Finite Group Databasebeta

← Group #10815958

Character table — Group #10815958

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222224444444444444444444444666666666666666688888888888888888888888812121212121212121212121216161616242424242424
order122244442222344446661212121222244466668888888812121212444444448888888822444466666121212121224242424242424244444888888886121212888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-11-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111-1-11-1-111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ71111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ9111111111-1-111-1-1111111111-111-11111-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-111-1-1-1-1
χ10111111111-1-111-1-1111111111-111-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-1-11111
χ11111111111-1-111-1-1111111111-111-11111-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-11-1-1-11-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-11-1-1-1-111
χ12111111111-1-111-1-1111111111-111-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-11-111-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-111111-1-1
χ13111111111-1-111-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111111-1-1-1-111-1-111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11-1-11111
χ14111111111-1-111-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1111111-1-1-1-11111-1-11111111-1-1111-1-1-1-1
χ15111111111-1-111-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-111111-1111-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-11111-1-1
χ16111111111-1-111-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-1-1-111-1-1-111-1-1-1-111111111111111-1-1-111-1-1-1-1-111
χ171111-1-1-1-1-111-11-1-111111-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-111iiii−i−i−i−iii−i−iii−i−i111-1-1-1-111111-1-1-1-111-1-111-1-1ii−i−ii−iii−i−ii−i11-1-1i−ii−ii−i
χ181111-1-1-1-1-111-11-1-111111-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-111−i−i−i−iiiii−i−iii−i−iii111-1-1-1-111111-1-1-1-111-1-111-1-1−i−iii−ii−i−iii−ii11-1-1−ii−ii−ii
χ191111-1-1-1-1-111-11-1-111111-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i−i−iii−i−iii1-1-11-11-111111-1-1-1-1-1-111-1-111ii−i−i−iiii−i−i−ii-1-111−iii−i−ii
χ201111-1-1-1-1-111-11-1-111111-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiiiii−i−iii−i−i1-1-11-11-111111-1-1-1-1-1-111-1-111−i−iiii−i−i−iiii−i-1-111i−i−iii−i
χ211111-1-1-1-1-111-11-1-111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-111iiii−i−i−i−iii−i−iii−i−i-1-1-1111-1-1-1-1-11111111-1-111-1-1ii−i−ii−i−i−iiii−i-1-111−ii−ii−ii
χ221111-1-1-1-1-111-11-1-111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-111−i−i−i−iiiii−i−iii−i−iii-1-1-1111-1-1-1-1-11111111-1-111-1-1−i−iii−iiii−i−i−ii-1-111i−ii−ii−i
χ231111-1-1-1-1-111-11-1-111111-1-1-1-1-1-1-1111-1-111-1-111-1-111-1-111iiii−i−i−i−i−i−iii−i−iii-111-11-1-1-1-1-1-111111-1-111-1-111ii−i−i−ii−i−iii−ii11-1-1i−i−iii−i
χ241111-1-1-1-1-111-11-1-111111-1-1-1-1-1-1-1111-1-111-1-111-1-111-1-111−i−i−i−iiiiiii−i−iii−i−i-111-11-1-1-1-1-1-111111-1-111-1-111−i−iiii−iii−i−ii−i11-1-1−iii−i−ii
χ251111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−iii−i−i−i−iii-1-11-111111-1-1-1-1-11111-1-1-1-111−i−iiii−iii−i−i−ii-11-11i−i−ii−ii
χ261111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii−i−iiiii−i−i-1-11-111111-1-1-1-1-11111-1-1-1-111ii−i−i−ii−i−iiii−i-11-11−iii−ii−i
χ271111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i−i−iiiii−i−i-11-111-1111-1-1-1-1-111-1-11111-1-1−i−iii−iiii−i−ii−i1-11-1−ii−iii−i
χ281111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiiiii−i−i−i−iii-11-111-1111-1-1-1-1-111-1-11111-1-1ii−i−ii−i−i−iii−ii1-11-1i−ii−i−ii
χ291111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1111111iiii−i−i−i−iii−i−i−i−iii11-11-1-11-1-111-111-1-111-1-1-1-111−i−iiii−i−i−iii−ii1-11-1−iii−ii−i
χ301111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii−i−iiiii−i−i11-11-1-11-1-111-111-1-111-1-1-1-111ii−i−i−iiii−i−ii−i1-11-1i−i−ii−ii
χ311111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i−i−iiiii−i−i1-11-1-111-1-111-111-1-1-1-11111-1-1−i−iii−ii−i−iiii−i-11-11i−ii−i−ii
