Finite Group Databasebeta

← Group #10713286

Character table — Group #10713286

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order1222222234444444466666668888888812121212121212124488881212121212121212242424242424242424242424242424244444444412121212121212121212121212121212161616161616161616161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91-1111-1-1-11-1-111-1-111-1-1111-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1i−ii−i
χ101-1111-1-1-11-1-111-1-111-1-1111-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ii−ii
χ111-1111-1-1-11-1-111-1-111-1-1111-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ii−ii
χ121-1111-1-1-11-1-111-1-111-1-1111-1-111-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111i−ii−i
χ131-1111-1-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−ii
χ141-1111-1-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−i
χ151-1111-1-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i
χ161-1111-1-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ19222222222-2-22222-2-222222220000000022222222-2-20000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222-2-22222-2-222222220000000022222222-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-2220000-2-22222-2-2000000000000000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-2220000-2-22222-2-20000000000000000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2922222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ31222-2-22-2-222-200002-22-22-2-22-22222-2-2-2-2000000000000002-200002-222-2-222-2-2000000002-22-200002-22-22-22-20000000000000000000000000000
χ32222-2-22-2-222-200002-22-22-2-22-22222-2-2-2-2000000000000002-200002-222-2-222-2-200000000-22-220000-22-22-22-220000000000000000000000000000
χ33222-2-22-2-222-200002-22-22-2-22-2-2-2-2-22222000000000000002-200002-2-2-222-2-2220000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ34222-2-22-2-222-200002-22-22-2-22-2-2-2-2-22222000000000000002-200002-2-2-222-2-222000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ35222-2-22-2-2-12-200002-2-11-111-112222-2-2-2-233−3−333−3−3000000-113−33−3-11-1-111-1-11133−3−333−3−32-22-20000-11-11-11-113−3−333−3−3300000000000000000000
χ36222-2-22-2-2-12-200002-2-11-111-112222-2-2-2-233−3−333−3−3000000-113−33−3-11-1-111-1-11133−3−333−3−3-22-2200001-11-11-11-1−333−3−333−300000000000000000000
χ37222-2-22-2-2-12-200002-2-11-111-112222-2-2-2-2−3−333−3−333000000-11−33−33-11-1-111-1-111−3−333−3−3332-22-20000-11-11-11-11−333−3−333−300000000000000000000
χ38222-2-22-2-2-12-200002-2-11-111-112222-2-2-2-2−3−333−3−333000000-11−33−33-11-1-111-1-111−3−333−3−333-22-2200001-11-11-11-13−3−333−3−3300000000000000000000
χ39222-2-22-2-2-12-200002-2-11-111-11-2-2-2-2222233−3−333−3−3000000-113−33−3-1111-1-111-1-1−3−333−3−33300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii00000000000000000000
χ40222-2-22-2-2-12-200002-2-11-111-11-2-2-2-2222233−3−333−3−3000000-113−33−3-1111-1-111-1-1−3−333−3−3330000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i00000000000000000000
χ41222-2-22-2-2-12-200002-2-11-111-11-2-2-2-22222−3−333−3−333000000-11−33−33-1111-1-111-1-133−3−333−3−300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii00000000000000000000
χ42222-2-22-2-2-12-200002-2-11-111-11-2-2-2-22222−3−333−3−333000000-11−33−33-1111-1-111-1-133−3−333−3−30000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i00000000000000000000
