Finite Group Databasebeta

← Group #13135711

Character table — Group #13135711

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222333344444446666666666666666666666888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order122344666883366812122424242466999121212121818181818181818182424242444121212122424363636363636727272727272727272727272121212123636363636363636363636361616161648484848484848488824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ611111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32
χ711111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ811111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ911111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ1011111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i32
χ1111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ1211111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311-111-1-1-11-1-111111-1111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-111111-1-111-1-111-1-11-11-111-1-111-1-111-1-1ii−i−iii−i−iii−i−ii−ii−ii−i
χ1411-111-1-1-11-1-111111-1111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-111111-1-111-1-111-1-11-11-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−ii−ii−ii
χ1511-111-1-1-11-1-111111-1111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-1-111111-1-111-1-111-1-1-11-11-1-111-1-111-1-111ii−i−iii−i−iii−i−i−ii−ii−ii
χ1611-111-1-1-11-1-111111-1111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-1-111111-1-111-1-111-1-1-11-11-1-111-1-111-1-111−i−iii−i−iii−i−iiii−ii−ii−i
χ1711-111-1-1-11-1-1−1−i32−1+i32−1−i32−1+i321-1111-1-11+i321−i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321+i321−i321−i321-111-1-1−1−i32−1+i32-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14i−iζ22−ζ22ζ14−ζ14
χ1811-111-1-1-11-1-1−1−i32−1+i32−1−i32−1+i321-1111-1-11+i321−i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321+i321−i321−i321-111-1-1−1−i32−1+i32-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ii−ζ22ζ22−ζ14ζ14
χ1911-111-1-1-11-1-1−1−i32−1+i32−1−i32−1+i321-1111-1-11+i321−i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321+i321−i321−i32-11-1-111−1−i32−1+i32-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14−ii−ζ22ζ22−ζ14ζ14
χ2011-111-1-1-11-1-1−1−i32−1+i32−1−i32−1+i321-1111-1-11+i321−i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i321+i321+i321−i321−i32-11-1-111−1−i32−1+i32-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14i−iζ22−ζ22ζ14−ζ14
χ2111-111-1-1-11-1-1−1+i32−1−i32−1+i32−1−i321-1111-1-11−i321+i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321−i321+i321+i321-111-1-1−1+i32−1−i32-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22i−iζ14−ζ14ζ22−ζ22
χ2211-111-1-1-11-1-1−1+i32−1−i32−1+i32−1−i321-1111-1-11−i321+i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321−i321+i321+i321-111-1-1−1+i32−1−i32-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ii−ζ14ζ14−ζ22ζ22
χ2311-111-1-1-11-1-1−1+i32−1−i32−1+i32−1−i321-1111-1-11−i321+i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321−i321+i321+i32-11-1-111−1+i32−1−i32-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22−ii−ζ14ζ14−ζ22ζ22
χ2411-111-1-1-11-1-1−1+i32−1−i32−1+i32−1−i321-1111-1-11−i321+i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i321−i321−i321+i321+i32-11-1-111−1+i32−1−i32-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22i−iζ14−ζ14ζ22−ζ22
χ25222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000
χ2722222222222−1−i3−1+i3−1−i3−1+i32222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3222222−1−i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000
χ2822222222222−1−i3−1+i3−1−i3−1+i32222222−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3-2-2-2-2-2-2−1−i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
χ2922222222222−1+i3−1−i3−1+i3−1−i32222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3222222−1+i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000
