Bilbao Crystallographic Server arrow COREPRESENTATIONS PG

Irreducible corepresentations of the Magnetic Point Group m-31' (N. 29.2.110)


Table of characters of the unitary symmetry operations


(1)
(2)
(3)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
GM1+
Ag
GM1+
1
1
1
1
1
1
1
1
1
1
1
1
1
1
GM1-
Au
GM1-
1
1
1
1
-1
-1
-1
-1
1
1
1
-1
-1
-1
GM2+GM3+
1Eg2Eg
GM2+GM3+
2
2
-1
-1
2
2
-1
-1
2
-1
-1
2
-1
-1
GM2-GM3-
1Eu2Eu
GM2-GM3-
2
2
-1
-1
-2
-2
1
1
2
-1
-1
-2
1
1
GM4+
Tg
GM4+
3
-1
0
0
3
-1
0
0
3
0
0
3
0
0
GM4-
Tu
GM4-
3
-1
0
0
-3
1
0
0
3
0
0
-3
0
0
GM5+
Eg
GM5
2
0
1
1
2
0
1
1
-2
-1
-1
-2
-1
-1
GM7+GM6+
2Fg1Fg
GM6GM7
4
0
-1
-1
4
0
-1
-1
-4
1
1
-4
1
1
GM5-
Eu
GM8
2
0
1
1
-2
0
-1
-1
-2
-1
-1
2
1
1
GM6-GM7-
1Fu2Fu
GM10GM9
4
0
-1
-1
-4
0
1
1
-4
1
1
4
-1
-1
The notation used in this table is an extension to corepresentations of the following notations used for irreducible representations:
(1): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press.
(2): Bradley CJ and Cracknell AP, (1972) The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, based on Mulliken RS (1933) Phys. Rev. 43, 279-302.
(3): A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love (1979) Kronecher Product Tables, 1, General Introduction and Tables of Irreducible Representations of Space groups. New York: IFI/Plenum, for the GM point.

Lists of unitary symmetry operations in the conjugacy classes

C1: 1
C2: 2001, 2010, 2100d2001d2010d2100
C3: 3+111, 3+111, 3+111, 3+111
C4: 3-111, 3-111, 3-111, 3-111
C51
C6: m001, m010, m100dm001dm010dm100
C73+1113+1113+1113+111
C83-1113-1113-1113-111
C9d1
C10d3+111d3+111d3+111d3+111
C11d3-111d3-111d3-111d3-111
C12d1
C13d3+111d3+111d3+111d3+111
C14d3-111d3-111d3-111d3-111

Matrices of the representations of the group

The antiunitary operations are written in red color
NMatrix presentationSeitz symbolGM1+GM1-GM2+GM3+GM2-GM3-GM4+GM4-GM5GM6GM7GM8GM10GM9
1
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
(
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
)
(
1 0
0 1
)
(
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
)
2
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2001
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-i 0
0 i
)
(
-i 0 0 0
0 i 0 0
0 0 i 0
0 0 0 -i
)
(
-i 0
0 i
)
(
-i 0 0 0
0 i 0 0
0 0 i 0
0 0 0 -i
)
3
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2010
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
(
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
)
(
0 -1
1 0
)
(
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
)
4
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2100
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -i
-i 0
)
(
0 -i 0 0
-i 0 0 0
0 0 0 i
0 0 i 0
)
(
0 -i
-i 0
)
(
0 -i 0 0
-i 0 0 0
0 0 0 i
0 0 i 0
)
5
(
0 0 1
1 0 0
0 1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3+111
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i11π/122/2
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei5π/122/2
)
6
(
0 0 1
-1 0 0
0 -1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3+-11-1
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i5π/122/2
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei11π/122/2
)
7
(
0 0 -1
-1 0 0
0 1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3+1-1-1
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i5π/122/2
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei11π/122/2
)
8
(
0 0 -1
1 0 0
0 -1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3+-1-11
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i11π/122/2
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei5π/122/2
)
9
(
0 1 0
0 0 1
1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3-111
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei11π/122/2
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i5π/122/2
)
10
(
0 -1 0
0 0 1
-1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3-1-1-1
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei5π/122/2
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i11π/122/2
)
11
(
0 1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3--1-11
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei11π/122/2
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i5π/122/2
)
12
(
0 -1 0
0 0 -1
