Finite Group Databasebeta

← Group #13167057

Character table — Group #13167057

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363672727272108108108108
order124423466612121212333366666666661212121212121212121212121212366661212121212224466666666666666661212121212121212121212121212121222446688881212242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ51111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-11-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-11-111-1-11-111-1-111-1-1
χ61111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-11-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-11-1-1-1111-1-1-111-1-111
χ71111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1-11-11-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-111-11-111-1-11-111-1-1-1-111
χ81111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1-11-11-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-111-11-1-1-1111-1-1-11111-1-1
χ911-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1i−ii−i11i−ii−ii−ii−i
χ1011-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−ii−ii11−ii−ii−ii−ii
χ1111-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1i−ii−i11i−ii−i−ii−ii
χ1211-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1−ii−ii11−ii−iii−ii−i
χ1311-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-11-1-11i−i−ii1-1i−i−iii−i−ii
χ1411-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-11-1-11−iii−i1-1−iii−i−iii−i
χ1511-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11-11-1-11i−i−ii1-1i−i−ii−iii−i
χ1611-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-11-11-1-11−iii−i1-1−iii−ii−i−ii
χ172222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-20000-2-200000000
χ1822222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-21100001100000000
χ1922222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-21100001100000000
χ2022222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-10000-1-100000000
χ2122222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-21111-2-21111-2-211111111-2-21111-2-211112222-1-10000-1-100000000
χ222222-22-2-2-2222-2-22222-2-2-2-2-2-22222222222-2-2-2-2-2-2222-2-2-22-222-2-20000000000000000000000000000000000002-2-22-220000-2200000000
χ232222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-1110000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32-2-221-100001-100000000
χ242222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-1110000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32-2-221-100001-100000000
χ252222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-1112-22-2-1-11122-1-1-1-1-2-21111-1-11122-1-1-1-1-2-21111-222-2-110000-1100000000
χ262222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-111-22-2211-1-1-2-2111122-1-1-1-111-1-1-2-2111122-1-1-1-1-222-2-110000-1100000000
χ2722-2-222-2222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000022-2-2220000-2-200000000
χ2822-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-211110000−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i322-2-2-1-100001100000000
χ2922-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-211110000i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i322-2-2-1-100001100000000
χ3022-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-2111122-2-2-1-1-1-122-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-222110000-1-100000000
χ3122-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-21111-2-2221111-2-21111-2-21111-1-1-1-122-1-1-1-122-1-1-1-1-2-222110000-1-100000000
χ3222-2-2-222-2-22-2-2222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-22-2-2-222-2-222000000000000000000000000000000000000-22-222-20000-2200000000
χ3322-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-22-22-1100001-100000000
χ3422-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-22-22-1100001-100000000
χ3522-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-12-2-22-1-11122-1-1-1-1-2-2111111-1-1-2-2111122-1-1-1-12-22-21-10000-1100000000
χ3622-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-1-222-211-1-1-2-2111122-1-1-1-1-1-11122-1-1-1-1-2-211112-22-21-10000-1100000000
χ37444444444444441-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000222200-1-1-1-10000
χ38444444444444441-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000-2-2-2-20011110000
χ3944444444444444-2111111111-2111111111111111-2-2-2-2-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ4044444444444444-2111111111-2111111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-211111111111100000000000000000000
