Finite Group Databasebeta

← Group #13167106

Character table — Group #13167106

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444488888888888888889999121212121212121212121212181818181818242424242424242424242424363636363636545454545454545472727272
order12223446663333666666666666121236661212121212121212121212122222444412121212121212124466661212121212121212121212122244121244444444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ511111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ711111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ811111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111
χ911-1-11i−i-11-11111-1-1-11-1111-1-1-1-1i−i11-1-1i−iiii−i−i−iii−i−i1-11-11-1i−i11-1-1ii−i−ii−i11-1-1111-1-1-1iii−i−i−i1-1i−ii−i11-1-1ii−i−i1-1i−i
χ1011-1-11i−i-11-11111-1-1-11-1111-1-1-1-1i−i11-1-1i−iiii−i−i−iii−i−i1-11-11-1i−i11-1-1ii−i−ii−i11-1-1111-1-1-1iii−i−i−i-11−iii−i-1-111−i−iii-11−ii
χ1111-1-11i−i-11-11111-1-1-11-1111-1-1-1-1i−i11-1-1i−iiii−i−i−iii−i−i1-11-1-11−ii-1-111−i−iiii−i11-1-1-1-1-1111−i−i−iiii1-1i−ii−i-1-111−i−iii1-1i−i
χ1211-1-11i−i-11-11111-1-1-11-1111-1-1-1-1i−i11-1-1i−iiii−i−i−iii−i−i1-11-1-11−ii-1-111−i−iiii−i11-1-1-1-1-1111−i−i−iiii-11−iii−i11-1-1ii−i−i-11−ii
χ1311-1-11−ii-11-11111-1-1-11-1111-1-1-1-1−ii11-1-1−ii−i−i−iiii−i−iii1-11-11-1−ii11-1-1−i−iii−ii11-1-1111-1-1-1−i−i−iiii1-1−ii−ii11-1-1−i−iii1-1−ii
χ1411-1-11−ii-11-11111-1-1-11-1111-1-1-1-1−ii11-1-1−ii−i−i−iiii−i−iii1-11-11-1−ii11-1-1−i−iii−ii11-1-1111-1-1-1−i−i−iiii-11i−i−ii-1-111ii−i−i-11i−i
χ1511-1-11−ii-11-11111-1-1-11-1111-1-1-1-1−ii11-1-1−ii−i−i−iiii−i−iii1-11-1-11i−i-1-111ii−i−i−ii11-1-1-1-1-1111iii−i−i−i1-1−ii−ii-1-111ii−i−i1-1−ii
χ1611-1-11−ii-11-11111-1-1-11-1111-1-1-1-1−ii11-1-1−ii−i−i−iiii−i−iii1-11-1-11i−i-1-111ii−i−i−ii11-1-1-1-1-1111iii−i−i−i-11i−i−ii11-1-1−i−iii-11i−i
χ1722222222222222222222222222222222222222222222-2-2-2-2000000000000-2-2-2-2-2-20000000000000000-2-2000000000000
χ1822222-2-22222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000022-2-2-2-2000000000000000022000000000000
χ192222-122-1-1-12-1-122-1-1222-1-12-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-10000-1-1000000000000
χ202222-122-1-1-12-1-122-1-1222-1-12-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-12222-2-2-2-21111111122-1-1-1-1-211-211-211-2110000-1-1000000000000
χ212222-122-1-1-12-1-122-1-1222-1-12-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3-2-211110−i3i30−i3i30−i3i30−i3i3000011000000000000
χ222222-122-1-1-12-1-122-1-1222-1-12-1-12-1-1-1-1-1-1222-1-12-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3-2-211110i3−i30i3−i30i3−i30i3−i3000011000000000000
