Finite Group Databasebeta

← Group #13138778

Character table — Group #13138778

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122244443666121212128824242424336666661212121212121212366612121212242424242424242424242424242424244444888888882444668812121212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1-11-111i−i11-1-111-1-1-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-11-11-1-1i−i11-1-1-1-11111ii−i−i−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii-111-1-1-1−ii-1-11111-1-111−i−iii−i−iiiii−i−i
χ121111-1-1-1-11111-1-1-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iiiii−i−i1-1-1111−ii-1-111-1-111-1-1−i−iiiii−i−i−i−iii
χ131111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1ii−i−iii−i−i-11-11-1-1−ii11-1-1-1-11111−i−iiiii−i−iii−i−i
χ141111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii1-11-111−ii11-1-111-1-1-1-1−i−iii−i−iii−i−iii
χ151111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111ii−i−i−i−iii1-1-1111i−i-1-111-1-111-1-1ii−i−i−i−iiiii−i−i
χ161111-1-1-1-11111-1-1-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111−i−iiiii−i−i-111-1-1-1i−i-1-11111-1-111ii−i−iii−i−i−i−iii
χ1722222222222222222222222-1-1-1222-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022222200-1-10000000000-1-10000-1-1-1-10000
χ1822222222222222222222222-1-1-1222-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2-2-20011000000000011000011110000
χ192222222222222222222222-1222-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000022220000002200000000-1-1-1-10000000000-1-1-1-1
χ202222222222222222222222-1222-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000111100000000001111
χ212222222222222222-2-2-2-2-2-22-1-1-1222-122-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111000000002222-2-200110000000000110000-1-1-1-10000
χ222222222222222222-2-2-2-2-2-22-1-1-1222-122-1-1-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-2-2-22200-1-10000000000-1-1000011110000
χ232222222222222222-2-2-2-2-2-2-1222-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100002222000000-2-20000000011110000000000-1-1-1-1
χ242222222222222222-2-2-2-2-2-2-1222-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-2-2-20000002200000000-1-1-1-100000000001111
χ252222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1-1-1222-1-2-21111-2-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii000000002i2i−2i−2i2-200-1-10000000000110000−i−iii0000
χ262222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1-1-1222-1-2-21111-2-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−2i−2i2i2i-2200110000000000-1-10000ii−i−i0000
χ272222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-1222-1-1-1211-2-2-2-211-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00002i2i−2i−2i0000002-200000000-1-1110000000000−i−iii
χ282222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-1222-1-1-1211-2-2-2-211-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i−2i2i2i000000-220000000011-1-10000000000ii−i−i
χ292222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-1222-1-2-21111-2-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i000000002i2i−2i−2i-2200110000000000-1-10000−i−iii0000
χ302222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1-1-1222-1-2-21111-2-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−2i−2i2i2i2-200-1-10000000000110000ii−i−i0000
χ312222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-1222-1-1-1211-2-2-2-211-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00002i2i−2i−2i000000-220000000011-1-10000000000−i−iii
χ322222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-1222-1-1-1211-2-2-2-211-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i−2i2i2i0000002-200000000-1-1110000000000ii−i−i
χ3322-2-222-2-222-2-222-2-200000022-2-22-2-22-2-222-2-2222-2-22-2-22200000000000000002i−2i2i−2i00000000000000002i−2i2i−2i000000000000000000
χ3422-2-222-2-222-2-222-2-200000022-2-22-2-22-2-222-2-2222-2-22-2-2220000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i000000000000000000
χ3522-2-2-2-22222-2-2-2-22200000022-2-22-2-2222-2-222-2-22-2-2222-2-200000000000000002i−2i−2i2i00000000000000002i−2i−2i2i000000000000000000
χ3622-2-2-2-22222-2-2-2-22200000022-2-22-2-2222-2-222-2-22-2-2222-2-20000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i000000000000000000
χ372-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ382-22-22i−2i2i−2i2-22-22i−2i2i−2i000000222-2-22-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ392-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i−ii−ii2i−2i-1-111−ii−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−i3i300000000003−30000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ402-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i−ii−ii2i−2i-1-111−ii−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i3−i30000000000−330000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ412-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i−ii−ii2i−2i-1-111−ii−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000i3−i30000000000−330000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ422-22-22i−2i2i−2i2-22-22i−2i2i−2i0000002-1-11-22-212i−2i−ii−ii2i−2i-1-111−ii−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−i3i300000000003−30000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ432-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ442-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ452-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2ii−ii−i−2i2i-1-111i−ii−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000i3−i300000000003−30000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ462-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2ii−ii−i−2i2i-1-111i−ii−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−i3i30000000000−330000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ472-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2ii−ii−i−2i2i-1-111i−ii−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−i3i30000000000−330000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ482-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000002-1-11-22-21−2i2ii−ii−i−2i2i-1-111i−ii−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000i3−i300000000003−30000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ492-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-2-22-2−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ502-2-222i−2i−2i2i2-2-222i−2i−2i2i00000022-22-2-22-2−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ512-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-12-2211-1-2i−i2i−2i−2i2i−ii-11-11i−i−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−i3i33−30000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ522-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-12-2211-1-2i−i2i−2i−2i2i−ii-11-11i−i−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000i3−i3−330000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ532-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-12-2211-1-2i−i2i−2i−2i2i−ii-11-11i−i−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000i3−i3−330000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ542-2-222i−2i−2i2i2-2-222i−2i−2i2i000000-12-2211-1-2i−i2i−2i−2i2i−ii-11-11i−i−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−i3i33−30000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ552-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-2-22-22i−2i−2i2i2i−2i−2i2i2-22-22i−2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ562-2-22−2i2i2i−2i2-2-22−2i2i2i−2i00000022-22-2-22-22i−2i−2i2i2i−2i−2i2i2-22-22i−2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ572-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-12-2211-1-2−ii−2i2i2i−2ii−i-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000i3−i33−30000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ582-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-12-2211-1-2−ii−2i2i2i−2ii−i-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−i3i3−330000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ592-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-12-2211-1-2−ii−2i2i2i−2ii−i-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−i3i3−330000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ602-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000-12-2211-1-2−ii−2i2i2i−2ii−i-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000i3−i33−30000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.