1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3--11-1
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei5π/122/2
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i11π/122/2
)
13
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
(
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
)
(
-1 0
0 -1
)
(
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 -1
)
14
(
1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m001
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
-i 0
0 i
)
(
-i 0 0 0
0 i 0 0
0 0 i 0
0 0 0 -i
)
(
i 0
0 -i
)
(
i 0 0 0
0 -i 0 0
0 0 -i 0
0 0 0 i
)
15
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m010
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
(
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
)
(
0 1
-1 0
)
(
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
)
16
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m100
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
0 -i
-i 0
)
(
0 -i 0 0
-i 0 0 0
0 0 0 i
0 0 i 0
)
(
0 i
i 0
)
(
0 i 0 0
i 0 0 0
0 0 0 -i
0 0 -i 0
)
17
(
0 0 -1
-1 0 0
0 -1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3+111
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i11π/122/2
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i5π/122/2 0 0
eiπ/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-i7π/122/2
)
18
(
0 0 -1
1 0 0
0 1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3+-11-1
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i5π/122/2
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i11π/122/2 0 0
ei7π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-iπ/122/2
)
19
(
0 0 1
1 0 0
0 -1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3+1-1-1
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i5π/122/2
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
ei7π/122/2 eiπ/122/2 0 0
e-i5π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-iπ/122/2
)
20
(
0 0 1
-1 0 0
0 1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3+-1-11
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i11π/122/2
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 ei7π/122/2 0 0
e-i11π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-i7π/122/2
)
21
(
0 -1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3-111
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei11π/122/2
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 eiπ/122/2
0 0 e-i5π/122/2 ei7π/122/2
)
22
(
0 1 0
0 0 -1
1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3-1-1-1
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei5π/122/2
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 e-i5π/122/2
0 0 eiπ/122/2 eiπ/122/2
)
23
(
0 -1 0
0 0 1
1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3--1-11
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei11π/122/2
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 e-i11π/122/2
0 0 ei7π/122/2 ei7π/122/2
)
24
(
0 1 0
0 0 1
-1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3--11-1
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei5π/122/2
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 ei7π/122/2
0 0 e-i11π/122/2 eiπ/122/2
)
25
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
(
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 -1
)
(
-1 0
0 -1
)
(
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 -1
)
26
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2001
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
i 0
0 -i
)
(
i 0 0 0
0 -i 0 0
0 0 -i 0
0 0 0 i
)
(
i 0
0 -i
)
(
i 0 0 0
0 -i 0 0
0 0 -i 0
0 0 0 i
)
27
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2010
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
(
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
)
(
0 1
-1 0
)
(
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
)
28
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2100
1
1
(
1 0
0 1
)
(
1 0
0 1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
0 i
i 0
)
(
0 i 0 0
i 0 0 0
0 0 0 -i
0 0 -i 0
)
(
0 i
i 0
)
(
0 i 0 0
i 0 0 0
0 0 0 -i
0 0 -i 0
)
29
(
0 0 1
1 0 0
0 1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3+111
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 e-i11π/122/2
0 0 ei7π/122/2 eiπ/122/2
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i5π/122/2 0 0
