Finite Group Databasebeta

← Group #11722614

Character table — Group #11722614

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1122222333344466666666666699999912121212121212121218181818181818181811222223333444666666666666999999121212121212121212181818181818181818
order12223463366661233366666661212441212121266666612121224466121212122222646666666126666666666121244121212126666661212122446612121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ31111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ41111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i321111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i32
χ51111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ61111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i321111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i32
χ7111-11-1111111-1-11111-11-1111-1-11111111-11-11-1-1-1-1-11-1-1-11-11-1111-11-1111111-1-11111-11-1111-1-11111111-11-11-1-1-1-1-11-1-1-11-11-1
χ8111-11-1111111-1-11111-11-1111-1-1-1-1-1-1-1-11-11-11-1-1-1-11-1111-11-11111-11-1111111-1-11111-11-1111-1-1-1-1-1-1-1-11-11-11-1-1-1-11-1111-11-11
χ9111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-11+i321−i32-11-11+i321−i32−1−i321+i32−1+i321−i32111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-11+i321−i32-11-11+i321−i32−1−i321+i32−1+i321−i32
χ10111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-11+i321−i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-11+i321−i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ11111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-11−i321+i32-11-11−i321+i32−1+i321−i32−1−i321+i32111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-11−i321+i32-11-11−i321+i32−1+i321−i32−1−i321+i32
χ12111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-11−i321+i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-11−i321+i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-111111-11-1111-11-11111-1-1111111-11-11-11-1-1-1-1-11-1-1-11-1111-111-111111-11-1111-11-11111-1-1111111-11-11-11-1-1-1-1-11-1-1-11-11
χ1411-111-111111-11-1111-11-11111-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1111-11-111-111-111111-11-1111-11-11111-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1111-11-1
χ1511-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32-11+i321−i32-1-111+i321−i321+i32−1−i321−i32−1+i3211-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32-11+i321−i32-1-111+i321−i321+i32−1−i321−i32−1+i32
χ1611-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-11+i321−i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i3211-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-11+i321−i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1711-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32-11−i321+i32-1-111−i321+i321−i32−1+i321+i32−1−i3211-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32-11−i321+i32-1-111−i321+i321−i32−1+i321+i32−1−i32
χ1811-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-11−i321+i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i3211-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-11−i321+i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-11111111-1-11111-1-1-1-111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111111-1-11111-1-1-1-111111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ2011-1-11111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-11111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-11111
χ2111-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i3211-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32
χ2211-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2311-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i3211-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i32
