Group #13019278 — 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	C₄₆	C₄₇	C₄₈	C₄₉	C₅₀	C₅₁	C₅₂	C₅₃	C₅₄	C₅₅	C₅₆	C₅₇	C₅₈	C₅₉	C₆₀	C₆₁	C₆₂	C₆₃	C₆₄	C₆₅	C₆₆	C₆₇	C₆₈	C₆₉	C₇₀	C₇₁
size	1	1	1	1	2	2	2	2	4	4	4	4	4	4	4	5	5	5	5	8	8	8	8	8	8	8	10	10	10	10	16	16	16	16	16	16	16	16	16	16	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20	32	32	40	40	40	40	40	40	40	40	40	40	40	40	40	80
order	1	2	2	2	4	4	4	4	2	2	4	5	10	10	10	4	4	4	4	4	8	8	20	20	20	20	2	2	4	4	4	10	10	20	20	20	40	40	40	40	4	4	4	8	8	8	8	8	8	8	8	8	8	8	8	20	20	4	8	8	8	8	8	8	8	8	8	8	8	8	2
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	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	-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	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	-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	$i$	$i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	1	1	-1	-1	-1	$i$	$i$	$i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	-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	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	1	1	-1	-1	-1	$- i$	$- i$	$- i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	-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	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-1	-1	-1	1	1	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	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	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-1	-1	-1	1	1	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	1
χ₉	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	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
χ₁₀	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	-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
χ₁₁	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	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
χ₁₂	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	-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
χ₁₃	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	$i$	$i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	-1	-1	1	-1	-1	$i$	$- i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$i$	$i$	1
χ₁₄	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	$- i$	$- i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	-1	-1	1	-1	-1	$- i$	$i$	$i$	$i$	$- i$	$- i$	$i$	$i$	$- i$	$- i$	1
χ₁₅	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	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	1	1	1	1	1	$i$	$- i$	$- i$	$- i$	$i$	$i$	$i$	$i$	$- i$	$- i$	-1
χ₁₆	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	$- i$	$- i$	$i$	$i$	$i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	1	1	1	1	1	$- i$	$i$	$i$	$i$	$- i$	$- i$	$- i$	$- i$	$i$	$i$	-1
χ₁₇	2	2	2	2	2	2	-2	-2	0	0	-2	2	2	2	2	2	2	2	2	0	0	0	2	2	-2	-2	-2	-2	2	2	0	0	0	-2	0	0	0	0	0	0	0	0	-2	2	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	0	0	-2	0	0	0	0	0	0	0
χ₁₈	2	2	2	2	2	2	-2	-2	0	0	-2	2	2	2	2	2	2	2	2	0	0	0	2	2	-2	-2	-2	-2	2	2	0	0	0	-2	0	0	0	0	0	0	0	0	-2	-2	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	2	0	0	0	0	0	0	0
