Finite Group Databasebeta

← Group #13166812

Character table — Group #13166812

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122444444444444881212121212121212121212121212121218181818242424243636363611112244444444444488121212121212121212121212121212121818181824242424363636361111224444444444448812121212121212121212121212121212181818182424242436363636
order122244336666661212121212124444444412121212121212124444121212128888366612123366666612121212121212121212121212121212121212121212121212121212121224242424366612123366666612121212121212121212121212121212121212121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ61111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ81111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ91-1-11i−i11-1-111-1-1ii−i−ii−ii−ii−i1-11-1ii−i−i11-1-1i−i1-11-1i−i1-1i−i1-1-11i−i11-1-111-1-1ii−i−ii−ii−ii−i1-11-1ii−i−i11-1-1i−i1-11-1i−i1-1i−i1-1-11i−i11-1-111-1-1ii−i−ii−ii−ii−i1-11-1ii−i−i11-1-1i−i1-11-1i−i1-1i−i
χ101-1-11i−i11-1-111-1-1ii−i−ii−ii−i−ii1-1-11−i−iii-1-111i−i1-11-1i−i-11−ii1-1-11i−i11-1-111-1-1ii−i−ii−ii−i−ii1-1-11−i−iii-1-111i−i1-11-1i−i-11−ii1-1-11i−i11-1-111-1-1ii−i−ii−ii−i−ii1-1-11−i−iii-1-111i−i1-11-1i−i-11−ii
χ111-1-11i−i11-1-111-1-1ii−i−ii−i−iii−i-111-1ii−i−i11-1-1i−i1-1-11−ii-11−ii1-1-11i−i11-1-111-1-1ii−i−ii−i−iii−i-111-1ii−i−i11-1-1i−i1-1-11−ii-11−ii1-1-11i−i11-1-111-1-1ii−i−ii−i−iii−i-111-1ii−i−i11-1-1i−i1-1-11−ii-11−ii
χ121-1-11i−i11-1-111-1-1ii−i−ii−i−ii−ii-11-11−i−iii-1-111i−i1-1-11−ii1-1i−i1-1-11i−i11-1-111-1-1ii−i−ii−i−ii−ii-11-11−i−iii-1-111i−i1-1-11−ii1-1i−i1-1-11i−i11-1-111-1-1ii−i−ii−i−ii−ii-11-11−i−iii-1-111i−i1-1-11−ii1-1i−i
χ131-1-11−ii11-1-111-1-1−i−iii−iii−ii−i-11-11ii−i−i-1-111−ii1-1-11i−i1-1−ii1-1-11−ii11-1-111-1-1−i−iii−iii−ii−i-11-11ii−i−i-1-111−ii1-1-11i−i1-1−ii1-1-11−ii11-1-111-1-1−i−iii−iii−ii−i-11-11ii−i−i-1-111−ii1-1-11i−i1-1−ii
χ141-1-11−ii11-1-111-1-1−i−iii−iii−i−ii-111-1−i−iii11-1-1−ii1-1-11i−i-11i−i1-1-11−ii11-1-111-1-1−i−iii−iii−i−ii-111-1−i−iii11-1-1−ii1-1-11i−i-11i−i1-1-11−ii11-1-111-1-1−i−iii−iii−i−ii-111-1−i−iii11-1-1−ii1-1-11i−i-11i−i
χ151-1-11−ii11-1-111-1-1−i−iii−ii−iii−i1-1-11ii−i−i-1-111−ii1-11-1−ii-11i−i1-1-11−ii11-1-111-1-1−i−iii−ii−iii−i1-1-11ii−i−i-1-111−ii1-11-1−ii-11i−i1-1-11−ii11-1-111-1-1−i−iii−ii−iii−i1-1-11ii−i−i-1-111−ii1-11-1−ii-11i−i
χ161-1-11−ii11-1-111-1-1−i−iii−ii−ii−ii1-11-1−i−iii11-1-1−ii1-11-1−ii1-1−ii1-1-11−ii11-1-111-1-1−i−iii−ii−ii−ii1-11-1−i−iii11-1-1−ii1-11-1−ii1-1−ii1-1-11−ii11-1-111-1-1−i−iii−ii−ii−ii1-11-1−i−iii11-1-1−ii1-11-1−ii1-1−ii
χ17222222222222222222220000000000000000-2-2-2-200000000222222222222222222220000000000000000-2-2-2-200000000222222222222222222220000000000000000-2-2-2-200000000
χ182222-2-222222222-2-2-2-2-2-2000000000000000022-2-2000000002222-2-222222222-2-2-2-2-2-2000000000000000022-2-2000000002222-2-222222222-2-2-2-2-2-2000000000000000022-2-200000000
χ192-2-222i−2i22-2-222-2-22i2i−2i−2i2i−2i0000000000000000−2i2i-22000000002-2-222i−2i22-2-222-2-22i2i−2i−2i2i−2i0000000000000000−2i2i-22000000002-2-222i−2i22-2-222-2-22i2i−2i−2i2i−2i0000000000000000−2i2i-2200000000
χ202-2-22−2i2i22-2-222-2-2−2i−2i2i2i−2i2i00000000000000002i−2i-22000000002-2-22−2i2i22-2-222-2-2−2i−2i2i2i−2i2i00000000000000002i−2i-22000000002-2-22−2i2i22-2-222-2-2−2i−2i2i2i−2i2i00000000000000002i−2i-2200000000