eiπ/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-i7π/122/2
)
30
(
0 0 1
-1 0 0
0 -1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3+-11-1
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 e-i5π/122/2
0 0 eiπ/122/2 ei7π/122/2
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i11π/122/2 0 0
ei7π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-iπ/122/2
)
31
(
0 0 -1
-1 0 0
0 1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3+1-1-1
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 ei7π/122/2
0 0 e-i11π/122/2 ei7π/122/2
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
ei7π/122/2 eiπ/122/2 0 0
e-i5π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-iπ/122/2
)
32
(
0 0 -1
1 0 0
0 -1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3+-1-11
1
1
(
ei2π/3 0
0 e-i2π/3
)
(
ei2π/3 0
0 e-i2π/3
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 eiπ/122/2
0 0 e-i5π/122/2 eiπ/122/2
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 ei7π/122/2 0 0
e-i11π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-i7π/122/2
)
33
(
0 1 0
0 0 1
1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3-111
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2 0 0
e-i11π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-iπ/122/2
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 eiπ/122/2
0 0 e-i5π/122/2 ei7π/122/2
)
34
(
0 -1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3-1-1-1
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2 0 0
ei7π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-i7π/122/2
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 e-i5π/122/2
0 0 eiπ/122/2 eiπ/122/2
)
35
(
0 1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3--1-11
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2 0 0
eiπ/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-iπ/122/2
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 e-i11π/122/2
0 0 ei7π/122/2 ei7π/122/2
)
36
(
0 -1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3--11-1
1
1
(
e-i2π/3 0
0 ei2π/3
)
(
e-i2π/3 0
0 ei2π/3
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2 0 0
e-i5π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-i7π/122/2
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 ei7π/122/2
0 0 e-i11π/122/2 eiπ/122/2
)
37
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
(
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 -1
)
(
1 0
0 1
)
(
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
)
38
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm001
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
i 0
0 -i
)
(
i 0 0 0
0 -i 0 0
0 0 -i 0
0 0 0 i
)
(
-i 0
0 i
)
(
-i 0 0 0
0 i 0 0
0 0 i 0
0 0 0 -i
)
39
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm010
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
(
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
)
(
0 -1
1 0
)
(
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
)
40
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm100
1
-1
(
1 0
0 1
)
(
-1 0
0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
0 i
i 0
)
(
0 i 0 0
i 0 0 0
0 0 0 -i
0 0 -i 0
)
(
0 -i
-i 0
)
(
0 -i 0 0
-i 0 0 0
0 0 0 i
0 0 i 0
)
41
(
0 0 -1
-1 0 0
0 -1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3+111
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
e-i7π/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 e-i11π/122/2
0 0 ei7π/122/2 eiπ/122/2
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
e-i11π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei5π/122/2
)
42
(
0 0 -1
1 0 0
0 1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3+-11-1
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
e-iπ/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 e-i5π/122/2
0 0 eiπ/122/2 ei7π/122/2
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
e-i5π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei11π/122/2
)
43
(
0 0 1
1 0 0
0 -1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3+1-1-1
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
e-iπ/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-i7π/122/2 0 0
0 0 eiπ/122/2 ei7π/122/2
0 0 e-i11π/122/2 ei7π/122/2
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
e-i5π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i11π/122/2 0 0
