Finite Group Databasebeta

← Group #13167623

Character table — Group #13167623

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112228888888899181818363636363636363636363636112228888888899181818363636363636363636363636112228888888899181818363636363636363636363636
order1224436661212121244224888888888888366121236661212121212126612242424242424242424242424366121236661212121212126612242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111
χ5111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1
χ6111-1-11111-1-1-1-111-1-1111-1-1-1-111-1-111111-1-11111-1-1-1-111-1-1111-1-1-1-111-1-111111-1-11111-1-1-1-111-1-1111-1-1-1-111-1-111
χ7111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-111111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-111111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-111
χ8111-1-11111-1-1-1-111-1-11-1-111-1-11111-1-1111-1-11111-1-1-1-111-1-11-1-111-1-11111-1-1111-1-11111-1-1-1-111-1-11-1-111-1-11111-1-1
χ911-11-11-1-1111-1-1-1-11-11i−ii−ii−ii−i1-11-111-11-11-1-1111-1-1-1-11-11i−ii−ii−ii−i1-11-111-11-11-1-1111-1-1-1-11-11i−ii−ii−ii−i1-11-1
χ1011-11-11-1-1111-1-1-1-11-11i−ii−i−ii−ii-11-1111-11-11-1-1111-1-1-1-11-11i−ii−i−ii−ii-11-1111-11-11-1-1111-1-1-1-11-11i−ii−i−ii−ii-11-11
χ1111-11-11-1-1111-1-1-1-11-11−ii−iii−ii−i-11-1111-11-11-1-1111-1-1-1-11-11−ii−iii−ii−i-11-1111-11-11-1-1111-1-1-1-11-11−ii−iii−ii−i-11-11
χ1211-11-11-1-1111-1-1-1-11-11−ii−ii−ii−ii1-11-111-11-11-1-1111-1-1-1-11-11−ii−ii−ii−ii1-11-111-11-11-1-1111-1-1-1-11-11−ii−ii−ii−ii1-11-1
χ1311-1-111-1-11-1-111-1-1-111i−i−iii−i−ii1-1-1111-1-111-1-11-1-111-1-1-111i−i−iii−i−ii1-1-1111-1-111-1-11-1-111-1-1-111i−i−iii−i−ii1-1-11
χ1411-1-111-1-11-1-111-1-1-111i−i−ii−iii−i-111-111-1-111-1-11-1-111-1-1-111i−i−ii−iii−i-111-111-1-111-1-11-1-111-1-1-111i−i−ii−iii−i-111-1
χ1511-1-111-1-11-1-111-1-1-111−iii−ii−i−ii-111-111-1-111-1-11-1-111-1-1-111−iii−ii−i−ii-111-111-1-111-1-11-1-111-1-1-111−iii−ii−i−ii-111-1
χ1611-1-111-1-11-1-111-1-1-111−iii−i−iii−i1-1-1111-1-111-1-11-1-111-1-1-111−iii−i−iii−i1-1-1111-1-111-1-11-1-111-1-1-111−iii−i−iii−i1-1-11
χ172222222222222-2-2-2-2-20000000000002222222222222-2-2-2-2-20000000000002222222222222-2-2-2-2-2000000000000
χ18222-2-22222-2-2-2-2-2-222-2000000000000222-2-22222-2-2-2-2-2-222-2000000000000222-2-22222-2-2-2-2-2-222-2000000000000
χ1922-22-22-2-2222-2-222-22-200000000000022-22-22-2-2222-2-222-22-200000000000022-22-22-2-2222-2-222-22-2000000000000
χ2022-2-222-2-22-2-222222-2-200000000000022-2-222-2-22-2-222222-2-200000000000022-2-222-2-22-2-222222-2-2000000000000
χ214-4000400-400004i−4i0000000000000004-4000400-400004i−4i0000000000000004-4000400-400004i−4i000000000000000
χ224-4000400-40000−4i4i0000000000000004-4000400-40000−4i4i0000000000000004-4000400-40000−4i4i000000000000000
χ2388888-1-1-1-1-1-1-1-10000000000000000088888-1-1-1-1-1-1-1-10000000000000000088888-1-1-1-1-1-1-1-100000000000000000
χ24888-8-8-1-1-1-1111100000000000000000888-8-8-1-1-1-1111100000000000000000888-8-8-1-1-1-1111100000000000000000
χ2588-88-8-111-1-1-1110000000000000000088-88-8-111-1-1-1110000000000000000088-88-8-111-1-1-11100000000000000000
χ2688-8-88-111-111-1-10000000000000000088-8-88-111-111-1-10000000000000000088-8-88-111-111-1-100000000000000000
χ278-8000-13-313i−3i3i−3i000000000000000008-8000-13-313i−3i3i−3i000000000000000008-8000-13-313i−3i3i−3i00000000000000000
χ288-8000-13-31−3i3i−3i3i000000000000000008-8000-13-31−3i3i−3i3i000000000000000008-8000-13-31−3i3i−3i3i00000000000000000
χ298-8000-1-3313i−3i−3i3i000000000000000008-8000-1-3313i−3i−3i3i000000000000000008-8000-1-3313i−3i−3i3i00000000000000000
χ308-8000-1-331−3i3i3i−3i000000000000000008-8000-1-331−3i3i3i−3i000000000000000008-8000-1-331−3i3i3i−3i00000000000000000