χ232222-1-2-2-1-1-12-1-122-1-1222-1-12-1-1211-1-1-1-1-2-2-211-2111111222222-2-2-1-1-1-11111-2-2-1-1-1-12-1-12-1-1-211-211000011000000000000
χ242222-1-2-2-1-1-12-1-122-1-1222-1-12-1-1211-1-1-1-1-2-2-211-21111112222-2-2221111-1-1-1-1-2-2-1-1-1-1-211-2112-1-12-1-1000011000000000000
χ252222-1-2-2-1-1-12-1-122-1-1222-1-12-1-1211-1-1-1-1-2-2-211-2111111-2-2-2-20000−i3i3−i3i3i3−i3i3−i32211110−i3i30−i3i30i3−i30i3−i30000-1-1000000000000
χ262222-1-2-2-1-1-12-1-122-1-1222-1-12-1-1211-1-1-1-1-2-2-211-2111111-2-2-2-20000i3−i3i3−i3−i3i3−i3i32211110i3−i30i3−i30−i3i30−i3i30000-1-1000000000000
χ2722-2-222i−2i-22-22222-2-2-22-2222-2-2-2-22i−2i22-2-22i−2i2i2i2i−2i−2i−2i2i2i−2i−2i-22-22000000000000−2i2i-2-2220000000000000000−2i2i000000000000
χ2822-2-22−2i2i-22-22222-2-2-22-2222-2-2-2-2−2i2i22-2-2−2i2i−2i−2i−2i2i2i2i−2i−2i2i2i-22-220000000000002i−2i-2-22200000000000000002i−2i000000000000
χ2922-2-2-12i−2i1-112-1-12-2112-22-1-1-211-2−ii-1-1112i−2i2i−i−i−2iii−i−iii2-22-22-22i−2i-1-111−i−iii2i−2i-1-1112-1-1-2112i−i−i−2iii0000−ii000000000000
χ3022-2-2-12i−2i1-112-1-12-2112-22-1-1-211-2−ii-1-1112i−2i2i−i−i−2iii−i−iii2-22-2-22−2i2i11-1-1ii−i−i2i−2i-1-111-2112-1-1−2iii2i−i−i0000−ii000000000000
χ3122-2-2-12i−2i1-112-1-12-2112-22-1-1-211-2−ii-1-1112i−2i2i−i−i−2iii−i−iii-22-220000−i3i3i3−i33−3−33−2i2i11-1-10−i3i30i3−i303−30−330000i−i000000000000
χ3222-2-2-12i−2i1-112-1-12-2112-22-1-1-211-2−ii-1-1112i−2i2i−i−i−2iii−i−iii-22-220000i3−i3−i3i3−333−3−2i2i11-1-10i3−i30−i3i30−3303−30000i−i000000000000
χ3322-2-2-1−2i2i1-112-1-12-2112-22-1-1-211-2i−i-1-111−2i2i−2iii2i−i−iii−i−i2-22-22-2−2i2i-1-111ii−i−i−2i2i-1-1112-1-1-211−2iii2i−i−i0000i−i000000000000
χ3422-2-2-1−2i2i1-112-1-12-2112-22-1-1-211-2i−i-1-111−2i2i−2iii2i−i−iii−i−i2-22-2-222i−2i11-1-1−i−iii−2i2i-1-111-2112-1-12i−i−i−2iii0000i−i000000000000
χ3522-2-2-1−2i2i1-112-1-12-2112-22-1-1-211-2i−i-1-111−2i2i−2iii2i−i−iii−i−i-22-220000−i3i3i3−i3−333−32i−2i11-1-10−i3i30i3−i30−3303−30000−ii000000000000
χ3622-2-2-1−2i2i1-112-1-12-2112-22-1-1-211-2i−i-1-111−2i2i−2iii2i−i−iii−i−i-22-220000i3−i3−i3i33−3−332i−2i11-1-10i3−i30−i3i303−30−330000−ii000000000000
χ372-22-2200-2-222222-2-2-2-22-2-2-2222-2002-2-2200000000000022-2-2000000000000002-22-20000000000000000002i−2i2i−2i00000000
χ382-22-2200-2-222222-2-2-2-22-2-2-2222-2002-2-2200000000000022-2-2000000000000002-22-2000000000000000000−2i2i−2i2i00000000
χ392-22-2200-2-222222-2-2-2-22-2-2-2222-2002-2-22000000000000-2-22200000000000000-22-2200000000000000000000002-22-20000
χ402-22-2200-2-222222-2-2-2-22-2-2-2222-2002-2-22000000000000-2-22200000000000000-22-220000000000000000000000-22-220000
χ412-2-222002-2-22222222-2-2-2-2-2-2-2-22002-22-20000000000002-2-22000000000000002-2-220000000000000000002i−2i−2i2i00000000