0 0 ei5π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei11π/122/2
)
44
(
0 0 1
-1 0 0
0 1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3+-1-11
1
-1
(
ei2π/3 0
0 e-i2π/3
)
(
e-iπ/3 0
0 eiπ/3
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
e-i7π/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-iπ/122/2 0 0
0 0 ei7π/122/2 eiπ/122/2
0 0 e-i5π/122/2 eiπ/122/2
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
e-i11π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i5π/122/2 0 0
0 0 ei11π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei5π/122/2
)
45
(
0 -1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3-111
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
ei7π/122/2 ei7π/122/2 0 0
e-i11π/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-iπ/122/2
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
ei11π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i5π/122/2
)
46
(
0 1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3-1-1-1
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
eiπ/122/2 e-i11π/122/2 0 0
ei7π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-i7π/122/2
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
ei5π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i11π/122/2
)
47
(
0 -1 0
0 0 1
1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3--1-11
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
ei7π/122/2 e-i5π/122/2 0 0
eiπ/122/2 eiπ/122/2 0 0
0 0 e-i7π/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-iπ/122/2
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
ei11π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei5π/122/2 0 0
0 0 e-i11π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i5π/122/2
)
48
(
0 1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3--11-1
1
-1
(
e-i2π/3 0
0 ei2π/3
)
(
eiπ/3 0
0 e-iπ/3
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
eiπ/122/2 eiπ/122/2 0 0
e-i5π/122/2 ei7π/122/2 0 0
0 0 e-iπ/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-i7π/122/2
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
ei5π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei11π/122/2 0 0
0 0 e-i5π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i11π/122/2
)
49
(
1 0 0
0 1 0
0 0 1
)
(
1 0
0 1
)
1'
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
(
0 1
-1 0
)
(
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0
)
(
0 -1
1 0
)
(
0 0 1 0
0 0 0 1
-1 0 0 0
0 -1 0 0
)
50
(
-1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
2'001
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
(
0 0 i 0
0 0 0 -i
i 0 0 0
0 -i 0 0
)
(
0 i
i 0
)
(
0 0 -i 0
0 0 0 i
-i 0 0 0
0 i 0 0
)
51
(
-1 0 0
0 1 0
0 0 -1
)
(
0 -1
1 0
)
2'010
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
(
1 0
0 1
)
(
0 0 0 1
0 0 -1 0
0 -1 0 0
1 0 0 0
)
(
-1 0
0 -1
)
(
0 0 0 -1
0 0 1 0
0 1 0 0
-1 0 0 0
)
52
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
2'100
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
(
0 0 0 i
0 0 i 0
0 i 0 0
i 0 0 0
)
(
-i 0
0 i
)
(
0 0 0 -i
0 0 -i 0
0 -i 0 0
-i 0 0 0
)
53
(
0 0 1
1 0 0
0 1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3'+111
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
0 0 e-i7π/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-iπ/122/2
e-i5π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i11π/122/2 0 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
0 0 e-i11π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i5π/122/2
e-iπ/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-i7π/122/2 0 0
)
54
(
0 0 1
-1 0 0
0 -1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3'+-11-1
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
0 0 e-iπ/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-i7π/122/2
e-i11π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i5π/122/2 0 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
0 0 e-i5π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i11π/122/2
e-i7π/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-iπ/122/2 0 0
)
55
(
0 0 -1
-1 0 0
0 1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3'+1-1-1
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
0 0 e-iπ/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-i7π/122/2
