| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{3^-{}_{\text{1-1-1}}\right\} & \left\{3_{\text{1-1-1}}\right\} & \left\{3^-{}_{\text{-11-1}}\right\} & \left\{3_{\text{-11-1}}\right\} & \left\{3^-{}_{\text{-1-11}}\right\} & \left\{3_{\text{-1-11}}\right\} & \left\{\bar{4}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{101},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{10-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{AI} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_2 & \text{AI} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{A}_3 & \text{BDI} & 4 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(\frac{1}{2},0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{\bar{4}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{C} & 2 & 0 & 0 & 0 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 \\ \text{B}_2 & \text{C} & 2 & 0 & 0 & 0 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\right\} & \left\{\bar{4}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{C}_1 & \text{AI} & 2 & 0 & 0 & 0 & \sqrt{2} & \sqrt{2} & 0 & 0 \\ \text{C}_2 & \text{AI} & 2 & 0 & 0 & 0 & -\sqrt{2} & -\sqrt{2} & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{2_{010}\right\} & \left\{2_{001}\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{4}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{100},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{010},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{101},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{10-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_2 & \text{C} & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 0 \\ \text{D}_3 & \text{CII} & 4 & 0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(\frac{t}{2},0,0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100}\right\} & \left\{m_{011},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ a_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010}\right\} \\ b_1 & \text{CI} & 1 & -\mathrm{i} \\ b_2 & \text{CI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ c_1 & \text{AI} & 1 & -\mathrm{i} e^{-\mathrm{i} \pi t} \\ c_2 & \text{AI} & 1 &\mathrm{i}e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ d_1 & \text{CI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{111}\right\} & \left\{3^-{}_{111}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} & \left\{m_{\text{10-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ e_1 & \text{A} & 1 & -1 & 1 & -\mathrm{i} e^{-\frac{3}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{3}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{3}{2}\mathrm{i}\pi t} \\ e_2 & \text{A} & 1 & -1 & 1 &\mathrm{i}e^{-\frac{3}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{3}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{3}{2}\mathrm{i}\pi t} \\ e_3 & \text{AIII} & 2 & 1 & -1 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1}{2},\frac{t}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{\text{01-1}},\left\{\frac{1}{2},\frac{1}{2},\frac{1}{2}\right\}\right\} \\ f_1 & \text{C} & 1 & -e^{-\mathrm{i} \pi t} \\ f_2 & \text{C} & 1 & e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |