Finite Group Databasebeta

← Group #13173213

Character table — Group #13173213

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122444444444488888888888899991818181818181818181836363636363611112244444444448888888888889999181818181818181818183636363636361111224444444444888888888888999918181818181818181818363636363636
order12224423346666666666121212121212121244444488888888248888366612126331266666666661212121212121212121212121212242424242424242461224242424366612126331266666666661212121212121212121212121212242424242424242461224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ5111111-111-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1111111-111-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1111111-111-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1
χ6111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii
χ8111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i
χ91111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-11111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-11111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-1
χ101111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-111111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-111111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-11
χ111111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii1111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii1111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii
χ121111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i1111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i1111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i
χ131111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-11-111111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-11-111111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-11-11
χ141111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-11-11111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-11-11111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-11-1
χ151111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-11−iii−i1111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-11−iii−i1111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-11−iii−i
χ161111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-11i−i−ii1111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-11i−i−ii1111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-11i−i−ii
χ1722-2-2000220-2-222-2-20000000000002i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000022-2-2000220-2-222-2-20000000000002i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000022-2-2000220-2-222-2-20000000000002i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ1822-2-2000220-2-222-2-20000000000002i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000022-2-2000220-2-222-2-20000000000002i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000022-2-2000220-2-222-2-20000000000002i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ1922-2-2000220-2-222-2-2000000000000−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000022-2-2000220-2-222-2-2000000000000−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000022-2-2000220-2-222-2-2000000000000−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ2022-2-2000220-2-222-2-2000000000000−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000022-2-2000220-2-222-2-2000000000000−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000022-2-2000220-2-222-2-2000000000000−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ212-22-22i−2i022022-2-2-2-200002i2i−2i−2i00002i−2i−2i2i2-2000000000000002-22-22i−2i022022-2-2-2-200002i2i−2i−2i00002i−2i−2i2i2-2000000000000002-22-22i−2i022022-2-2-2-200002i2i−2i−2i00002i−2i−2i2i2-200000000000000
χ222-22-22i−2i022022-2-2-2-200002i2i−2i−2i0000−2i2i2i−2i-22000000000000002-22-22i−2i022022-2-2-2-200002i2i−2i−2i0000−2i2i2i−2i-22000000000000002-22-22i−2i022022-2-2-2-200002i2i−2i−2i0000−2i2i2i−2i-2200000000000000
χ232-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i00002i−2i−2i2i-22000000000000002-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i00002i−2i−2i2i-22000000000000002-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i00002i−2i−2i2i-2200000000000000
χ242-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i0000−2i2i2i−2i2-2000000000000002-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i0000−2i2i2i−2i2-2000000000000002-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i0000−2i2i2i−2i2-200000000000000
χ252-2-22000220-2-2-2-22200000000000022-2-20000002i−2i2i−2i0000002-2-22000220-2-2-2-22200000000000022-2-20000002i−2i2i−2i0000002-2-22000220-2-2-2-22200000000000022-2-20000002i−2i2i−2i000000
χ262-2-22000220-2-2-2-22200000000000022-2-2000000−2i2i−2i2i0000002-2-22000220-2-2-2-22200000000000022-2-2000000−2i2i−2i2i0000002-2-22000220-2-2-2-22200000000000022-2-2000000−2i2i−2i2i000000
χ272-2-22000220-2-2-2-222000000000000-2-2220000002-2-220000002-2-22000220-2-2-2-222000000000000-2-2220000002-2-220000002-2-22000220-2-2-2-222000000000000-2-2220000002-2-22000000