χ₁₉	2	2	2	2	2	2	-2	-2	0	0	-2	2	2	2	2	-2	-2	-2	-2	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	-2	0	0	0	0	0	0	0	0	2	$2 i$	$2 i$	$- 2 i$	$- 2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	0	0	$2 i$	0	0	0	0	0	0	0
χ₂₀	2	2	2	2	2	2	-2	-2	0	0	-2	2	2	2	2	-2	-2	-2	-2	0	0	0	2	2	-2	-2	2	2	-2	-2	0	0	0	-2	0	0	0	0	0	0	0	0	2	$- 2 i$	$- 2 i$	$2 i$	$2 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	0	0	$- 2 i$	0	0	0	0	0	0	0
χ₂₁	2	2	2	2	-2	-2	2	2	2	2	-2	2	2	2	2	2	2	2	2	-2	0	0	-2	-2	2	2	2	2	-2	-2	0	2	2	-2	-2	-2	0	0	0	0	2	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₂	2	2	2	2	-2	-2	2	2	2	2	-2	2	2	2	2	-2	-2	-2	-2	-2	0	0	-2	-2	2	2	-2	-2	2	2	0	2	2	-2	-2	-2	0	0	0	0	-2	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₃	2	2	2	2	-2	-2	2	2	-2	-2	-2	2	2	2	2	2	2	2	2	2	0	0	-2	-2	2	2	2	2	-2	-2	0	-2	-2	-2	2	2	0	0	0	0	-2	-2	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₄	2	2	2	2	-2	-2	2	2	-2	-2	-2	2	2	2	2	-2	-2	-2	-2	2	0	0	-2	-2	2	2	-2	-2	2	2	0	-2	-2	-2	2	2	0	0	0	0	2	2	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₂₅	2	2	2	2	-2	-2	-2	-2	0	0	2	2	2	2	2	2	2	2	2	0	0	0	-2	-2	-2	-2	-2	-2	-2	-2	0	0	0	2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	-2	0	2	-2	0	0	0	0	0
χ₂₆	2	2	2	2	-2	-2	-2	-2	0	0	2	2	2	2	2	2	2	2	2	0	0	0	-2	-2	-2	-2	-2	-2	-2	-2	0	0	0	2	0	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-2	2	0	-2	2	0	0	0	0	0
χ₂₇	2	2	2	2	-2	-2	-2	-2	0	0	2	2	2	2	2	-2	-2	-2	-2	0	0	0	-2	-2	-2	-2	2	2	2	2	0	0	0	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$2 i$	$- 2 i$	0	$- 2 i$	$2 i$	0	0	0	0	0
χ₂₈	2	2	2	2	-2	-2	-2	-2	0	0	2	2	2	2	2	-2	-2	-2	-2	0	0	0	-2	-2	-2	-2	2	2	2	2	0	0	0	2	0	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- 2 i$	$2 i$	0	$2 i$	$- 2 i$	0	0	0	0	0
χ₂₉	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	$1 - i$	$1 - i$	$- 1 + i$	$- 1 + i$	$1 + i$	$1 + i$	$- 1 - i$	$- 1 - i$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₀	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	$- 1 + i$	$- 1 + i$	$1 - i$	$1 - i$	$- 1 - i$	$- 1 - i$	$1 + i$	$1 + i$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₁	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	$- 1 + i$	$- 1 + i$	$1 - i$	$1 - i$	$- 1 - i$	$- 1 - i$	$1 + i$	$1 + i$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₂	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$2 i$	$- 2 i$	$2 i$	$- 2 i$	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	0	0	$2 i$	$- 2 i$	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	$1 - i$	$1 - i$	$- 1 + i$	$- 1 + i$	$1 + i$	$1 + i$	$- 1 - i$	$- 1 - i$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₃	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	$1 + i$	$1 + i$	$- 1 - i$	$- 1 - i$	$1 - i$	$1 - i$	$- 1 + i$	$- 1 + i$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₄	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	$i \sqrt{2}$	$- i \sqrt{2}$	2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	$- 1 - i$	$- 1 - i$	$1 + i$	$1 + i$	$- 1 + i$	$- 1 + i$	$1 - i$	$1 - i$	0	0	0	$- \sqrt{2}$	$\sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₅	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	$- 1 - i$	$- 1 - i$	$1 + i$	$1 + i$	$- 1 + i$	$- 1 + i$	$1 - i$	$1 - i$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₆	2	2	-2	-2	2	-2	0	0	0	0	0	2	-2	2	-2	$- 2 i$	$2 i$	$- 2 i$	$2 i$	0	$- i \sqrt{2}$	$i \sqrt{2}$	2	-2	0	0	0	0	$- 2 i$	$2 i$	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	$1 + i$	$1 + i$	$- 1 - i$	$- 1 - i$	$1 - i$	$1 - i$	$- 1 + i$	$- 1 + i$	0	0	0	$\sqrt{2}$	$- \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0
