Finite Group Databasebeta

← Group #13167613

Character table — Group #13167613

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112488888888991836363636367272727211248888888899183636363636727272721124888888889918363636363672727272
order124836121224242424224448884444361224361212242424246612121224242412121212361224361212242424246612121224242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111111111111111111111-1-1-1-111111111111111111111-1-1-1-1
χ3111111111111111-1-11-1-111-1-1111111111111111-1-11-1-111-1-1111111111111111-1-11-1-111-1-1
χ4111111111111111-1-11-1-1-1-111111111111111111-1-11-1-1-1-111111111111111111-1-11-1-1-1-111
χ5111-11111-1-1-1-111111-1-1-11-11-1111-11111-1-1-1-111111-1-1-11-11-1111-11111-1-1-1-111111-1-1-11-11-1
χ6111-11111-1-1-1-111111-1-1-1-11-11111-11111-1-1-1-111111-1-1-1-11-11111-11111-1-1-1-111111-1-1-1-11-11
χ7111-11111-1-1-1-1111-1-1-1111-1-11111-11111-1-1-1-1111-1-1-1111-1-11111-11111-1-1-1-1111-1-1-1111-1-11
χ8111-11111-1-1-1-1111-1-1-111-111-1111-11111-1-1-1-1111-1-1-111-111-1111-11111-1-1-1-1111-1-1-111-111-1
χ9222222222222-2-2-200-2000000222222222222-2-2-200-2000000222222222222-2-2-200-2000000
χ10222-22222-2-2-2-2-2-2-2002000000222-22222-2-2-2-2-2-2-2002000000222-22222-2-2-2-2-2-2-2002000000
χ1122-2022-2-2000022-22-2000000022-2022-2-2000022-22-2000000022-2022-2-2000022-22-20000000
χ1222-2022-2-2000022-2-22000000022-2022-2-2000022-2-22000000022-2022-2-2000022-2-220000000
χ1322-2022-2-20000-2-220002-2000022-2022-2-20000-2-220002-2000022-2022-2-20000-2-220002-20000
χ1422-2022-2-20000-2-22000-22000022-2022-2-20000-2-22000-22000022-2022-2-20000-2-22000-220000
χ154-4004-40000004-400000000004-4004-40000004-400000000004-4004-40000004-40000000000
χ164-4004-4000000-4400000000004-4004-4000000-4400000000004-4004-4000000-440000000000
χ178888-1-1-1-1-1-1-1-10000000000008888-1-1-1-1-1-1-1-10000000000008888-1-1-1-1-1-1-1-1000000000000
χ18888-8-1-1-1-11111000000000000888-8-1-1-1-11111000000000000888-8-1-1-1-11111000000000000
χ1988-80-1-1113i3i−3i−3i00000000000088-80-1-1113i3i−3i−3i00000000000088-80-1-1113i3i−3i−3i000000000000
χ2088-80-1-111−3i−3i3i3i00000000000088-80-1-111−3i−3i3i3i00000000000088-80-1-111−3i−3i3i3i000000000000
χ218-800-113i−3i3ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ130000000000008-800-113i−3i3ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ130000000000008-800-113i−3i3ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000
χ228-800-113i−3i−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ130000000000008-800-113i−3i−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ130000000000008-800-113i−3i−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000
χ238-800-11−3i3i3ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ230000000000008-800-11−3i3i3ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ230000000000008-800-11−3i3i3ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000
χ248-800-11−3i3i−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ230000000000008-800-11−3i3i−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ230000000000008-800-11−3i3i−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000
χ25111111111111111111111111−1+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+i32−1−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
χ2611111111111111111111-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i32
