Finite Group Databasebeta

← Group #72500

Character table — Group #72500

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222224444444444888888881111222222222244444444448888888811112222222222444444444488888888
order1222224444444422222244448888888836666612121212121212126666661212121224242424242424243666661212121212121212666666121212122424242424242424
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
χ51111111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1111111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1111111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i
χ61111111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1111111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1111111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii
χ71111111111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1111111111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1111111111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111-1-1-1-11111-1-11111-1-1-1-11-11-11-11-1111111-1-1-1-11111-1-11111-1-1-1-11-11-11-11-1111111-1-1-1-11111-1-11111-1-1-1-11-11-11-11-1
χ10111111-1-1-1-11111-1-11111-1-1-1-1-11-11-11-11111111-1-1-1-11111-1-11111-1-1-1-1-11-11-11-11111111-1-1-1-11111-1-11111-1-1-1-1-11-11-11-11
χ11111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11
χ12111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-1111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-1111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-1
χ13111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ14111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ15111111-1-1-1-1-1-1-1-111-1-11111-1-1i−i−ii−iii−i111111-1-1-1-1-1-1-1-111-1-11111-1-1i−i−ii−iii−i111111-1-1-1-1-1-1-1-111-1-11111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-1-1-111-1-11111-1-1−iii−ii−i−ii111111-1-1-1-1-1-1-1-111-1-11111-1-1−iii−ii−i−ii111111-1-1-1-1-1-1-1-111-1-11111-1-1−iii−ii−i−ii
χ172222-2-222-2-222-2-22-200000000000000002222-2-222-2-222-2-22-200000000000000002222-2-222-2-222-2-22-20000000000000000
χ182222-2-222-2-2-2-222-2200000000000000002222-2-222-2-2-2-222-2200000000000000002222-2-222-2-2-2-222-220000000000000000
χ192222-2-2-2-22222-2-2-2200000000000000002222-2-2-2-22222-2-2-2200000000000000002222-2-2-2-22222-2-2-220000000000000000
χ202222-2-2-2-222-2-2222-200000000000000002222-2-2-2-222-2-2222-200000000000000002222-2-2-2-222-2-2222-20000000000000000
χ212-2-222-200002-22-20000002-22-2000000002-2-222-200002-22-20000002-22-2000000002-2-222-200002-22-20000002-22-200000000
χ222-2-222-200002-22-2000000-22-22000000002-2-222-200002-22-2000000-22-22000000002-2-222-200002-22-2000000-22-2200000000
χ232-2-222-20000-22-220000002-2-22000000002-2-222-20000-22-220000002-2-22000000002-2-222-20000-22-220000002-2-2200000000
χ242-2-222-20000-22-22000000-222-2000000002-2-222-20000-22-22000000-222-2000000002-2-222-20000-22-22000000-222-200000000
χ252-2-22-2200002-2-22002-22-20000000000002-2-22-2200002-2-22002-22-20000000000002-2-22-2200002-2-22002-22-2000000000000
χ262-2-22-2200002-2-2200-22-220000000000002-2-22-2200002-2-2200-22-220000000000002-2-22-2200002-2-2200-22-22000000000000
χ272-2-22-220000-222-2002-2-220000000000002-2-22-220000-222-2002-2-220000000000002-2-22-220000-222-2002-2-22000000000000
χ282-2-22-220000-222-200-222-20000000000002-2-22-220000-222-200-222-20000000000002-2-22-220000-222-200-222-2000000000000
χ2944-4-400004i−4i000000000000000000000044-4-400004i−4i000000000000000000000044-4-400004i−4i0000000000000000000000
χ3044-4-40000−4i4i000000000000000000000044-4-40000−4i4i000000000000000000000044-4-40000−4i4i0000000000000000000000
χ314-44-4004i−4i0000000000000000000000004-44-4004i−4i0000000000000000000000004-44-4004i−4i000000000000000000000000
χ324-44-400−4i4i0000000000000000000000004-44-400−4i4i0000000000000000000000004-44-400−4i4i000000000000000000000000
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
χ371111111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i−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+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−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−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ381111111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−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+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−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−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ391111111111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii−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−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−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+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ401111111111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−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−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−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+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ41111111-1-1-1-11111-1-11111-1-1-1-11-11-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ42111111-1-1-1-11111-1-11111-1-1-1-1-11-11-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+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−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ43111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11−1+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−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+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−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ44111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-1−1+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−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−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+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
χ45111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii−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+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7−1−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−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11
χ46111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i−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−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−1−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−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11
χ47111111-1-1-1-1-1-1-1-111-1-11111-1-1i−i−ii−iii−i−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11
χ48111111-1-1-1-1-1-1-1-111-1-11111-1-1−iii−ii−i−ii−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−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11
χ492222-2-222-2-222-2-22-20000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i30000000000000000
χ502222-2-222-2-2-2-222-220000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i30000000000000000
χ512222-2-2-2-22222-2-2-220000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i30000000000000000
χ522222-2-2-2-222-2-2222-20000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i30000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i30000000000000000
χ532-2-222-200002-22-20000002-22-200000000−1+i31−i31−i3−1+i3−1+i31−i30000−1+i31−i3−1+i31−i3000000−1+i31−i3−1+i31−i300000000−1−i31+i31+i3−1−i3−1−i31+i30000−1−i31+i3−1−i31+i3000000−1−i31+i3−1−i31+i300000000
χ542-2-222-200002-22-2000000-22-2200000000−1+i31−i31−i3−1+i3−1+i31−i30000−1+i31−i3−1+i31−i30000001−i3−1+i31−i3−1+i300000000−1−i31+i31+i3−1−i3−1−i31+i30000−1−i31+i3−1−i31+i30000001+i3−1−i31+i3−1−i300000000
χ552-2-222-20000-22-220000002-2-2200000000−1+i31−i31−i3−1+i3−1+i31−i300001−i3−1+i31−i3−1+i3000000−1+i31−i31−i3−1+i300000000−1−i31+i31+i3−1−i3−1−i31+i300001+i3−1−i31+i3−1−i3000000−1−i31+i31+i3−1−i300000000
χ562-2-222-20000-22-22000000-222-200000000−1+i31−i31−i3−1+i3−1+i31−i300001−i3−1+i31−i3−1+i30000001−i3−1+i3−1+i31−i300000000−1−i31+i31+i3−1−i3−1−i31+i300001+i3−1−i31+i3−1−i30000001+i3−1−i3−1−i31+i300000000
χ572-2-22-2200002-2-22002-22-2000000000000−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3−1+i300−1+i31−i3−1+i31−i3000000000000−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3−1−i300−1−i31+i3−1−i31+i3000000000000
χ582-2-22-2200002-2-2200-22-22000000000000−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3−1+i3001−i3−1+i31−i3−1+i3000000000000−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3−1−i3001+i3−1−i31+i3−1−i3000000000000
χ592-2-22-220000-222-2002-2-22000000000000−1+i31−i31−i3−1+i31−i3−1+i300001−i3−1+i3−1+i31−i300−1+i31−i31−i3−1+i3000000000000−1−i31+i31+i3−1−i31+i3−1−i300001+i3−1−i3−1−i31+i300−1−i31+i31+i3−1−i3000000000000
χ602-2-22-220000-222-200-222-2000000000000−1+i31−i31−i3−1+i31−i3−1+i300001−i3−1+i3−1+i31−i3001−i3−1+i3−1+i31−i3000000000000−1−i31+i31+i3−1−i31+i3−1−i300001+i3−1−i3−1−i31+i3001+i3−1−i3−1−i31+i3000000000000
χ6144-4-400004i−4i0000000000000000000000−2+2i3−2+2i32−2i32−2i300004ζ7−4ζ70000000000000000000000−2−2i3−2−2i32+2i32+2i300004ζ11−4ζ110000000000000000000000
χ6244-4-40000−4i4i0000000000000000000000−2+2i3−2+2i32−2i32−2i30000−4ζ74ζ70000000000000000000000−2−2i3−2−2i32+2i32+2i30000−4ζ114ζ110000000000000000000000
χ634-44-4004i−4i000000000000000000000000−2+2i32−2i3−2+2i32−2i3004ζ7−4ζ7000000000000000000000000−2−2i32+2i3−2−2i32+2i3004ζ11−4ζ11000000000000000000000000
χ644-44-400−4i4i000000000000000000000000−2+2i32−2i3−2+2i32−2i300−4ζ74ζ7000000000000000000000000−2−2i32+2i3−2−2i32+2i300−4ζ114ζ11000000000000000000000000
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