χ4144444-24-2-2-2-2-2-2-2-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-211112222−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ4244444-24-2-2-2-2-2-2-2-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-21111-2-2-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ4344444-24-2-2-2-2-2-2-2-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-211112222−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ4444444-24-2-2-2-2-2-2-2-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-21111-2-2-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ454444-44-4-4-4444-4-41-2-2-22222221-2-2-2-2-2-2-2-2-2222222111-1-1-11-111-1-100000000000000000000000000000000000000000022-2-200-1-1110000
χ464444-44-4-4-4444-4-41-2-2-22222221-2-2-2-2-2-2-2-2-2222222111-1-1-11-111-1-1000000000000000000000000000000000000000000-2-2220011-1-10000
χ474444-44-4-4-4444-4-4-2111-1-1-1-1-1-1-2111111111-1-1-1-1-1-1-2-2-2222-22-2-2222-22-222-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1-1-111111100000000000000000000
χ484444-44-4-4-4444-4-4-2111-1-1-1-1-1-1-2111111111-1-1-1-1-1-1-2-2-2222-22-2-222-22-22-2-222111111-1-1-1-1-1-1-2-222111111-1-1-1-1-1-100000000000000000000
χ494444-4-2-422-2-2-222-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-12-22-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ504444-4-2-422-2-2-222-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-1-22-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3200000000000000000000
χ514444-4-2-422-2-2-222-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-12-22-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ524444-4-2-422-2-2-222-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-1-22-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3200000000000000000000
χ5344-4-444-4444-4-4-4-41-2-2-2-2-2-2-2-2-21-2-2-2222222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ5444-4-444-4444-4-4-4-41-2-2-2-2-2-2-2-2-21-2-2-2222222222222-1-111111-1-1-1-1-1000000000000000000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ5544-4-444-4444-4-4-4-4-2111111111-2111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-22222222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000
χ5644-4-444-4444-4-4-4-4-2111111111-2111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-222222-2-222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ5744-4-44-2-4-2-2-22222-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ5844-4-44-2-4-2-2-22222-21−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-1-2-2221+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ5944-4-44-2-4-2-2-22222-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32221-21112-1-1-1-122-2-2−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ6044-4-44-2-4-2-2-22222-21−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32221-21112-1-1-1-1-2-2221−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ6144-4-4-444-4-44-4-4441-2-2-22222221-2-2-2222222-2-2-2-2-2-2-1-11-1-1-111-1-1110000000000000000000000000000000000000000002i−2i−2i2i00−iii−i0000
χ6244-4-4-444-4-44-4-4441-2-2-22222221-2-2-2222222-2-2-2-2-2-2-1-11-1-1-111-1-111000000000000000000000000000000000000000000−2i2i2i−2i00i−i−ii0000
χ6344-4-4-444-4-44-4-444-2111-1-1-1-1-1-1-2111-1-1-1-1-1-111111122-2222-2-222-2-22-2-2222-2-2-1-1-1-1-1-1111111-2-222111111-1-1-1-1-1-100000000000000000000
χ6444-4-4-444-4-44-4-444-2111-1-1-1-1-1-1-2111-1-1-1-1-1-111111122-2222-2-222-2-2-222-2-2-222111111-1-1-1-1-1-122-2-2-1-1-1-1-1-111111100000000000000000000
χ6544-4-4-4-2422-222-2-2-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i322212-1-11-2-1-1112-2-22−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3200000000000000000000
χ6644-4-4-4-2422-222-2-2-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i322212-1-11-2-1-111-222-21+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ6744-4-4-4-2422-222-2-2-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i322212-1-11-2-1-1112-2-22−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3200000000000000000000
χ6844-4-4-4-2422-222-2-2-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i322212-1-11-2-1-111-222-21−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ694-44i−4i04000-44i−4i004444000000-4-4-4-44i−4i4i−4i4i−4i0000004i−4i4000-404i−4i0000000000000000000000000000000000000000000000000000000000
χ704-44i−4i04000-44i−4i00-21113-33-33-32-1-1-1i−ii−ii−i3i−3i3i−3i3i−3i−2i2i-200020−2i2i0000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300003−33−33−33−33−33−300000000000000000000