e-i11π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i5π/122/2 0 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
0 0 e-i5π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i11π/122/2
e-i7π/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-iπ/122/2 0 0
)
56
(
0 0 -1
1 0 0
0 -1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3'+-1-11
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
0 0 e-i7π/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-iπ/122/2
e-i5π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i11π/122/2 0 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
0 0 e-i11π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i5π/122/2
e-iπ/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-i7π/122/2 0 0
)
57
(
0 1 0
0 0 1
1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3'-111
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
0 0 ei7π/122/2 ei7π/122/2
0 0 e-i11π/122/2 eiπ/122/2
ei5π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei11π/122/2 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
0 0 ei11π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei5π/122/2
eiπ/122/2 eiπ/122/2 0 0
e-i5π/122/2 ei7π/122/2 0 0
)
58
(
0 -1 0
0 0 1
-1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3'-1-1-1
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
0 0 eiπ/122/2 e-i11π/122/2
0 0 ei7π/122/2 ei7π/122/2
ei11π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei5π/122/2 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
0 0 ei5π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei11π/122/2
ei7π/122/2 e-i5π/122/2 0 0
eiπ/122/2 eiπ/122/2 0 0
)
59
(
0 1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3'--1-11
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
0 0 ei7π/122/2 e-i5π/122/2
0 0 eiπ/122/2 eiπ/122/2
ei5π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei11π/122/2 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
0 0 ei11π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei5π/122/2
eiπ/122/2 e-i11π/122/2 0 0
ei7π/122/2 ei7π/122/2 0 0
)
60
(
0 -1 0
0 0 -1
1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3'--11-1
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
0 0 eiπ/122/2 eiπ/122/2
0 0 e-i5π/122/2 ei7π/122/2
ei11π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei5π/122/2 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
0 0 ei5π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei11π/122/2
ei7π/122/2 ei7π/122/2 0 0
e-i11π/122/2 eiπ/122/2 0 0
)
61
(
-1 0 0
0 -1 0
0 0 -1
)
(
1 0
0 1
)
1'
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
0 1
-1 0
)
(
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0
)
(
0 1
-1 0
)
(
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0
)
62
(
1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
m'001
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
0 -i
-i 0
)
(
0 0 i 0
0 0 0 -i
i 0 0 0
0 -i 0 0
)
(
0 -i
-i 0
)
(
0 0 i 0
0 0 0 -i
i 0 0 0
0 -i 0 0
)
63
(
1 0 0
0 -1 0
0 0 1
)
(
0 -1
1 0
)
m'010
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0
0 1
)
(
0 0 0 1
0 0 -1 0
0 -1 0 0
1 0 0 0
)
(
1 0
0 1
)
(
0 0 0 1
0 0 -1 0
0 -1 0 0
1 0 0 0
)
64
(
-1 0 0
0 1 0
0 0 1
)
(
0 -i
-i 0
)
m'100
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
(
0 0 0 i
0 0 i 0
0 i 0 0
i 0 0 0
)
(
i 0
0 -i
)
(
0 0 0 i
0 0 i 0
0 i 0 0
i 0 0 0
)
65
(
0 0 -1
-1 0 0
0 -1 0
)
(
(1-i)/2 -(1+i)/2
(1-i)/2 (1+i)/2
)
3'+111
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
0 0 e-i7π/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-iπ/122/2
e-i5π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i11π/122/2 0 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
0 0 eiπ/122/2 e-i5π/122/2
0 0 eiπ/122/2 ei7π/122/2
ei11π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei5π/122/2 0 0
)
66
(
0 0 -1
1 0 0
0 1 0
)
(
(1+i)/2 -(1-i)/2
(1+i)/2 (1-i)/2
)
3'+-11-1
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
0 0 e-iπ/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-i7π/122/2
e-i11π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i5π/122/2 0 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
0 0 ei7π/122/2 e-i11π/122/2
0 0 ei7π/122/2 eiπ/122/2
ei5π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei11π/122/2 0 0
)
67
