N  Matrix presentation  Seitz symbol  GM_{1}  GM_{2}  GM_{3}  GM_{4}  GM_{5}  GM_{6}  GM_{7}  GM_{8} 
1    1          1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 

2    2_{001}          i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 

3    2_{010}          0  1  0  0  1  0  0  0  0  0  0  i  0  0  i  0 
 

4    2_{100}          0  i  0  0  i  0  0  0  0  0  0  1  0  0  1  0 
 

5    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 3^{+}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2 
 

6    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 3^{+}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2 
 

7    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 3^{+}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2 
 

8    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 3^{+}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2 
 

9    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 3^{}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2 
 

10    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 3^{}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2 
 

11    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 3^{}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2 
 

12    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 3^{}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2 
 

13    m_{110}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

14    m_{110}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

15    4^{}_{001}          0  0  0  1  0  0  1  0  0  i  0  0  i  0  0  0 
 

16    4^{+}_{001}          0  0  0  i  0  0  i  0  0  1  0  0  1  0  0  0 
 

17    4^{}_{100}          0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0 
 

18    m_{011}          0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

19    m_{011}          0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

20    4^{+}_{100}          0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0 
 

21    4^{+}_{010}          0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

22    i√2/2  i√2/2  i√2/2  i√2/2 
 
 m_{101}          0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0 
 

23    4^{}_{010}          0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

24    i√2/2  i√2/2  i√2/2  i√2/2 
 
 m_{101}          0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

25    ^{d}1_{}          1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 

26    ^{d}2_{001}          i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 

27    ^{d}2_{010}          0  1  0  0  1  0  0  0  0  0  0  i  0  0  i  0 
 

28    ^{d}2_{100}          0  i  0  0  i  0  0  0  0  0  0  1  0  0  1  0 
 

29    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 ^{d}3^{+}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2 
 

30    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 ^{d}3^{+}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2 
 

31    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 ^{d}3^{+}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2 
 

32    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 ^{d}3^{+}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2 
 

33    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 ^{d}3^{}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2 
 

34    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 ^{d}3^{}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2 
 

35    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 ^{d}3^{}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2 
 

36    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 ^{d}3^{}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2 
 

37    ^{d}m_{110}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

38    ^{d}m_{110}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

39    (1+i)√2/2  0  0  (1i)√2/2 
 
 ^{d}4^{}_{001}          0  0  0  1  0  0  1  0  0  i  0  0  i  0  0  0 
 

40    (1i)√2/2  0  0  (1+i)√2/2 
 
 ^{d}4^{+}_{001}          0  0  0  i  0  0  i  0  0  1  0  0  1  0  0  0 
 

41    √2/2  i√2/2  i√2/2  √2/2 
 
 ^{d}4^{}_{100}          0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

42    ^{d}m_{011}          0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

43    ^{d}m_{011}          0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

44    ^{d}4^{+}_{100}          0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

45    ^{d}4^{+}_{010}          0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

46    ^{d}m_{101}          0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

47    ^{d}4^{}_{010}          0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

48    ^{d}m_{101}          0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0 
 

49    2'_{110}          e^{iπ/4}  0  0  0  0  e^{i3π/4}  0  0  0  0  e^{i3π/4}  0  0  0  0  e^{iπ/4} 
 

50    2'_{110}          e^{i3π/4}  0  0  0  0  e^{iπ/4}  0  0  0  0  e^{i3π/4}  0  0  0  0  e^{iπ/4} 
 

51    4^{'}_{001}          0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  0  0  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0 
 

52    4^{'+}_{001}          0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  0  0  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0 
 

53    4^{'}_{100}          e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2 
 

54    2'_{011}          e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2 
 

55    2'_{011}          e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2 
 

56    4^{'+}_{100}          e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2 
 

57    4^{'+}_{010}          e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2 
 

58    i√2/2  i√2/2  i√2/2  i√2/2 
 
 2'_{101}          e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2 
 

59    4^{'}_{010}          e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2 
 

60    i√2/2  i√2/2  i√2/2  i√2/2 
 
 2'_{101}          e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2 
 

61    1'_{}          0  0  e^{i3π/4}  0  0  0  0  e^{iπ/4}  e^{iπ/4}  0  0  0  0  e^{i3π/4}  0  0 
 