χ4322-22-2-2-222002i−2i2i−2i002-2-22-2-222−22−22−22−22i−2i2i−2i2i−2i2i−2i00−i2i2−i2i2000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ4422-22-2-2-222002i−2i2i−2i002-2-22-2-222−22−22−22−22i−2i2i−2i2i−2i2i−2i00−i2i2−i2i2000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ4522-22-2-2-222002i−2i2i−2i002-2-22-2-22−22−22−22−222i−2i2i−2i2i−2i2i−2i00i2−i2i2−i200000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ4622-22-2-2-222002i−2i2i−2i002-2-22-2-22−22−22−22−222i−2i2i−2i2i−2i2i−2i00i2−i2i2−i200000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ4722-22-2-2-22200−2i2i−2i2i002-2-22-2-222−22−22−22−2−2i2i−2i2i−2i2i−2i2i00i2−i2i2−i2000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ4822-22-2-2-22200−2i2i−2i2i002-2-22-2-222−22−22−22−2−2i2i−2i2i−2i2i−2i2i00i2−i2i2−i2000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ4922-22-2-2-22200−2i2i−2i2i002-2-22-2-22−22−22−22−22−2i2i−2i2i−2i2i−2i2i00−i2i2−i2i200000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ5022-22-2-2-22200−2i2i−2i2i002-2-22-2-22−22−22−22−22−2i2i−2i2i−2i2i−2i2i00−i2i2−i2i200000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ512-2222-2-2-222222-2-2-2-2-2-2222-2-2000000002222-2-2-2-2-22000022-2-222-2-2000000000000000000000000000000000000000022−2−2−2−22222−2−2−2−2220000
χ522-2222-2-2-222222-2-2-2-2-2-2222-2-2000000002222-2-2-2-2-22000022-2-222-2-20000000000000000000000000000000000000000−2−22222−2−2−2−22222−2−20000
χ532-2222-2-2-2222-2-222-2-2-2-2222-2-200000000-2-2-2-222222-200002222-2-2-2-2000000000000000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ542-2222-2-2-2222-2-222-2-2-2-2222-2-200000000-2-2-2-222222-200002222-2-2-2-20000000000000000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ552-2222-2-2-22-2-222-2-222-2-2222-2-2-2-22222-2-22222-2-2-2-22-2-2-222-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ562-2222-2-2-22-2-2-2-22222-2-2222-2-2-2-22222-2-2-2-2-2-22222-2222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ572-2222-2-2-2-1-2-222-2-22211-1-1-11122-2-2-2-222-1-1-1-111112-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ582-2222-2-2-2-1-2-222-2-22211-1-1-11122-2-2-2-222-1-1-1-111112-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ592-2222-2-2-2-1-2-222-2-22211-1-1-111-2-22222-2-2-1-1-1-111112-2-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ602-2222-2-2-2-1-2-222-2-22211-1-1-111-2-22222-2-2-1-1-1-111112-2-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ612-2222-2-2-2-1-2-2-2-2222211-1-1-11122-2-2-2-2221111-1-1-1-1-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ622-2222-2-2-2-1-2-2-2-2222211-1-1-11122-2-2-2-2221111-1-1-1-1-22-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ632-2222-2-2-2-1-2-2-2-2222211-1-1-111-2-22222-2-21111-1-1-1-1-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ642-2222-2-2-2-1-2-2-2-2222211-1-1-111-2-22222-2-21111-1-1-1-1-2222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ652-22-2-2-2222-2200002-2-222-2-2-2222-2-222-2-200000000000000-2200002-222-2-2-2-222000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ662-22-2-2-2222-2200002-2-222-2-2-2222-2-222-2-200000000000000-2200002-222-2-2-2-22200000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ672-22-2-2-2222-2200002-2-222-2-2-22-2-222-2-22200000000000000-2200002-2-2-22222-2-20000000000002-2-22000000002-22-2-22-2200000000000000000000
χ682-22-2-2-2222-2200002-2-222-2-2-22-2-222-2-22200000000000000-2200002-2-2-22222-2-2000000000000-222-200000000-22-222-22-200000000000000000000
χ692-22-2-2-222-1-2200002-21-1-1111-122-2-222-2-233−3−3−3−3330000001-13−3−33-11-1-11111-1-133−3−3−3−3332i−2i−2i2i0000−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i300000000000000000000
