Group #69377 — character table

	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈	C₉	C₁₀	C₁₁	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉	C₂₀	C₂₁	C₂₂	C₂₃	C₂₄	C₂₅	C₂₆	C₂₇	C₂₈	C₂₉	C₃₀	C₃₁	C₃₂	C₃₃	C₃₄	C₃₅	C₃₆	C₃₇	C₃₈	C₃₉	C₄₀	C₄₁	C₄₂	C₄₃	C₄₄	C₄₅
size	1	1	2	2	2	2	2	2	2	2	2	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	6	6	12	12	12	12	12	12	12	16	16	32	32	48	48
order	1	2	3	4	6	8	8	16	16	16	16	12	24	24	32	32	32	32	48	48	48	48	96	96	96	96	96	96	96	96	2	4	8	16	16	32	32	32	32	2	2	6	6	2	4
χ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
χ₂	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1
χ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	-1
χ₄	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1
χ₅	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	-1	-1	1	-1	1	-1	1	-1
χ₆	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	-1	-1	-1	-1	-1	1	-1	1	-1	1
χ₇	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	1	-1	1	-1	-1	1
χ₈	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	-1	1	-1	1	1	-1
χ₉	2	2	2	2	2	2	2	-2	-2	-2	-2	2	2	2	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	2	2	2	-2	-2	0	0	0	0	0	0	0	0	0	0
χ₁₀	2	2	2	2	2	2	2	-2	-2	-2	-2	2	2	2	0	0	0	0	-2	-2	-2	-2	0	0	0	0	0	0	0	0	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	0	0
χ₁₁	2	2	2	2	2	-2	-2	0	0	0	0	2	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	2	2	-2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₂	2	2	2	2	2	-2	-2	0	0	0	0	2	-2	-2	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₃	2	2	2	2	2	-2	-2	0	0	0	0	2	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	2	2	-2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0
χ₁₄	2	2	2	2	2	-2	-2	0	0	0	0	2	-2	-2	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0
χ₁₅	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	0	0	0	0	0
χ₁₆	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	-2	2	0	$- \sqrt{2}$	$\sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	0	0	0	0	0
χ₁₇	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	2	-2	0	$\sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	0	0	0	0	0
χ₁₈	2	2	2	-2	2	0	0	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	-2	0	0	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	-2	2	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	0	0	0	0	0
χ₁₉	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	0	0	0	0	0
χ₂₀	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	-2	2	0	$\sqrt{2}$	$- \sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	0	0	0	0	0
χ₂₁	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	2	-2	0	$- \sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	0	0	0	0	0
χ₂₂	2	2	2	-2	2	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	-2	0	0	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	-2	2	0	$\sqrt{2}$	$- \sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	0	0	0	0	0
χ₂₃	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	2	2	-1	-1	0	0
χ₂₄	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	2	2	2	2	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	-2	-2	1	1	0	0
χ₂₅	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	-2	-2	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	2	-2	-1	1	0	0
χ₂₆	2	2	-1	2	-1	2	2	2	2	2	2	-1	-1	-1	-2	-2	-2	-2	-1	-1	-1	-1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	-2	2	1	-1	0	0
χ₂₇	4	4	-2	4	-2	4	4	-4	-4	-4	-4	-2	-2	-2	0	0	0	0	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₈	4	4	-2	4	-2	-4	-4	0	0	0	0	-2	2	2	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₉	4	4	-2	4	-2	-4	-4	0	0	0	0	-2	2	2	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	4	4	-2	-4	-2	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	2	0	0	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	4	4	-2	-4	-2	0	0	$2 \sqrt{2}$	$2 \sqrt{2}$	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	2	0	0	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	4	4	-2	-4	-2	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	2	0	0	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	4	4	-2	-4	-2	0	0	$- 2 \sqrt{2}$	$- 2 \sqrt{2}$	$2 \sqrt{2}$	$2 \sqrt{2}$	2	0	0	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	4	-4	4	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	4	-4	4	0	-4	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	0	$2 \sqrt{2}$	$- 2 \sqrt{2}$	0	0	0	0	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	4	-4	4	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	4	-4	4	0	-4	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	0	$- 2 \sqrt{2}$	$2 \sqrt{2}$	0	0	0	0	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₈	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₃₉	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₀	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₁	4	-4	-2	0	2	$2 \sqrt{2}$	$- 2 \sqrt{2}$	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₂	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₃	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₄	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₅	4	-4	-2	0	2	$- 2 \sqrt{2}$	$2 \sqrt{2}$	−2ζ²²+2ζ²⁶+2ζ⁵⁸−2ζ⁸⁶	2ζ²²−2ζ²⁶−2ζ⁵⁸+2ζ⁸⁶	−2ζ⁵⁰+2ζ⁶²−2ζ⁸²+2ζ⁹⁴	2ζ⁵⁰−2ζ⁶²+2ζ⁸²−2ζ⁹⁴	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	ζ²²−ζ²⁶−ζ⁵⁸+ζ⁸⁶	−ζ²²+ζ²⁶+ζ⁵⁸−ζ⁸⁶	ζ⁵⁰−ζ⁶²+ζ⁸²−ζ⁹⁴	−ζ⁵⁰+ζ⁶²−ζ⁸²+ζ⁹⁴	−ζ²³−ζ²⁵+ζ⁵⁵+ζ⁸⁹	ζ²³+ζ²⁵−ζ⁵⁵−ζ⁸⁹	ζ¹⁷+ζ³¹−ζ⁴⁹−ζ⁹⁵	−ζ¹⁷−ζ³¹+ζ⁴⁹+ζ⁹⁵	−ζ¹⁹−ζ²⁹+ζ⁶¹+ζ⁸³	ζ¹⁹+ζ²⁹−ζ⁶¹−ζ⁸³	−ζ⁵³+ζ⁵⁹+ζ⁸⁵−ζ⁹¹	ζ⁵³−ζ⁵⁹−ζ⁸⁵+ζ⁹¹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #69377