χ714-44i−4i04000-44i−4i00-21113-33-33-32-1-1-1i−ii−ii−i3i−3i3i−3i3i−3i−2i2i-200020−2i2i0000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000−33−33−33−33−33−3300000000000000000000
χ724-44i−4i04000-44i−4i00-2111-33-33-332-1-1-1i−ii−ii−i−3i3i−3i3i−3i3i−2i2i-200020−2i2i0000000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i300003−33−33−3−33−33−3300000000000000000000
χ734-44i−4i04000-44i−4i00-2111-33-33-332-1-1-1i−ii−ii−i−3i3i−3i3i−3i3i−2i2i-200020−2i2i0000000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i30000−33−33−333−33−33−300000000000000000000
χ744-44i−4i0-20−2i32i32−2i2i23−2344-2-200−2i32i32i3−2i3-4-4224i−4i−2i2i−2i2i0023−23−23234i−4i-20−2i32i320−2i2i23−2300000000000000000000000000000000000000000000000000000000
χ754-44i−4i0-20−2i32i32−2i2i23−23-21−1−3i32−1+3i323-3−3−i323+i32−3+i323−i322-11+3i321−3i32i−i−ζ7+2ζ11ζ7−2ζ112ζ7−ζ11−2ζ7+ζ113i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2i2i10i3−i3-10i−i−3300000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i3200003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000000000
χ764-44i−4i0-20−2i32i32−2i2i23−23-21−1−3i32−1+3i323-3−3−i323+i32−3+i323−i322-11+3i321−3i32i−i−ζ7+2ζ11ζ7−2ζ112ζ7−ζ11−2ζ7+ζ113i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2i2i10i3−i3-10i−i−3300000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i320000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000000000
χ774-44i−4i0-20−2i32i32−2i2i23−23-21−1+3i32−1−3i32-333−i32−3+i323+i32−3−i322-11−3i321+3i32i−i2ζ7−ζ11−2ζ7+ζ11−ζ7+2ζ11ζ7−2ζ11−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11−2i2i10i3−i3-10i−i−3300000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i3200003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000000000
χ784-44i−4i0-20−2i32i32−2i2i23−23-21−1+3i32−1−3i32-333−i32−3+i323+i32−3−i322-11−3i321+3i32i−i2ζ7−ζ11−2ζ7+ζ11−ζ7+2ζ11ζ7−2ζ11−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11−2i2i10i3−i3-10i−i−3300000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i320000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000000000
χ794-44i−4i0-202i3−2i32−2i2i−232344-2-2002i3−2i3−2i32i3-4-4224i−4i−2i2i−2i2i00−232323−234i−4i-202i3−2i320−2i2i−232300000000000000000000000000000000000000000000000000000000
χ804-44i−4i0-202i3−2i32−2i2i−2323-21−1−3i32−1+3i32-333+i32−3−i323−i32−3+i322-11+3i321−3i32i−i−ζ7+2ζ11ζ7−2ζ112ζ7−ζ11−2ζ7+ζ11−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ11−2i2i10−i3i3-10i−i3−300000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i3200003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000000000
χ814-44i−4i0-202i3−2i32−2i2i−2323-21−1−3i32−1+3i32-333+i32−3−i323−i32−3+i322-11+3i321−3i32i−i−ζ7+2ζ11ζ7−2ζ112ζ7−ζ11−2ζ7+ζ11−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ11−2i2i10−i3i3-10i−i3−300000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i320000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000000000
χ824-44i−4i0-202i3−2i32−2i2i−2323-21−1+3i32−1−3i323-3−3+i323−i32−3−i323+i322-11−3i321+3i32i−i2ζ7−ζ11−2ζ7+ζ11−ζ7+2ζ11ζ7−2ζ113i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−2i2i10−i3i3-10i−i3−300000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i3200003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000000000
χ834-44i−4i0-202i3−2i32−2i2i−2323-21−1+3i32−1−3i323-3−3+i323−i32−3−i323+i322-11−3i321+3i32i−i2ζ7−ζ11−2ζ7+ζ11−ζ7+2ζ11ζ7−2ζ113i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−2i2i10−i3i3-10i−i3−300000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i320000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000000000
χ844-4−4i4i04000-4−4i4i004444000000-4-4-4-4−4i4i−4i4i−4i4i000000−4i4i4000-40−4i4i0000000000000000000000000000000000000000000000000000000000
χ854-4−4i4i04000-4−4i4i00-21113-33-33-32-1-1-1−ii−ii−ii−3i3i−3i3i−3i3i2i−2i-2000202i−2i0000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000−33−33−33−33−33−3300000000000000000000
χ864-4−4i4i04000-4−4i4i00-21113-33-33-32-1-1-1−ii−ii−ii−3i3i−3i3i−3i3i2i−2i-2000202i−2i0000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300003−33−33−33−33−33−300000000000000000000
χ874-4−4i4i04000-4−4i4i00-2111-33-33-332-1-1-1−ii−ii−ii3i−3i3i−3i3i−3i2i−2i-2000202i−2i0000000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i30000−33−33−333−33−33−300000000000000000000
χ884-4−4i4i04000-4−4i4i00-2111-33-33-332-1-1-1−ii−ii−ii3i−3i3i−3i3i−3i2i−2i-2000202i−2i0000000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i300003−33−33−3−33−33−3300000000000000000000