χ702-22-2-2-222-1-2200002-21-1-1111-122-2-222-2-233−3−3−3−3330000001-13−3−33-11-1-11111-1-133−3−3−3−333−2i2i2i−2i0000i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i300000000000000000000
χ712-22-2-2-222-1-2200002-21-1-1111-122-2-222-2-2−3−33333−3−30000001-1−333−3-11-1-11111-1-1−3−33333−3−32i−2i−2i2i0000−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i300000000000000000000
χ722-22-2-2-222-1-2200002-21-1-1111-122-2-222-2-2−3−33333−3−30000001-1−333−3-11-1-11111-1-1−3−33333−3−3−2i2i2i−2i0000i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i300000000000000000000
χ732-22-2-2-222-1-2200002-21-1-1111-1-2-222-2-22233−3−3−3−3330000001-13−3−33-1111-1-1-1-111−3−33333−3−300002-2-22−333−33−3−33-11-111-11-100000000000000000000
χ742-22-2-2-222-1-2200002-21-1-1111-1-2-222-2-22233−3−3−3−3330000001-13−3−33-1111-1-1-1-111−3−33333−3−30000-222-23−3−33−333−31-11-1-11-1100000000000000000000
χ752-22-2-2-222-1-2200002-21-1-1111-1-2-222-2-222−3−33333−3−30000001-1−333−3-1111-1-1-1-11133−3−3−3−33300002-2-223−3−33−333−3-11-111-11-100000000000000000000
χ762-22-2-2-222-1-2200002-21-1-1111-1-2-222-2-222−3−33333−3−30000001-1−333−3-1111-1-1-1-11133−3−3−3−3330000-222-2−333−33−3−331-11-1-11-1100000000000000000000
χ772-2-22-222-22002i−2i−2i2i00-22-22-22-22−2−22−222−22i−2i2i−2i−2i2i−2i2i00−i2i2i2−i2000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ782-2-22-222-22002i−2i−2i2i00-22-22-22-22−2−22−222−22i−2i2i−2i−2i2i−2i2i00−i2i2i2−i2000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ792-2-22-222-22002i−2i−2i2i00-22-22-22-2−222−22−2−222i−2i2i−2i−2i2i−2i2i00i2−i2−i2i200000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ802-2-22-222-22002i−2i−2i2i00-22-22-22-2−222−22−2−222i−2i2i−2i−2i2i−2i2i00i2−i2−i2i200000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ812-2-22-222-2200−2i2i2i−2i00-22-22-22-22−2−22−222−2−2i2i−2i2i2i−2i2i−2i00i2−i2−i2i2000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ822-2-22-222-2200−2i2i2i−2i00-22-22-22-22−2−22−222−2−2i2i−2i2i2i−2i2i−2i00i2−i2−i2i2000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ832-2-22-222-2200−2i2i2i−2i00-22-22-22-2−222−22−2−22−2i2i−2i2i2i−2i2i−2i00−i2i2i2−i200000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ842-2-22-222-2200−2i2i2i−2i00-22-22-22-2−222−22−2−22−2i2i−2i2i2i−2i2i−2i00−i2i2i2−i200000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ8544444444-2-4-44444-4-4-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2-4-4000022222222000000000000000000000000000000000000000000000000000000000000
χ8644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2000000002222222244000022-2-2-2-222000000000000000000000000000000000000000000000000000000000000
χ87444-4-44-4-44-440000-444-44-4-44-40000000000000000000000-440000-44000000000000000000000000000000000000000000000000000000000000
χ88444-4-44-4-4-2-440000-44-22-222-22000000002323−23−232323−23−230000002-2−2323−23232-2000000000000000000000000000000000000000000000000000000000000
χ89444-4-44-4-4-2-440000-44-22-222-2200000000−23−232323−23−2323230000002-223−2323−232-2000000000000000000000000000000000000000000000000000000000000
χ9044-44-4-4-44-2004i−4i4i−4i00-222-222-222−2222−2222−2222−22−2i2i−2i2i−2i2i−2i2i00−2i22i2−2i22i200000000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000000000000000
χ9144-44-4-4-44-2004i−4i4i−4i00-222-222-2−2222−2222−2222−2222−2i2i−2i2i−2i2i−2i2i002i2−2i22i2−2i2000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000000000000000