(
0 0 1
1 0 0
0 -1 0
)
(
(1+i)/2 (1-i)/2
-(1+i)/2 (1-i)/2
)
3'+1-1-1
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
0 0 e-iπ/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-i7π/122/2
e-i11π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i5π/122/2 0 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
0 0 ei7π/122/2 eiπ/122/2
0 0 e-i5π/122/2 eiπ/122/2
ei5π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei11π/122/2 0 0
)
68
(
0 0 1
-1 0 0
0 1 0
)
(
(1-i)/2 (1+i)/2
-(1-i)/2 (1+i)/2
)
3'+-1-11
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
0 0 e-i7π/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-iπ/122/2
e-i5π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i11π/122/2 0 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
0 0 eiπ/122/2 ei7π/122/2
0 0 e-i11π/122/2 ei7π/122/2
ei11π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei5π/122/2 0 0
)
69
(
0 -1 0
0 0 -1
-1 0 0
)
(
(1+i)/2 (1+i)/2
-(1-i)/2 (1-i)/2
)
3'-111
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
0 0 ei7π/122/2 ei7π/122/2
0 0 e-i11π/122/2 eiπ/122/2
ei5π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei11π/122/2 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
0 0 e-iπ/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-i7π/122/2
e-i11π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i5π/122/2 0 0
)
70
(
0 1 0
0 0 -1
1 0 0
)
(
(1-i)/2 -(1-i)/2
(1+i)/2 (1+i)/2
)
3'-1-1-1
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
0 0 eiπ/122/2 e-i11π/122/2
0 0 ei7π/122/2 ei7π/122/2
ei11π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei5π/122/2 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
0 0 e-i7π/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-iπ/122/2
e-i5π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i11π/122/2 0 0
)
71
(
0 -1 0
0 0 1
1 0 0
)
(
(1+i)/2 -(1+i)/2
(1-i)/2 (1-i)/2
)
3'--1-11
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
0 0 ei7π/122/2 e-i5π/122/2
0 0 eiπ/122/2 eiπ/122/2
ei5π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei11π/122/2 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
0 0 e-iπ/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-i7π/122/2
e-i11π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i5π/122/2 0 0
)
72
(
0 1 0
0 0 1
-1 0 0
)
(
(1-i)/2 (1-i)/2
-(1+i)/2 (1+i)/2
)
3'--11-1
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
0 0 eiπ/122/2 eiπ/122/2
0 0 e-i5π/122/2 ei7π/122/2
ei11π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei5π/122/2 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
0 0 e-i7π/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-iπ/122/2
e-i5π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i11π/122/2 0 0
)
73
(
1 0 0
0 1 0
0 0 1
)
(
-1 0
0 -1
)
d1'
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
1 0 0
0 1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 -1
)
(
0 -1
1 0
)
(
0 0 1 0
0 0 0 1
-1 0 0 0
0 -1 0 0
)
(
0 1
-1 0
)
(
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0
)
74
(
-1 0 0
0 -1 0
0 0 1
)
(
i 0
0 -i
)
d2'001
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
1 0 0
0 -1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
(
0 0 -i 0
0 0 0 i
-i 0 0 0
0 i 0 0
)
(
0 -i
-i 0
)
(
0 0 i 0
0 0 0 -i
i 0 0 0
0 -i 0 0
)
75
(
-1 0 0
0 1 0
0 0 -1
)
(
0 1
-1 0
)
d2'010
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
-1 0 0
0 -1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 -1
)
(
-1 0
0 -1
)
(
0 0 0 -1
0 0 1 0
0 1 0 0
-1 0 0 0
)
(
1 0
0 1
)
(
0 0 0 1
0 0 -1 0
0 -1 0 0
1 0 0 0
)
76
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
d2'100
1
-1
(
0 1
1 0
)
(
0 -1
-1 0
)
(
-1 0 0
0 1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 1
)
(
-i 0
0 i
)
(
0 0 0 -i
0 0 -i 0
0 -i 0 0
-i 0 0 0
)
(
i 0
0 -i
)
(
0 0 0 i
0 0 i 0
0 i 0 0
i 0 0 0
)
77
(
0 0 1
1 0 0
0 1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3'+111
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 -1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
0 0 ei5π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei11π/122/2
ei7π/122/2 e-i11π/122/2 0 0
ei7π/122/2 eiπ/122/2 0 0
)
(
eiπ/42/2 e-iπ/42/2
e-i3π/42/2 e-iπ/42/2
)
(
0 0 eiπ/122/2 e-i5π/122/2
0 0 eiπ/122/2 ei7π/122/2
ei11π/122/2 e-i7π/122/2 0 0
ei11π/122/2 ei5π/122/2 0 0
)
