Finite Group Databasebeta

← Group #72713

Character table — Group #72713

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222224444444444888888881111222222222244444444448888888811112222222222444444444488888888
order1222224444444444888888884444888836666612121212121212121212242424242424242412121212242424243666661212121212121212121224242424242424241212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-11111111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-11111111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1
χ61111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1111111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111
χ71111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111
χ81111111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-11111111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1
χ9111111-111-1-1-1-1-11-1ii−i−iii−i−i1-11-1i−ii−i111111-111-1-1-1-1-11-1ii−i−iii−i−i1-11-1i−ii−i111111-111-1-1-1-1-11-1ii−i−iii−i−i1-11-1i−ii−i
χ10111111-111-1-1-1-1-11-1ii−i−iii−i−i-11-11−ii−ii111111-111-1-1-1-1-11-1ii−i−iii−i−i-11-11−ii−ii111111-111-1-1-1-1-11-1ii−i−iii−i−i-11-11−ii−ii
χ11111111-111-1-1-1-1-11-1−i−iii−i−iii1-11-1−ii−ii111111-111-1-1-1-1-11-1−i−iii−i−iii1-11-1−ii−ii111111-111-1-1-1-1-11-1−i−iii−i−iii1-11-1−ii−ii
χ12111111-111-1-1-1-1-11-1−i−iii−i−iii-11-11i−ii−i111111-111-1-1-1-1-11-1−i−iii−i−iii-11-11i−ii−i111111-111-1-1-1-1-11-1−i−iii−i−iii-11-11i−ii−i
χ13111111-1-1-111-1-1-1-11ii−i−i−i−iii1-1-11i−i−ii111111-1-1-111-1-1-1-11ii−i−i−i−iii1-1-11i−i−ii111111-1-1-111-1-1-1-11ii−i−i−i−iii1-1-11i−i−ii
χ14111111-1-1-111-1-1-1-11ii−i−i−i−iii-111-1−iii−i111111-1-1-111-1-1-1-11ii−i−i−i−iii-111-1−iii−i111111-1-1-111-1-1-1-11ii−i−i−i−iii-111-1−iii−i
χ15111111-1-1-111-1-1-1-11−i−iiiii−i−i1-1-11−iii−i111111-1-1-111-1-1-1-11−i−iiiii−i−i1-1-11−iii−i111111-1-1-111-1-1-1-11−i−iiiii−i−i1-1-11−iii−i
χ16111111-1-1-111-1-1-1-11−i−iiiii−i−i-111-1i−i−ii111111-1-1-111-1-1-1-11−i−iiiii−i−i-111-1i−i−ii111111-1-1-111-1-1-1-11−i−iiiii−i−i-111-1i−i−ii
χ172222-2-2222-2-2-2-22-2200000000000000002222-2-2222-2-2-2-22-2200000000000000002222-2-2222-2-2-2-22-220000000000000000
χ182222-2-22-2-222-2-222-200000000000000002222-2-22-2-222-2-222-200000000000000002222-2-22-2-222-2-222-20000000000000000
χ192222-2-2-2222222-2-2-200000000000000002222-2-2-2222222-2-2-200000000000000002222-2-2-2222222-2-2-20000000000000000
χ202222-2-2-2-2-2-2-222-22200000000000000002222-2-2-2-2-2-2-222-22200000000000000002222-2-2-2-2-2-2-222-2220000000000000000
χ2122-2-22-2200002-2-20000002-22-20000000022-2-22-2200002-2-20000002-22-20000000022-2-22-2200002-2-20000002-22-200000000
χ2222-2-22-2200002-2-2000000-22-220000000022-2-22-2200002-2-2000000-22-220000000022-2-22-2200002-2-2000000-22-2200000000
χ2322-2-22-2-20000-2220000002i−2i−2i2i0000000022-2-22-2-20000-2220000002i−2i−2i2i0000000022-2-22-2-20000-2220000002i−2i−2i2i00000000
χ2422-2-22-2-20000-222000000−2i2i2i−2i0000000022-2-22-2-20000-222000000−2i2i2i−2i0000000022-2-22-2-20000-222000000−2i2i2i−2i00000000
χ2522-2-2-2220000-22-2002-22-200000000000022-2-2-2220000-22-2002-22-200000000000022-2-2-2220000-22-2002-22-2000000000000
χ2622-2-2-2220000-22-200-22-2200000000000022-2-2-2220000-22-200-22-2200000000000022-2-2-2220000-22-200-22-22000000000000
χ2722-2-2-22-200002-22002i−2i−2i2i00000000000022-2-2-22-200002-22002i−2i−2i2i00000000000022-2-2-22-200002-22002i−2i−2i2i000000000000
χ2822-2-2-22-200002-2200−2i2i2i−2i00000000000022-2-2-22-200002-2200−2i2i2i−2i00000000000022-2-2-22-200002-2200−2i2i2i−2i000000000000
χ294-44-4000004i−4i0000000000000000000004-44-4000004i−4i0000000000000000000004-44-4000004i−4i000000000000000000000
χ304-44-400000−4i4i0000000000000000000004-44-400000−4i4i0000000000000000000004-44-400000−4i4i000000000000000000000
χ314-4-440004i−4i000000000000000000000004-4-440004i−4i000000000000000000000004-4-440004i−4i00000000000000000000000
χ324-4-44000−4i4i000000000000000000000004-4-44000−4i4i000000000000000000000004-4-44000−4i4i00000000000000000000000
χ3311111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ34111111111111111111111111-1-1-1-1-1-1-1-1−1+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+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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ351111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−1+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+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ361111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+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+i321−i321−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−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−i32−1−i32−1−i32