χ2411-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222-1-1-12222-1-1-122000000-1-1-1-1-1-1-1-1-100000000022222222222222-1-1-12222-1-1-122000000-1-1-1-1-1-1-1-1-1000000000
χ262222222−1−i3−1+i3−1−i3−1+i3222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i3000000-1-11+i321+i321−i321−i32-11+i321−i320000000002222222−1−i3−1+i3−1−i3−1+i3222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i3000000-1-11+i321+i321−i321−i32-11+i321−i32000000000
χ272222222−1+i3−1−i3−1+i3−1−i3222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i3000000-1-11−i321−i321+i321+i32-11−i321+i320000000002222222−1+i3−1−i3−1+i3−1−i3222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i3000000-1-11−i321−i321+i321+i32-11−i321+i32000000000
χ28222-22-2222222-2-2-1-1-12-22-2-1-1-1-2-2000000-11-11-11111000000000222-22-2222222-2-2-1-1-12-22-2-1-1-1-2-2000000-11-11-11111000000000
χ29222-22-22−1−i3−1+i3−1−i3−1+i32-2-2-11+i321−i32−1−i31+i3−1+i31−i3-11+i321−i321+i31−i3000000-111+i32−1−i321−i32−1+i321−1−i32−1+i32000000000222-22-22−1−i3−1+i3−1−i3−1+i32-2-2-11+i321−i32−1−i31+i3−1+i31−i3-11+i321−i321+i31−i3000000-111+i32−1−i321−i32−1+i321−1−i32−1+i32000000000
χ30222-22-22−1+i3−1−i3−1+i3−1−i32-2-2-11−i321+i32−1+i31−i3−1−i31+i3-11−i321+i321−i31+i3000000-111−i32−1+i321+i32−1−i321−1+i32−1−i32000000000222-22-22−1+i3−1−i3−1+i3−1−i32-2-2-11−i321+i32−1+i31−i3−1−i31+i3-11−i321+i321−i31+i3000000-111−i32−1+i321+i32−1−i321−1+i32−1−i32000000000
χ3122-222-222222-22-2-1-1-1-22-22-1-1-1-2-20000001-11-11-111100000000022-222-222222-22-2-1-1-1-22-22-1-1-1-2-20000001-11-11-1111000000000
χ3222-222-22−1−i3−1+i3−1−i3−1+i3-22-2-11+i321−i321+i3−1−i31−i3−1+i3-11+i321−i321+i31−i30000001-1−1−i321+i32−1+i321−i321−1−i32−1+i3200000000022-222-22−1−i3−1+i3−1−i3−1+i3-22-2-11+i321−i321+i3−1−i31−i3−1+i3-11+i321−i321+i31−i30000001-1−1−i321+i32−1+i321−i321−1−i32−1+i32000000000
χ3322-222-22−1+i3−1−i3−1+i3−1−i3-22-2-11−i321+i321−i3−1+i31+i3−1−i3-11−i321+i321−i31+i30000001-1−1+i321−i32−1−i321+i321−1+i32−1−i3200000000022-222-22−1+i3−1−i3−1+i3−1−i3-22-2-11−i321+i321−i3−1+i31+i3−1−i3-11−i321+i321−i31+i30000001-1−1+i321−i32−1−i321+i321−1+i32−1−i32000000000
χ3422-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122000000111111-1-1-100000000022-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122000000111111-1-1-1000000000
χ3522-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-11+i321−i321+i31+i31−i31−i3-11+i321−i32−1−i3−1+i300000011−1−i32−1−i32−1+i32−1+i32-11+i321−i3200000000022-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-11+i321−i321+i31+i31−i31−i3-11+i321−i32−1−i3−1+i300000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000000
χ3622-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-11−i321+i321−i31−i31+i31+i3-11−i321+i32−1+i3−1−i300000011−1+i32−1+i32−1−i32−1−i32-11−i321+i3200000000022-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-11−i321+i321−i31−i31+i31+i3-11−i321+i32−1+i3−1−i300000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000000
χ372-20020-222-2-20002220000-2-2-2002i−2i2i−2i2i−2i0000000000000000002-20020-222-2-20002220000-2-2-2002i−2i2i−2i2i−2i000000000000000000
χ382-20020-222-2-20002220000-2-2-200−2i2i−2i2i−2i2i0000000000000000002-20020-222-2-20002220000-2-2-200−2i2i−2i2i−2i2i000000000000000000
χ392-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i3002i−2i2ζ11−2ζ112ζ7−2ζ70000000000000000002-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i3002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000
χ402-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i300−2i2i−2ζ112ζ11−2ζ72ζ70000000000000000002-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i300−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000
χ412-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i3002i−2i2ζ7−2ζ72ζ11−2ζ110000000000000000002-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i3002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000
