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

25    m'_{110}        
26    m'_{110}        
27    4^{'+}_{001}        
28    4^{'}_{001}        
29    m'_{011}        e^{i2π/3}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{i2π/3}√2/2 
 
  e^{i2π/3}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i2π/3}√2/2 
 

30    4^{'+}_{100}        e^{i5π/6}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/6}√2/2 
 
  e^{iπ/6}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{i5π/6}√2/2 
 

31    4^{'}_{100}        e^{iπ/6}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{i5π/6}√2/2 
 
  e^{i5π/6}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/6}√2/2 
 

32    m'_{011}        e^{i2π/3}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i2π/3}√2/2 
 
  e^{i2π/3}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{i2π/3}√2/2 
 

33    i√2/2  i√2/2  i√2/2  i√2/2 
 
 m'_{101}        e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{i5π/6}√2/2 
 
  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{iπ/6}√2/2 
 

34    4^{'}_{010}        e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{i2π/3}√2/2 
 
  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{i2π/3}√2/2 
 

35    i√2/2  i√2/2  i√2/2  i√2/2 
 
 m'_{101}        e^{iπ/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2 
 
  e^{i5π/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2 
 

36    4^{'+}_{010}        e^{iπ/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2 
 
  e^{iπ/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2 
 

37    ^{d}m'_{110}        
38    ^{d}m'_{110}        
39    (1i)√2/2  0  0  (1+i)√2/2 
 
 ^{d}4^{'+}_{001}        
40    (1+i)√2/2  0  0  (1i)√2/2 
 
 ^{d}4^{'}_{001}        
41    ^{d}m'_{011}        e^{iπ/3}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{iπ/3}√2/2 
 
  e^{iπ/3}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/3}√2/2 
 

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

43    √2/2  i√2/2  i√2/2  √2/2 
 
 ^{d}4^{'}_{100}        e^{i5π/6}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{iπ/6}√2/2 
 
  e^{iπ/6}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i5π/6}√2/2 
 

44    ^{d}m'_{011}        e^{iπ/3}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/3}√2/2 
 
  e^{iπ/3}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{iπ/3}√2/2 
 

45    ^{d}m'_{101}        e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{iπ/6}√2/2 
 
  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{i5π/6}√2/2 
 

46    ^{d}4^{'}_{010}        e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{iπ/3}√2/2 
 
  e^{iπ/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{iπ/3}√2/2 
 

47    ^{d}m'_{101}        e^{i5π/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2  e^{iπ/6}√2/2 
 
  e^{iπ/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2  e^{i5π/6}√2/2 
 

48    ^{d}4^{'+}_{010}        e^{i2π/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2 
 
  e^{i2π/3}√2/2  e^{i2π/3}√2/2  e^{iπ/3}√2/2  e^{i2π/3}√2/2 
 