χ371111111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ381111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i321−i321−i32−1+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−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
χ391111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−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+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+i321+i321+i321+i32−1−i32−1−i32
χ401111111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−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+i32
χ41111111-111-1-1-1-1-11-1ii−i−iii−i−i1-11-1i−ii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ42111111-111-1-1-1-1-11-1ii−i−iii−i−i-11-11−ii−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ43111111-111-1-1-1-1-11-1−i−iii−i−iii1-11-1−ii−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ44111111-111-1-1-1-1-11-1−i−iii−i−iii-11-11i−ii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ45111111-1-1-111-1-1-1-11ii−i−i−i−iii1-1-11i−i−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ46111111-1-1-111-1-1-1-11ii−i−i−i−iii-111-1−iii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11
χ47111111-1-1-111-1-1-1-11−i−iiiii−i−i1-1-11−iii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ48111111-1-1-111-1-1-1-11−i−iiiii−i−i-111-1i−i−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11
χ492222-2-2222-2-2-2-22-220000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i3−1−i30000000000000000
χ502222-2-22-2-222-2-222-20000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i30000000000000000
χ512222-2-2-2222222-2-2-20000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000000000
χ522222-2-2-2-2-2-2-222-2220000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i30000000000000000
χ5322-2-22-2200002-2-20000002-22-200000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3000000−1+i31−i3−1+i31−i300000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3000000−1−i31+i3−1−i31+i300000000
χ5422-2-22-2200002-2-2000000-22-2200000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i30000001−i3−1+i31−i3−1+i300000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i30000001+i3−1−i31+i3−1−i300000000
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χ5622-2-22-2-20000-222000000−2i2i2i−2i00000000−1+i3−1+i31−i31−i3−1+i31−i31−i300001−i3−1+i3−1+i3000000−2ζ72ζ72ζ7−2ζ700000000−1−i3−1−i31+i31+i3−1−i31+i31+i300001+i3−1−i3−1−i3000000−2ζ112ζ112ζ11−2ζ1100000000
χ5722-2-2-2220000-22-2002-22-2000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i300001−i3−1+i31−i300−1+i31−i3−1+i31−i3000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i300001+i3−1−i31+i300−1−i31+i3−1−i31+i3000000000000
χ5822-2-2-2220000-22-200-22-22000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i300001−i3−1+i31−i3001−i3−1+i31−i3−1+i3000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i300001+i3−1−i31+i3001+i3−1−i31+i3−1−i3000000000000
χ5922-2-2-22-200002-22002i−2i−2i2i000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i30000−1+i31−i3−1+i3002ζ7−2ζ7−2ζ72ζ7000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i30000−1−i31+i3−1−i3002ζ11−2ζ11−2ζ112ζ11000000000000
χ6022-2-2-22-200002-2200−2i2i2i−2i000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i30000−1+i31−i3−1+i300−2ζ72ζ72ζ7−2ζ7000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i30000−1−i31+i3−1−i300−2ζ112ζ112ζ11−2ζ11000000000000
χ614-44-4000004i−4i000000000000000000000−2+2i32−2i3−2+2i32−2i3000004ζ7−4ζ7000000000000000000000−2−2i32+2i3−2−2i32+2i3000004ζ11−4ζ11000000000000000000000
χ624-44-400000−4i4i000000000000000000000−2+2i32−2i3−2+2i32−2i300000−4ζ74ζ7000000000000000000000−2−2i32+2i3−2−2i32+2i300000−4ζ114ζ11000000000000000000000
χ634-4-440004i−4i00000000000000000000000−2+2i32−2i32−2i3−2+2i30004ζ7−4ζ700000000000000000000000−2−2i32+2i32+2i3−2−2i30004ζ11−4ζ1100000000000000000000000
χ644-4-44000−4i4i00000000000000000000000−2+2i32−2i32−2i3−2+2i3000−4ζ74ζ700000000000000000000000−2−2i32+2i32+2i3−2−2i3000−4ζ114ζ1100000000000000000000000
χ6511111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ66111111111111111111111111-1-1-1-1-1-1-1-1−1−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−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+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ671111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−1−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−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ681111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1−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−i321+i321+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+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+i32−1+i32−1+i32