χ894-4−4i4i0-20−2i32i322i−2i−232344-2-200−2i32i32i3−2i3-4-422−4i4i2i−2i2i−2i00−232323−23−4i4i-20−2i32i3202i−2i−232300000000000000000000000000000000000000000000000000000000
χ904-4−4i4i0-20−2i32i322i−2i−2323-21−1−3i32−1+3i323-3−3−i323+i32−3+i323−i322-11+3i321−3i32−iiζ7−2ζ11−ζ7+2ζ11−2ζ7+ζ112ζ7−ζ11−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112i−2i10i3−i3-10−ii3−300000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i320000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000000000
χ914-4−4i4i0-20−2i32i322i−2i−2323-21−1−3i32−1+3i323-3−3−i323+i32−3+i323−i322-11+3i321−3i32−iiζ7−2ζ11−ζ7+2ζ11−2ζ7+ζ112ζ7−ζ11−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112i−2i10i3−i3-10−ii3−300000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i3200003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000000000
χ924-4−4i4i0-20−2i32i322i−2i−2323-21−1+3i32−1−3i32-333−i32−3+i323+i32−3−i322-11−3i321+3i32−ii−2ζ7+ζ112ζ7−ζ11ζ7−2ζ11−ζ7+2ζ113i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ112i−2i10i3−i3-10−ii3−300000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i320000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000000000
χ934-4−4i4i0-20−2i32i322i−2i−2323-21−1+3i32−1−3i32-333−i32−3+i323+i32−3−i322-11−3i321+3i32−ii−2ζ7+ζ112ζ7−ζ11ζ7−2ζ11−ζ7+2ζ113i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ112i−2i10i3−i3-10−ii3−300000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i3200003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000000000
χ944-4−4i4i0-202i3−2i322i−2i23−2344-2-2002i3−2i3−2i32i3-4-422−4i4i2i−2i2i−2i0023−23−2323−4i4i-202i3−2i3202i−2i23−2300000000000000000000000000000000000000000000000000000000
χ954-4−4i4i0-202i3−2i322i−2i23−23-21−1−3i32−1+3i32-333+i32−3−i323−i32−3+i322-11+3i321−3i32−iiζ7−2ζ11−ζ7+2ζ11−2ζ7+ζ112ζ7−ζ113i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ112i−2i10−i3i3-10−ii−3300000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i320000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000000000
χ964-4−4i4i0-202i3−2i322i−2i23−23-21−1−3i32−1+3i32-333+i32−3−i323−i32−3+i322-11+3i321−3i32−iiζ7−2ζ11−ζ7+2ζ11−2ζ7+ζ112ζ7−ζ113i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ112i−2i10−i3i3-10−ii−3300000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i3200003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000000000
χ974-4−4i4i0-202i3−2i322i−2i23−23-21−1+3i32−1−3i323-3−3+i323−i32−3−i323+i322-11−3i321+3i32−ii−2ζ7+ζ112ζ7−ζ11ζ7−2ζ11−ζ7+2ζ11−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ112i−2i10−i3i3-10−ii−3300000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i320000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000000000000000
χ984-4−4i4i0-202i3−2i322i−2i23−23-21−1+3i32−1−3i323-3−3+i323−i32−3−i323+i322-11−3i321+3i32−ii−2ζ7+ζ112ζ7−ζ11ζ7−2ζ11−ζ7+2ζ11−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ112i−2i10−i3i3-10−ii−3300000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i3200003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000000000000000
χ9988888-48-4-4-4-4-4-4-42-422-4-422222-422-4-42222-4-4222222-12-1-1-12-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1008888-8-4-844-4-4-4442-42244-2-2-2-22-422-4-4222244-2-2-2-222-1-211-1-2-1-11100000000000000000000000000000000000000000000000000000000
χ10188-8-88-4-8-4-4-444442-422-4-422222-42244-2-2-2-244-2-2-2-2-2-2-12-1-1-1-2111100000000000000000000000000000000000000000000000000000000
χ10288-8-8-8-4844-444-4-42-42244-2-2-2-22-42244-2-2-2-2-4-42222-2-2-1-211-1211-1-100000000000000000000000000000000000000000000000000000000
χ1038-88i−8i08000-88i−8i002-4-4-4000000-2444−4i4i−4i4i−4i4i0000002i−2i2000-202i−2i0000000000000000000000000000000000000000000000000000000000
χ1048-88i−8i0-40−4i34i34−4i4i43−432-422002i3−2i3−2i32i3-24-2-2−4i4i2i−2i2i−2i00−232323−232i−2i-10−i3i310−ii3−300000000000000000000000000000000000000000000000000000000
χ1058-88i−8i0-404i3−4i34−4i4i−43432-42200−2i32i32i3−2i3-24-2-2−4i4i2i−2i2i−2i0023−23−23232i−2i-10i3−i310−ii−3300000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i08000-8−8i8i002-4-4-4000000-24444i−4i4i−4i4i−4i000000−2i2i2000-20−2i2i0000000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-40−4i34i344i−4i−43432-422002i3−2i3−2i32i3-24-2-24i−4i−2i2i−2i2i0023−23−2323−2i2i-10−i3i310i−i−3300000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-404i3−4i344i−4i43−432-42200−2i32i32i3−2i3-24-2-24i−4i−2i2i−2i2i00−232323−23−2i2i-10i3−i310i−i3−300000000000000000000000000000000000000000000000000000000

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