Finite Group Databasebeta

← Group #11923408

Character table — Group #11923408

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222444444444444666688888888888888121212121212121212121212121216161616161616161616161616161616363636364848484848484848
order122344612122334666661212122244336666121212121212121224446666881212121266666666121212121212121222881212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111−1−i32−1+i321111−1−i32−1+i321111111−1−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+i3211111111111111−1−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−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ41111111111−1−i32−1+i321111−1−i32−1+i321111111−1−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+i3211-1-11111-1-11111−1−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+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ51111111111−1+i32−1−i321111−1+i32−1−i321111111−1+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−i3211111111111111−1+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+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ61111111111−1+i32−1−i321111−1+i32−1−i321111111−1+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−i3211-1-11111-1-11111−1+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−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ7111111111-111-11-1-1111-1-1111111111111111111-1-11111-1-1-1-111-1-1-1-11-1-11-1-1-1-11-1-11-1-111-1-11111-1-1-1-1
χ8111111111-111-11-1-1111-1-1111111111111111111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-11-1-11-1-1-1-111-1-1-1-11111
χ9111111111-1−1−i32−1+i32-11-1-1−1−i32−1+i321-1-11111−1−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+i32-1-11111-1-1-1-111-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ10111111111-1−1−i32−1+i32-11-1-1−1−i32−1+i321-1-11111−1−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+i32-1-1-1-111-1-11111-1-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ11111111111-1−1+i32−1−i32-11-1-1−1+i32−1−i321-1-11111−1+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−i32-1-11111-1-1-1-111-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ12111111111-1−1+i32−1−i32-11-1-1−1+i32−1−i321-1-11111−1+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−i32-1-1-1-111-1-11111-1-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311-11-111-1-1111-1-111111-1-11-11-111-1-111-1-1-1-1-1-111-111-11-1-1-11-11-11111-111-111-1-11-1-11-1-11-11-11-11-11-11-1
χ1411-11-111-1-1111-1-111111-1-11-11-111-1-111-1-1-1-1-1-111-11-111-1-1-1-111-11111-111-111-1-11-1-11-1-1-11-11-11-11-11-11
χ1511-11-111-1-11−1−i32−1+i32-1-111−1−i32−1+i321-1-11-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32-111-11-1-1-11-11-111−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ1611-11-111-1-11−1−i32−1+i32-1-111−1−i32−1+i321-1-11-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32-11-111-1-1-1-111-111−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1711-11-111-1-11−1+i32−1−i32-1-111−1+i32−1−i321-1-11-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32-111-11-1-1-11-11-111−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ1811-11-111-1-11−1+i32−1−i32-1-111−1+i32−1−i321-1-11-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32-11-111-1-1-1-111-111−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1911-11-111-1-1-1111-1-1-1111111-11-111-1-111-1-1-1-1-1-1111-11-11-111-111-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-11-1-11-11
χ2011-11-111-1-1-1111-1-1-1111111-11-111-1-111-1-1-1-1-1-1111-1-111-1111-11-1-1-1-1-1-1-1-1-1-1-111111111-111-1-11-111-11-1
χ2111-11-111-1-1-1−1−i32−1+i321-1-1-1−1−i32−1+i321111-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321-11-11-111-111-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ2211-11-111-1-1-1−1−i32−1+i321-1-1-1−1−i32−1+i321111-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321-1-111-1111-11-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ2311-11-111-1-1-1−1+i32−1−i321-1-1-1−1+i32−1−i321111-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321-11-11-111-111-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ2411-11-111-1-1-1−1+i32−1−i321-1-1-1−1+i32−1−i321111-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321-1-111-1111-11-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ252222-2-22-2-2022020022-200-2-222222222-2-2-2-2-2-2-2-20000-2-2000022000020020000-200-200000000000000