χ3022222222222−1+i3−1−i3−1+i3−1−i32222222−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3-2-2-2-2-2-2−1+i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000
χ31222222222-2-22222-222-2-2-2-2222222222222222222-2-2-2-2000000-2-2222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ32222222222-2-22222-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2-1-1-1-1-1-11111111111110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ33222222222-2-22222-222-2-2-2-222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2-1-1-1-1-1-11111111111110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ34222222222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-2-2−1−i3−1+i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i31+i31+i31−i31−i30000001+i31−i32−1−i3−1+i32−1−i3−1+i3-2-2-2-21+i31+i31+i31+i31−i31−i31−i31−i30000000000000000000000000000000000
χ35222222222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31+i31−i31−i30000001+i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32000000000000000000
χ36222222222-2-2−1−i3−1+i3−1−i3−1+i3-222-2-2-2-2−1−i3−1+i3-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+i31+i31−i31−i30000001+i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i32000000000000000000
χ37222222222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-2-2−1+i3−1−i32−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i31−i31−i31+i31+i30000001−i31+i32−1+i3−1−i32−1+i3−1−i3-2-2-2-21−i31−i31−i31−i31+i31+i31+i31+i30000000000000000000000000000000000
χ38222222222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31−i31+i31+i30000001−i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i32000000000000000000
χ39222222222-2-2−1+i3−1−i3−1+i3−1−i3-222-2-2-2-2−1+i3−1−i3-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−i31−i31+i31+i30000001−i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i32000000000000000000
χ402222-2-22220022220-2-2000022222-2-2-2-2222222222000000000000-2-2-2-2-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ412222-2-22220022220-2-2000022222-2-2-2-2222222222000000000000-2-2-2-2-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ422222-2-222200−1−i3−1+i3−1−i3−1+i30-2-20000−1−i3−1+i32−1−i3−1+i31+i31−i31+i31−i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i3000000000000-21+i31−i3-21+i31−i30000000000000000000000000000−i2i2−i2i2ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000
χ432222-2-222200−1−i3−1+i3−1−i3−1+i30-2-20000−1−i3−1+i32−1−i3−1+i31+i31−i31+i31−i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i3000000000000-21+i31−i3-21+i31−i30000000000000000000000000000i2−i2i2−i2−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000
χ442222-2-222200−1+i3−1−i3−1+i3−1−i30-2-20000−1+i3−1−i32−1+i3−1−i31−i31+i31−i31+i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i3000000000000-21−i31+i3-21−i31+i30000000000000000000000000000−i2i2−i2i2ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000
χ452222-2-222200−1+i3−1−i3−1+i3−1−i30-2-20000−1+i3−1−i32−1+i3−1−i31−i31+i31−i31+i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i3000000000000-21−i31+i3-21−i31+i30000000000000000000000000000i2−i2i2−i2−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000
χ4622-222-2-2-22222222-2-22-2-222-2-222222-2-2-2-2-2-2-2-22222222000000-2-2-2-2-2222-2-222-2-222-2-2220000000000000000000000000000000000
χ4722-222-2-2-22222222-2-22-2-222-2-2-1-1-122-2-2111111-1-1-12222000000-2-2111-1-1-111-1-111-1-111-1-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ4822-222-2-2-22222222-2-22-2-222-2-2-1-1-122-2-2111111-1-1-12222000000-2-2111-1-1-111-1-111-1-111-1-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ4922-222-2-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-2-2221+i31−i32−1−i3−1+i3−1−i3−1+i31+i31−i3-2-21+i31+i31−i31−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i30000001+i31−i3-21+i31−i32−1−i3−1+i3-2-2221+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i30000000000000000000000000000000000