χ422-2-222002-2-22222222-2-2-2-2-2-2-2-22002-22-20000000000002-2-22000000000000002-2-22000000000000000000−2i2i2i−2i00000000
χ432-2-222002-2-22222222-2-2-2-2-2-2-2-22002-22-2000000000000-222-200000000000000-222-200000000000000000000002i−2i−2i2i0000
χ442-2-222002-2-22222222-2-2-2-2-2-2-2-22002-22-2000000000000-222-200000000000000-222-20000000000000000000000−2i2i2i−2i0000
χ454444444444111-2111-2-2111111-244-2-2-2-2-2-2111111-2-2-2-20000222222222222000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ464444444444111-2111-2-2111111-244-2-2-2-2-2-2111111-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000111111111111000000000000000000
χ474444444444-2-2-21-2-2-211-2-2-2-2-2-2144111111-2-2-2-2-2-21111000000000000000000000000000000000022220000000000-1-1-1-1
χ484444444444-2-2-21-2-2-211-2-2-2-2-2-2144111111-2-2-2-2-2-211110000000000000000000000000000000000-2-2-2-200000000001111
χ4944444-4-4444111-2111-2-2111111-2-4-4-2-2-2-222-1-1-1-1-1-12222000022-2-22222-2-2-2-2000000-1-1-1-1-1-1111111000000000000000000
χ5044444-4-4444111-2111-2-2111111-2-4-4-2-2-2-222-1-1-1-1-1-122220000-2-222-2-2-2-22222000000111111-1-1-1-1-1-1000000000000000000
χ5144444-4-4444-2-2-21-2-2-211-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-1000000000000000000000000000000000022-2-20000000000-1-111
χ5244444-4-4444-2-2-21-2-2-211-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-10000000000000000000000000000000000-2-222000000000011-1-1
χ534444-244-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-21−1−3i32−1+3i321−1−3i32−1+3i32111100002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ544444-244-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-21−1−3i32−1+3i321−1−3i32−1+3i3211110000-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i30000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ554444-244-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-21−1+3i32−1−3i321−1+3i32−1−3i32111100002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ564444-244-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-21−1+3i32−1−3i321−1+3i32−1−3i3211110000-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i30000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ574444-2-4-4-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-11+3i321−3i32-11+3i321−3i32-1-1-1-1000022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ584444-2-4-4-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-11+3i321−3i32-11+3i321−3i32-1-1-1-10000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i30000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ594444-2-4-4-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-11−3i321+3i32-11−3i321