χ214444441-21-21-2-21-2-2-2-21122002200000000000000-1-1-1-100004444441-21-21-2-21-2-2-2-21122002200000000000000-1-1-1-100004444441-21-21-2-21-2-2-2-21122002200000000000000-1-1-1-10000
χ224444441-21-21-2-21-2-2-2-211-2-200-2-200000000000000111100004444441-21-21-2-21-2-2-2-211-2-200-2-200000000000000111100004444441-21-21-2-21-2-2-2-211-2-200-2-20000000000000011110000
χ23444444-21-21-211-21111-2-200220022-1-1-1-1-1-1-1-1000000000000444444-21-21-211-21111-2-200220022-1-1-1-1-1-1-1-1000000000000444444-21-21-211-21111-2-200220022-1-1-1-1-1-1-1-1000000000000
χ24444444-21-21-211-21111-2-200-2-200-2-211111111000000000000444444-21-21-211-21111-2-200-2-200-2-211111111000000000000444444-21-21-211-21111-2-200-2-200-2-211111111000000000000
χ254444-4-41-21-21-2-212222-1-12200-2-20000000000000011-1-100004444-4-41-21-21-2-212222-1-12200-2-20000000000000011-1-100004444-4-41-21-21-2-212222-1-12200-2-20000000000000011-1-10000
χ264444-4-41-21-21-2-212222-1-1-2-2002200000000000000-1-11100004444-4-41-21-21-2-212222-1-1-2-2002200000000000000-1-11100004444-4-41-21-21-2-212222-1-1-2-2002200000000000000-1-1110000
χ274444-4-4-21-21-211-2-1-1-1-122002200-2-2-1-1-1-111110000000000004444-4-4-21-21-211-2-1-1-1-122002200-2-2-1-1-1-111110000000000004444-4-4-21-21-211-2-1-1-1-122002200-2-2-1-1-1-11111000000000000
χ284444-4-4-21-21-211-2-1-1-1-12200-2-200221111-1-1-1-10000000000004444-4-4-21-21-211-2-1-1-1-12200-2-200221111-1-1-1-10000000000004444-4-4-21-21-211-2-1-1-1-12200-2-200221111-1-1-1-1000000000000
χ2944-4-40044-44-4-4-44000000000000000000000000000000000044-4-40044-44-4-4-44000000000000000000000000000000000044-4-40044-44-4-4-440000000000000000000000000000000000
χ3044-4-400-21212-1-1-23-33-300000000003−33−33−33−300000000000044-4-400-21212-1-1-23-33-300000000003−33−33−33−300000000000044-4-400-21212-1-1-23-33-300000000003−33−33−33−3000000000000
χ3144-4-400-21212-1-1-23-33-30000000000−33−33−33−3300000000000044-4-400-21212-1-1-23-33-30000000000−33−33−33−3300000000000044-4-400-21212-1-1-23-33-30000000000−33−33−33−33000000000000
χ3244-4-400-21212-1-1-2-33-3300000000003−33−3−33−3300000000000044-4-400-21212-1-1-2-33-3300000000003−33−3−33−3300000000000044-4-400-21212-1-1-2-33-3300000000003−33−3−33−33000000000000
χ3344-4-400-21212-1-1-2-33-330000000000−33−333−33−300000000000044-4-400-21212-1-1-2-33-330000000000−33−333−33−300000000000044-4-400-21212-1-1-2-33-330000000000−33−333−33−3000000000000
χ344-44-400444-4-4-44-400000000000000000000000000000000004-44-400444-4-4-44-400000000000000000000000000000000004-44-400444-4-4-44-40000000000000000000000000000000000
χ354-44-400-21-2-12-1123i−3i−3i3i0000000000−i3i3i3−i3−333−30000000000004-44-400-21-2-12-1123i−3i−3i3i0000000000−i3i3i3−i3−333−30000000000004-44-400-21-2-12-1123i−3i−3i3i0000000000−i3i3i3−i3−333−3000000000000
χ364-44-400-21-2-12-1123i−3i−3i3i0000000000i3−i3−i3i33−3−330000000000004-44-400-21-2-12-1123i−3i−3i3i0000000000i3−i3−i3i33−3−330000000000004-44-400-21-2-12-1123i−3i−3i3i0000000000i3−i3−i3i33−3−33000000000000
χ374-44-400-21-2-12-112−3i3i3i−3i0000000000−i3i3i3−i33−3−330000000000004-44-400-21-2-12-112−3i3i3i−3i0000000000−i3i3i3−i33−3−330000000000004-44-400-21-2-12-112−3i3i3i−3i0000000000−i3i3i3−i33−3−33000000000000
