Finite Group Databasebeta

← Group #73167

Character table — Group #73167

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111122222222222244444444444444446666666666666666888888888888888888888888
order1222222244444444444433666666666666664444444444444444121212121212121212121212121212121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111−1−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+i321111111111111111−1−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
χ311111111111111111111−1+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−i321111111111111111−1+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
χ4111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1-1-1-1-1−1−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+i3211111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ6111111111111-1-1-1-1-1-1-1-1−1+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−i3211111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ711111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111-1-1-1-11111-1-1-1-1−1−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+i321111-1-1-1-11111-1-1-1-11+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ911111111-1-1-1-11111-1-1-1-1−1+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−i321111-1-1-1-11111-1-1-1-11−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ1011111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-11111−1−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+i321111-1-1-1-1-1-1-1-111111+i321+i321+i321+i321+i321+i321+i321+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
χ1211111111-1-1-1-1-1-1-1-11111−1+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−i321111-1-1-1-1-1-1-1-111111−i321−i321−i321−i321−i321−i321−i321−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
χ1311-1-111-1-111-1-1ii−i−iii−i−i1111-1-111-1-11-1-11-1-111-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1411-1-111-1-111-1-1ii−i−iii−i−i−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-111-1-1ii−i−iii−i−i−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ1511-1-111-1-111-1-1ii−i−iii−i−i−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-111-1-1ii−i−iii−i−i−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ1611-1-111-1-111-1-1−i−iii−i−iii1111-1-111-1-11-1-11-1-111-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1711-1-111-1-111-1-1−i−iii−i−iii−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-111-1-1−i−iii−i−iii−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ1811-1-111-1-111-1-1−i−iii−i−iii−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-111-1-1−i−iii−i−iii−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ1911-1-111-1-1-1-111ii−i−i−i−iii1111-1-111-1-11-1-11-1-111-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii
χ2011-1-111-1-1-1-111ii−i−i−i−iii−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1-1-111ii−i−i−i−iii1+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ2111-1-111-1-1-1-111ii−i−i−i−iii−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1-1-111ii−i−i−i−iii1−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ2211-1-111-1-1-1-111−i−iiiii−i−i1111-1-111-1-11-1-11-1-111-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i
χ2311-1-111-1-1-1-111−i−iiiii−i−i−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1-1-111−i−iiiii−i−i1+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ2411-1-111-1-1-1-111−i−iiiii−i−i−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1-1-111−i−iiiii−i−i1−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ251-11-11-11-1i−ii−i1-11-1i−ii−i111-11-11-11-1-11-1-11-11-11-1i−ii−i1-11-1i−ii−ii−ii−i1-11-1i−ii−ii−ii−i1-11-1i−ii−i
χ261-11-11-11-1i−ii−i1-11-1i−ii−i−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321-11-1i−ii−i1-11-1i−ii−iζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ271-11-11-11-1i−ii−i1-11-1i−ii−i−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321-11-1i−ii−i1-11-1i−ii−iζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ281-11-11-11-1i−ii−i-11-11−ii−ii111-11-11-11-1-11-1-11-11-11-1i−ii−i-11-11−ii−iii−ii−i-11-11−ii−iii−ii−i-11-11−ii−ii
χ291-11-11-11-1i−ii−i-11-11−ii−ii−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321-11-1i−ii−i-11-11−ii−iiζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ301-11-11-11-1i−ii−i-11-11−ii−ii−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321-11-1i−ii−i-11-11−ii−iiζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ311-11-11-11-1−ii−ii1-11-1−ii−ii111-11-11-11-1-11-1-11-11-11-1−ii−ii1-11-1−ii−ii−ii−ii1-11-1−ii−ii−ii−ii1-11-1−ii−ii
χ321-11-11-11-1−ii−ii1-11-1−ii−ii−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321-11-1−ii−ii1-11-1−ii−ii−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ331-11-11-11-1−ii−ii1-11-1−ii−ii−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321-11-1−ii−ii1-11-1−ii−ii−ζ7ζ7−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ341-11-11-11-1−ii−ii-11-11i−ii−i111-11-11-11-1-11-1-11-11-11-1−ii−ii-11-11i−ii−i−ii−ii-11-11i−ii−i−ii−ii-11-11i−ii−i