χ9244-44-4-4-44-200−4i4i−4i4i00-222-222-222−2222−2222−2222−222i−2i2i−2i2i−2i2i−2i002i2−2i22i2−2i200000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000000000000000
χ9344-44-4-4-44-200−4i4i−4i4i00-222-222-2−2222−2222−2222−22222i−2i2i−2i2i−2i2i−2i00−2i22i2−2i22i2000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000000000000000
χ9444-4-44-44-440000000044-4-44-4-422−2222−22−2222−2222000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000000000000000
χ9544-4-44-44-440000000044-4-44-4-4−2222−222222−2222−220000000000000000000000−222222−22−222222−220000000000000000000000000000000000000000000000000000
χ9644-4-44-44-4-200000000-2-222-22222−2222−22−2222−2222−2i32i32i3−2i3−2i32i32i3−2i300000000000000−222−2−222−2i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000000000
χ9744-4-44-44-4-200000000-2-222-22222−2222−22−2222−22222i3−2i3−2i32i32i3−2i3−2i32i300000000000000−222−2−222−2−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000000000
χ9844-4-44-44-4-200000000-2-222-222−2222−222222−2222−22−2i32i32i3−2i3−2i32i32i3−2i3000000000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000000000
χ9944-4-44-44-4-200000000-2-222-222−2222−222222−2222−222i3−2i3−2i32i32i3−2i3−2i32i3000000000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000000000
χ1004-4444-4-4-4-24444-4-4-4-422-2-2-22200000000-2-2-2-22222-440000-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ1014-4444-4-4-4-244-4-444-4-422-2-2-222000000002222-2-2-2-24-40000-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-4-44444-40000-44-444-4-4-4400000000000000000000004-40000-44000000000000000000000000000000000000000000000000000000000000
χ1034-44-4-4-444-24-40000-442-2-2222-2000000002323−23−23−23−232323000000-22−232323−232-2000000000000000000000000000000000000000000000000000000000000
χ1044-44-4-4-444-24-40000-442-2-2222-200000000−23−2323232323−23−23000000-2223−23−23232-2000000000000000000000000000000000000000000000000000000000000
χ1054-4-44-444-4-2004i−4i−4i4i002-22-22-2222−22−2222−222222−22−2i2i−2i2i2i−2i2i−2i00−2i22i22i2−2i200000000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000000000000000
χ1064-4-44-444-4-2004i−4i−4i4i002-22-22-22−222222−2222−22−2222−2i2i−2i2i2i−2i2i−2i002i2−2i2−2i22i2000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000000000000000
χ1074-4-44-444-4-200−4i4i4i−4i002-22-22-2222−22−2222−222222−222i−2i2i−2i−2i2i−2i2i002i2−2i2−2i22i200000000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000000000000000
χ1084-4-44-444-4-200−4i4i4i−4i002-22-22-22−222222−2222−22−22222i−2i2i−2i−2i2i−2i2i00−2i22i22i2−2i2000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000000000000000
χ1094-4-4-444-44400000000-4-4-4-444422−22−222222−22−2222000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000000000000000
χ1104-4-4-444-44400000000-4-4-4-4444−222222−22−222222−220000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000000000000000
χ1114-4-4-444-44-2000000002222-2-2-222−22−222222−22−2222−2i32i32i3−2i32i3−2i3−2i32i300000000000000−222−22−2−22i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000000000000000
χ1124-4-4-444-44-2000000002222-2-2-222−22−222222−22−22222i3−2i3−2i32i3−2i32i32i3−2i300000000000000−222−22−2−22−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000000000000000
χ1134-4-4-444-44-2000000002222-2-2-2−222222−22−222222−22−2i32i32i3−2i32i3−2i3−2i32i3000000000000002−2−22−222−2−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000000000000000
χ1144-4-4-444-44-2000000002222-2-2-2−222222−22−222222−222i3−2i3−2i32i3−2i32i32i3−2i3000000000000002−2−22−222−2i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.