χ384-44-400-21-2-12-112−3i3i3i−3i0000000000i3−i3−i3i3−333−30000000000004-44-400-21-2-12-112−3i3i3i−3i0000000000i3−i3−i3i3−333−30000000000004-44-400-21-2-12-112−3i3i3i−3i0000000000i3−i3−i3i3−333−3000000000000
χ394-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i2i−2i002-200000000000000-11−ii00004-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i2i−2i002-200000000000000-11−ii00004-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i2i−2i002-200000000000000-11−ii0000
χ404-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i−2i2i00-22000000000000001-1i−i00004-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i−2i2i00-22000000000000001-1i−i00004-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i−2i2i00-22000000000000001-1i−i0000
χ414-4-444i−4i-212-1-21-12ii−i−i−2i2i002i−2i002-2−i−iii-1-1110000000000004-4-444i−4i-212-1-21-12ii−i−i−2i2i002i−2i002-2−i−iii-1-1110000000000004-4-444i−4i-212-1-21-12ii−i−i−2i2i002i−2i002-2−i−iii-1-111000000000000
χ424-4-444i−4i-212-1-21-12ii−i−i−2i2i00−2i2i00-22ii−i−i11-1-10000000000004-4-444i−4i-212-1-21-12ii−i−i−2i2i00−2i2i00-22ii−i−i11-1-10000000000004-4-444i−4i-212-1-21-12ii−i−i−2i2i00−2i2i00-22ii−i−i11-1-1000000000000
χ434-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii2i−2i00-22000000000000001-1−ii00004-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii2i−2i00-22000000000000001-1−ii00004-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii2i−2i00-22000000000000001-1−ii0000
χ444-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii−2i2i002-200000000000000-11i−i00004-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii−2i2i002-200000000000000-11i−i00004-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii−2i2i002-200000000000000-11i−i0000
χ454-4-44−4i4i-212-1-21-12−i−iii2i−2i002i−2i00-22−i−iii11-1-10000000000004-4-44−4i4i-212-1-21-12−i−iii2i−2i002i−2i00-22−i−iii11-1-10000000000004-4-44−4i4i-212-1-21-12−i−iii2i−2i002i−2i00-22−i−iii11-1-1000000000000
χ464-4-44−4i4i-212-1-21-12−i−iii2i−2i00−2i2i002-2ii−i−i-1-1110000000000004-4-44−4i4i-212-1-21-12−i−iii2i−2i00−2i2i002-2ii−i−i-1-1110000000000004-4-44−4i4i-212-1-21-12−i−iii2i−2i00−2i2i002-2ii−i−i-1-111000000000000
χ4788-8-8002-4-2-4-2442000000000000000000000000000000000088-8-8002-4-2-4-2442000000000000000000000000000000000088-8-8002-4-2-4-24420000000000000000000000000000000000
χ488-88-8002-424-24-4-200000000000000000000000000000000008-88-8002-424-24-4-200000000000000000000000000000000008-88-8002-424-24-4-20000000000000000000000000000000000
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
χ501111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−1+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+i321−i321−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+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−i321+i321+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−i321+i321+i321+i321+i32
