Finite Group Databasebeta

← Group #11721636

Character table — Group #11721636

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1122333366666699999911223333666666999999224466661212121212121818181818182244666612121212121218181818181822446666121212121212181818181818
order123633663336664412121212226666666666664412121212226666666666664412121212226666666666664412121212441212121212121212121212124412121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ31111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ41111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32
χ51111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ61111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32
χ71-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i
χ81-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii
χ91-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ7
χ101-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ7
χ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ11
χ121-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ11
χ1322222222-1-1-1-1-1-100000022222222-1-1-1-1-1-100000022222222-1-1-1-1-1-100000022222222-1-1-1-1-1-100000022222222-1-1-1-1-1-1000000
χ142222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i32000000
χ152222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i32000000
χ162-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-1111000000
χ172-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i32000000
χ182-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i32000000
χ1966-3-3000000000000000066-3-3000000000000000066-3-3000000000000000066-3-3000000000000000066-3-30000000000000000
χ206-6-3300000000000000006-6-3300000000000000006-6-3300000000000000006-6-3300000000000000006-6-330000000000000000
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ231111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32
χ241111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32
χ251111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32
χ261111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32
χ271-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i1-11-111-1-1111-1-1-1i−ii−ii−i-11-11-1-111-1-1-1111−ii−ii−ii-11-11-1-111-1-1-1111−ii−ii−ii
χ281-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii1-11-111-1-1111-1-1-1−ii−ii−ii-11-11-1-111-1-1-1111i−ii−ii−i-11-11-1-111-1-1-1111i−ii−ii−i
χ291-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32i−iζ11−ζ11ζ7−ζ7-11-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32−ii−ζ11ζ11−ζ7ζ7-11-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32−ii−ζ11ζ11−ζ7ζ7
χ301-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ71-11-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32−ii−ζ11ζ11−ζ7ζ7-11-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32i−iζ11−ζ11ζ7−ζ7-11-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32i−iζ11−ζ11ζ7−ζ7
χ311-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32i−iζ7−ζ7ζ11−ζ11-11-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32−ii−ζ7ζ7−ζ11ζ11-11-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32−ii−ζ7ζ7−ζ11ζ11
χ321-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ111-11-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32−ii−ζ7ζ7−ζ11ζ11-11-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32i−iζ7−ζ7ζ11−ζ11-11-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32i−iζ7−ζ7ζ11−ζ11
χ3322222222-1-1-1-1-1-100000022222222-1-1-1-1-1-100000022222222-1-1-1-1-1-1000000-2-2-2-2-2-2-2-2111111000000-2-2-2-2-2-2-2-2111111000000
χ342222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i320000002222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i32000000-2-2-2-21+i31−i31+i31−i31−1−i32−1+i321−1−i32−1+i32000000-2-2-2-21+i31−i31+i31−i31−1−i32−1+i321−1−i32−1+i32000000
χ352222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i320000002222−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i32000000-2-2-2-21−i31+i31−i31+i31−1+i32−1−i321−1+i32−1−i32000000-2-2-2-21−i31+i31−i31+i31−1+i32−1−i321−1+i32−1−i32000000
χ362-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-11110000002-22-222-2-2-1-1-1111000000-22-22-2-222111-1-1-1000000-22-22-2-222111-1-1-1000000
χ372-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i320000002-22-2−1−i3−1+i31+i31−i3-11+i321−i321−1−i32−1+i32000000-22-221+i31−i3−1−i3−1+i31−1−i32−1+i32-11+i321−i32000000-22-221+i31−i3−1−i3−1+i31−1−i32−1+i32-11+i321−i32000000
χ382-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i320000002-22-2−1+i3−1−i31−i31+i3-11−i321+i321−1+i32−1−i32000000-22-221−i31+i3−1+i3−1−i31−1+i32−1−i32-11−i321+i32000000-22-221−i31+i3−1+i3−1−i31−1+i32−1−i32-11−i321+i32000000
χ3966-3-3000000000000000066-3-3000000000000000066-3-30000000000000000-6-6330000000000000000-6-6330000000000000000
χ406-6-3300000000000000006-6-3300000000000000006-6-330000000000000000-663-30000000000000000-663-30000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4211111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ431111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32
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χ451111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32
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χ892-22-2−1−i3−1+i31+i31−i32−1−i3−1+i3-21+i31−i32i−2i2ζ11−2ζ112ζ7−2ζ7-22-221+i31−i3−1−i3−1+i3-21+i31−i32−1−i3−1+i3−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000000000000000000000000000000000
χ902-22-2−1−i3−1+i31+i31−i32−1−i3−1+i3-21+i31−i3−2i2i−2ζ112ζ11−2ζ72ζ7-22-221+i31−i3−1−i3−1+i3-21+i31−i32−1−i3−1+i32i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000000000000000000000000000000000
χ912-22-2−1+i3−1−i31−i31+i32−1+i3−1−i3-21−i31+i32i−2i2ζ7−2ζ72ζ11−2ζ11-22-221−i31+i3−1+i3−1−i3-21−i31+i32−1+i3−1−i3−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000000000000000000000000000000000
χ922-22-2−1+i3−1−i31−i31+i32−1+i3−1−i3-21−i31+i3−2i2i−2ζ72ζ7−2ζ112ζ11-22-221−i31+i3−1+i3−1−i3-21−i31+i32−1+i3−1−i32i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000000000000000000000000000000000
χ9344444444-2-2-2-2-2-2000000-4-4-4-4-4-4-4-4222222000000000000000000000000000000000000000000000000000000000000000000
χ944444−2−2i3−2+2i3−2−2i3−2+2i3-21+i31−i3-21+i31−i3000000-4-4-4-42+2i32−2i32+2i32−2i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000000000000000000000000000000000000000
χ954444−2+2i3−2−2i3−2+2i3−2−2i3-21−i31+i3-21−i31+i3000000-4-4-4-42−2i32+2i32−2i32+2i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000000000000000000000000000000000000000
χ964-44-444-4-4-2-2-2222000000-44-44-4-444222-2-2-2000000000000000000000000000000000000000000000000000000000000000000
χ974-44-4−2−2i3−2+2i32+2i32−2i3-21+i31−i32−1−i3−1+i3000000-44-442+2i32−2i3−2−2i3−2+2i32−1−i3−1+i3-21+i31−i3000000000000000000000000000000000000000000000000000000000000000000
χ984-44-4−2+2i3−2−2i32−2i32+2i3-21−i31+i32−1+i3−1−i3000000-44-442−2i32+2i3−2+2i3−2−2i32−1+i3−1−i3-21−i31+i3000000000000000000000000000000000000000000000000000000000000000000
χ991212-6-60000000000000000-12-12660000000000000000000000000000000000000000000000000000000000000000000000000000
χ10012-12-660000000000000000-12126-60000000000000000000000000000000000000000000000000000000000000000000000000000

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