χ₃₇	2	-2	-2	2	0	0	-2	2	2	-2	0	2	-2	-2	2	2	2	-2	-2	0	0	0	0	0	-2	2	2	-2	0	0	0	2	-2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0
χ₃₈	2	-2	-2	2	0	0	-2	2	2	-2	0	2	-2	-2	2	2	2	-2	-2	0	0	0	0	0	-2	2	2	-2	0	0	0	2	-2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0
χ₃₉	2	-2	-2	2	0	0	-2	2	2	-2	0	2	-2	-2	2	-2	-2	2	2	0	0	0	0	0	-2	2	-2	2	0	0	0	2	-2	0	0	0	0	0	0	0	-2	2	0	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	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0
χ₄₀	2	-2	-2	2	0	0	-2	2	2	-2	0	2	-2	-2	2	-2	-2	2	2	0	0	0	0	0	-2	2	-2	2	0	0	0	2	-2	0	0	0	0	0	0	0	-2	2	0	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	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0
χ₄₁	2	-2	-2	2	0	0	-2	2	-2	2	0	2	-2	-2	2	2	2	-2	-2	0	0	0	0	0	-2	2	2	-2	0	0	0	-2	2	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0
χ₄₂	2	-2	-2	2	0	0	-2	2	-2	2	0	2	-2	-2	2	2	2	-2	-2	0	0	0	0	0	-2	2	2	-2	0	0	0	-2	2	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	0
χ₄₃	2	-2	-2	2	0	0	-2	2	-2	2	0	2	-2	-2	2	-2	-2	2	2	0	0	0	0	0	-2	2	-2	2	0	0	0	-2	2	0	0	0	0	0	0	0	2	-2	0	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	$- \sqrt{2}$	$\sqrt{2}$	$\sqrt{2}$	$- \sqrt{2}$	0
χ₄₄	2	-2	-2	2	0	0	-2	2	-2	2	0	2	-2	-2	2	-2	-2	2	2	0	0	0	0	0	-2	2	-2	2	0	0	0	-2	2	0	0	0	0	0	0	0	2	-2	0	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	$\sqrt{2}$	$- \sqrt{2}$	$- \sqrt{2}$	$\sqrt{2}$	0
χ₄₅	4	4	4	4	4	4	4	4	4	4	4	-1	-1	-1	-1	0	0	0	0	4	4	4	-1	-1	-1	-1	0	0	0	0	4	-1	-1	-1	-1	-1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₆	4	4	4	4	4	4	4	4	4	4	4	-1	-1	-1	-1	0	0	0	0	4	-4	-4	-1	-1	-1	-1	0	0	0	0	-4	-1	-1	-1	-1	-1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₇	4	4	4	4	4	4	4	4	-4	-4	4	-1	-1	-1	-1	0	0	0	0	-4	4	4	-1	-1	-1	-1	0	0	0	0	-4	1	1	-1	1	1	-1	-1	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₈	4	4	4	4	4	4	4	4	-4	-4	4	-1	-1	-1	-1	0	0	0	0	-4	-4	-4	-1	-1	-1	-1	0	0	0	0	4	1	1	-1	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₄₉	4	4	4	4	-4	-4	4	4	4	4	-4	-1	-1	-1	-1	0	0	0	0	-4	0	0	1	1	-1	-1	0	0	0	0	0	-1	-1	1	1	1	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₀	4	4	4	4	-4	-4	4	4	4	4	-4	-1	-1	-1	-1	0	0	0	0	-4	0	0	1	1	-1	-1	0	0	0	0	0	-1	-1	1	1	1	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₁	4	4	4	4	-4	-4	4	4	-4	-4	-4	-1	-1	-1	-1	0	0	0	0	4	0	0	1	1	-1	-1	0	0	0	0	0	1	1	1	-1	-1	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₂	4	4	4	4	-4	-4	4	4	-4	-4	-4	-1	-1	-1	-1	0	0	0	0	4	0	0	1	1	-1	-1	0	0	0	0	0	1	1	1	-1	-1	$- \sqrt{5}$	$\sqrt{5}$	$- \sqrt{5}$	$\sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	$\sqrt{5}$	$- \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₃	4	4	-4	-4	-4	4	0	0	0	0	0	4	-4	