χ422-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i300−2i2i−2ζ72ζ7−2ζ112ζ110000000000000000002-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i300−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000
χ434-40040-444-4-4000-2-2-20000222000000000000000000000000004-40040-444-4-4000-2-2-2000022200000000000000000000000000
χ444-40040-4−2−2i3−2+2i32+2i32−2i3000-21+i31−i300002−1−i3−1+i3000000000000000000000000004-40040-4−2−2i3−2+2i32+2i32−2i3000-21+i31−i300002−1−i3−1+i300000000000000000000000000
χ454-40040-4−2+2i3−2−2i32−2i32+2i3000-21−i31+i300002−1+i3−1−i3000000000000000000000000004-40040-4−2+2i3−2−2i32−2i32+2i3000-21−i31+i300002−1+i3−1−i300000000000000000000000000
χ466666-36-30000-3-3-30000000000000000000000000000000000006666-36-30000-3-3-3000000000000000000000000000000000000
χ47666-6-3-6-30000-333000000000000000000000000000000000000666-6-3-6-30000-333000000000000000000000000000000000000
χ4866-66-3-6-300003-3300000000000000000000000000000000000066-66-3-6-300003-33000000000000000000000000000000000000
χ4966-6-6-36-3000033-300000000000000000000000000000000000066-6-6-36-3000033-3000000000000000000000000000000000000
χ5012-1200-606000000000000000000000000000000000000000000012-1200-6060000000000000000000000000000000000000000000
χ5111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5211111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111111
χ531111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321−i321+i321+i321−i321−i32-11+i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-11+i321−i32-1-1-11+i321−i321+i321+i321−i321−i32
χ541111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321−i321+i321+i321−i321−i32-11+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ551111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-11−i321+i32-1-1-11−i321+i321−i321−i321+i321+i32
χ561111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ57111-11-1111111-1-11111-11-1111-1-11111111-11-11-1-1-1-1-11-1-1-11-11-1-1-1-11-11-1-1-1-1-1-111-1-1-1-11-11-1-1-111-1-1-1-1-1-1-11-11-111111-1111-11-11
χ58111-11-1111111-1-11111-11-1111-1-1-1-1-1-1-1-11-11-11-1-1-1-11-1111-11-11-1-1-11-11-1-1-1-1-1-111-1-1-1-11-11-1-1-111111111-11-11-11111-11-1-1-11-11-1
χ59111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-11+i321−i32-11-11+i321−i32−1−i321+i32−1+i321−i32-1-1-11-11-11+i321−i321+i321−i32-111-11+i321−i321+i32−1−i321−i32−1+i32-11+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i321−1−i32−1+i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ60111-11-11−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i321+i32−1+i321−i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-11+i321−i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32-1-1-11-11-11+i321−i321+i321−i32-111-11+i321−i321+i32−1−i321−i32−1+i32-11+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i321−1−i32−1+i32-11-11+i321−i32−1−i321+i32−1+i321−i32
χ61111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-11−i321+i32-11-11−i321+i32−1+i321−i32−1−i321+i32-1-1-11-11-11−i321+i321−i321+i32-111-11−i321+i321−i32−1+i321+i32−1−i32-11−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i321−1+i32−1−i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ62111-11-11−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i321−i32−1−i321+i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-11−i321+i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32-1-1-11-11-11−i321+i321−i321+i32-111-11−i321+i321−i32−1+i321+i32−1−i32-11−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i321−1+i32−1−i32-11-11−i321+i32−1+i321−i32−1−i321+i32
χ6311-111-111111-11-1111-11-11111-1-1111111-11-11-11-1-1-1-1-11-1-1-11-11-1-11-1-11-1-1-1-1-11-11-1-1-11-11-1-1-1-111-1-1-1-1-1-11-11-11-111111-1111-11-1
