Finite Group Databasebeta

← Group #11709366

Character table — Group #11709366

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222244444444444444444444444466668888888888888888888888881212121212121616161616161616161616161616161624242424
order1222444444448888888822334466666688881212121212121212224412121212121212122424242424242424242424242424242444888866661212121224242424242424242488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111−1−i32−1+i3211−1−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+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+i32111111−1−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
χ31111111111111111111111−1+i32−1−i3211−1+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−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−i32111111−1+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
χ411111111111111111111-1-111-1-1111111-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111111111-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1−1−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−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+i321111111+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1
χ611111111111111111111-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1−1+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+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−i321111111−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1
χ7111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ8111111111111-1-1-1-1-1-1-1-111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i3211-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1
χ9111111111111-1-1-1-1-1-1-1-111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i3211-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-1-1−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i3211-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-1-1−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i3211-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111
χ131111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1111111ii−i−i-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1111-1-1-1-1ii−i−iii−i−i-11i−i
χ141111-1-1-1-111-1-1iiii−i−i−i−i11−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32ii−i−i1+i321+i321−i321−i321+i321+i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ141-1ii−i−i−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11i−i
χ151111-1-1-1-111-1-1iiii−i−i−i−i11−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32ii−i−i1−i321−i321+i321+i321−i321−i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ221-1ii−i−i−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11i−i
χ161111-1-1-1-111-1-1iiii−i−i−i−i-1-11111111111−i−iii-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i-1-1-1-11111−i−iii−i−iii1-1−ii
χ171111-1-1-1-111-1-1iiii−i−i−i−i-1-1−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−i−iii1+i321+i321−i321−i321+i321+i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ141-1ii−i−i1+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ141-1−ii
χ181111-1-1-1-111-1-1iiii−i−i−i−i-1-1−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−i−iii1−i321−i321+i321+i321−i321−i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ221-1ii−i−i1−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ221-1−ii
χ191111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1111111−i−iii-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1111-1-1-1-1−i−iii−i−iii-11−ii
χ201111-1-1-1-111-1-1−i−i−i−iiiii11−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−i−iii1+i321+i321−i321−i321+i321+i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ141-1−i−iii−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11−ii
χ211111-1-1-1-111-1-1−i−i−i−iiiii11−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−i−iii1−i321−i321+i321+i321−i321−i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ221-1−i−iii−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11−ii
χ221111-1-1-1-111-1-1−i−i−i−iiiii-1-11111111111ii−i−i-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii-1-1-1-11111ii−i−iii−i−i1-1i−i
χ231111-1-1-1-111-1-1−i−i−i−iiiii-1-1−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32ii−i−i1+i321+i321−i321−i321+i321+i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ141-1−i−iii1+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141-1i−i
χ241111-1-1-1-111-1-1−i−i−i−iiiii-1-1−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32ii−i−i1−i321−i321+i321+i321−i321−i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ221-1−i−iii1−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221-1i−i
χ2522222222-2-2-2-2000000000022002222220000222222222222-2-2-2-2-2-2-2-20000000000000000-2-2000000000000000000000000