χ31111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ321111111111111111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ33111111111111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ34111111111111111111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ35111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ36111-1-11111-1-1-1-111-1-1111-1-1-1-111-1-111−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ37111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-111−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ38111-1-11111-1-1-1-111-1-11-1-111-1-11111-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ3911-11-11-1-1111-1-1-1-11-11i−ii−ii−ii−i1-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32
χ4011-11-11-1-1111-1-1-1-11-11i−ii−i−ii−ii-11-11−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32
χ4111-11-11-1-1111-1-1-1-11-11−ii−iii−ii−i-11-11−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32
χ4211-11-11-1-1111-1-1-1-11-11−ii−ii−ii−ii1-11-1−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32
χ4311-1-111-1-11-1-111-1-1-111i−i−iii−i−ii1-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32
χ4411-1-111-1-11-1-111-1-1-111i−i−ii−iii−i-111-1−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32
χ4511-1-111-1-11-1-111-1-1-111−iii−ii−i−ii-111-1−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32
χ4611-1-111-1-11-1-111-1-1-111−iii−i−iii−i1-1-11−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32
χ472222222222222-2-2-2-2-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3000000000000
χ48222-2-22222-2-2-2-2-2-222-2000000000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i3000000000000
χ4922-22-22-2-2222-2-222-22-2000000000000−1+i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i3000000000000−1−i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i3000000000000
χ5022-2-222-2-22-2-222222-2-2000000000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3000000000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3000000000000
χ514-4000400-400004i−4i000000000000000−2+2i32−2i3000−2+2i3002−2i300004ζ7−4ζ7000000000000000−2−2i32+2i3000−2−2i3002+2i300004ζ11−4ζ11000000000000000
χ524-4000400-40000−4i4i000000000000000−2+2i32−2i3000−2+2i3002−2i30000−4ζ74ζ7000000000000000−2−2i32+2i3000−2−2i3002+2i30000−4ζ114ζ11000000000000000
χ5388888-1-1-1-1-1-1-1-100000000000000000−4+4i3−4+4i3−4+4i3−4+4i3−4+4i31−i321−i321−i321−i321−i321−i321−i321−i3200000000000000000−4−4i3−4−4i3−4−4i3−4−4i3−4−4i31+i321+i321+i321+i321+i321+i321+i321+i3200000000000000000
χ54888-8-8-1-1-1-1111100000000000000000−4+4i3−4+4i3−4+4i34−4i34−4i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i3200000000000000000−4−4i3−4−4i3−4−4i34+4i34+4i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i3200000000000000000
χ5588-88-8-111-1-1-11100000000000000000−4+4i3−4+4i34−4i3−4+4i34−4i31−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i3200000000000000000−4−4i3−4−4i34+4i3−4−4i34+4i31+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i3200000000000000000
χ5688-8-88-111-111-1-100000000000000000−4+4i3−4+4i34−4i34−4i3−4+4i31−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i3200000000000000000−4−4i3−4−4i34+4i34+4i3−4−4i31+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i3200000000000000000
χ578-8000-13-313i−3i3i−3i00000000000000000−4+4i34−4i30001−i32−3+3i323−3i32−1+i323ζ7−3ζ73ζ7−3ζ700000000000000000−4−4i34+4i30001+i32−3−3i323+3i32−1−i323ζ11−3ζ113ζ11−3ζ1100000000000000000
χ588-8000-13-31−3i3i−3i3i00000000000000000−4+4i34−4i30001−i32−3+3i323−3i32−1+i32−3ζ73ζ7−3ζ73ζ700000000000000000−4−4i34+4i30001+i32−3−3i323+3i32−1−i32−3ζ113ζ11−3ζ113ζ1100000000000000000
χ598-8000-1-3313i−3i−3i3i00000000000000000−4+4i34−4i30001−i323−3i32−3+3i32−1+i323ζ7−3ζ7−3ζ73ζ700000000000000000−4−4i34+4i30001+i323+3i32−3−3i32−1−i323ζ11−3ζ11−3ζ113ζ1100000000000000000
χ608-8000-1-331−3i3i3i−3i00000000000000000−4+4i34−4i30001−i323−3i32−3+3i32−1+i32−3ζ73ζ73ζ7−3ζ700000000000000000−4−4i34+4i30001+i323+3i32−3−3i32−1−i32−3ζ113ζ113ζ11−3ζ1100000000000000000
