Point Group D4

**Characters of symmetric powers**
Power To	E	2C₄	C₂	2C'₂	2C''₂
1	2	0	-2	0	0
2	3	-1	3	1	1
3	4	0	-4	0	0
4	5	1	5	1	1
5	6	0	-6	0	0
6	7	-1	7	1	1
7	8	0	-8	0	0
8	9	1	9	1	1
9	10	0	-10	0	0
10	11	-1	11	1	1
11	12	0	-12	0	0
12	13	1	13	1	1
13	14	0	-14	0	0
14	15	-1	15	1	1
15	16	0	-16	0	0
16	17	1	17	1	1
17	18	0	-18	0	0
18	19	-1	19	1	1
19	20	0	-20	0	0
20	21	1	21	1	1

**Decomposition to irreducible representations**
Power To	A₁	A₂	B₁	B₂	E
1	0	0	0	0	1	E
2	1	0	1	1	0	A₁⊕B₁⊕B₂
3	0	0	0	0	2	2E
4	2	1	1	1	0	2A₁⊕A₂⊕B₁⊕B₂
5	0	0	0	0	3	3E
6	2	1	2	2	0	2A₁⊕A₂⊕2B₁⊕2B₂
7	0	0	0	0	4	4E
8	3	2	2	2	0	3A₁⊕2A₂⊕2B₁⊕2B₂
9	0	0	0	0	5	5E
10	3	2	3	3	0	3A₁⊕2A₂⊕3B₁⊕3B₂
11	0	0	0	0	6	6E
12	4	3	3	3	0	4A₁⊕3A₂⊕3B₁⊕3B₂
13	0	0	0	0	7	7E
14	4	3	4	4	0	4A₁⊕3A₂⊕4B₁⊕4B₂
15	0	0	0	0	8	8E
16	5	4	4	4	0	5A₁⊕4A₂⊕4B₁⊕4B₂
17	0	0	0	0	9	9E
18	5	4	5	5	0	5A₁⊕4A₂⊕5B₁⊕5B₂
19	0	0	0	0	10	10E
20	6	5	5	5	0	6A₁⊕5A₂⊕5B₁⊕5B₂

Results for Point Group D₄

Power To	E	2C₄	C₂	2C'₂	2C''₂
1	2	0	-2	0	0
2	3	-1	3	1	1
3	4	0	-4	0	0
4	5	1	5	1	1
5	6	0	-6	0	0
6	7	-1	7	1	1
7	8	0	-8	0	0
8	9	1	9	1	1
9	10	0	-10	0	0
10	11	-1	11	1	1
11	12	0	-12	0	0
12	13	1	13	1	1
13	14	0	-14	0	0
14	15	-1	15	1	1
15	16	0	-16	0	0
16	17	1	17	1	1
17	18	0	-18	0	0
18	19	-1	19	1	1
19	20	0	-20	0	0
20	21	1	21	1	1

Power To	E	2C₄	C₂	2C'₂	2C''₂
1	2	0	-2	0	0
2	3	-1	3	1	1
3	4	0	-4	0	0
4	5	1	5	1	1
5	6	0	-6	0	0
6	7	-1	7	1	1
7	8	0	-8	0	0
8	9	1	9	1	1
9	10	0	-10	0	0
10	11	-1	11	1	1
11	12	0	-12	0	0
12	13	1	13	1	1
13	14	0	-14	0	0
14	15	-1	15	1	1
15	16	0	-16	0	0
16	17	1	17	1	1
17	18	0	-18	0	0
18	19	-1	19	1	1
19	20	0	-20	0	0
20	21	1	21	1	1

Power To	E	2C₄	C₂	2C'₂	2C''₂
1	2	0	-2	0	0
2	3	-1	3	1	1
3	4	0	-4	0	0
4	5	1	5	1	1
5	6	0	-6	0	0
6	7	-1	7	1	1
7	8	0	-8	0	0
8	9	1	9	1	1
9	10	0	-10	0	0
10	11	-1	11	1	1
11	12	0	-12	0	0
12	13	1	13	1	1
13	14	0	-14	0	0
14	15	-1	15	1	1
15	16	0	-16	0	0
16	17	1	17	1	1
17	18	0	-18	0	0
18	19	-1	19	1	1
19	20	0	-20	0	0
20	21	1	21	1	1