4	-4	$4 i$	$- 4 i$	$4 i$	$- 4 i$	0	0	0	-4	4	0	0	0	0	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₄	4	4	-4	-4	-4	4	0	0	0	0	0	4	-4	4	-4	$- 4 i$	$4 i$	$- 4 i$	$4 i$	0	0	0	-4	4	0	0	0	0	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₅	4	-4	4	-4	0	0	0	0	0	0	0	4	4	-4	-4	$4 i$	$- 4 i$	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₆	4	-4	4	-4	0	0	0	0	0	0	0	4	4	-4	-4	$4 i$	$- 4 i$	$- 4 i$	$4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₇	4	-4	4	-4	0	0	0	0	0	0	0	4	4	-4	-4	$- 4 i$	$4 i$	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₈	4	-4	4	-4	0	0	0	0	0	0	0	4	4	-4	-4	$- 4 i$	$4 i$	$4 i$	$- 4 i$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	−2ζ⁷−2ζ²³−2ζ³¹−2ζ³⁹	2ζ⁷+2ζ²³+2ζ³¹+2ζ³⁹	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	−2ζ¹³−2ζ²¹−2ζ²⁹−2ζ³⁷	2ζ¹³+2ζ²¹+2ζ²⁹+2ζ³⁷	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₅₉	4	-4	-4	4	0	0	4	-4	0	0	0	4	-4	-4	4	4	4	-4	-4	0	0	0	0	0	4	-4	-4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₀	4	-4	-4	4	0	0	4	-4	0	0	0	4	-4	-4	4	-4	-4	4	4	0	0	0	0	0	4	-4	4	-4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₁	8	8	8	8	8	8	-8	-8	0	0	-8	-2	-2	-2	-2	0	0	0	0	0	0	0	-2	-2	2	2	0	0	0	0	0	0	0	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₂	8	8	8	8	-8	-8	-8	-8	0	0	8	-2	-2	-2	-2	0	0	0	0	0	0	0	2	2	2	2	0	0	0	0	0	0	0	-2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₃	8	8	-8	-8	8	-8	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	$4 i \sqrt{2}$	$- 4 i \sqrt{2}$	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{2}$	$- i \sqrt{2}$	$i \sqrt{2}$	$i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₄	8	8	-8	-8	8	-8	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	$- 4 i \sqrt{2}$	$4 i \sqrt{2}$	-2	2	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{2}$	$i \sqrt{2}$	$- i \sqrt{2}$	$- i \sqrt{2}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₅	8	8	-8	-8	-8	8	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	$i \sqrt{10}$	$- i \sqrt{10}$	$- i \sqrt{10}$	$i \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₆	8	8	-8	-8	-8	8	0	0	0	0	0	-2	2	-2	2	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	0	0	0	0	0	0	0	$- i \sqrt{10}$	$i \sqrt{10}$	$i \sqrt{10}$	$- i \sqrt{10}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₇	8	-8	-8	8	0	0	8	-8	0	0	0	-2	2	2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	$2 i \sqrt{5}$	$- 2 i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₈	8	-8	-8	8	0	0	8	-8	0	0	0	-2	2	2	-2	0	0	0	0	0	0	0	0	0	-2	2	0	0	0	0	0	0	0	0	$- 2 i \sqrt{5}$	$2 i \sqrt{5}$	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₆₉	8	-8	-8	8	0	0	-8	8	8	-8	0	-2	2	2	-2	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	-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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₇₀	8	-8	-8	8	0	0	-8	8	-8	8	0	-2	2	2	-2	0	0	0	0	0	0	0	0	0	2	-2	0	0	0	0	0	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	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
χ₇₁	16	-16	16	-16	0	0	0	0	0	0	0	-4	-4	4	4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Character table — Group #13019278