Character table for $C_{41}:C_{20}$

The row representing the character 820.7.20a1 is highlighted below.

1A

2A

4A1

4A-1

5A1

5A-1

5A2

5A-2

10A1

10A-1

10A3

10A-3

20A1

20A-1

20A3

20A-3

20A7

20A-7

20A9

20A-9

41A1

41A3

Size

1

41

41

41

41

41

41

41

41

41

41

41

41

41

41

41

41

41

41

41

20

20

2 P

1A

1A

2A

2A

5A2

5A-2

5A-1

5A1

5A1

5A-1

5A-2

5A2

10A1

10A-1

10A3

10A-3

10A-3

10A3

10A-1

10A1

41A1

41A3

5 P

1A

2A

4A1

4A-1

1A

1A

1A

1A

2A

2A

2A

2A

4A1

4A-1

4A-1

4A1

4A-1

4A1

4A1

4A-1

41A1

41A3

41 P

1A

2A

4A1

4A-1

5A1

5A-1

5A2

5A-2

10A1

10A-1

10A3

10A-3

20A1

20A-1

20A3

20A-3

20A7

20A-7

20A9

20A-9

1A

1A

Type

820.7.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

820.7.1b

R

$1$

$1$

$-1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$-1$

$1$

$1$

820.7.1c1

C

$1$

$-1$

$-i$

$i$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$i$

$-i$

$i$

$-i$

$-i$

$i$

$-i$

$i$

$1$

$1$

820.7.1c2

C

$1$

$-1$

$i$

$-i$

$1$

$1$

$1$

$1$

$-1$

$-1$

$-1$

$-1$

$-i$

$i$

$-i$

$i$

$i$

$-i$

$i$

$-i$

$1$

$1$

820.7.1d1

C

$1$

$1$

$1$

$1$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

$1$

$1$

820.7.1d2

C

$1$

$1$

$1$

$1$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^2$

$1$

$1$

820.7.1d3

C

$1$

$1$

$1$

$1$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

$1$

$1$

820.7.1d4

C

$1$

$1$

$1$

$1$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

${\zeta }_5$

${\zeta }_5$

$1$

$1$

820.7.1e1

C

$1$

$1$

$-1$

$-1$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5^2$

${\zeta }_5^{-2}$

$-{\zeta }_5^2$

$-{\zeta }_5^2$

$-{\zeta }_5$

$-{\zeta }_5$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^{-2}$

$1$

$1$

820.7.1e2

C

$1$

$1$

$-1$

$-1$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^{-2}$

${\zeta }_5^2$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^{-1}$

$-{\zeta }_5$

$-{\zeta }_5$

$-{\zeta }_5^2$

$-{\zeta }_5^2$

$1$

$1$

820.7.1e3

C

$1$

$1$

$-1$

$-1$

${\zeta }_5^{-1}$

${\zeta }_5$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5$

${\zeta }_5^{-1}$

$-{\zeta }_5$

$-{\zeta }_5$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^2$

$-{\zeta }_5^2$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^{-1}$

$1$

$1$

820.7.1e4

C

$1$

$1$

$-1$

$-1$

${\zeta }_5$

${\zeta }_5^{-1}$

${\zeta }_5^2$

${\zeta }_5^{-2}$

${\zeta }_5^{-2}$