χ27111111111111111-1-11-1-111-1-1−1+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+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ28111111111111111-1-11-1-1-1-111−1+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+i321−i321−i32−1+i321−i321−i321−i321−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−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ29111-11111-1-1-1-111111-1-1-11-11-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32
χ30111-11111-1-1-1-111111-1-1-1-11-11−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32
χ31111-11111-1-1-1-1111-1-1-1111-1-11−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ32111-11111-1-1-1-1111-1-1-111-111-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ33222222222222-2-2-200-2000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3001−i3000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3001+i3000000
χ34222-22222-2-2-2-2-2-2-2002000000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i300−1+i3000000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i300−1−i3000000
χ3522-2022-2-2000022-22-20000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i30000−1+i3−1+i31−i3−1+i31−i30000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i30000−1−i3−1−i31+i3−1−i31+i30000000
χ3622-2022-2-2000022-2-220000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i30000−1+i3−1+i31−i31−i3−1+i30000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i30000−1−i3−1−i31+i31+i3−1−i30000000
χ3722-2022-2-20000-2-220002-20000−1+i3−1+i31−i30−1+i3−1+i31−i31−i300001−i31−i3−1+i3000−1+i31−i30000−1−i3−1−i31+i30−1−i3−1−i31+i31+i300001+i31+i3−1−i3000−1−i31+i30000
χ3822-2022-2-20000-2-22000-220000−1+i3−1+i31−i30−1+i3−1+i31−i31−i300001−i31−i3−1+i30001−i3−1+i30000−1−i3−1−i31+i30−1−i3−1−i31+i31+i300001+i31+i3−1−i30001+i3−1−i30000
χ394-4004-40000004-40000000000−2+2i32−2i300−2+2i32−2i3000000−2+2i32−2i30000000000−2−2i32+2i300−2−2i32+2i3000000−2−2i32+2i30000000000
χ404-4004-4000000-440000000000−2+2i32−2i300−2+2i32−2i30000002−2i3−2+2i30000000000−2−2i32+2i300−2−2i32+2i30000002+2i3−2−2i30000000000
χ418888-1-1-1-1-1-1-1-1000000000000−4+4i3−4+4i3−4+4i3−4+4i31−i321−i321−i321−i321−i321−i321−i321−i32000000000000−4−4i3−4−4i3−4−4i3−4−4i31+i321+i321+i321+i321+i321+i321+i321+i32000000000000
χ42888-8-1-1-1-11111000000000000−4+4i3−4+4i3−4+4i34−4i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000−4−4i3−4−4i3−4−4i34+4i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ4388-80-1-1113i3i−3i−3i000000000000−4+4i3−4+4i34−4i301−i321−i32−1+i32−1+i323ζ143ζ14−3ζ14−3ζ14000000000000−4−4i3−4−4i34+4i301+i321+i32−1−i32−1−i323ζ223ζ22−3ζ22−3ζ22000000000000
χ4488-80-1-111−3i−3i3i3i000000000000−4+4i3−4+4i34−4i301−i321−i32−1+i32−1+i32−3ζ14−3ζ143ζ143ζ14000000000000−4−4i3−4−4i34+4i301+i321+i32−1−i32−1−i32−3ζ22−3ζ223ζ223ζ22000000000000
χ458-800-113i−3i3ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000−4+4i34−4i3001−i32−1+i323ζ14−3ζ14−3ζ233ζ23−3ζ53ζ5000000000000−4−4i34+4i3001+i32−1−i323ζ22−3ζ22−3ζ73ζ7−3ζ133ζ13000000000000
χ468-800-113i−3i−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000−4+4i34−4i3001−i32−1+i323ζ14−3ζ143ζ23−3ζ233ζ5−3ζ5000000000000−4−4i34+4i3001+i32−1−i323ζ22−3ζ223ζ7−3ζ73ζ13−3ζ13000000000000
χ478-800-11−3i3i3ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000−4+4i34−4i3001−i32−1+i32−3ζ143ζ14−3ζ53ζ5−3ζ233ζ23000000000000−4−4i34+4i3001+i32−1−i32−3ζ223ζ22−3ζ133ζ13−3ζ73ζ7000000000000
χ488-800-11−3i3i−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000−4+4i34−4i3001−i32−1+i32−3ζ143ζ143ζ5−3ζ53ζ23−3ζ23000000000000−4−4i34+4i3001+i32−1−i32−3ζ223ζ223ζ13−3ζ133ζ7−3ζ7000000000000
χ49111111111111111111111111−1−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−i32−1+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
χ5011111111111111111111-1-1-1-1−1−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i32