χ691111111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ701111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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−i321+i321+i32−1−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+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
χ711111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+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−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−i321−i321−i321−i32−1+i32−1+i32
χ721111111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+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−i32
χ73111111-111-1-1-1-1-11-1ii−i−iii−i−i1-11-1i−ii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ74111111-111-1-1-1-1-11-1ii−i−iii−i−i-11-11−ii−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ75111111-111-1-1-1-1-11-1−i−iii−i−iii1-11-1−ii−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ76111111-111-1-1-1-1-11-1−i−iii−i−iii-11-11i−ii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ77111111-1-1-111-1-1-1-11ii−i−i−i−iii1-1-11i−i−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ78111111-1-1-111-1-1-1-11ii−i−i−i−iii-111-1−iii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7
χ79111111-1-1-111-1-1-1-11−i−iiiii−i−i1-1-11−iii−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ80111111-1-1-111-1-1-1-11−i−iiiii−i−i-111-1i−i−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7
χ812222-2-2222-2-2-2-22-220000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i3−1−i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i3−1+i30000000000000000
χ822222-2-22-2-222-2-222-20000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i30000000000000000
χ832222-2-2-2222222-2-2-20000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000000000
χ842222-2-2-2-2-2-2-222-2220000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i30000000000000000
χ8522-2-22-2200002-2-20000002-22-200000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3000000−1−i31+i3−1−i31+i300000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3000000−1+i31−i3−1+i31−i300000000
χ8622-2-22-2200002-2-2000000-22-2200000000−1−i3−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i30000001+i3−1−i31+i3−1−i300000000−1+i3−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i30000001−i3−1+i31−i3−1+i300000000
χ8722-2-22-2-20000-2220000002i−2i−2i2i00000000−1−i3−1−i31+i31+i3−1−i31+i31+i300001+i3−1−i3−1−i30000002ζ11−2ζ11−2ζ112ζ1100000000−1+i3−1+i31−i31−i3−1+i31−i31−i300001−i3−1+i3−1+i30000002ζ7−2ζ7−2ζ72ζ700000000
χ8822-2-22-2-20000-222000000−2i2i2i−2i00000000−1−i3−1−i31+i31+i3−1−i31+i31+i300001+i3−1−i3−1−i3000000−2ζ112ζ112ζ11−2ζ1100000000−1+i3−1+i31−i31−i3−1+i31−i31−i300001−i3−1+i3−1+i3000000−2ζ72ζ72ζ7−2ζ700000000
χ8922-2-2-2220000-22-2002-22-2000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i300001+i3−1−i31+i300−1−i31+i3−1−i31+i3000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i300001−i3−1+i31−i300−1+i31−i3−1+i31−i3000000000000
χ9022-2-2-2220000-22-200-22-22000000000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i300001+i3−1−i31+i3001+i3−1−i31+i3−1−i3000000000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i300001−i3−1+i31−i3001−i3−1+i31−i3−1+i3000000000000
χ9122-2-2-22-200002-22002i−2i−2i2i000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i30000−1−i31+i3−1−i3002ζ11−2ζ11−2ζ112ζ11000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i30000−1+i31−i3−1+i3002ζ7−2ζ7−2ζ72ζ7000000000000
χ9222-2-2-22-200002-2200−2i2i2i−2i000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i30000−1−i31+i3−1−i300−2ζ112ζ112ζ11−2ζ11000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i30000−1+i31−i3−1+i300−2ζ72ζ72ζ7−2ζ7000000000000
χ934-44-4000004i−4i000000000000000000000−2−2i32+2i3−2−2i32+2i3000004ζ11−4ζ11000000000000000000000−2+2i32−2i3−2+2i32−2i3000004ζ7−4ζ7000000000000000000000
χ944-44-400000−4i4i000000000000000000000−2−2i32+2i3−2−2i32+2i300000−4ζ114ζ11000000000000000000000−2+2i32−2i3−2+2i32−2i300000−4ζ74ζ7000000000000000000000
χ954-4-440004i−4i00000000000000000000000−2−2i32+2i32+2i3−2−2i30004ζ11−4ζ1100000000000000000000000−2+2i32−2i32−2i3−2+2i30004ζ7−4ζ700000000000000000000000
χ964-4-44000−4i4i00000000000000000000000−2−2i32+2i32+2i3−2−2i3000−4ζ114ζ1100000000000000000000000−2+2i32−2i32−2i3−2+2i3000−4ζ74ζ700000000000000000000000

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