χ5022-222-2-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-2-2221+i31−i3-11+i321−i32−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i3−1−i3−1+i3−1+i30000001+i31−i31−1−i32−1+i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i320000−i3i3i3−i3−3+i323−i323−i32−3+i323+i32−3−i32−3−i323+i32000000000000000000
χ5122-222-2-2-2222−1−i3−1+i3−1−i3−1+i3-2-22-2-2221+i31−i3-11+i321−i32−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i32−1−i3−1−i3−1+i3−1+i30000001+i31−i31−1−i32−1+i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i320000i3−i3−i3i33−i32−3+i32−3+i323−i32−3−i323+i323+i32−3−i32000000000000000000
χ5222-222-2-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-2-2221−i31+i32−1+i3−1−i3−1+i3−1−i31−i31+i3-2-21−i31−i31+i31+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i30000001−i31+i3-21−i31+i32−1+i3−1−i3-2-2221−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i30000000000000000000000000000000000
χ5322-222-2-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-2-2221−i31+i3-11−i321+i32−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i3−1+i3−1−i3−1−i30000001−i31+i31−1+i32−1−i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i320000−i3i3i3−i33+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i32000000000000000000
χ5422-222-2-2-2222−1+i3−1−i3−1+i3−1−i3-2-22-2-2221−i31+i3-11−i321+i32−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i32−1+i3−1+i3−1−i3−1−i30000001−i31+i31−1+i32−1−i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i320000i3−i3−i3i3−3−i323+i323+i32−3−i323−i32−3+i32−3+i323−i32000000000000000000
χ5522-222-2-2-22-2-222222-2222-2-2-2-2-1-1-122-2-2111111-1-1-1-2-2-2-22-222-2-222111-1-1-1-1-111-1-111-1-1112-22-2-1-111-1-111-1-111000000000000000000
χ5622-222-2-2-22-2-222222-2222-2-2-2-2-1-1-122-2-2111111-1-1-1-2-2-2-2-22-2-22222111-1-1-1-1-111-1-111-1-111-22-2211-1-111-1-111-1-1000000000000000000
χ5722-222-2-2-22-2-2−1−i3−1+i3−1−i3−1+i32-2222-2-21+i31−i3-11+i321−i32−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i31+i31−i31−i32-222-2-2−1−i3−1+i31−1−i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i31+i3−1+i31−i3-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000000
χ5822-222-2-2-22-2-2−1−i3−1+i3−1−i3−1+i32-2222-2-21+i31−i3-11+i321−i32−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i31+i31−i31−i3-22-2-222−1−i3−1+i31−1−i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i3−1−i31−i3−1+i311-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000000000
χ5922-222-2-2-22-2-2−1+i3−1−i3−1+i3−1−i32-2222-2-21−i31+i3-11−i321+i32−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i31−i31+i31+i32-222-2-2−1+i3−1−i31−1+i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i31−i3−1−i31+i3-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000000
χ6022-222-2-2-22-2-2−1+i3−1−i3−1+i3−1−i32-2222-2-21−i31+i3-11−i321+i32−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i31−i31+i31+i3-22-2-222−1+i3−1−i31−1+i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i3−1+i31+i3−1−i311-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000000000
χ6122-22-22-2-2200222202-20000-2-2222-2-222-2-2-2-2-2-2222000000000000222-2-2-200000000000000000000000000002−2−222−2−222−2−22000000
χ6222-22-22-2-2200222202-20000-2-2222-2-222-2-2-2-2-2-2222000000000000222-2-2-20000000000000000000000000000−222−2−222−2−222−2000000
χ6322-22-22-2-2200−1−i3−1+i3−1−i3−1+i302-200001+i31−i32−1−i3−1+i31+i31−i3−1−i3−1+i3-2-21+i31+i31−i31−i32−1−i3−1+i30000000000002−1−i3−1+i3-21+i31−i300000000000000000000000000002−2−22−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000
χ6422-22-22-2-2200−1−i3−1+i3−1−i3−1+i302-200001+i31−i32−1−i3−1+i31+i31−i3−1−i3−1+i3-2-21+i31+i31−i31−i32−1−i3−1+i30000000000002−1−i3−1+i3-21+i31−i30000000000000000000000000000−222−2ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000
