Character table for $C_5:F_5$

The column representing the conjugacy class 4A1 is highlighted below.

		1A	2A	4A1	4A-1	5A1	5A2	5B	5C1	5C-1	5C2	5C-2	10A1	10A3
	Size	1	5	25	25	2	2	4	4	4	4	4	10	10
	2 P	1A	1A	2A	2A	5A2	5A1	5B	5C2	5C-2	5C-1	5C1	5A1	5A2
	5 P	1A	2A	4A1	4A-1	1A	1A	1A	1A	1A	1A	1A	2A	2A
	Type
100.10.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
100.10.1b	R	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
100.10.1c1	C	$1$	$-1$	$-i$	$i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
100.10.1c2	C	$1$	$-1$	$i$	$-i$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
100.10.2a1	R	$2$	$2$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$
100.10.2a2	R	$2$	$2$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$
100.10.2b1	S	$2$	$-2$	$0$	$0$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$-{\zeta }_5^{-1}-{\zeta }_5$	$-{\zeta }_5^{-2}-{\zeta }_5^2$
100.10.2b2	S	$2$	$-2$	$0$	$0$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-2}+{\zeta }_5^2$	${\zeta }_5^{-1}+{\zeta }_5$	$2$	${\zeta }_5^{-1}+{\zeta }_5$	${\zeta }_5^{-2}+{\zeta }_5^2$	$-{\zeta }_5^{-2}-{\zeta }_5^2$	$-{\zeta }_5^{-1}-{\zeta }_5$
100.10.4a	R	$4$	$0$	$0$	$0$	$4$	$4$	$-1$	$-1$	$-1$	$-1$	$-1$	$0$	$0$
100.10.4b1	C	$4$	$0$	$0$	$0$	$2{\zeta }_5^{-2}+2{\zeta }_5^2$	$2{\zeta }_5^{-1}+2{\zeta }_5$	${\zeta }_5^{-2}-{\zeta }_5-{\zeta }_5^2$	${\zeta }_5^{-2}+1+2{\zeta }_5$	$-1$	$-2{\zeta }_5^{-2}-1-2{\zeta }_5-{\zeta }_5^2$	$1+{\zeta }_5+2{\zeta }_5^2$	$0$	$0$
100.10.4b2	C	$4$	$0$	$0$	$0$	$2{\zeta }_5^{-2}+2{\zeta }_5^2$	$2{\zeta }_5^{-1}+2{\zeta }_5$	$1+{\zeta }_5+2{\zeta }_5^2$	$-2{\zeta }_5^{-2}-1-2{\zeta }_5-{\zeta }_5^2$	$-1$	${\zeta }_5^{-2}+1+2{\zeta }_5$	${\zeta }_5^{-2}-{\zeta }_5-{\zeta }_5^2$	$0$	$0$
100.10.4b3	C	$4$	$0$	$0$	$0$	$2{\zeta }_5^{-1}+2{\zeta }_5$	$2{\zeta }_5^{-2}+2{\zeta }_5^2$	$-2{\zeta }_5^{-2}-1-2{\zeta }_5-{\zeta }_5^2$	${\zeta }_5^{-2}-{\zeta }_5-{\zeta }_5^2$	$-1$	$1+{\zeta }_5+2{\zeta }_5^2$	${\zeta }_5^{-2}+1+2{\zeta }_5$	$0$	$0$
100.10.4b4	C	$4$	$0$	$0$	$0$	$2{\zeta }_5^{-1}+2{\zeta }_5$	$2{\zeta }_5^{-2}+2{\zeta }_5^2$	${\zeta }_5^{-2}+1+2{\zeta }_5$	$1+{\zeta }_5+2{\zeta }_5^2$	$-1$	${\zeta }_5^{-2}-{\zeta }_5-{\zeta }_5^2$	$-2{\zeta }_5^{-2}-1-2{\zeta }_5-{\zeta }_5^2$	$0$	$0$