78
(
0 0 1
-1 0 0
0 -1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3'+-11-1
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
0 0 ei11π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei5π/122/2
eiπ/122/2 e-i5π/122/2 0 0
eiπ/122/2 ei7π/122/2 0 0
)
(
e-iπ/42/2 eiπ/42/2
ei3π/42/2 eiπ/42/2
)
(
0 0 ei7π/122/2 e-i11π/122/2
0 0 ei7π/122/2 eiπ/122/2
ei5π/122/2 e-iπ/122/2 0 0
ei5π/122/2 ei11π/122/2 0 0
)
79
(
0 0 -1
-1 0 0
0 1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3'+1-1-1
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
0 0 ei11π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei5π/122/2
eiπ/122/2 ei7π/122/2 0 0
e-i11π/122/2 ei7π/122/2 0 0
)
(
ei3π/42/2 eiπ/42/2
ei3π/42/2 e-i3π/42/2
)
(
0 0 ei7π/122/2 eiπ/122/2
0 0 e-i5π/122/2 eiπ/122/2
ei5π/122/2 ei11π/122/2 0 0
e-i7π/122/2 ei11π/122/2 0 0
)
80
(
0 0 -1
1 0 0
0 -1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3'+-1-11
1
-1
(
0 ei2π/3
e-i2π/3 0
)
(
0 e-iπ/3
eiπ/3 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 -1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
0 0 ei5π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei11π/122/2
ei7π/122/2 eiπ/122/2 0 0
e-i5π/122/2 eiπ/122/2 0 0
)
(
e-i3π/42/2 e-iπ/42/2
e-i3π/42/2 ei3π/42/2
)
(
0 0 eiπ/122/2 ei7π/122/2
0 0 e-i11π/122/2 ei7π/122/2
ei11π/122/2 ei5π/122/2 0 0
e-iπ/122/2 ei5π/122/2 0 0
)
81
(
0 1 0
0 0 1
1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3'-111
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 1 0
0 0 1
1 0 0
)
(
0 -1 0
0 0 -1
-1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
0 0 e-i5π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i11π/122/2
e-i7π/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-iπ/122/2 0 0
)
(
e-i3π/42/2 eiπ/42/2
ei3π/42/2 ei3π/42/2
)
(
0 0 e-iπ/122/2 e-iπ/122/2
0 0 ei5π/122/2 e-i7π/122/2
e-i11π/122/2 e-i11π/122/2 0 0
ei7π/122/2 e-i5π/122/2 0 0
)
82
(
0 -1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3'-1-1-1
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 1 0
0 0 1
-1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
0 0 e-i11π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i5π/122/2
e-iπ/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-i7π/122/2 0 0
)
(
e-iπ/42/2 e-iπ/42/2
e-i3π/42/2 eiπ/42/2
)
(
0 0 e-i7π/122/2 ei5π/122/2
0 0 e-iπ/122/2 e-iπ/122/2
e-i5π/122/2 ei7π/122/2 0 0
e-i11π/122/2 e-i11π/122/2 0 0
)
83
(
0 1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3'--1-11
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 1 0
0 0 -1
1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
0 0 e-i5π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i11π/122/2
e-i7π/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-iπ/122/2 0 0
)
(
eiπ/42/2 eiπ/42/2
ei3π/42/2 e-iπ/42/2
)
(
0 0 e-iπ/122/2 ei11π/122/2
0 0 e-i7π/122/2 e-i7π/122/2
e-i11π/122/2 eiπ/122/2 0 0
e-i5π/122/2 e-i5π/122/2 0 0
)
84
(
0 -1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3'--11-1
1
-1
(
0 e-i2π/3
ei2π/3 0
)
(
0 eiπ/3
e-iπ/3 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 -1 0
0 0 1
1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
0 0 e-i11π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i5π/122/2
e-iπ/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-i7π/122/2 0 0
)
(
ei3π/42/2 e-iπ/42/2
e-i3π/42/2 e-i3π/42/2
)
(
0 0 e-i7π/122/2 e-i7π/122/2
0 0 ei11π/122/2 e-iπ/122/2
e-i5π/122/2 e-i5π/122/2 0 0
eiπ/122/2 e-i11π/122/2 0 0
)
85
(
-1 0 0
0 -1 0
0 0 -1
)
(
-1 0
0 -1
)
d1'
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
1 0 0
0 1 0
0 0 1
)
(
1 0 0
0 1 0
0 0 1
)
(
0 -1
1 0
)
(
0 0 1 0
0 0 0 1
-1 0 0 0
0 -1 0 0
)
(
0 -1
1 0
)
(
0 0 1 0
0 0 0 1
-1 0 0 0
0 -1 0 0
)
86
(
1 0 0
0 1 0
0 0 -1
)
(
i 0
0 -i
)
dm'001
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
1 0 0
0 -1 0
0 0 -1
)
(
1 0 0
0 -1 0
0 0 -1
)
(
0 i
i 0
)
(
0 0 -i 0
0 0 0 i
-i 0 0 0
0 i 0 0
)
(
0 i
i 0
)
(
0 0 -i 0
0 0 0 i
-i 0 0 0
0 i 0 0
)
87
(
1 0 0
0 -1 0
0 0 1
)
(
0 1
-1 0
)
dm'010
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0 0
0 -1 0
0 0 1
)
(
-1 0
0 -1
)
(
0 0 0 -1
0 0 1 0
0 1 0 0
-1 0 0 0
)
(
-1 0
0 -1
)
(
0 0 0 -1
0 0 1 0
0 1 0 0
-1 0 0 0
)
88
(
-1 0 0
0 1 0
0 0 1
)
(
0 i
i 0
)
dm'100
1
1
(
0 1
1 0
)
(
0 1
1 0
)
(
-1 0 0
0 1 0
0 0 -1
)
(
-1 0 0
0 1 0
0 0 -1