χ321111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-1-1-11111-1-11111−i−i−i−iiiiiii−i−i−i−iii1-11-1-111-1-111-111-1-1-1-11111-1-1ii−i−ii−iii−i−i−ii-11-11−ii−iii−i
χ33222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-10000000000000000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1000000
χ34222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000000000002-2-2-22-2-1-1-1-1-1-1-1-1-1-1111111110000000000001111000000
χ35222222222222-12222-1-1-1-1-1-1-12-2-22-2-2-1-1-1-122222222-1-1-1-10000000000000000-2-2-2-2-2-2-11111-11111-1-1-1-1-1-1-1-10000000000001111000000
χ36222222222222-12222-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-10000000000000000-2222-22-11111-1111111111111000000000000-1-1-1-1000000
χ37222222222-2-22-1-2-222-1-1-1-1-1-1-1-222-222-1-1112222-2-2-2-211-1-10000000000000000-2-222-2-21-1-1111-1-111-1-1-1-111110000000000001-1-11000000
χ38222222222-2-22-1-2-222-1-1-1-1-1-1-1-222-222-1-111-2-2-2-2222211-1-10000000000000000-22-2-2-221-1-1111-1-1111111-1-1-1-1000000000000-111-1000000
χ39222222222-2-22-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1112222-2-2-2-211-1-1000000000000000022-2-222111-1-1111-1-1-1-1-1-11111000000000000-111-1000000
χ40222222222-2-22-1-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111-2-2-2-2222211-1-100000000000000002-2222-2111-1-1111-1-11111-1-1-1-10000000000001-1-11000000
χ4122222222-222-2222-2-22222222-200-200-2-2220000000022-2-20000000022222222000000-20000-20000000000000000-2-20000-2-20000000000
χ4222222222-222-2222-2-22222222-200-200-2-2220000000022-2-200000000-2-2-2-2-2-2-2-2000000-20000-20000000000000000220000220000000000
χ4322222222-2-2-2-22-2-2-2-22222222200200-2-2-2-200000000-2-2-2-2000000002222-2-2-2-20000002000020000000000000000-2-20000220000000000
χ4422222222-2-2-2-22-2-2-2-22222222200200-2-2-2-200000000-2-2-2-200000000-2-2-2-222220000002000020000000000000000220000-2-20000000000
χ452222-2-2-2-222222-2-2-2-2222-2-2-2-2200-200222200000000-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i00000020000-20000000000000000−2i2i0000−2i2i0000000000
χ462222-2-2-2-222222-2-2-2-2222-2-2-2-2200-200222200000000-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i00000020000-200000000000000002i−2i00002i−2i0000000000
χ472222-2-2-2-22-2-22222-2-2222-2-2-2-2-20020022-2-20000000022-2-2000000002i2i−2i−2i−2i−2i2i2i000000-2000020000000000000000−2i2i00002i−2i0000000000
χ482222-2-2-2-22-2-22222-2-2222-2-2-2-2-20020022-2-20000000022-2-200000000−2i−2i2i2i2i2i−2i−2i000000-20000200000000000000002i−2i0000−2i2i0000000000
χ492222-2-2-2-2-222-2-1-2-222-1-1-11111-2222-2-211-1-122-2-222-2-211-1-10000000000000000222-2-2-21-1-1-1-1-11111-1-111-1-111000000000000-1-111000000
χ502222-2-2-2-2-222-2-1-2-222-1-1-11111-2222-2-211-1-1-2-222-2-22211-1-100000000000000002-2-22-221-1-1-1-1-1111111-1-111-1-100000000000011-1-1000000
χ512222-2-2-2-2-222-2-1-2-222-1-1-11111-2-2-222211-1-122-2-222-2-211-1-10000000000000000-2-2-222211111-1-1-1-1-1-1-111-1-11100000000000011-1-1000000
χ522222-2-2-2-2-222-2-1-2-222-1-1-11111-2-2-222211-1-1-2-222-2-22211-1-10000000000000000-222-22-211111-1-1-1-1-111-1-111-1-1000000000000-1-111000000
χ532222-2-2-2-2-2-2-2-2-12222-1-1-11111222-2-2-2111122-2-2-2-222-1-1-1-10000000000000000-2-22-222-1-1-111111-1-1-1-11111-1-10000000000001-11-1000000
χ542222-2-2-2-2-2-2-2-2-12222-1-1-11111222-2-2-21111-2-22222-2-2-1-1-1-10000000000000000-22-222-2-1-1-111111-1-111-1-1-1-111000000000000-11-11000000
χ552222-2-2-2-2-2-2-2-2-12222-1-1-111112-2-2-222111122-2-2-2-222-1-1-1-1000000000000000022-22-2-2-111-1-11-1-111-1-11111-1-1000000000000-11-11000000
χ562222-2-2-2-2-2-2-2-2-12222-1-1-111112-2-2-2221111-2-22222-2-2-1-1-1-100000000000000002-22-2-22-111-1-11-1-11111-1-1-1-1110000000000001-11-1000000
χ5722-2-22i−2i2i−2i02-2022i−2i002-2-22i2i−2i−2i000000002-22−2−i2i22−2−i2i22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002−2−i2i22−2−i2i21+i−1−i1−i−1+i000000000000000000
χ5822-2-22i−2i2i−2i02-2022i−2i002-2-22i2i−2i−2i000000002-22−2−i2i22−2−i2i22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002−2−i2i22−2−i2i2−1−i1+i−1+i1−i000000000000000000