χ6411-111-111111-11-1111-11-11111-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1111-11-1-1-11-1-11-1-1-1-1-11-11-1-1-11-11-1-1-1-1111111111-11-11-1111-1-11-1-1-11-11
χ6511-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32-11+i321−i32-1-111+i321−i321+i32−1−i321−i32−1+i32-1-11-1-11-11+i321−i321+i321−i321-11-11+i321−i32−1−i321+i32−1+i321−i32-11+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i321−1−i32−1+i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ6611-111-11−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-11+i321−i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11-1-11-11+i321−i321+i321−i321-11-11+i321−i32−1−i321+i32−1+i321−i32-11+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i321−1−i32−1+i32-1-111+i321−i321+i32−1−i321−i32−1+i32
χ6711-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32-11−i321+i32-1-111−i321+i321−i32−1+i321+i32−1−i32-1-11-1-11-11−i321+i321−i321+i321-11-11−i321+i32−1+i321−i32−1−i321+i32-11−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i321−1+i32−1−i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ6811-111-11−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-11−i321+i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11-1-11-11−i321+i321−i321+i321-11-11−i321+i32−1+i321−i32−1−i321+i32-11−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i321−1+i32−1−i32-1-111−i321+i321−i32−1+i321+i32−1−i32
χ6911-1-11111111-1-11111-1-1-1-111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111
χ7011-1-11111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-11111-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1111111111111-1-1-11-1-111-1-1-1-1
χ7111-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32-1-111-1-1-11+i321−i321+i321−i3211-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ7211-1-1111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32-1-111-1-1-11+i321−i321+i321−i3211-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i321-1-1−1−i32−1+i321+i321+i321−i321−i32
χ7311-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i32-1-111-1-1-11−i321+i321−i321+i3211-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ7411-1-1111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32-1-111-1-1-11−i321+i321−i321+i3211-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i321-1-1−1+i32−1−i321−i321−i321+i321+i32
χ7522222222222222-1-1-12222-1-1-122000000-1-1-1-1-1-1-1-1-1000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2111-2-2-2-2111-2-2000000111111111000000000
χ762222222−1−i3−1+i3−1−i3−1+i3222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32−1−i3−1+i3000000-1-11+i321+i321−i321−i32-11+i321−i32000000000-2-2-2-2-2-2-21+i31−i31+i31−i3-2-2-21−1−i32−1+i321+i31+i31−i31−i31−1−i32−1+i321+i31−i300000011−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32000000000
χ772222222−1+i3−1−i3−1+i3−1−i3222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32−1+i3−1−i3000000-1-11−i321−i321+i321+i32-11−i321+i32000000000-2-2-2-2-2-2-21−i31+i31−i31+i3-2-2-21−1+i32−1−i321−i31−i31+i31+i31−1+i32−1−i321−i31+i300000011−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32000000000
χ78222-22-2222222-2-2-1-1-12-22-2-1-1-1-2-2000000-11-11-11111000000000-2-2-22-22-2-2-2-2-2-222111-22-22111220000001-11-11-1-1-1-1000000000
χ79222-22-22−1−i3−1+i3−1−i3−1+i32-2-2-11+i321−i32−1−i31+i3−1+i31−i3-11+i321−i321+i31−i3000000-111+i32−1−i321−i32−1+i321−1−i32−1+i32000000000-2-2-22-22-21+i31−i31+i31−i3-2221−1−i32−1+i321+i3−1−i31−i3−1+i31−1−i32−1+i32−1−i3−1+i30000001-1−1−i321+i32−1+i321−i32-11+i321−i32000000000
χ80222-22-22−1+i3−1−i3−1+i3−1−i32-2-2-11−i321+i32−1+i31−i3−1−i31+i3-11−i321+i321−i31+i3000000-111−i32−1+i321+i32−1−i321−1+i32−1−i32000000000-2-2-22-22-21−i31+i31−i31+i3-2221−1+i32−1−i321−i3−1+i31+i3−1−i31−1+i32−1−i32−1+i3−1−i30000001-1−1+i321−i32−1−i321+i32-11−i321+i32000000000