χ351-11-11-11-1−ii−ii-11-11i−ii−i−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321-11-1−ii−ii-11-11i−ii−i−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ361-11-11-11-1−ii−ii-11-11i−ii−i−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321-11-1−ii−ii-11-11i−ii−i−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ371-1-111-1-11i−i−iii−i−ii-111-1111-1-111-1-11-1-11-1-111-1-11i−i−iii−i−ii-111-1i−i−iii−i−ii-111-1i−i−iii−i−ii-111-1
χ381-1-111-1-11i−i−iii−i−ii-111-1−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-11i−i−iii−i−ii-111-1ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32
χ391-1-111-1-11i−i−iii−i−ii-111-1−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-11i−i−iii−i−ii-111-1ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32
χ401-1-111-1-11i−i−ii−iii−i1-1-11111-1-111-1-11-1-11-1-111-1-11i−i−ii−iii−i1-1-11i−i−ii−iii−i1-1-11i−i−ii−iii−i1-1-11
χ411-1-111-1-11i−i−ii−iii−i1-1-11−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-11i−i−ii−iii−i1-1-11ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32
χ421-1-111-1-11i−i−ii−iii−i1-1-11−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-11i−i−ii−iii−i1-1-11ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i32
χ431-1-111-1-11−iii−ii−i−ii1-1-11111-1-111-1-11-1-11-1-111-1-11−iii−ii−i−ii1-1-11−iii−ii−i−ii1-1-11−iii−ii−i−ii1-1-11
χ441-1-111-1-11−iii−ii−i−ii1-1-11−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-11−iii−ii−i−ii1-1-11−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32
χ451-1-111-1-11−iii−ii−i−ii1-1-11−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-11−iii−ii−i−ii1-1-11−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32
χ461-1-111-1-11−iii−i−iii−i-111-1111-1-111-1-11-1-11-1-111-1-11−iii−i−iii−i-111-1−iii−i−iii−i-111-1−iii−i−iii−i-111-1
χ471-1-111-1-11−iii−i−iii−i-111-1−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321-1-11−iii−i−iii−i-111-1−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32
χ481-1-111-1-11−iii−i−iii−i-111-1−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321-1-11−iii−i−iii−i-111-1−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i32
χ49333333333333333333330000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ50333333333333-3-3-3-3-3-3-3-30000000000000000-1-1-1-1-1-1-1-111111111000000000000000000000000
χ5133333333-3-3-3-33333-3-3-3-30000000000000000-1-1-1-11111-1-1-1-11111000000000000000000000000
χ5233333333-3-3-3-3-3-3-3-333330000000000000000-1-1-1-111111111-1-1-1-1000000000000000000000000
χ5333-3-333-3-333-3-33i3i−3i−3i3i3i−3i−3i0000000000000000-1-111-1-111−i−iii−i−iii000000000000000000000000
χ5433-3-333-3-333-3-3−3i−3i3i3i−3i−3i3i3i0000000000000000-1-111-1-111ii−i−iii−i−i000000000000000000000000
χ5533-3-333-3-3-3-3333i3i−3i−3i−3i−3i3i3i0000000000000000-1-11111-1-1−i−iiiii−i−i000000000000000000000000
χ5633-3-333-3-3-3-333−3i−3i3i3i3i3i−3i−3i0000000000000000-1-11111-1-1ii−i−i−i−iii000000000000000000000000
χ573-33-33-33-33i−3i3i−3i3-33-33i−3i3i−3i0000000000000000-11-11−ii−ii-11-11−ii−ii000000000000000000000000
χ583-33-33-33-33i−3i3i−3i-33-33−3i3i−3i3i0000000000000000-11-11−ii−ii1-11-1i−ii−i000000000000000000000000
χ593-33-33-33-3−3i3i−3i3i3-33-3−3i3i−3i3i0000000000000000-11-11i−ii−i-11-11i−ii−i000000000000000000000000
χ603-33-33-33-3−3i3i−3i3i-33-333i−3i3i−3i0000000000000000-11-11i−ii−i1-11-1−ii−ii000000000000000000000000
χ613-3-333-3-333i−3i−3i3i3i−3i−3i3i-333-30000000000000000-111-1−iii−i−iii−i1-1-11000000000000000000000000
χ623-3-333-3-333i−3i−3i3i−3i3i3i−3i3-3-330000000000000000-111-1−iii−ii−i−ii-111-1000000000000000000000000
χ633-3-333-3-33−3i3i3i−3i3i−3i−3i3i3-3-330000000000000000-111-1i−i−ii−iii−i-111-1000000000000000000000000
χ643-3-333-3-33−3i3i3i−3i−3i3i3i−3i-333-30000000000000000-111-1i−i−iii−i−ii1-1-11000000000000000000000000
χ65444-4-4-4-44000000000000-2-2222-2222-2-2-22-2-220000000000000000000000000000000000000000
χ66444-4-4-4-440000000000001+i31−i3−1−i3−1−i3−1−i31+i3−1+i3−1+i3−1+i31−i31+i31+i3−1−i31−i31−i3−1+i30000000000000000000000000000000000000000
χ67444-4-4-4-440000000000001−i31+i3−1+i3−1+i3−1+i31−i3−1−i3−1−i3−1−i31+i31−i31−i3−1+i31+i31+i3−1−i30000000000000000000000000000000000000000
χ6844-44-4-44-4000000000000-2-222-2222-22-22-2-22-20000000000000000000000000000000000000000
χ6944-44-4-44-40000000000001+i31−i3−1−i3−1−i31+i3−1−i3−1+i3−1+i31−i3−1+i31+i3−1−i31+i31−i3−1+i31−i30000000000000000000000000000000000000000
χ7044-44-4-44-40000000000001−i31+i3−1+i3−1+i31−i3−1+i3−1−i3−1−i31+i3−1−i31−i3−1+i31−i31+i3−1−i31+i30000000000000000000000000000000000000000
χ714-444-44-4-4000000000000-2-22-2222-2222-2-22-2-20000000000000000000000000000000000000000
χ724-444-44-4-40000000000001+i31−i3−1−i31+i3−1−i3−1−i3−1+i31−i3−1+i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000000000000000000000000000000000000000
χ734-444-44-4-40000000000001−i31+i3−1+i31−i3−1+i3−1+i3−1−i31+i3−1−i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000000000000000000000000000000000000000
χ744-4-4-4-4444000000000000-2-22-2-2-22-2-2-22222220000000000000000000000000000000000000000
χ754-4-4-4-44440000000000001+i31−i3−1−i31+i31+i31+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000000000000000000000000000000000000
χ764-4-4-4-44440000000000001−i31+i3−1+i31−i31−i31−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000000000000000000000000000000000000

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