N  Matrix presentation  Seitz symbol  GM_{1}^{+}  GM_{1}^{}  GM_{2}^{+}GM_{3}^{+}  GM_{2}^{}GM_{3}^{}  GM_{4}^{+}  GM_{4}^{}  GM_{5}  GM_{6}GM_{7}  GM_{8}  GM_{10}GM_{9} 
1    1          1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  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 
 
   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  1  0  0  1  0 
 
   0  1  0  0  1  0  0  0  0  0  0  1  0  0  1  0 
 

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

13    1_{}          1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 
   1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 

14    m_{001}          i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 
   i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 

15    m_{010}          0  1  0  0  1  0  0  0  0  0  0  1  0  0  1  0 
 
   0  1  0  0  1  0  0  0  0  0  0  1  0  0  1  0 
 

16    m_{100}          0  i  0  0  i  0  0  0  0  0  0  i  0  0  i  0 
 
   0  i  0  0  i  0  0  0  0  0  0  i  0  0  i  0 
 

17    (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^{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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2 
 

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

19    (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^{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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2 
 

20    (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^{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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2 
 

21    (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^{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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2 
 

22    (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^{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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2 
 

23    (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^{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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2 
 

24    (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^{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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2 
 

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

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

37    ^{d}1_{}          1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 
   1  0  0  0  0  1  0  0  0  0  1  0  0  0  0  1 
 

38    ^{d}m_{001}          i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 
   i  0  0  0  0  i  0  0  0  0  i  0  0  0  0  i 
 

39    ^{d}m_{010}          0  1  0  0  1  0  0  0  0  0  0  1  0  0  1  0 
 
   0  1  0  0  1  0  0  0  0  0  0  1  0  0  1  0 
 

40    ^{d}m_{100}          0  i  0  0  i  0  0  0  0  0  0  i  0  0  i  0 
 
   0  i  0  0  i  0  0  0  0  0  0  i  0  0  i  0 
 

41    (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^{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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2 
 

42    (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^{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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2 
 

43    (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^{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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2 
 

44    (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^{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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2 
 

45    (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^{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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2 
 

46    (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^{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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2 
 

47    (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^{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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2 
 

48    (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^{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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2 
 

49    1'_{}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 
   0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

50    2'_{001}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 
   0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

51    2'_{010}          0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 
   0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 

52    2'_{100}          0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 
   0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 

53    (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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0 
 

54    (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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

55    (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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

56    (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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

57    (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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

58    (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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0 
 

59    (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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0 
 

60    (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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0 
 

61    1'_{}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 
   0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

62    m'_{001}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 
   0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

63    m'_{010}          0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 
   0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 

64    m'_{100}          0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 
   0  0  0  i  0  0  i  0  0  i  0  0  i  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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0 
 

73    ^{d}1'_{}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 
   0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

74    ^{d}2'_{001}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 
   0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

75    ^{d}2'_{010}          0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 
   0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 

76    ^{d}2'_{100}          0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 
   0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 

77    (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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

78    (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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

79    (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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

80    (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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i5π/12}√2/2  0  0 
 

81    (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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

82    (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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i11π/12}√2/2  0  0 
 

83    (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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i5π/12}√2/2  0  0 
 

84    (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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i11π/12}√2/2  0  0 
 

85    ^{d}1'_{}          0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 
   0  0  1  0  0  0  0  1  1  0  0  0  0  1  0  0 
 

86    ^{d}m'_{001}          0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 
   0  0  i  0  0  0  0  i  i  0  0  0  0  i  0  0 
 

87    ^{d}m'_{010}          0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 
   0  0  0  1  0  0  1  0  0  1  0  0  1  0  0  0 
 

88    ^{d}m'_{100}          0  0  0  i  0  0  i  0  0  i  0  0  i  0  0  0 
 
   0  0  0  i  0  0  i  0  0  i  0  0  i  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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{iπ/12}√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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{i7π/12}√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 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√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 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√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 
 
  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^{i5π/12}√2/2  0  0  e^{iπ/12}√2/2  e^{iπ/12}√2/2  0  0 
 
  e^{i3π/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{i3π/4}√2/2 
 
  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^{i11π/12}√2/2  0  0  e^{i7π/12}√2/2  e^{i7π/12}√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 
 
  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^{iπ/12}√2/2  0  0  e^{i5π/12}√2/2  e^{i7π/12}√2/2  0  0 
 
  e^{iπ/4}√2/2  e^{i3π/4}√2/2  e^{iπ/4}√2/2  e^{iπ/4}√2/2 
 
  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^{i7π/12}√2/2  0  0  e^{i11π/12}√2/2  e^{iπ/12}√2/2  0  0 
 