χ282-2-22000220-2-2-2-222000000000000-2-222000000-222-20000002-2-22000220-2-2-2-222000000000000-2-222000000-222-20000002-2-22000220-2-2-2-222000000000000-2-222000000-222-2000000
χ2944444441-241-21-21-211-2-21-21-211-2-20000000000000000000044444441-241-21-21-211-2-21-21-211-2-20000000000000000000044444441-241-21-21-211-2-21-21-211-2-200000000000000000000
χ304444444-214-21-21-21-2-211-21-21-2-211000000000000000000004444444-214-21-21-21-2-211-21-21-2-211000000000000000000004444444-214-21-21-21-2-211-21-21-2-21100000000000000000000
χ31444444-41-2-41-21-21-2-1-1221-21-2-1-12200000000000000000000444444-41-2-41-21-21-2-1-1221-21-2-1-12200000000000000000000444444-41-2-41-21-21-2-1-1221-21-2-1-12200000000000000000000
χ32444444-4-21-4-21-21-2122-1-1-21-2122-1-100000000000000000000444444-4-21-4-21-21-2122-1-1-21-2122-1-100000000000000000000444444-4-21-4-21-21-2122-1-1-21-2122-1-100000000000000000000
χ334444-4-441-2-41-21-21-211-2-2-12-12-1-122000000000000000000004444-4-441-2-41-21-21-211-2-2-12-12-1-122000000000000000000004444-4-441-2-41-21-21-211-2-2-12-12-1-12200000000000000000000
χ344444-4-44-21-4-21-21-21-2-2112-12-122-1-1000000000000000000004444-4-44-21-4-21-21-21-2-2112-12-122-1-1000000000000000000004444-4-44-21-4-21-21-21-2-2112-12-122-1-100000000000000000000
χ354444-4-4-41-241-21-21-2-1-122-12-1211-2-2000000000000000000004444-4-4-41-241-21-21-2-1-122-12-1211-2-2000000000000000000004444-4-4-41-241-21-21-2-1-122-12-1211-2-200000000000000000000
χ364444-4-4-4-214-21-21-2122-1-12-12-1-2-211000000000000000000004444-4-4-4-214-21-21-2122-1-12-12-1-2-211000000000000000000004444-4-4-4-214-21-21-2122-1-12-12-1-2-21100000000000000000000
χ374-44-44i−4i01-201-2-12-123-300i−2i−i2i3i−3i00000000000000000000004-44-44i−4i01-201-2-12-123-300i−2i−i2i3i−3i00000000000000000000004-44-44i−4i01-201-2-12-123-300i−2i−i2i3i−3i0000000000000000000000
χ384-44-44i−4i01-201-2-12-12-3300i−2i−i2i−3i3i00000000000000000000004-44-44i−4i01-201-2-12-12-3300i−2i−i2i−3i3i00000000000000000000004-44-44i−4i01-201-2-12-12-3300i−2i−i2i−3i3i0000000000000000000000
χ394-44-44i−4i0-210-212-12-1003-3−2ii2i−i003i−3i000000000000000000004-44-44i−4i0-210-212-12-1003-3−2ii2i−i003i−3i000000000000000000004-44-44i−4i0-210-212-12-1003-3−2ii2i−i003i−3i00000000000000000000
χ404-44-44i−4i0-210-212-12-100-33−2ii2i−i00−3i3i000000000000000000004-44-44i−4i0-210-212-12-100-33−2ii2i−i00−3i3i000000000000000000004-44-44i−4i0-210-212-12-100-33−2ii2i−i00−3i3i00000000000000000000
χ414-44-4−4i4i01-201-2-12-123-300−i2ii−2i−3i3i00000000000000000000004-44-4−4i4i01-201-2-12-123-300−i2ii−2i−3i3i00000000000000000000004-44-4−4i4i01-201-2-12-123-300−i2ii−2i−3i3i0000000000000000000000
χ424-44-4−4i4i01-201-2-12-12-3300−i2ii−2i3i−3i00000000000000000000004-44-4−4i4i01-201-2-12-12-3300−i2ii−2i3i−3i00000000000000000000004-44-4−4i4i01-201-2-12-12-3300−i2ii−2i3i−3i0000000000000000000000
χ434-44-4−4i4i0-210-212-12-1003-32i−i−2ii00−3i3i000000000000000000004-44-4−4i4i0-210-212-12-1003-32i−i−2ii00−3i3i000000000000000000004-44-4−4i4i0-210-212-12-1003-32i−i−2ii00−3i3i00000000000000000000
χ444-44-4−4i4i0-210-212-12-100-332i−i−2ii003i−3i000000000000000000004-44-4−4i4i0-210-212-12-100-332i−i−2ii003i−3i000000000000000000004-44-4−4i4i0-210-212-12-100-332i−i−2ii003i−3i00000000000000000000
χ4588-8-80002-40-242-4-240000000000000000000000000000000088-8-80002-40-242-4-240000000000000000000000000000000088-8-80002-40-242-4-2400000000000000000000000000000000
χ4688-8-8000-4204-2-424-20000000000000000000000000000000088-8-8000-4204-2-424-20000000000000000000000000000000088-8-8000-4204-2-424-200000000000000000000000000000000
χ478-8-880002-40-24-242-4000000000000000000000000000000008-8-880002-40-24-242-4000000000000000000000000000000008-8-880002-40-24-242-400000000000000000000000000000000
χ488-8-88000-4204-24-2-42000000000000000000000000000000008-8-88000-4204-24-2-42000000000000000000000000000000008-8-88000-4204-24-2-4200000000000000000000000000000000
χ49111111111111111111111111111111111111111111111111−1+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+i32−1−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
χ501111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1−1+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+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−i321−i321−i321−i321−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−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+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ511111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i−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+i321−i321−i321−i321−i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ141−i321−i32ζ14ζ14−ζ14−ζ14−1−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−i321+i321+i321+i321+i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ221+i321+i32ζ22ζ22−ζ22−ζ22
χ521111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii−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+i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ141−i321−i32−ζ14−ζ14ζ14ζ14−1−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−i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ221+i321+i32−ζ22−ζ22ζ22ζ22
