1 & -1 & 1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & -1 & 1 & 1 \\ \text{B}_3 & \text{A} & 1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & 1 & -1 & -1 & -1 & 1 & 1 \\ \text{B}_4 & \text{A} & 1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & 1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 \\ \text{B}_5 & \text{A} & 1 & 1 & 1 & -1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & -1 & 1 & 1 & 1 \\ \text{B}_6 & \text{A} & 1 & 1 & 1 & -1 & 1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & 1 & -1 & -1 & -1 \\ \text{B}_7 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \text{B}_8 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{B}_9 & \text{A} & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ \text{B}_{10} & \text{A} & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & -2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{\text{1-10}}\right\} & \left\{2_{\text{01-1}}\right\} & \left\{2_{\text{10-1}}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{\bar{1}\right\} & \left\{m_{\text{1-10}}\right\} & \left\{m_{\text{01-1}}\right\} & \left\{m_{\text{10-1}}\right\} & \left\{\bar{3}_{111}\right\} & \left\{\bar{3}^-{}_{111}\right\} \\ \text{C}_1 & \text{A} & 1 & -1 & -1 & -1 & 1 & 1 & -1 & 1 & 1 & 1 & -1 & -1 \\ \text{C}_2 & \text{A} & 1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & 1 \\ \text{C}_3 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \text{C}_4 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{C}_5 & \text{A} & 2 & 0 & 0 & 0 & -1 & -1 & -2 & 0 & 0 & 0 & 1 & 1 \\ \text{C}_6 & \text{A} & 2 & 0 & 0 & 0 & -1 & -1 & 2 & 0 & 0 & 0 & -1 & -1 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},1,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{011}\right\} & \left\{2_{\text{01-1}}\right\} & \left\{\bar{4}_{100}\right\} & \left\{\bar{4}^-{}_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{001}\right\} \\ \text{D}_1 & \text{A} & 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\ \text{D}_2 & \text{A} & 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\ \text{D}_3 & \text{A} & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\ \text{D}_4 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \text{D}_5 & \text{C} & 2 & -2 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,t,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{010}\right\} & \left\{4^-{}_{010}\right\} & \left\{2_{010}\right\} & \left\{m_{100}\right\} & \left\{m_{001}\right\} & \left\{m_{101}\right\} & \left\{m_{\text{10-1}}\right\} \\ a_1 & \text{A} & 1 & -1 & -1 & 1 & -1 & -1 & 1 & 1 \\ a_2 & \text{A} & 1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 \\ a_3 & \text{A} & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\ a_4 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ a_5 & \text{D} & 2 & 0 & 0 & -2 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(b\) | \(\left(t,t,0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110}\right\} & \left\{m_{001}\right\} & \left\{m_{\text{1-10}}\right\} \\ b_1 & \text{A} & 1 & -1 & -1 & 1 \\ b_2 & \text{A} & 1 & -1 & 1 & -1 \\ b_3 & \text{A} & 1 & 1 & -1 & -1 \\ b_4 & \text{A} & 1 & 1 & 1 & 1 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},1,0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{001}\right\} \\ c_1 & \text{A} & 1 & -1 & -1 & 1 \\ c_2 & \text{A} & 1 & -1 & 1 & -1 \\ c_3 & \text{A} & 1 & 1 & -1 & -1 \\ c_4 & \text{A} & 1 & 1 & 1 & 1 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{m_{\text{1-10}}\right\} & \left\{m_{\text{01-1}}\right\} & \left\{m_{\text{10-1}}\right\} \\ d_1 & \text{A} & 1 & 1 & 1 & -1 & -1 & -1 \\ d_2 & \text{A} & 1 & 1 & 1 & 1 & 1 & 1 \\ d_3 & \text{D} & 2 & -1 & -1 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(e\) | \(\left(1-\frac{t}{2},1-\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{\text{1-10}}\right\} \\ e_1 & \text{A} & 1 & -1 \\ e_2 & \text{A} & 1 & 1 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1}{2},1-\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{\text{01-1}}\right\} \\ f_1 & \text{C} & 1 & -1 \\ f_2 & \text{C} & 1 & 1 \\ \end{array} \right)\) |