χ61111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ621111111111111111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ63111111111111111111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ64111111111111111111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ65111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ66111-1-11111-1-1-1-111-1-1111-1-1-1-111-1-111−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ67111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-111−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ68111-1-11111-1-1-1-111-1-11-1-111-1-11111-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ6911-11-11-1-1111-1-1-1-11-11i−ii−ii−ii−i1-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32
χ7011-11-11-1-1111-1-1-1-11-11i−ii−i−ii−ii-11-11−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32
χ7111-11-11-1-1111-1-1-1-11-11−ii−iii−ii−i-11-11−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32
χ7211-11-11-1-1111-1-1-1-11-11−ii−ii−ii−ii1-11-1−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32
χ7311-1-111-1-11-1-111-1-1-111i−i−iii−i−ii1-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32
χ7411-1-111-1-11-1-111-1-1-111i−i−ii−iii−i-111-1−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32
χ7511-1-111-1-11-1-111-1-1-111−iii−ii−i−ii-111-1−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32
χ7611-1-111-1-11-1-111-1-1-111−iii−i−iii−i1-1-11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32
χ772222222222222-2-2-2-2-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3000000000000
χ78222-2-22222-2-2-2-2-2-222-2000000000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i3000000000000
χ7922-22-22-2-2222-2-222-22-2000000000000−1−i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i31+i3000000000000−1+i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i31−i3000000000000
χ8022-2-222-2-22-2-222222-2-2000000000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3000000000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3000000000000
χ814-4000400-400004i−4i000000000000000−2−2i32+2i3000−2−2i3002+2i300004ζ11−4ζ11000000000000000−2+2i32−2i3000−2+2i3002−2i300004ζ7−4ζ7000000000000000
χ824-4000400-40000−4i4i000000000000000−2−2i32+2i3000−2−2i3002+2i30000−4ζ114ζ11000000000000000−2+2i32−2i3000−2+2i3002−2i30000−4ζ74ζ7000000000000000
χ8388888-1-1-1-1-1-1-1-100000000000000000−4−4i3−4−4i3−4−4i3−4−4i3−4−4i31+i321+i321+i321+i321+i321+i321+i321+i3200000000000000000−4+4i3−4+4i3−4+4i3−4+4i3−4+4i31−i321−i321−i321−i321−i321−i321−i321−i3200000000000000000
χ84888-8-8-1-1-1-1111100000000000000000−4−4i3−4−4i3−4−4i34+4i34+4i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i3200000000000000000−4+4i3−4+4i3−4+4i34−4i34−4i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i3200000000000000000
χ8588-88-8-111-1-1-11100000000000000000−4−4i3−4−4i34+4i3−4−4i34+4i31+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i3200000000000000000−4+4i3−4+4i34−4i3−4+4i34−4i31−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i3200000000000000000
χ8688-8-88-111-111-1-100000000000000000−4−4i3−4−4i34+4i34+4i3−4−4i31+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i3200000000000000000−4+4i3−4+4i34−4i34−4i3−4+4i31−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i3200000000000000000
χ878-8000-13-313i−3i3i−3i00000000000000000−4−4i34+4i30001+i32−3−3i323+3i32−1−i323ζ11−3ζ113ζ11−3ζ1100000000000000000−4+4i34−4i30001−i32−3+3i323−3i32−1+i323ζ7−3ζ73ζ7−3ζ700000000000000000
χ888-8000-13-31−3i3i−3i3i00000000000000000−4−4i34+4i30001+i32−3−3i323+3i32−1−i32−3ζ113ζ11−3ζ113ζ1100000000000000000−4+4i34−4i30001−i32−3+3i323−3i32−1+i32−3ζ73ζ7−3ζ73ζ700000000000000000
χ898-8000-1-3313i−3i−3i3i00000000000000000−4−4i34+4i30001+i323+3i32−3−3i32−1−i323ζ11−3ζ11−3ζ113ζ1100000000000000000−4+4i34−4i30001−i323−3i32−3+3i32−1+i323ζ7−3ζ7−3ζ73ζ700000000000000000
χ908-8000-1-331−3i3i3i−3i00000000000000000−4−4i34+4i30001+i323+3i32−3−3i32−1−i32−3ζ113ζ113ζ11−3ζ1100000000000000000−4+4i34−4i30001−i323−3i32−3+3i32−1+i32−3ζ73ζ73ζ7−3ζ700000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.