χ2622222222-2-2-2-20000000000−1−i3−1+i300−1−i3−1−i3−1+i3−1+i3−1−i3−1+i30000−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i322221+i31+i31−i31−i31+i31+i31−i31−i30000000000000000-2-2000000000000000000000000
χ2722222222-2-2-2-20000000000−1+i3−1−i300−1+i3−1+i3−1−i3−1−i3−1+i3−1−i30000−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i322221−i31−i31+i31+i31−i31−i31+i31+i30000000000000000-2-2000000000000000000000000
χ282222-2-2-2-2-2-222000000000022002222220000-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000-22000000000000000000000000
χ292222-2-2-2-2-2-2220000000000−1−i3−1+i300−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300001+i31+i31−i31−i31+i31+i31−i31−i3-2-2221+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i30000000000000000-22000000000000000000000000
χ302222-2-2-2-2-2-2220000000000−1+i3−1−i300−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300001−i31−i31+i31+i31−i31−i31+i31+i3-2-2221−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i30000000000000000-22000000000000000000000000
χ3122-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-2-1-12i−2i1-11-1112ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13i−ii−ii−ii−i00001-11-1i−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000001-11-1i−ii−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ3222-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-21+i321−i322i−2i−1−i321+i32−1+i321−i32−1−i32−1+i322ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ζ22−ζ22ζ14−ζ14ζ22−ζ22ζ14−ζ140000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14−ζ7−ζ7ζ7ζ7ζ13ζ13−ζ13−ζ13−ζ23−ζ23ζ23ζ23ζ5ζ5−ζ5−ζ5000000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ50000
χ3322-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-21−i321+i322i−2i−1+i321−i32−1−i321+i32−1+i32−1−i322ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ζ14−ζ14ζ22−ζ22ζ14−ζ14ζ22−ζ220000−1+i321−i32−1−i321+i32ζ14−ζ14ζ22−ζ22−ζ23−ζ23ζ23ζ23ζ5ζ5−ζ5−ζ5−ζ7−ζ7ζ7ζ7ζ13ζ13−ζ13−ζ13000000−1+i321−i32−1−i321+i32ζ14−ζ14ζ22−ζ22−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ130000
χ3422-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13-22-1-1−2i2i1-11-111−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13i−ii−ii−ii−i00001-11-1i−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000-11-11−ii−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ3522-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13-221+i321−i32−2i2i−1−i321+i32−1+i321−i32−1−i32−1+i32−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ22−ζ22ζ14−ζ14ζ22−ζ22ζ14−ζ140000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14−ζ7−ζ7ζ7ζ7ζ13ζ13−ζ13−ζ13−ζ23−ζ23ζ23ζ23ζ5ζ5−ζ5−ζ50000001+i32−1−i321−i32−1+i32−ζ22ζ22−ζ14ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ50000
χ3622-2-22i−2i2i−2i2-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13-221−i321+i32−2i2i−1+i321−i32−1−i321+i32−1+i32−1−i32−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ14−ζ14ζ22−ζ22ζ14−ζ14ζ22−ζ220000−1+i321−i32−1−i321+i32ζ14−ζ14ζ22−ζ22−ζ23−ζ23ζ23ζ23ζ5ζ5−ζ5−ζ5−ζ7−ζ7ζ7ζ7ζ13ζ13−ζ13−ζ130000001−i32−1+i321+i32−1−i32−ζ14ζ14−ζ22ζ22ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ130000
χ3722-2-22i−2i2i−2i2-22i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132-2-1-12i−2i1-11-111−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13i−ii−ii−ii−i00001-11-1i−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000001-11-1i−ii−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ3822-2-22i−2i2i−2i2-22i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132-21+i321−i322i−2i−1−i321+i32−1+i321−i32−1−i32−1+i32−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ22−ζ22ζ14−ζ14ζ22−ζ22ζ14−ζ140000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14ζ7ζ7−ζ7−ζ7−ζ13−ζ13ζ13ζ13ζ23ζ23−ζ23−ζ23−ζ5−ζ5ζ5ζ5000000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ50000
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χ9366666666-6-6-6-600000000000000000000000000000000-2-2-2-200000000000000000000000022000000000000000000000000
χ946666-6-6-6-6-6-6660000000000000000000000000000000022-2-20000000000000000000000002-2000000000000000000000000
χ956-6-6666-6-60000−3i23i2−3i23i2−3i23i2−3i23i2000000000000000000000000-22-2200000000000000000000000000i2−i2i2−i200000000000000000000
χ966-6-6666-6-600003i2−3i23i2−3i23i2−3i23i2−3i2000000000000000000000000-22-2200000000000000000000000000−i2i2−i2i200000000000000000000
χ976-6-66-6-666000032−3232−32−3232−32320000000000000000000000002-2-2200000000000000000000000000−222−200000000000000000000
χ986-6-66-6-6660000−3232−323232−3232−320000000000000000000000002-2-22000000000000000000000000002−2−2200000000000000000000

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