χ6522-22-22-2-2200−1+i3−1−i3−1+i3−1−i302-200001−i31+i32−1+i3−1−i31−i31+i3−1+i3−1−i3-2-21−i31−i31+i31+i32−1+i3−1−i30000000000002−1+i3−1−i3-21−i31+i300000000000000000000000000002−2−22ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000
χ6622-22-22-2-2200−1+i3−1−i3−1+i3−1−i302-200001−i31+i32−1+i3−1−i31−i31+i3−1+i3−1−i3-2-21−i31−i31+i31+i32−1+i3−1−i30000000000002−1+i3−1−i3-21−i31+i30000000000000000000000000000−222−2−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000
χ674444-4-44440044440-4-4000044-2-2-2-4-4-4-4-2-2-2-2-2-2-2-2-20000000000002222220000000000000000000000000000000000000000000000
χ684444-4-444400−2−2i3−2+2i3−2−2i3−2+2i30-4-40000−2−2i3−2+2i3-21+i31−i32+2i32−2i32+2i32−2i3-2-21+i31+i31−i31−i3-21+i31−i30000000000002−1−i3−1+i32−1−i3−1+i30000000000000000000000000000000000000000000000
χ694444-4-444400−2+2i3−2−2i3−2+2i3−2−2i30-4-40000−2+2i3−2−2i3-21−i31+i32−2i32+2i32−2i32+2i3-2-21−i31−i31+i31+i3-21−i31+i30000000000002−1+i3−1−i32−1+i3−1−i30000000000000000000000000000000000000000000000
χ7044-44-44-4-4400444404-40000-4-4-2-2-2-4-444222222-2-2-2000000000000-2-2-22220000000000000000000000000000000000000000000000
χ7144-44-44-4-4400−2−2i3−2+2i3−2−2i3−2+2i304-400002+2i32−2i3-21+i31−i32+2i32−2i3−2−2i3−2+2i322−1−i3−1−i3−1+i3−1+i3-21+i31−i3000000000000-21+i31−i32−1−i3−1+i30000000000000000000000000000000000000000000000
χ7244-44-44-4-4400−2+2i3−2−2i3−2+2i3−2−2i304-400002−2i32+2i3-21−i31+i32−2i32+2i3−2+2i3−2−2i322−1+i3−1+i3−1−i3−1−i3-21−i31+i3000000000000-21−i31+i32−1+i3−1−i30000000000000000000000000000000000000000000000
χ734-4040000-422−2244-4-40000022−22004440000000000-4-4-422−2222−22000000000000000022−220022−220022−220000000000000000000000000000000000
χ744-4040000-422−2244-4-40000022−2200-2-2-20000−2i32i3−2i32i3−2i32i322222−2222−2200000000000000i6−i6−22i6−i6−22i6−i6−220000000000000000000000000000000000
χ754-4040000-422−2244-4-40000022−2200-2-2-200002i3−2i32i3−2i32i3−2i322222−2222−2200000000000000−i6i6−22−i6i6−22−i6i6−220000000000000000000000000000000000
χ764-4040000-422−22−2−2i3−2+2i32+2i32−2i30000022−22004−2−2i3−2+2i30000000000-42+2i32−2i3−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ23000000000000000022−2200−2ζ7+2ζ132ζ7−2ζ13002ζ5−2ζ23−2ζ5+2ζ230000000000000000000000000000000000
χ774-4040000-422−22−2−2i3−2+2i32+2i32−2i30000022−2200-21+i31−i30000−2i32i3−3+i33−i33+i3−3−i32−1−i3−1+i3−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ2300000000000000i6−i6−22−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ7−ζ13−ζ7+ζ13ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23−ζ5+ζ23ζ5−ζ230000000000000000000000000000000000
χ784-4040000-422−22−2−2i3−2+2i32+2i32−2i30000022−2200-21+i31−i300002i3−2i33−i3−3+i3−3−i33+i32−1−i3−1+i3−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ2300000000000000−i6i6−222ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23ζ7−ζ13−ζ7+ζ13−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ23−ζ5+ζ23ζ5−ζ230000000000000000000000000000000000
χ794-4040000-422−22−2+2i3−2−2i32−2i32+2i30000022−22004−2+2i3−2−2i30000000000-42−2i32+2i32ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ13000000000000000022−22002ζ5−2ζ23−2ζ5+2ζ2300−2ζ7+2ζ132ζ7−2ζ130000000000000000000000000000000000
χ804-4040000-422−22−2+2i3−2−2i32−2i32+2i30000022−2200-21−i31+i30000−2i32i33+i3−3−i3−3+i33−i32−1+i3−1−i32ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ1300000000000000i6−i6−22ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23−ζ5+ζ23ζ5−ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ7−ζ13−ζ7+ζ130000000000000000000000000000000000
χ814-4040000-422−22−2+2i3−2−2i32−2i32+2i30000022−2200-21−i31+i300002i3−2i3−3−i33+i33−i3−3+i32−1+i3−1−i32ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ1300000000000000−i6i6−22−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ23−ζ5+ζ23ζ5−ζ232ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23ζ7−ζ13−ζ7+ζ130000000000000000000000000000000000