${\zeta }_5^2$

${\zeta }_5^{-1}$

${\zeta }_5$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^{-1}$

$-{\zeta }_5^2$

$-{\zeta }_5^2$

$-{\zeta }_5^{-2}$

$-{\zeta }_5^{-2}$

$-{\zeta }_5$

$-{\zeta }_5$

$1$

$1$

820.7.1f1

C

$1$

$-1$

$-{\zeta }_{20}^5$

${\zeta }_{20}^5$

$-{\zeta }_{20}^2$

${\zeta }_{20}^8$

${\zeta }_{20}^4$

$-{\zeta }_{20}^6$

${\zeta }_{20}^6$

$-{\zeta }_{20}^4$

$-{\zeta }_{20}^8$

${\zeta }_{20}^2$

$-{\zeta }_{20}^3$

${\zeta }_{20}^3$

${\zeta }_{20}^9$

$-{\zeta }_{20}^9$

$-{\zeta }_{20}$

${\zeta }_{20}$

${\zeta }_{20}^7$

$-{\zeta }_{20}^7$

$1$

$1$

820.7.1f2

C

$1$

$-1$

${\zeta }_{20}^5$

$-{\zeta }_{20}^5$

${\zeta }_{20}^8$

$-{\zeta }_{20}^2$

$-{\zeta }_{20}^6$

${\zeta }_{20}^4$

$-{\zeta }_{20}^4$

${\zeta }_{20}^6$

${\zeta }_{20}^2$

$-{\zeta }_{20}^8$

${\zeta }_{20}^7$

$-{\zeta }_{20}^7$

$-{\zeta }_{20}$

${\zeta }_{20}$

${\zeta }_{20}^9$

$-{\zeta }_{20}^9$

$-{\zeta }_{20}^3$

${\zeta }_{20}^3$

$1$

$1$

820.7.1f3

C

$1$

$-1$

$-{\zeta }_{20}^5$

${\zeta }_{20}^5$

${\zeta }_{20}^8$

$-{\zeta }_{20}^2$

$-{\zeta }_{20}^6$

${\zeta }_{20}^4$

$-{\zeta }_{20}^4$

${\zeta }_{20}^6$

${\zeta }_{20}^2$

$-{\zeta }_{20}^8$

$-{\zeta }_{20}^7$

${\zeta }_{20}^7$

${\zeta }_{20}$

$-{\zeta }_{20}$

$-{\zeta }_{20}^9$

${\zeta }_{20}^9$

${\zeta }_{20}^3$

$-{\zeta }_{20}^3$

$1$

$1$

820.7.1f4

C

$1$

$-1$

${\zeta }_{20}^5$

$-{\zeta }_{20}^5$

$-{\zeta }_{20}^2$

${\zeta }_{20}^8$

${\zeta }_{20}^4$

$-{\zeta }_{20}^6$

${\zeta }_{20}^6$

$-{\zeta }_{20}^4$

$-{\zeta }_{20}^8$

${\zeta }_{20}^2$

${\zeta }_{20}^3$

$-{\zeta }_{20}^3$

$-{\zeta }_{20}^9$

${\zeta }_{20}^9$

${\zeta }_{20}$

$-{\zeta }_{20}$

$-{\zeta }_{20}^7$

${\zeta }_{20}^7$

$1$

$1$

820.7.1f5

C

$1$

$-1$

$-{\zeta }_{20}^5$

${\zeta }_{20}^5$

$-{\zeta }_{20}^6$

${\zeta }_{20}^4$

$-{\zeta }_{20}^2$

${\zeta }_{20}^8$

$-{\zeta }_{20}^8$

${\zeta }_{20}^2$

$-{\zeta }_{20}^4$

${\zeta }_{20}^6$

${\zeta }_{20}^9$

$-{\zeta }_{20}^9$

$-{\zeta }_{20}^7$

${\zeta }_{20}^7$

${\zeta }_{20}^3$

$-{\zeta }_{20}^3$

$-{\zeta }_{20}$

${\zeta }_{20}$

$1$

$1$

820.7.1f6

C

$1$

$-1$

${\zeta }_{20}^5$

$-{\zeta }_{20}^5$

${\zeta }_{20}^4$

$-{\zeta }_{20}^6$

${\zeta }_{20}^8$

$-{\zeta }_{20}^2$

${\zeta }_{20}^2$

$-{\zeta }_{20}^8$

${\zeta }_{20}^6$

$-{\zeta }_{20}^4$

$-{\zeta }_{20}$

${\zeta }_{20}$

${\zeta }_{20}^3$

$-{\zeta }_{20}^3$

$-{\zeta }_{20}^7$

${\zeta }_{20}^7$