)
(
-i 0
0 i
)
(
0 0 0 -i
0 0 -i 0
0 -i 0 0
-i 0 0 0
)
(
-i 0
0 i
)
(
0 0 0 -i
0 0 -i 0
0 -i 0 0
-i 0 0 0
)
89
(
0 0 -1
-1 0 0
0 -1 0
)
(
-(1-i)/2 (1+i)/2
-(1-i)/2 -(1+i)/2
)
d3'+111
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 1
1 0 0
0 1 0
)
(
0 0 1
1 0 0
0 1 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
0 0 ei5π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei11π/122/2
ei7π/122/2 e-i11π/122/2 0 0
ei7π/122/2 eiπ/122/2 0 0
)
(
e-i3π/42/2 ei3π/42/2
eiπ/42/2 ei3π/42/2
)
(
0 0 e-i11π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i5π/122/2
e-iπ/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-i7π/122/2 0 0
)
90
(
0 0 -1
1 0 0
0 1 0
)
(
-(1+i)/2 (1-i)/2
-(1+i)/2 -(1-i)/2
)
d3'+-11-1
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
0 0 -1
1 0 0
0 -1 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
0 0 ei11π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei5π/122/2
eiπ/122/2 e-i5π/122/2 0 0
eiπ/122/2 ei7π/122/2 0 0
)
(
ei3π/42/2 e-i3π/42/2
e-iπ/42/2 e-i3π/42/2
)
(
0 0 e-i5π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i11π/122/2
e-i7π/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-iπ/122/2 0 0
)
91
(
0 0 1
1 0 0
0 -1 0
)
(
-(1+i)/2 -(1-i)/2
(1+i)/2 -(1-i)/2
)
d3'+1-1-1
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
0 0 1
-1 0 0
0 -1 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
0 0 ei11π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei5π/122/2
eiπ/122/2 ei7π/122/2 0 0
e-i11π/122/2 ei7π/122/2 0 0
)
(
e-iπ/42/2 e-i3π/42/2
e-iπ/42/2 eiπ/42/2
)
(
0 0 e-i5π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i11π/122/2
e-i7π/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-iπ/122/2 0 0
)
92
(
0 0 1
-1 0 0
0 1 0
)
(
-(1-i)/2 -(1+i)/2
(1-i)/2 -(1+i)/2
)
d3'+-1-11
1
1
(
0 ei2π/3
e-i2π/3 0
)
(
0 ei2π/3
e-i2π/3 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
0 0 -1
-1 0 0
0 1 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
0 0 ei5π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei11π/122/2
ei7π/122/2 eiπ/122/2 0 0
e-i5π/122/2 eiπ/122/2 0 0
)
(
eiπ/42/2 ei3π/42/2
eiπ/42/2 e-iπ/42/2
)
(
0 0 e-i11π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i5π/122/2
e-iπ/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-i7π/122/2 0 0
)
93
(
0 -1 0
0 0 -1
-1 0 0
)
(
-(1+i)/2 -(1+i)/2
(1-i)/2 -(1-i)/2
)
d3'-111
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 1 0
0 0 1
1 0 0
)
(
0 1 0
0 0 1
1 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
0 0 e-i5π/122/2 e-i5π/122/2
0 0 eiπ/122/2 e-i11π/122/2
e-i7π/122/2 e-i7π/122/2 0 0
ei11π/122/2 e-iπ/122/2 0 0
)
(
eiπ/42/2 e-i3π/42/2
e-iπ/42/2 e-iπ/42/2
)
(
0 0 ei11π/122/2 ei11π/122/2
0 0 e-i7π/122/2 ei5π/122/2
eiπ/122/2 eiπ/122/2 0 0
e-i5π/122/2 ei7π/122/2 0 0
)
94
(
0 1 0
0 0 -1
1 0 0
)
(
-(1-i)/2 (1-i)/2
-(1+i)/2 -(1+i)/2
)
d3'-1-1-1
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
0 -1 0
0 0 -1
1 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
0 0 e-i11π/122/2 eiπ/122/2
0 0 e-i5π/122/2 e-i5π/122/2
e-iπ/122/2 ei11π/122/2 0 0
e-i7π/122/2 e-i7π/122/2 0 0
)
(
ei3π/42/2 ei3π/42/2
eiπ/42/2 e-i3π/42/2
)
(
0 0 ei5π/122/2 e-i7π/122/2
0 0 ei11π/122/2 ei11π/122/2
ei7π/122/2 e-i5π/122/2 0 0
eiπ/122/2 eiπ/122/2 0 0
)
95
(
0 -1 0
0 0 1
1 0 0
)
(
-(1+i)/2 (1+i)/2
-(1-i)/2 -(1-i)/2
)
d3'--1-11
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
0 -1 0
0 0 1
-1 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
0 0 e-i5π/122/2 ei7π/122/2
0 0 e-i11π/122/2 e-i11π/122/2
e-i7π/122/2 ei5π/122/2 0 0
e-iπ/122/2 e-iπ/122/2 0 0
)
(
e-i3π/42/2 e-i3π/42/2
e-iπ/42/2 ei3π/42/2
)
(
0 0 ei11π/122/2 e-iπ/122/2
0 0 ei5π/122/2 ei5π/122/2
eiπ/122/2 e-i11π/122/2 0 0
ei7π/122/2 ei7π/122/2 0 0
)
96
(
0 1 0
0 0 1
-1 0 0
)
(
-(1-i)/2 -(1-i)/2
(1+i)/2 -(1+i)/2
)
d3'--11-1
1
1
(
0 e-i2π/3
ei2π/3 0
)
(
0 e-i2π/3
ei2π/3 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
0 1 0
0 0 -1
-1 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
0 0 e-i11π/122/2 e-i11π/122/2
0 0 ei7π/122/2 e-i5π/122/2
e-iπ/122/2 e-iπ/122/2 0 0
ei5π/122/2 e-i7π/122/2 0 0
)
(
e-iπ/42/2 ei3π/42/2
eiπ/42/2 eiπ/42/2
)
(
0 0 ei5π/122/2 ei5π/122/2
0 0 e-iπ/122/2 ei11π/122/2
ei7π/122/2 ei7π/122/2 0 0
e-i11π/122/2 eiπ/122/2 0 0
)
k-Subgroupsmag
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