+3i32-1-1-1-1000022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ604444-2-4-4-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-11−3i321+3i32-11−3i321+3i32-1-1-1-10000-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i30000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ6144-4-444i−4i-44-4111-2-1-1-1-22111-1-1-124i−4i-2-222−2i2iiii−i−i−i−2i−2i2i2i00002-22i−2i22-2-22i2i−2i−2i000000-1-1-1111−i−i−iiii000000000000000000
χ6244-4-444i−4i-44-4111-2-1-1-1-22111-1-1-124i−4i-2-222−2i2iiii−i−i−i−2i−2i2i2i0000-22−2i2i-2-222−2i−2i2i2i000000111-1-1-1iii−i−i−i000000000000000000
χ6344-4-444i−4i-44-4-2-2-212221-1-2-2-2222-14i−4i11-1-1i−i−2i−2i−2i2i2i2iii−i−i00000000000000000000000000000000002-22i−2i0000000000-11−ii
χ6444-4-444i−4i-44-4-2-2-212221-1-2-2-2222-14i−4i11-1-1i−i−2i−2i−2i2i2i2iii−i−i0000000000000000000000000000000000-22−2i2i00000000001-1i−i
χ6544-4-44−4i4i-44-4111-2-1-1-1-22111-1-1-12−4i4i-2-2222i−2i−i−i−iiii2i2i−2i−2i00002-2−2i2i22-2-2−2i−2i2i2i000000-1-1-1111iii−i−i−i000000000000000000
χ6644-4-44−4i4i-44-4111-2-1-1-1-22111-1-1-12−4i4i-2-2222i−2i−i−i−iiii2i2i−2i−2i0000-222i−2i-2-2222i2i−2i−2i000000111-1-1-1−i−i−iiii000000000000000000
χ6744-4-44−4i4i-44-4-2-2-212221-1-2-2-2222-1−4i4i11-1-1−ii2i2i2i−2i−2i−2i−i−iii00000000000000000000000000000000002-2−2i2i0000000000-11i−i
χ6844-4-44−4i4i-44-4-2-2-212221-1-2-2-2222-1−4i4i11-1-1−ii2i2i2i−2i−2i−2i−i−iii0000000000000000000000000000000000-222i−2i00000000001-1−ii
χ6944-4-4-24i−4i2-221−1−3i32−1+3i32-2-11+3i321−3i32-221−1−3i32−1+3i32-11+3i321−3i322−2i2i11-1-1−2i2ii−ζ7+2ζ112ζ7−ζ11−iζ7−2ζ11−2ζ7+ζ11ii−i−i00002-22i−2i−1−i3−1+i31+i31−i32ζ112ζ7−2ζ11−2ζ7000000-11+i321−i321−1−i32−1+i32−i−ζ11−ζ7iζ11ζ7000000000000000000
χ7044-4-4-24i−4i2-221−1−3i32−1+3i32-2-11+3i321−3i32-221−1−3i32−1+3i32-11+3i321−3i322−2i2i11-1-1−2i2ii−ζ7+2ζ112ζ7−ζ11−iζ7−2ζ11−2ζ7+ζ11ii−i−i0000-22−2i2i1+i31−i3−1−i3−1+i3−2ζ11−2ζ72ζ112ζ70000001−1−i32−1+i32-11+i321−i32iζ11ζ7−i−ζ11−ζ7000000000000000000
χ7144-4-4-24i−4i2-221−1+3i32−1−3i32-2-11−3i321+3i32-221−1+3i32−1−3i32-11−3i321+3i322−2i2i11-1-1−2i2ii2ζ7−ζ11−ζ7+2ζ11−i−2ζ7+ζ11ζ7−2ζ11ii−i−i00002-22i−2i−1+i3−1−i31−i31+i32ζ72ζ11−2ζ7−2ζ11000000-11−i321+i321−1+i32−1−i32−i−ζ7−ζ11iζ7ζ11000000000000000000
χ7244-4-4-24i−4i2-221−1+3i32−1−3i32-2-11−3i321+3i32-221−1+3i32−1−3i32-11−3i321+3i322−2i2i11-1-1−2i2ii2ζ7−ζ11−ζ7+2ζ11−i−2ζ7+ζ11ζ7−2ζ11ii−i−i0000-22−2i2i1−i31+i3−1+i3−1−i3−2ζ7−2ζ112ζ72ζ110000001−1+i32−1−i32-11−i321+i32iζ7ζ11−i−ζ7−ζ11000000000000000000
χ7344-4-4-2−4i4i2-221−1−3i32−1+3i32-2-11+3i321−3i32-221−1−3i32−1+3i32-11+3i321−3i3222i−2i11-1-12i−2i−iζ7−2ζ11−2ζ7+ζ11i−ζ7+2ζ112ζ7−ζ11−i−iii00002-2−2i2i−1−i3−1+i31+i31−i3−2ζ11−2ζ72ζ112ζ7000000-11+i321−i321−1−i32−1+i32iζ11ζ7−i−ζ11−ζ7000000000000000000