62    m'_{001}          0  0  e^{i3π/4}  0  0  0  0  e^{iπ/4}  e^{i3π/4}  0  0  0  0  e^{iπ/4}  0  0 
 

63    m'_{010}          0  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  0 
 

64    m'_{100}          0  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  0 
 

65    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 3^{'+}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0 
 

66    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 3^{'+}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0 
 

67    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 3^{'+}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2  e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0 
 

68    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 3^{'+}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2  e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0 
 

69    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 3^{'}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2  e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0 
 

70    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 3^{'}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2  e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0 
 

71    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 3^{'}_{111}        e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0 
 

72    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 3^{'}_{111}        e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0 
 

73    ^{d}2'_{110}          e^{i3π/4}  0  0  0  0  e^{iπ/4}  0  0  0  0  e^{iπ/4}  0  0  0  0  e^{i3π/4} 
 

74    ^{d}2'_{110}          e^{iπ/4}  0  0  0  0  e^{i3π/4}  0  0  0  0  e^{iπ/4}  0  0  0  0  e^{i3π/4} 
 

75    (1+i)√2/2  0  0  (1i)√2/2 
 
 ^{d}4^{'}_{001}          0  e^{i3π/4}  0  0  e^{i3π/4}  0  0  0  0  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0 
 

76    (1i)√2/2  0  0  (1+i)√2/2 
 
 ^{d}4^{'+}_{001}          0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  0  0  0  0  e^{i3π/4}  0  0  e^{i3π/4}  0 
 

77    √2/2  i√2/2  i√2/2  √2/2 
 
 ^{d}4^{'}_{100}          e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2 
 

78    ^{d}2'_{011}          e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2 
 

79    ^{d}2'_{011}          e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2 
 

80    ^{d}4^{'+}_{100}          e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2 
 

81    ^{d}4^{'+}_{010}          e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2 
 

82    ^{d}2'_{101}          e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2 
 

83    ^{d}4^{'}_{010}          e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2 
 

84    ^{d}2'_{101}          e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2 
 

85    ^{d}1'_{}          0  0  e^{iπ/4}  0  0  0  0  e^{i3π/4}  e^{i3π/4}  0  0  0  0  e^{iπ/4}  0  0 
 

86    ^{d}m'_{001}          0  0  e^{iπ/4}  0  0  0  0  e^{i3π/4}  e^{iπ/4}  0  0  0  0  e^{i3π/4}  0  0 
 

87    ^{d}m'_{010}          0  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  0 
 

88    ^{d}m'_{100}          0  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  e^{iπ/4}  0  0  0 
 

89    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 ^{d}3^{'+}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0 
 

90    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 ^{d}3^{'+}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{iπ/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{i2π/3}√2/2  0  0 
 

91    (1+i)/2  (1i)/2  (1+i)/2  (1i)/2 
 
 ^{d}3^{'+}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{i5π/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i5π/6}√2/2  e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0 
 

92    (1i)/2  (1+i)/2  (1i)/2  (1+i)/2 
 
 ^{d}3^{'+}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{i2π/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/3}√2/2  e^{i5π/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i5π/6}√2/2  0  0 
 

93    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 ^{d}3^{'}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{iπ/6}√2/2  e^{iπ/3}√2/2  e^{iπ/3}√2/2  0  0  e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0 
 

94    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 ^{d}3^{'}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{i2π/3}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/3}√2/2  e^{iπ/6}√2/2  e^{i5π/6}√2/2  0  0  e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0 
 

95    (1+i)/2  (1+i)/2  (1i)/2  (1i)/2 
 
 ^{d}3^{'}_{111}        e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  0  0  e^{iπ/6}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  0  0  e^{i2π/3}√2/2  e^{i2π/3}√2/2  0  0 
 

96    (1i)/2  (1i)/2  (1+i)/2  (1+i)/2 
 
 ^{d}3^{'}_{111}        e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  0  0  e^{i2π/3}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/3}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  0  0  e^{i5π/6}√2/2  e^{iπ/6}√2/2  0  0 
 