χ262222-2-22-2-20−1−i3−1+i30200−1−i3−1+i3-200-2-222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i31+i31+i31−i31−i31+i31−i30000-2-20000220000−1−i300−1+i300001+i3001−i300000000000000
χ272222-2-22-2-20−1+i3−1−i30200−1+i3−1−i3-200-2-222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i31−i31−i31+i31+i31−i31+i30000-2-20000220000−1+i300−1−i300001−i3001+i300000000000000
χ28222-122-1-1-12222-1-1-122-1-1-12222-1-122-1-122-1-1-1-1222200-1-1-1-100-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ29222-122-1-1-12−1−i3−1+i32-1-1-1−1−i3−1+i3-1-1-122221+i321−i32−1−i3−1+i31+i321−i32−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i32200-1-1-1-100-1-1-1-1−1−i3−1+i31+i321+i321+i321−i321−i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i32000000000000
χ30222-122-1-1-12−1+i3−1−i32-1-1-1−1+i3−1−i3-1-1-122221−i321+i32−1+i3−1−i31−i321+i32−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i32200-1-1-1-100-1-1-1-1−1+i3−1−i31−i321−i321−i321+i321+i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i32000000000000
χ31222-122-1-1-1-222-2-11122-1112222-1-122-1-122-1-1-1-122-2-200-1-11100-1-111-2-2-111-111-2-2-111-111000000000000
χ32222-122-1-1-1-2−1−i3−1+i3-2-111−1−i3−1+i3-11122221+i321−i32−1−i3−1+i31+i321−i32−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i3-2-200-1-11100-1-1111+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i32000000000000
χ33222-122-1-1-1-2−1+i3−1−i3-2-111−1+i3−1−i3-11122221−i321+i32−1+i3−1−i31−i321+i32−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i3-2-200-1-11100-1-1111−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i32000000000000
χ34222-1-2-2-1110220-1−i3i3221−i3i3-2-222-1-122-1-1-2-21111-2-2000011−i3i300-1-1−i3i300-1−i3i3-1−i3i3001−i3i31−i3i3000000000000
χ35222-1-2-2-1110220-1i3−i3221i3−i3-2-222-1-122-1-1-2-21111-2-2000011i3−i300-1-1i3−i300-1i3−i3-1i3−i3001i3−i31i3−i3000000000000
χ36222-1-2-2-1110−1−i3−1+i30-1−i3i3−1−i3−1+i31−i3i3-2-2221+i321−i32−1−i3−1+i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i31−i3000011−i3i300-1-1−i3i3001+i32−3+i323−i321−i323+i32−3−i3200−1−i32−3+i323−i32−1+i323+i32−3−i32000000000000
χ37222-1-2-2-1110−1−i3−1+i30-1i3−i3−1−i3−1+i31i3−i3-2-2221+i321−i32−1−i3−1+i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i31−i3000011i3−i300-1-1i3−i3001+i323−i32−3+i321−i32−3−i323+i3200−1−i323−i32−3+i32−1+i32−3−i323+i32000000000000
χ38222-1-2-2-1110−1+i3−1−i30-1−i3i3−1+i3−1−i31−i3i3-2-2221−i321+i32−1+i3−1−i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i31+i3000011−i3i300-1-1−i3i3001−i323+i32−3−i321+i32−3+i323−i3200−1+i323+i32−3−i32−1−i32−3+i323−i32000000000000
χ39222-1-2-2-1110−1+i3−1−i30-1i3−i3−1+i3−1−i31i3−i3-2-2221−i321+i32−1+i3−1−i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i31+i3000011i3−i300-1-1i3−i3001−i32−3−i323+i321+i323−i32−3+i3200−1+i32−3−i323+i32−1−i323−i32−3+i32000000000000
χ4022-222-22220220-20022-200-222-222-2-222222222-2-20000-2200002-20000-200-20000-200-200000000000000
χ4122-222-22220−1−i3−1+i30-200−1−i3−1+i3-200-222-2−1−i3−1+i31+i31−i3−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i30000-2200002-200001+i3001−i300001+i3001−i300000000000000
χ4222-222-22220−1+i3−1−i30-200−1+i3−1−i3-200-222-2−1+i3−1−i31−i31+i3−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i30000-2200002-200001−i3001+i300001−i3001+i300000000000000
χ4322-2-12-2-1-1-102201−i3i3221i3−i3-222-2-1-1-2-2-1-122-1-1-1-1-2-200001-1i3−i300-11−i3i3001−i3i31−i3i3001i3−i31i3−i3000000000000
χ4422-2-12-2-1-1-102201i3−i3221−i3i3-222-2-1-1-2-2-1-122-1-1-1-1-2-200001-1−i3i300-11i3−i3001i3−i31i3−i3001−i3i31−i3i3000000000000
χ4522-2-12-2-1-1-10−1−i3−1+i301−i3i3−1−i3−1+i31i3−i3-222-21+i321−i321+i31−i31+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i31−i300001-1i3−i300-11−i3i300−1−i32−3+i323−i32−1+i323+i32−3−i3200−1−i323−i32−3+i32−1+i32−3−i323+i32000000000000
χ4622-2-12-2-1-1-10−1−i3−1+i301i3−i3−1−i3−1+i31−i3i3-222-21+i321−i321+i31−i31+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i31−i300001-1−i3i300-11i3−i300−1−i323−i32−3+i32−1+i32−3−i323+i3200−1−i32−3+i323−i32−1+i323+i32−3−i32000000000000
χ4722-2-12-2-1-1-10−1+i3−1−i301−i3i3−1+i3−1−i31i3−i3-222-21−i321+i321−i31+i31−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i31+i300001-1i3−i300-11−i3i300−1+i323+i32−3−i32−1−i32−3+i323−i3200−1+i32−3−i323+i32−1−i323−i32−3+i32000000000000
χ4822-2-12-2-1-1-10−1+i3−1−i301i3−i3−1+i3−1−i31−i3i3-222-21−i321+i321−i31+i31−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i31+i300001-1−i3i300-11i3−i300−1+i32−3−i323+i32−1−i323−i32−3+i3200−1+i323+i32−3−i32−1−i32−3+i323−i32000000000000