χ5111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1−1+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−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+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ5211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−1+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+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ531111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ541111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ551111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−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−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+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+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
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χ10011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−1−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−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ1011111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ1021111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ1031111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+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+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−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−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ1041111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ1051-1-11i−i11-1-111-1-1ii−i−ii−ii−ii−i1-11-1ii−i−i11-1-1i−i1-11-1i−i1-1i−i−1−i321+i321+i32−1−i32ζ11−ζ11−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1−i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1+i321−i321−i32−1+i32ζ7−ζ7−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1+i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7
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χ119444444-21-21-211-21111-2-200220022-1-1-1-1-1-1-1-1000000000000−2−2i3−2−2i3−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i32−1−i321+i31+i300−1−i3−1−i300−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32000000000000−2+2i3−2+2i3−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i32−1+i321−i31−i300−1+i3−1+i300−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32000000000000
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χ1234444-4-4-21-21-211-2-1-1-1-122002200-2-2-1-1-1-11111000000000000−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i321+i321+i321+i32−1−i3−1−i300−1−i3−1−i3001+i31+i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i321−i321−i321−i32−1+i3−1+i300−1+i3−1+i3001−i31−i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ1244444-4-4-21-21-211-2-1-1-1-12200-2-200221111-1-1-1-1000000000000−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i321+i321+i321+i32−1−i3−1−i3001+i31+i300−1−i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32000000000000−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i321−i321−i321−i32−1+i3−1+i3001−i31−i300−1+i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32000000000000
χ12544-4-40044-44-4-4-440000000000000000000000000000000000−2−2i3−2−2i32+2i32+2i300−2−2i3−2−2i32+2i3−2−2i32+2i32+2i32+2i3−2−2i30000000000000000000000000000000000−2+2i3−2+2i32−2i32−2i300−2+2i3−2+2i32−2i3−2+2i32−2i32−2i32−2i3−2+2i30000000000000000000000000000000000