${\zeta }_{20}^9$

$-{\zeta }_{20}^9$

$1$

$1$

820.7.1f7

C

$1$

$-1$

$-{\zeta }_{20}^5$

${\zeta }_{20}^5$

${\zeta }_{20}^4$

$-{\zeta }_{20}^6$

${\zeta }_{20}^8$

$-{\zeta }_{20}^2$

${\zeta }_{20}^2$

$-{\zeta }_{20}^8$

${\zeta }_{20}^6$

$-{\zeta }_{20}^4$

${\zeta }_{20}$

$-{\zeta }_{20}$

$-{\zeta }_{20}^3$

${\zeta }_{20}^3$

${\zeta }_{20}^7$

$-{\zeta }_{20}^7$

$-{\zeta }_{20}^9$

${\zeta }_{20}^9$

$1$

$1$

820.7.1f8

C

$1$

$-1$

${\zeta }_{20}^5$

$-{\zeta }_{20}^5$

$-{\zeta }_{20}^6$

${\zeta }_{20}^4$

$-{\zeta }_{20}^2$

${\zeta }_{20}^8$

$-{\zeta }_{20}^8$

${\zeta }_{20}^2$

$-{\zeta }_{20}^4$

${\zeta }_{20}^6$

$-{\zeta }_{20}^9$

${\zeta }_{20}^9$

${\zeta }_{20}^7$

$-{\zeta }_{20}^7$

$-{\zeta }_{20}^3$

${\zeta }_{20}^3$

${\zeta }_{20}$

$-{\zeta }_{20}$

$1$

$1$

820.7.20a1

R

$20$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

${\zeta }_{41}^{-19}+{\zeta }_{41}^{-17}+{\zeta }_{41}^{-15}+{\zeta }_{41}^{-14}+{\zeta }_{41}^{-13}+{\zeta }_{41}^{-12}+{\zeta }_{41}^{-11}+{\zeta }_{41}^{-7}+{\zeta }_{41}^{-6}+{\zeta }_{41}^{-3}+{\zeta }_{41}^3+{\zeta }_{41}^6+{\zeta }_{41}^7+{\zeta }_{41}^{11}+{\zeta }_{41}^{12}+{\zeta }_{41}^{13}+{\zeta }_{41}^{14}+{\zeta }_{41}^{15}+{\zeta }_{41}^{17}+{\zeta }_{41}^{19}$

$-{\zeta }_{41}^{-19}-{\zeta }_{41}^{-17}-{\zeta }_{41}^{-15}-{\zeta }_{41}^{-14}-{\zeta }_{41}^{-13}-{\zeta }_{41}^{-12}-{\zeta }_{41}^{-11}-{\zeta }_{41}^{-7}-{\zeta }_{41}^{-6}-{\zeta }_{41}^{-3}-1-{\zeta }_{41}^3-{\zeta }_{41}^6-{\zeta }_{41}^7-{\zeta }_{41}^{11}-{\zeta }_{41}^{12}-{\zeta }_{41}^{13}-{\zeta }_{41}^{14}-{\zeta }_{41}^{15}-{\zeta }_{41}^{17}-{\zeta }_{41}^{19}$

820.7.20a2

R

$20$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$-{\zeta }_{41}^{-19}-{\zeta }_{41}^{-17}-{\zeta }_{41}^{-15}-{\zeta }_{41}^{-14}-{\zeta }_{41}^{-13}-{\zeta }_{41}^{-12}-{\zeta }_{41}^{-11}-{\zeta }_{41}^{-7}-{\zeta }_{41}^{-6}-{\zeta }_{41}^{-3}-1-{\zeta }_{41}^3-{\zeta }_{41}^6-{\zeta }_{41}^7-{\zeta }_{41}^{11}-{\zeta }_{41}^{12}-{\zeta }_{41}^{13}-{\zeta }_{41}^{14}-{\zeta }_{41}^{15}-{\zeta }_{41}^{17}-{\zeta }_{41}^{19}$

${\zeta }_{41}^{-19}+{\zeta }_{41}^{-17}+{\zeta }_{41}^{-15}+{\zeta }_{41}^{-14}+{\zeta }_{41}^{-13}+{\zeta }_{41}^{-12}+{\zeta }_{41}^{-11}+{\zeta }_{41}^{-7}+{\zeta }_{41}^{-6}+{\zeta }_{41}^{-3}+{\zeta }_{41}^3+{\zeta }_{41}^6+{\zeta }_{41}^7+{\zeta }_{41}^{11}+{\zeta }_{41}^{12}+{\zeta }_{41}^{13}+{\zeta }_{41}^{14}+{\zeta }_{41}^{15}+{\zeta }_{41}^{17}+{\zeta }_{41}^{19}$