χ4922-2-1-22-111222-21-1-122-1112-22-2-1-1-2-2-1-1-2-2111122-2200-111100-11-1-1221-1-11-1-1-2-2-111-111000000000000
χ5022-2-1-22-1112−1−i3−1+i3-21-1-1−1−i3−1+i3-1112-22-21+i321−i321+i31−i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-2200-111100-11-1-1−1−i3−1+i3−1−i321+i321+i32−1+i321−i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i32000000000000
χ5122-2-1-22-1112−1+i3−1−i3-21-1-1−1+i3−1−i3-1112-22-21−i321+i321−i31+i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-2200-111100-11-1-1−1+i3−1−i3−1+i321−i321−i32−1−i321+i321+i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i32000000000000
χ5222-2-1-22-111-222211122-1-1-12-22-2-1-1-2-2-1-1-2-21111222-200-11-1-100-1111-2-211111122-1-1-1-1-1-1000000000000
χ5322-2-1-22-111-2−1−i3−1+i32111−1−i3−1+i3-1-1-12-22-21+i321−i321+i31−i31+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i32-200-11-1-100-11111+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i3−1+i31+i321+i321+i321−i321−i321−i32000000000000
χ5422-2-1-22-111-2−1+i3−1−i32111−1+i3−1−i3-1-1-12-22-21−i321+i321−i31+i31−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i32-200-11-1-100-11111−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i3−1−i31−i321−i321−i321+i321+i321+i32000000000000
χ55333333333300333300333-1-1-1-100000000000000-1-133-1-1-1-133-1-1-1-10000000000000000-1-1-1-100000000
χ56333333333300333300333-1-1-1-100000000000000-1-1-3-3-1-1-1-1-3-3-1-1-1-10000000000000000111100000000
χ57333333333-300-33-3-3003-3-3-1-1-1-1000000000000001133-1-111-3-3-1-1110000000000000000-1-11100000000
χ58333333333-300-33-3-3003-3-3-1-1-1-10000000000000011-3-3-1-11133-1-111000000000000000011-1-100000000
χ5933-33-333-3-3300-3-333003-3-3-11-11000000000000001-13-3-11113-3-11-1-10000000000000000-11-1100000000
χ6033-33-333-3-3300-3-333003-3-3-11-11000000000000001-1-33-1111-33-11-1-100000000000000001-11-100000000
χ6133-33-333-3-3-3003-3-3-300333-11-1100000000000000-113-3-11-1-1-33-11110000000000000000-111-100000000
χ6233-33-333-3-3-3003-3-3-300333-11-1100000000000000-11-33-11-1-13-3-111100000000000000001-1-1100000000
χ636666-6-66-6-6000060000-60022-2-2000000000000000000220000-2-2000000000000000000000000000000
χ64666-366-3-3-36006-3-3-300-3-3-3-2-2-2-200000000000000-2-20011110011110000000000000000000000000000
χ65666-366-3-3-3-600-6-33300-333-2-2-2-200000000000000220011-1-10011-1-10000000000000000000000000000
χ66666-3-6-6-3330000-3−3i33i3003−3i33i322-2-2000000000000000000-1-1i3−i30011i3−i30000000000000000000000000000
χ67666-3-6-6-3330000-33i3−3i30033i3−3i322-2-2000000000000000000-1-1−i3i30011−i3i30000000000000000000000000000
χ6866-666-66660000-60000-6002-2-220000000000000000002-20000-22000000000000000000000000000000
χ6966-6-36-6-3-3-300003−3i33i30033i3−3i32-2-22000000000000000000-11−i3i3001-1i3−i30000000000000000000000000000
χ7066-6-36-6-3-3-3000033i3−3i3003−3i33i32-2-22000000000000000000-11i3−i3001-1−i3i30000000000000000000000000000
χ7166-6-3-66-333600-63-3-300-333-22-22000000000000002-2001-1-1-1001-1110000000000000000000000000000
χ7266-6-3-66-333-600633300-3-3-3-22-2200000000000000-22001-111001-1-1-10000000000000000000000000000
χ738-80800-8000-4-40000440000000-4-4004400000000000000000000000000000000000000000000000000
χ748-80800-80002+2i32−2i30000−2−2i3−2+2i300000002+2i32−2i300−2−2i3−2+2i300000000000000000000000000000000000000000000000000
χ758-80800-80002−2i32+2i30000−2+2i3−2−2i300000002−2i32+2i300−2+2i3−2−2i300000000000000000000000000000000000000000000000000
χ768-80-400443−430-4-400004400000002200-2-20023−2323−2300000000000000000000000000000000000000000000
χ778-80-400443−4302+2i32−2i30000−2−2i3−2+2i30000000−1−i3−1+i3001+i31−i3004ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ1100000000000000000000000000000000000000000000
χ788-80-400443−4302−2i32+2i30000−2+2i3−2−2i30000000−1+i3−1−i3001−i31+i300−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ1100000000000000000000000000000000000000000000
χ798-80-4004−43430-4-400004400000002200-2-200−2323−232300000000000000000000000000000000000000000000
χ808-80-4004−434302+2i32−2i30000−2−2i3−2+2i30000000−1−i3−1+i3001+i31−i300−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ1100000000000000000000000000000000000000000000
χ818-80-4004−434302−2i32+2i30000−2+2i3−2−2i30000000−1+i3−1−i3001−i31+i3002ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ1100000000000000000000000000000000000000000000

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