χ51111111111111111-1-11-1-111-1-1−1−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−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ52111111111111111-1-11-1-1-1-111−1−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−i321+i321+i32−1−i321+i321+i321+i321+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+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ53111-11111-1-1-1-111111-1-1-11-11-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32
χ54111-11111-1-1-1-111111-1-1-1-11-11−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32
χ55111-11111-1-1-1-1111-1-1-1111-1-11−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ56111-11111-1-1-1-1111-1-1-111-111-1−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ57222222222222-2-2-200-2000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3001+i3000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3001−i3000000
χ58222-22222-2-2-2-2-2-2-2002000000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i300−1−i3000000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i300−1+i3000000
χ5922-2022-2-2000022-22-20000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i30000−1−i3−1−i31+i3−1−i31+i30000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i30000−1+i3−1+i31−i3−1+i31−i30000000
χ6022-2022-2-2000022-2-220000000−1−i3−1−i31+i30−1−i3−1−i31+i31+i30000−1−i3−1−i31+i31+i3−1−i30000000−1+i3−1+i31−i30−1+i3−1+i31−i31−i30000−1+i3−1+i31−i31−i3−1+i30000000
χ6122-2022-2-20000-2-220002-20000−1−i3−1−i31+i30−1−i3−1−i31+i31+i300001+i31+i3−1−i3000−1−i31+i30000−1+i3−1+i31−i30−1+i3−1+i31−i31−i300001−i31−i3−1+i3000−1+i31−i30000
χ6222-2022-2-20000-2-22000-220000−1−i3−1−i31+i30−1−i3−1−i31+i31+i300001+i31+i3−1−i30001+i3−1−i30000−1+i3−1+i31−i30−1+i3−1+i31−i31−i300001−i31−i3−1+i30001−i3−1+i30000
χ634-4004-40000004-40000000000−2−2i32+2i300−2−2i32+2i3000000−2−2i32+2i30000000000−2+2i32−2i300−2+2i32−2i3000000−2+2i32−2i30000000000
χ644-4004-4000000-440000000000−2−2i32+2i300−2−2i32+2i30000002+2i3−2−2i30000000000−2+2i32−2i300−2+2i32−2i30000002−2i3−2+2i30000000000
χ658888-1-1-1-1-1-1-1-1000000000000−4−4i3−4−4i3−4−4i3−4−4i31+i321+i321+i321+i321+i321+i321+i321+i32000000000000−4+4i3−4+4i3−4+4i3−4+4i31−i321−i321−i321−i321−i321−i321−i321−i32000000000000
χ66888-8-1-1-1-11111000000000000−4−4i3−4−4i3−4−4i34+4i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000−4+4i3−4+4i3−4+4i34−4i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ6788-80-1-1113i3i−3i−3i000000000000−4−4i3−4−4i34+4i301+i321+i32−1−i32−1−i323ζ223ζ22−3ζ22−3ζ22000000000000−4+4i3−4+4i34−4i301−i321−i32−1+i32−1+i323ζ143ζ14−3ζ14−3ζ14000000000000
χ6888-80-1-111−3i−3i3i3i000000000000−4−4i3−4−4i34+4i301+i321+i32−1−i32−1−i32−3ζ22−3ζ223ζ223ζ22000000000000−4+4i3−4+4i34−4i301−i321−i32−1+i32−1+i32−3ζ14−3ζ143ζ143ζ14000000000000
χ698-800-113i−3i3ζ7+3ζ23−3ζ7−3ζ233ζ5+3ζ13−3ζ5−3ζ13000000000000−4−4i34+4i3001+i32−1−i323ζ22−3ζ22−3ζ73ζ7−3ζ133ζ13000000000000−4+4i34−4i3001−i32−1+i323ζ14−3ζ14−3ζ233ζ23−3ζ53ζ5000000000000
χ708-800-113i−3i−3ζ7−3ζ233ζ7+3ζ23−3ζ5−3ζ133ζ5+3ζ13000000000000−4−4i34+4i3001+i32−1−i323ζ22−3ζ223ζ7−3ζ73ζ13−3ζ13000000000000−4+4i34−4i3001−i32−1+i323ζ14−3ζ143ζ23−3ζ233ζ5−3ζ5000000000000
χ718-800-11−3i3i3ζ5+3ζ13−3ζ5−3ζ133ζ7+3ζ23−3ζ7−3ζ23000000000000−4−4i34+4i3001+i32−1−i32−3ζ223ζ22−3ζ133ζ13−3ζ73ζ7000000000000−4+4i34−4i3001−i32−1+i32−3ζ143ζ14−3ζ53ζ5−3ζ233ζ23000000000000
χ728-800-11−3i3i−3ζ5−3ζ133ζ5+3ζ13−3ζ7−3ζ233ζ7+3ζ23000000000000−4−4i34+4i3001+i32−1−i32−3ζ223ζ223ζ13−3ζ133ζ7−3ζ7000000000000−4+4i34−4i3001−i32−1+i32−3ζ143ζ143ζ5−3ζ53ζ23−3ζ23000000000000

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