χ8122-222-222222-22-2-1-1-1-22-22-1-1-1-2-20000001-11-11-1111000000000-2-22-2-22-2-2-2-2-22-221112-22-211122000000-11-11-11-1-1-1000000000
χ8222-222-22−1−i3−1+i3−1−i3−1+i3-22-2-11+i321−i321+i3−1−i31−i3−1+i3-11+i321−i321+i31−i30000001-1−1−i321+i32−1+i321−i321−1−i32−1+i32000000000-2-22-2-22-21+i31−i31+i31−i32-221−1−i32−1+i32−1−i31+i3−1+i31−i31−1−i32−1+i32−1−i3−1+i3000000-111+i32−1−i321−i32−1+i32-11+i321−i32000000000
χ8322-222-22−1+i3−1−i3−1+i3−1−i3-22-2-11−i321+i321−i3−1+i31+i3−1−i3-11−i321+i321−i31+i30000001-1−1+i321−i32−1−i321+i321−1+i32−1−i32000000000-2-22-2-22-21−i31+i31−i31+i32-221−1+i32−1−i32−1+i31−i3−1−i31+i31−1+i32−1−i32−1+i3−1−i3000000-111−i32−1+i321+i32−1−i32-11−i321+i32000000000
χ8422-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122000000111111-1-1-1000000000-2-222-2-2-2-2-2-2-222-21112222111-2-2000000-1-1-1-1-1-1111000000000
χ8522-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-11+i321−i321+i31+i31−i31−i3-11+i321−i32−1−i3−1+i300000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000000-2-222-2-2-21+i31−i31+i31−i322-21−1−i32−1+i32−1−i3−1−i3−1+i3−1+i31−1−i32−1+i321+i31−i3000000-1-11+i321+i321−i321−i321−1−i32−1+i32000000000
χ8622-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-11−i321+i321−i31−i31+i31+i3-11−i321+i32−1+i3−1−i300000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000000-2-222-2-2-21−i31+i31−i31+i322-21−1+i32−1−i32−1+i3−1+i3−1−i3−1−i31−1+i32−1−i321−i31+i3000000-1-11−i321−i321+i321+i321−1+i32−1−i32000000000
χ872-20020-222-2-20002220000-2-2-2002i−2i2i−2i2i−2i000000000000000000-2200-202-2-222000-2-2-2000022200−2i2i−2i2i−2i2i000000000000000000
χ882-20020-222-2-20002220000-2-2-200−2i2i−2i2i−2i2i000000000000000000-2200-202-2-222000-2-2-20000222002i−2i2i−2i2i−2i000000000000000000
χ892-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i3002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000-2200-2021+i31−i3−1−i3−1+i3000-21+i31−i300002−1−i3−1+i300−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000
χ902-20020-2−1−i3−1+i31+i31−i30002−1−i3−1+i30000-21+i31−i300−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000-2200-2021+i31−i3−1−i3−1+i3000-21+i31−i300002−1−i3−1+i3002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000
χ912-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i3002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000-2200-2021−i31+i3−1+i3−1−i3000-21−i31+i300002−1+i3−1−i300−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000
χ922-20020-2−1+i3−1−i31−i31+i30002−1+i3−1−i30000-21−i31+i300−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000-2200-2021−i31+i3−1+i3−1−i3000-21−i31+i300002−1+i3−1−i3002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000
χ934-40040-444-4-4000-2-2-2000022200000000000000000000000000-4400-404-4-4440002220000-2-2-200000000000000000000000000
χ944-40040-4−2−2i3−2+2i32+2i32−2i3000-21+i31−i300002−1−i3−1+i300000000000000000000000000-4400-4042+2i32−2i3−2−2i3−2+2i30002−1−i3−1+i30000-21+i31−i300000000000000000000000000
χ954-40040-4−2+2i3−2−2i32−2i32+2i3000-21−i31+i300002−1+i3−1−i300000000000000000000000000-4400-4042−2i32+2i3−2+2i3−2−2i30002−1+i3−1−i30000-21−i31+i300000000000000000000000000
χ966666-36-30000-3-3-3000000000000000000000000000000000000-6-6-6-63-630000333000000000000000000000000000000000000
χ97666-6-3-6-30000-333000000000000000000000000000000000000-6-6-6636300003-3-3000000000000000000000000000000000000
χ9866-66-3-6-300003-33000000000000000000000000000000000000-6-66-63630000-33-3000000000000000000000000000000000000
χ9966-6-6-36-3000033-3000000000000000000000000000000000000-6-6663-630000-3-33000000000000000000000000000000000000
χ10012-1200-6060000000000000000000000000000000000000000000-12120060-60000000000000000000000000000000000000000000

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