χ691111111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i−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−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+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+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ701111111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−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−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+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+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ711111111111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii−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+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1+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−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ721111111111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−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+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1+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−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ73111111-1-1-1-11111-1-11111-1-1-1-11-11-11-11-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+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−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ74111111-1-1-1-11111-1-11111-1-1-1-1-11-11-11-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−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+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ75111111-1-1-1-11111-1-1-1-1-1-111111-11-1-11-11−1−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+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−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+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ76111111-1-1-1-11111-1-1-1-1-1-11111-11-111-11-1−1−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+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+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−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ77111111-1-1-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii−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−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11−1+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+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7
χ78111111-1-1-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i−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−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−1+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−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7
χ79111111-1-1-1-1-1-1-1-111-1-11111-1-1i−i−ii−iii−i−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7
χ80111111-1-1-1-1-1-1-1-111-1-11111-1-1−iii−ii−i−ii−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7
χ812222-2-222-2-222-2-22-20000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i30000000000000000
χ822222-2-222-2-2-2-222-220000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i3−1−i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i3−1+i30000000000000000
χ832222-2-2-2-22222-2-2-220000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i30000000000000000
χ842222-2-2-2-222-2-2222-20000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i30000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i30000000000000000
χ852-2-222-200002-22-20000002-22-200000000−1−i31+i31+i3−1−i3−1−i31+i30000−1−i31+i3−1−i31+i3000000−1−i31+i3−1−i31+i300000000−1+i31−i31−i3−1+i3−1+i31−i30000−1+i31−i3−1+i31−i3000000−1+i31−i3−1+i31−i300000000
χ862-2-222-200002-22-2000000-22-2200000000−1−i31+i31+i3−1−i3−1−i31+i30000−1−i31+i3−1−i31+i30000001+i3−1−i31+i3−1−i300000000−1+i31−i31−i3−1+i3−1+i31−i30000−1+i31−i3−1+i31−i30000001−i3−1+i31−i3−1+i300000000
χ872-2-222-20000-22-220000002-2-2200000000−1−i31+i31+i3−1−i3−1−i31+i300001+i3−1−i31+i3−1−i3000000−1−i31+i31+i3−1−i300000000−1+i31−i31−i3−1+i3−1+i31−i300001−i3−1+i31−i3−1+i3000000−1+i31−i31−i3−1+i300000000
χ882-2-222-20000-22-22000000-222-200000000−1−i31+i31+i3−1−i3−1−i31+i300001+i3−1−i31+i3−1−i30000001+i3−1−i3−1−i31+i300000000−1+i31−i31−i3−1+i3−1+i31−i300001−i3−1+i31−i3−1+i30000001−i3−1+i3−1+i31−i300000000
χ892-2-22-2200002-2-22002-22-2000000000000−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3−1−i300−1−i31+i3−1−i31+i3000000000000−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3−1+i300−1+i31−i3−1+i31−i3000000000000
χ902-2-22-2200002-2-2200-22-22000000000000−1−i31+i31+i3−1−i31+i3−1−i30000−1−i31+i31+i3−1−i3001+i3−1−i31+i3−1−i3000000000000−1+i31−i31−i3−1+i31−i3−1+i30000−1+i31−i31−i3−1+i3001−i3−1+i31−i3−1+i3000000000000
χ912-2-22-220000-222-2002-2-22000000000000−1−i31+i31+i3−1−i31+i3−1−i300001+i3−1−i3−1−i31+i300−1−i31+i31+i3−1−i3000000000000−1+i31−i31−i3−1+i31−i3−1+i300001−i3−1+i3−1+i31−i300−1+i31−i31−i3−1+i3000000000000
χ922-2-22-220000-222-200-222-2000000000000−1−i31+i31+i3−1−i31+i3−1−i300001+i3−1−i3−1−i31+i3001+i3−1−i3−1−i31+i3000000000000−1+i31−i31−i3−1+i31−i3−1+i300001−i3−1+i3−1+i31−i3001−i3−1+i3−1+i31−i3000000000000
χ9344-4-400004i−4i0000000000000000000000−2−2i3−2−2i32+2i32+2i300004ζ11−4ζ110000000000000000000000−2+2i3−2+2i32−2i32−2i300004ζ7−4ζ70000000000000000000000
χ9444-4-40000−4i4i0000000000000000000000−2−2i3−2−2i32+2i32+2i30000−4ζ114ζ110000000000000000000000−2+2i3−2+2i32−2i32−2i30000−4ζ74ζ70000000000000000000000
χ954-44-4004i−4i000000000000000000000000−2−2i32+2i3−2−2i32+2i3004ζ11−4ζ11000000000000000000000000−2+2i32−2i3−2+2i32−2i3004ζ7−4ζ7000000000000000000000000
χ964-44-400−4i4i000000000000000000000000−2−2i32+2i3−2−2i32+2i300−4ζ114ζ11000000000000000000000000−2+2i32−2i3−2+2i32−2i300−4ζ74ζ7000000000000000000000000

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