Rational character table for $(C_4\times C_8).D_4$

The row representing the character 256.507.8a is highlighted below.

		1A	2A	2B	2C	2D	4A	4B	4C	4D	4E	4F	8A	8B	8C	16A
	Size	1	1	2	16	16	4	4	4	16	16	64	8	8	32	64
	2 P	1A	1A	1A	1A	1A	2B	2A	2B	2B	2A	2D	4B	4B	4C	8A
256.507.1a		$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
256.507.1b		$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
256.507.1c		$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$
256.507.1d		$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$
256.507.1e		$2$	$2$	$2$	$-2$	$-2$	$2$	$2$	$2$	$-2$	$2$	$0$	$-2$	$-2$	$2$	$0$
256.507.1f		$2$	$2$	$2$	$2$	$-2$	$2$	$2$	$2$	$2$	$2$	$0$	$-2$	$-2$	$-2$	$0$
256.507.2a		$2$	$2$	$2$	$0$	$-2$	$2$	$2$	$2$	$0$	$-2$	$0$	$2$	$2$	$0$	$0$
256.507.2b		$2$	$2$	$2$	$0$	$2$	$2$	$2$	$2$	$0$	$-2$	$0$	$-2$	$-2$	$0$	$0$
256.507.4a		$4$	$4$	$4$	$0$	$0$	$-4$	$4$	$-4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
256.507.4b		$4$	$4$	$4$	$-2$	$0$	$0$	$-4$	$0$	$2$	$0$	$0$	$0$	$0$	$0$	$0$
256.507.4c		$4$	$4$	$4$	$2$	$0$	$0$	$-4$	$0$	$-2$	$0$	$0$	$0$	$0$	$0$	$0$
256.507.4d		$8$	$8$	$-8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$-4$	$4$	$0$	$0$
256.507.4e		$8$	$8$	$-8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$4$	$-4$	$0$	$0$
256.507.4f		$16$	$-16$	$0$	$0$	$0$	$8$	$0$	$-8$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
256.507.8a		$8$	$-8$	$0$	$0$	$0$	$-4$	$0$	$4$	$0$	$0$	$0$	$0$	$0$	$0$	$0$