| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{\frac{1}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{3}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001},\left\{\frac{3}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{A}_1 & \text{AI} & 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1 \\ \text{A}_2 & \text{AI} & 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\ \text{A}_3 & \text{AI} & 1 & -\mathrm{i} &\mathrm{i}& -1 & -1 &\mathrm{i}& -\mathrm{i} & 1 \\ \text{A}_4 & \text{AI} & 1 & -\mathrm{i} &\mathrm{i}& -1 & 1 & -\mathrm{i} &\mathrm{i}& -1 \\ \text{A}_5 & \text{AI} & 1 &\mathrm{i}& -\mathrm{i} & -1 & -1 & -\mathrm{i} &\mathrm{i}& 1 \\ \text{A}_6 & \text{AI} & 1 &\mathrm{i}& -\mathrm{i} & -1 & 1 &\mathrm{i}& -\mathrm{i} & -1 \\ \text{A}_7 & \text{AI} & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\ \text{A}_8 & \text{AI} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \end{array} \right)\) |
| B | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{B}_1 & \text{BDI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(0,0,1\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{\frac{1}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{3}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001},\left\{\frac{3}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ \text{C}_1 & \text{AI} & 2 & 0 & 0 & -2 & 0 & 0 & 0 & 0 \\ \text{C}_2 & \text{AI} & 2 & 0 & 0 & 2 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} & \left\{\bar{4}_{001},\left\{\frac{3}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} & \left\{\bar{4}^-{}_{001},\left\{\frac{1}{4},\frac{1}{4},\frac{3}{4}\right\}\right\} \\ \text{D}_1 & \text{D} & 1 & -1 & -\mathrm{i} & -\mathrm{i} \\ \text{D}_2 & \text{D} & 1 & -1 &\mathrm{i}&\mathrm{i}\\ \text{D}_3 & \text{AIII} & 1 & 1 & -1 & 1 \\ \text{D}_4 & \text{AIII} & 1 & 1 & 1 & -1 \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{\bar{1}\right\} \\ \text{E}_1 & \text{D} & 1 & -1 \\ \text{E}_2 & \text{D} & 1 & 1 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,0,t\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{\frac{1}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{\frac{3}{4},\frac{3}{4},\frac{1}{4}\right\}\right\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ a_1 & \text{AI} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} & -e^{-\frac{1}{2}\mathrm{i}\pi t} & 1 \\ a_2 & \text{AI} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -1 \\ a_3 & \text{AI} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & -1 \\ a_4 & \text{AI} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} & e^{-\frac{1}{2}\mathrm{i}\pi t} & 1 \\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ b_1 & \text{BDI} & 1 & -1 \\ b_2 & \text{BDI} & 1 & 1 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ c_1 & \text{BDI} & 1 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ d_1 & \text{AI} & 1 & -e^{-\frac{1}{2}\mathrm{i}\pi t} \\ d_2 & \text{AI} & 1 & e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},1-\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ e_1 & \text{AIII} & 1 & e^{\frac{i \pi t}{2}} \\ e_2 & \text{AIII} & 1 & -e^{\frac{i \pi t}{2}} \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ f_1 & \text{DIII} & 1 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,t,0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{001},\left\{0,\frac{1}{2},0\right\}\right\} \\ g_1 & \text{AI} & 1 & -e^{-\mathrm{i} \pi t} \\ g_2 & \text{AI} & 1 & e^{-\mathrm{i} \pi t} \\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ h_1 & \text{BDI} & 1 \\ \end{array} \right)\) |