χ5922-2-22i−2i2i−2i02-2022i−2i002-2-22i2i−2i−2i000000002-2−22i2−i2−22i2−i22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−22i2−i2−22i2−i21+i−1−i1−i−1+i000000000000000000
χ6022-2-22i−2i2i−2i02-2022i−2i002-2-22i2i−2i−2i000000002-2−22i2−i2−22i2−i22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−22i2−i2−22i2−i2−1−i1+i−1+i1−i000000000000000000
χ6122-2-22i−2i2i−2i0-2202−2i2i002-2-22i2i−2i−2i00000000-222−2−i2i2−22i2−i2−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002−2−i2i2−22i2−i2−1−i1+i−1+i1−i000000000000000000
χ6222-2-22i−2i2i−2i0-2202−2i2i002-2-22i2i−2i−2i00000000-222−2−i2i2−22i2−i2−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002−2−i2i2−22i2−i21+i−1−i1−i−1+i000000000000000000
χ6322-2-22i−2i2i−2i0-2202−2i2i002-2-22i2i−2i−2i00000000-22−22i2−i22−2−i2i2−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−22i2−i22−2−i2i2−1−i1+i−1+i1−i000000000000000000
χ6422-2-22i−2i2i−2i0-2202−2i2i002-2-22i2i−2i−2i00000000-22−22i2−i22−2−i2i2−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−22i2−i22−2−i2i21+i−1−i1−i−1+i000000000000000000
χ6522-2-2−2i2i−2i2i02-202−2i2i002-2-2−2i−2i2i2i000000002-22−2i2−i22−2i2−i2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000002−2i2−i22−2i2−i21−i−1+i1+i−1−i000000000000000000
χ6622-2-2−2i2i−2i2i02-202−2i2i002-2-2−2i−2i2i2i000000002-22−2i2−i22−2i2−i2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002−2i2−i22−2i2−i2−1+i1−i−1−i1+i000000000000000000
χ6722-2-2−2i2i−2i2i02-202−2i2i002-2-2−2i−2i2i2i000000002-2−22−i2i2−22−i2i2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−22−i2i2−22−i2i21−i−1+i1+i−1−i000000000000000000
χ6822-2-2−2i2i−2i2i02-202−2i2i002-2-2−2i−2i2i2i000000002-2−22−i2i2−22−i2i2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−22−i2i2−22−i2i2−1+i1−i−1−i1+i000000000000000000
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χ8144444444-444-4-244-4-4-2-2-2-2-2-2-2-400-40022-2-200000000-2-22200000000000000000000002000020000000000000000000000000000000000
χ8244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-240040022220000000022220000000000000000000000-20000-20000000000000000000000000000000000
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χ9244-4-4−4i4i−4i4i0-440-24i−4i00-2222i2i−2i−2i000000002-2−2222−2i22i222−222i2−2i2−2i2i00000000000000000000000000000000002−2i2−i2−22−i2i20000000000000000000000
χ934-44-44i−4i−4i4i000040000-44-44i−4i−4i4i00000000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000000000000
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χ964-44-4−4i4i4i−4i000040000-44-4−4i4i4i−4i0000000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000000000000000
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χ984-4-4444-4-4400-4-2004-422-2-22-220-440-44-22000000000000-22000000000000000000000002-20002-200000000000000000000000000000000
χ994-4-4444-4-4-4004400-44-4-444-44-4000000-44000000000000-4400000000000000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-4-4004-200-4422-2-22-220000002-20000000000002-20000000000000000000000000−2i32i3000−2i32i3000000000000000000000000000000
χ1014-4-4444-4-4-4004-200-4422-2-22-220000002-20000000000002-200000000000000000000000002i3−2i30002i3−2i3000000000000000000000000000000
χ1024-4-44-4-444400-4400-44-4-44-44-440000004-4000000000000-4400000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-4-444400-4-200-4422-22-22-2000000-220000000000002-20000000000000000000000000−2i32i30002i3−2i3000000000000000000000000000000
χ1044-4-44-4-444400-4-200-4422-22-22-2000000-220000000000002-200000000000000000000000002i3−2i3000−2i32i3000000000000000000000000000000
χ1054-4-44-4-444-4004-2004-422-22-22-204-40-442-2000000000000-2200000000000000000000000-220002-200000000000000000000000000000000
χ1064-4-44-4-444-4004-2004-422-22-22-20-4404-42-2000000000000-22000000000000000000000002-2000-2200000000000000000000000000000000
χ1078-88-88i−8i−8i8i0000-400004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8−8i8i8i−8i0000-400004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.