N 
Matrix presentation 
Seitz Symbol 
GM_{1}(1)  GM_{2}(0)  GM_{3}(0)  GM_{4}(1)  GM_{5}(1)  GM_{6}(0)  GM_{7}(0) 
1    1        
2    2_{001}        
3    2_{010}        
4    2_{100}        
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  e^{i5π/12}√2/2  e^{i11π/12}√2/2 
 
  e^{i11π/12}√2/2  e^{i7π/12}√2/2  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  e^{i11π/12}√2/2  e^{i5π/12}√2/2 
 
  e^{i5π/12}√2/2  e^{iπ/12}√2/2  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  e^{iπ/12}√2/2  e^{i5π/12}√2/2 
 
  e^{i5π/12}√2/2  e^{i11π/12}√2/2  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  e^{i7π/12}√2/2  e^{i11π/12}√2/2 
 
  e^{i11π/12}√2/2  e^{i5π/12}√2/2  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  e^{iπ/12}√2/2  e^{i11π/12}√2/2 
 
  e^{i11π/12}√2/2  e^{i11π/12}√2/2  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  e^{i5π/12}√2/2  e^{i5π/12}√2/2 
 
  e^{i5π/12}√2/2  e^{i7π/12}√2/2  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  e^{i11π/12}√2/2  e^{i11π/12}√2/2 
 
  e^{i11π/12}√2/2  e^{iπ/12}√2/2  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  e^{i7π/12}√2/2  e^{i5π/12}√2/2 
 
  e^{i5π/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i11π/12}√2/2 
 

13    ^{d}1_{}        
14    ^{d}2_{001}        
15    ^{d}2_{010}        
16    ^{d}2_{100}        
17    (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  e^{i7π/12}√2/2  e^{iπ/12}√2/2 
 
  e^{iπ/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{i7π/12}√2/2 
 

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

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

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

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

22    (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  e^{i7π/12}√2/2  e^{i7π/12}√2/2 
 
  e^{i7π/12}√2/2  e^{i5π/12}√2/2  e^{iπ/12}√2/2  e^{iπ/12}√2/2 
 

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

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