χ12644-4-400-21212-1-1-23-33-300000000003−33−33−33−3000000000000−2−2i3−2−2i32+2i32+2i3001+i3−1−i32−1−i3−1−i32−1−i31+i321+i321+i3−3−3i323+3i32−3−3i323+3i3200000000002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11000000000000−2+2i3−2+2i32−2i32−2i3001−i3−1+i32−1+i3−1+i32−1+i31−i321−i321−i3−3+3i323−3i32−3+3i323−3i320000000000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ12744-4-400-21212-1-1-23-33-30000000000−33−33−33−33000000000000−2−2i3−2−2i32+2i32+2i3001+i3−1−i32−1−i3−1−i32−1−i31+i321+i321+i3−3−3i323+3i32−3−3i323+3i320000000000−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i3−2+2i32−2i32−2i3001−i3−1+i32−1+i3−1+i32−1+i31−i321−i321−i3−3+3i323−3i32−3+3i323−3i320000000000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ12844-4-400-21212-1-1-2-33-3300000000003−33−3−33−33000000000000−2−2i3−2−2i32+2i32+2i3001+i3−1−i32−1−i3−1−i32−1−i31+i321+i321+i33+3i32−3−3i323+3i32−3−3i3200000000002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i3−2+2i32−2i32−2i3001−i3−1+i32−1+i3−1+i32−1+i31−i321−i321−i33−3i32−3+3i323−3i32−3+3i320000000000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
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χ1304-44-400444-4-4-44-40000000000000000000000000000000000−2−2i32+2i3−2−2i32+2i300−2−2i3−2−2i3−2−2i32+2i32+2i32+2i3−2−2i32+2i30000000000000000000000000000000000−2+2i32−2i3−2+2i32−2i300−2+2i3−2+2i3−2+2i32−2i32−2i32−2i3−2+2i32−2i30000000000000000000000000000000000
χ1314-44-400-21-2-12-1123i−3i−3i3i0000000000−i3i3i3−i3−333−3000000000000−2−2i32+2i3−2−2i32+2i3001+i3−1−i321+i31+i32−1−i31+i32−1−i32−1−i33ζ11−3ζ11−3ζ113ζ110000000000−3+i323−i323−i32−3+i32−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i3−2+2i32−2i3001−i3−1+i321−i31−i32−1+i31−i32−1+i32−1+i33ζ7−3ζ7−3ζ73ζ700000000003+i32−3−i32−3−i323+i32ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ1324-44-400-21-2-12-1123i−3i−3i3i0000000000i3−i3−i3i33−3−33000000000000−2−2i32+2i3−2−2i32+2i3001+i3−1−i321+i31+i32−1−i31+i32−1−i32−1−i33ζ11−3ζ11−3ζ113ζ1100000000003−i32−3+i32−3+i323−i322ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i3−2+2i32−2i3001−i3−1+i321−i31−i32−1+i31−i32−1+i32−1+i33ζ7−3ζ7−3ζ73ζ70000000000−3−i323+i323+i32−3−i32−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ1334-44-400-21-2-12-112−3i3i3i−3i0000000000−i3i3i3−i33−3−33000000000000−2−2i32+2i3−2−2i32+2i3001+i3−1−i321+i31+i32−1−i31+i32−1−i32−1−i3−3ζ113ζ113ζ11−3ζ110000000000−3+i323−i323−i32−3+i322ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i3−2+2i32−2i3001−i3−1+i321−i31−i32−1+i31−i32−1+i32−1+i3−3ζ73ζ73ζ7−3ζ700000000003+i32−3−i32−3−i323+i32−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
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χ1354-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i2i−2i002-200000000000000-11−ii0000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ11−1−i321+i31+i32−1−i3−1−i321+i3−1−i31+i32−2ζ11−2ζ112ζ112ζ11ζ11−ζ112ζ11−2ζ1100−1−i31+i3000000000000001+i32−1−i32−ζ11ζ110000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ7−1+i321−i31−i32−1+i3−1+i321−i3−1+i31−i32−2ζ7−2ζ72ζ72ζ7ζ7−ζ72ζ7−2ζ700−1+i31−i3000000000000001−i32−1+i32−ζ7ζ70000
χ1364-4-444i−4i1-2-121-22-1−2i−2i2i2ii−i−2i2i00-22000000000000001-1i−i0000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ11−1−i321+i31+i32−1−i3−1−i321+i3−1−i31+i32−2ζ11−2ζ112ζ112ζ11ζ11−ζ11−2ζ112ζ11001+i3−1−i300000000000000−1−i321+i32ζ11−ζ110000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ7−1+i321−i31−i32−1+i3−1+i321−i3−1+i31−i32−2ζ7−2ζ72ζ72ζ7ζ7−ζ7−2ζ72ζ7001−i3−1+i300000000000000−1+i321−i32ζ7−ζ70000