χ7444-4-4-2−4i4i2-221−1−3i32−1+3i32-2-11+3i321−3i32-221−1−3i32−1+3i32-11+3i321−3i3222i−2i11-1-12i−2i−iζ7−2ζ11−2ζ7+ζ11i−ζ7+2ζ112ζ7−ζ11−i−iii0000-222i−2i1+i31−i3−1−i3−1+i32ζ112ζ7−2ζ11−2ζ70000001−1−i32−1+i32-11+i321−i32−i−ζ11−ζ7iζ11ζ7000000000000000000
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χ774-44-4-20022-24-2-24-422-44-4224-2-2-400-222-200000000000044-4-400000000000000-22-22000000000000000000000000000000
χ784-44-4-20022-24-2-24-422-44-4224-2-2-400-222-2000000000000-4-444000000000000002-22-2000000000000000000000000000000
χ794-4-44-200-2224-2-244-2-2-4-4-422-422400-22-220000000000004-4-4400000000000000-222-2000000000000000000000000000000
χ804-4-44-200-2224-2-244-2-2-4-4-422-422400-22-22000000000000-444-4000000000000002-2-22000000000000000000000000000000
χ818888-488-4-4-4-4222-42222-422-4222-4-4-1-1-1-122-422-422-1-1-1-10000000000000000000000000000000000000000000000000000
χ828888-4-8-8-4-4-4-4222-42222-422-422244-1-1-1-1-2-24-2-24-2-211110000000000000000000000000000000000000000000000000000
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χ8488-8-8-4−8i8i4-44-42224-2-22-2-4224-2-2-24i−4i-1-111−2i2i4i−2i−2i−4i2i2iii−i−i0000000000000000000000000000000000000000000000000000
χ858-88-8800-8-88222-4-2-2-24-4-2-2-2222400-444-40000000000000000000000000000000000000000000000000000000000000000
χ868-88-8800-8-88-4-4-42444-22444-4-4-4-2002-2-220000000000000000000000000000000000000000000000000000000000000000
χ878-88-8-40044-42−1−3i3−1+3i3-4-21+3i31−3i34-4-21+3i31−3i32−1−3i3−1+3i34002-2-220000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-40044-42−1+3i3−1−3i3-4-21−3i31+3i34-4-21−3i31+3i32−1+3i3−1−3i34002-2-220000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-40044-4-42224-2-2-224-2-2-422-200-111-100000000−3i33i3−3i33i30000000000000000000000000000000000000000000000000000
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χ918-8-888008-8-8222-422244-2-2-2-2-2-2-400-44-440000000000000000000000000000000000000000000000000000000000000000
χ928-8-888008-8-8-4-4-42-4-4-4-2-24444442002-22-20000000000000000000000000000000000000000000000000000000000000000
χ938-8-88-400-4442−1−3i3−1+3i3-42−1−3i3−1+3i344-21+3i31−3i3-21+3i31−3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ948-8-88-400-4442−1+3i3−1−3i3-42−1+3i3−1−3i344-21−3i31+3i3-21−3i31+3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-400-444-4222-422-2-24-2-24-2-2200-11-110000000033−33−33330000000000000000000000000000000000000000000000000000
χ968-8-88-400-444-4222-422-2-24-2-24-2-2200-11-1100000000−333333−330000000000000000000000000000000000000000000000000000

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