χ824-4040000-4−222244-4-400000−2222004440000000000-4-4-4−2222−22220000000000000000−222200−222200−22220000000000000000000000000000000000
χ834-4040000-4−222244-4-400000−222200-2-2-20000−2i32i3−2i32i3−2i32i3222−2222−222200000000000000−i6i62−2−i6i62−2−i6i62−20000000000000000000000000000000000
χ844-4040000-4−222244-4-400000−222200-2-2-200002i3−2i32i3−2i32i3−2i3222−2222−222200000000000000i6−i62−2i6−i62−2i6−i62−20000000000000000000000000000000000
χ854-4040000-4−2222−2−2i3−2+2i32+2i32−2i300000−2222004−2−2i3−2+2i30000000000-42+2i32−2i32ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ230000000000000000−2222002ζ7−2ζ13−2ζ7+2ζ1300−2ζ5+2ζ232ζ5−2ζ230000000000000000000000000000000000
χ864-4040000-4−2222−2−2i3−2+2i32+2i32−2i300000−222200-21+i31−i30000−2i32i3−3+i33−i33+i3−3−i32−1−i3−1+i32ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ2300000000000000−i6i62−22ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23−ζ7+ζ13ζ7−ζ13−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ23ζ5−ζ23−ζ5+ζ230000000000000000000000000000000000
χ874-4040000-4−2222−2−2i3−2+2i32+2i32−2i300000−222200-21+i31−i300002i3−2i33−i3−3+i3−3−i33+i32−1−i3−1+i32ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ2300000000000000i6−i62−2−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23−ζ7+ζ13ζ7−ζ13ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5−ζ23−ζ5+ζ230000000000000000000000000000000000
χ884-4040000-4−2222−2+2i3−2−2i32−2i32+2i300000−2222004−2+2i3−2−2i30000000000-42−2i32+2i3−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ130000000000000000−222200−2ζ5+2ζ232ζ5−2ζ23002ζ7−2ζ13−2ζ7+2ζ130000000000000000000000000000000000
χ894-4040000-4−2222−2+2i3−2−2i32−2i32+2i300000−222200-21−i31+i30000−2i32i33+i3−3−i3−3+i33−i32−1+i3−1−i3−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ1300000000000000−i6i62−2−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ23ζ5−ζ23−ζ5+ζ232ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23−ζ7+ζ13ζ7−ζ130000000000000000000000000000000000
χ904-4040000-4−2222−2+2i3−2−2i32−2i32+2i300000−222200-21−i31+i300002i3−2i3−3−i33+i33−i3−3+i32−1+i3−1−i3−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ1300000000000000i6−i62−2ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5−ζ23−ζ5+ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23−ζ7+ζ13ζ7−ζ130000000000000000000000000000000000
χ91666-366-3-3-36600006-3-3-3-3-3-3000000000000000000000066-3-3-3-3000000000000000000000000000000000000000000000000000000
χ92666-366-3-3-36600006-3-3-3-3-3-30000000000000000000000-6-63333000000000000000000000000000000000000000000000000000000
χ93666-366-3-3-3-6-60000-6-3-33333000000000000000000000000−3i33i3−3i33i3000000000000000000000000000000000000000000000000000000
χ94666-366-3-3-3-6-60000-6-3-333330000000000000000000000003i3−3i33i3−3i3000000000000000000000000000000000000000000000000000000
χ9566-6-36-633-3660000-63-333-3-3000000000000000000000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000
χ9666-6-36-633-3660000-63-333-3-30000000000000000000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000
χ9766-6-36-633-3-6-6000063-3-3-33300000000000000000000006-6-3-333000000000000000000000000000000000000000000000000000000
χ9866-6-36-633-3-6-6000063-3-3-3330000000000000000000000-6633-3-3000000000000000000000000000000000000000000000000000000
χ99121212-6-12-12-6-6-600000006600000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1001212-12-6-121266-60000000-6600000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10112-120-600−6i36i3662−6200000003i6−3i6−32320000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-120-600−6i36i36−62620000000−3i63i632−320000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-120-6006i3−6i3662−620000000−3i63i6−32320000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-120-6006i3−6i36−626200000003i6−3i632−320000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.