χ1374-4-444i−4i-212-1-21-12ii−i−i−2i2i002i−2i002-2−i−iii-1-111000000000000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ111+i3−1−i32−1−i31+i321+i3−1−i321+i32−1−i3ζ11ζ11−ζ11−ζ11−2ζ112ζ11002ζ11−2ζ1100−1−i31+i3−ζ11−ζ11ζ11ζ111+i321+i32−1−i32−1−i32000000000000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ71−i3−1+i32−1+i31−i321−i3−1+i321−i32−1+i3ζ7ζ7−ζ7−ζ7−2ζ72ζ7002ζ7−2ζ700−1+i31−i3−ζ7−ζ7ζ7ζ71−i321−i32−1+i32−1+i32000000000000
χ1384-4-444i−4i-212-1-21-12ii−i−i−2i2i00−2i2i00-22ii−i−i11-1-1000000000000−2−2i32+2i32+2i3−2−2i34ζ11−4ζ111+i3−1−i32−1−i31+i321+i3−1−i321+i32−1−i3ζ11ζ11−ζ11−ζ11−2ζ112ζ1100−2ζ112ζ11001+i3−1−i3ζ11ζ11−ζ11−ζ11−1−i32−1−i321+i321+i32000000000000−2+2i32−2i32−2i3−2+2i34ζ7−4ζ71−i3−1+i32−1+i31−i321−i3−1+i321−i32−1+i3ζ7ζ7−ζ7−ζ7−2ζ72ζ700−2ζ72ζ7001−i3−1+i3ζ7ζ7−ζ7−ζ7−1+i32−1+i321−i321−i32000000000000
χ1394-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii2i−2i00-22000000000000001-1−ii0000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ11−1−i321+i31+i32−1−i3−1−i321+i3−1−i31+i322ζ112ζ11−2ζ11−2ζ11−ζ11ζ112ζ11−2ζ11001+i3−1−i300000000000000−1−i321+i32−ζ11ζ110000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ7−1+i321−i31−i32−1+i3−1+i321−i3−1+i31−i322ζ72ζ7−2ζ7−2ζ7−ζ7ζ72ζ7−2ζ7001−i3−1+i300000000000000−1+i321−i32−ζ7ζ70000
χ1404-4-44−4i4i1-2-121-22-12i2i−2i−2i−ii−2i2i002-200000000000000-11i−i0000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ11−1−i321+i31+i32−1−i3−1−i321+i3−1−i31+i322ζ112ζ11−2ζ11−2ζ11−ζ11ζ11−2ζ112ζ1100−1−i31+i3000000000000001+i32−1−i32ζ11−ζ110000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ7−1+i321−i31−i32−1+i3−1+i321−i3−1+i31−i322ζ72ζ7−2ζ7−2ζ7−ζ7ζ7−2ζ72ζ700−1+i31−i3000000000000001−i32−1+i32ζ7−ζ70000
χ1414-4-44−4i4i-212-1-21-12−i−iii2i−2i002i−2i00-22−i−iii11-1-1000000000000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ111+i3−1−i32−1−i31+i321+i3−1−i321+i32−1−i3−ζ11−ζ11ζ11ζ112ζ11−2ζ11002ζ11−2ζ11001+i3−1−i3−ζ11−ζ11ζ11ζ11−1−i32−1−i321+i321+i32000000000000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ71−i3−1+i32−1+i31−i321−i3−1+i321−i32−1+i3−ζ7−ζ7ζ7ζ72ζ7−2ζ7002ζ7−2ζ7001−i3−1+i3−ζ7−ζ7ζ7ζ7−1+i32−1+i321−i321−i32000000000000
χ1424-4-44−4i4i-212-1-21-12−i−iii2i−2i00−2i2i002-2ii−i−i-1-111000000000000−2−2i32+2i32+2i3−2−2i3−4ζ114ζ111+i3−1−i32−1−i31+i321+i3−1−i321+i32−1−i3−ζ11−ζ11ζ11ζ112ζ11−2ζ1100−2ζ112ζ1100−1−i31+i3ζ11ζ11−ζ11−ζ111+i321+i32−1−i32−1−i32000000000000−2+2i32−2i32−2i3−2+2i3−4ζ74ζ71−i3−1+i32−1+i31−i321−i3−1+i321−i32−1+i3−ζ7−ζ7ζ7ζ72ζ7−2ζ700−2ζ72ζ700−1+i31−i3ζ7ζ7−ζ7−ζ71−i321−i32−1+i32−1+i32000000000000
χ14388-8-8002-4-2-4-24420000000000000000000000000000000000−4−4i3−4−4i34+4i34+4i300−1−i32+2i31+i32+2i31+i3−2−2i3−2−2i3−1−i30000000000000000000000000000000000−4+4i3−4+4i34−4i34−4i300−1+i32−2i31−i32−2i31−i3−2+2i3−2+2i3−1+i30000000000000000000000000000000000
χ1448-88-8002-424-24-4-20000000000000000000000000000000000−4−4i34+4i3−4−4i34+4i300−1−i32+2i3−1−i3−2−2i31+i3−2−2i32+2i31+i30000000000000000000000000000000000−4+4i34−4i3−4+4i34−4i300−1+i32−2i3−1+i3−2+2i31−i3−2+2i32−2i31−i30000000000000000000000000000000000

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