χ53111111-111-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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−i321+i321+i321+i321+i321+i321+i32
χ54111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−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−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ55111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i32−1+i32−ζ14−ζ14ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i32−1−i32−ζ22−ζ22ζ22ζ22
χ56111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i32−1+i32ζ14ζ14−ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i32−1−i32ζ22ζ22−ζ22−ζ22
χ571111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32
χ581111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ591111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+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−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ14−1+i321−i32ζ14−ζ14−ζ14ζ14−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−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+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ22−1−i321+i32ζ22−ζ22−ζ22ζ22
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χ102111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+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+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ103111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i32−1−i32−ζ22−ζ22ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i32−1+i32−ζ14−ζ14ζ14ζ14
χ104111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i32−1−i32ζ22ζ22−ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i32−1+i32ζ14ζ14−ζ14−ζ14
χ1051111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32
χ1061111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ1071111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−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+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ22−1−i321+i32ζ22−ζ22−ζ22ζ22−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+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−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ14−1+i321−i32ζ14−ζ14−ζ14ζ14
χ1081111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−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+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ22−1−i321+i32−ζ22ζ22ζ22−ζ22−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+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−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ14−1+i321−i32−ζ14ζ14ζ14−ζ14
χ1091111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-11-11−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ1101111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-11-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ1111111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-11−iii−i−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ221+i32−1−i32−ζ22ζ22ζ22−ζ22−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ141−i32−1+i32−ζ14ζ14ζ14−ζ14
χ1121111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-11i−i−ii−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ221+i32−1−i32ζ22−ζ22−ζ22ζ22−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ141−i32−1+i32ζ14−ζ14−ζ14ζ14
χ11322-2-2000220-2-222-2-20000000000002i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−1−i3−1−i31+i31+i3000−1−i3−1−i301+i31+i3−1−i3−1−i31+i31+i30000000000002ζ22−2ζ222ζ22−2ζ2200−2ζ72ζ7−2ζ132ζ130000000000−1+i3−1+i31−i31−i3000−1+i3−1+i301−i31−i3−1+i3−1+i31−i31−i30000000000002ζ14−2ζ142ζ14−2ζ1400−2ζ232ζ23−2ζ52ζ50000000000
χ11422-2-2000220-2-222-2-20000000000002i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−1−i3−1−i31+i31+i3000−1−i3−1−i301+i31+i3−1−i3−1−i31+i31+i30000000000002ζ22−2ζ222ζ22−2ζ22002ζ7−2ζ72ζ13−2ζ130000000000−1+i3−1+i31−i31−i3000−1+i3−1+i301−i31−i3−1+i3−1+i31−i31−i30000000000002ζ14−2ζ142ζ14−2ζ14002ζ23−2ζ232ζ5−2ζ50000000000
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χ1182-22-22i−2i022022-2-2-2-200002i2i−2i−2i0000−2i2i2i−2i-2200000000000000−1−i31+i3−1−i31+i32ζ22−2ζ220−1−i3−1−i30−1−i3−1−i31+i31+i31+i31+i300002ζ222ζ22−2ζ22−2ζ220000−2ζ222ζ222ζ22−2ζ221+i3−1−i300000000000000−1+i31−i3−1+i31−i32ζ14−2ζ140−1+i3−1+i30−1+i3−1+i31−i31−i31−i31−i300002ζ142ζ14−2ζ14−2ζ140000−2ζ142ζ142ζ14−2ζ141−i3−1+i300000000000000
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χ1212-2-22000220-2-2-2-22200000000000022-2-20000002i−2i2i−2i000000−1−i31+i31+i3−1−i3000−1−i3−1−i301+i31+i31+i31+i3−1−i3−1−i3000000000000−1−i3−1−i31+i31+i30000002ζ22−2ζ222ζ22−2ζ22000000−1+i31−i31−i3−1+i3000−1+i3−1+i301−i31−i31−i31−i3−1+i3−1+i3000000000000−1+i3−1+i31−i31−i30000002ζ14−2ζ142ζ14−2ζ14000000
χ1222-2-22000220-2-2-2-22200000000000022-2-2000000−2i2i−2i2i000000−1−i31+i31+i3−1−i3000−1−i3−1−i301+i31+i31+i31+i3−1−i3−1−i3000000000000−1−i3−1−i31+i31+i3000000−2ζ222ζ22−2ζ222ζ22000000−1+i31−i31−i3−1+i3000−1+i3−1+i301−i31−i31−i31−i3−1+i3−1+i3000000000000−1+i3−1+i31−i31−i3000000−2ζ142ζ14−2ζ142ζ14000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.