Finite Group Databasebeta

← Group #13168437

Character table — Group #13168437

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121218181818181824242424242436363636363636363636367272108108
order122233344666666666121212123336666666661212121212121212121212124444121212123666121212121212224466661212121212121212121212121212121212121212121212121212121212124444446666664441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-11-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111111-1-1
χ91111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11-111-1-1-11-111-1-111-1-11-11-1
χ101111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-11-1-111-1-1111-1-1-1-111-11-11
χ111111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-111-1-1-111-1-1111-1-11
χ121111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-1111-11-1-11111-1-1-111-1
χ131111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-111-1-11-11-1-11111-1-1-11-11
χ141111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-1-11111-1-1-111-1-1111-11-1
χ151111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1111-111-1-1-1-1111-1-1-1-111-111-1
χ161111111-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-11-1-111-11-111-1-111-1-11-1-11
χ17222222-122222-1-122-1222222-1-1-1-12-1-122-1-122-1-12222-1-1-1-122000000-1-1-1-1-1-1-1-1-1-122022222-1-1-1-10022220000-1-1-1-1-1-1-1-100000000000000-1-1-1-1-1-102200000000-1-100
χ18222222-122222-1-122-1222222-1-1-1-12-1-122-1-122-1-12222-1-1-1-122000000-1-1-1-1-1-1-1-1-1-1-2-202-2-2-2-2-1-1-1-10022220000-1-1-1-1-1-1-1-1000000000000001111110-2-2000000001100
χ19222222-122222-1-122-1222222-1-1-1-12-1-122-1-122-1-12222-1-1-1-1-2-2000000-1-1-1-1-1-1-1-1-1-1220-22222111100-2-2-2-200001111111100000000000000-1-1-1-1-1-10-2-2000000001100
χ20222222-122222-1-122-1222222-1-1-1-12-1-122-1-122-1-12222-1-1-1-1-2-2000000-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2111100-2-2-2-20000111111110000000000000011111102200000000-1-100
χ21222222-1-2-2222-1-122-12-2-2-2-22-1-1-1-12-1-122-1-1-2-211-2-2-2-2111122000000-1-1-1-11111112-20-222-2-2-1-1110022-2-20000-1-1-1-1111100000000000000-11-1-11102-200000000-1100
χ22222222-1-2-2222-1-122-12-2-2-2-22-1-1-1-12-1-122-1-1-2-211-2-2-2-2111122000000-1-1-1-1111111-220-2-2-222-1-1110022-2-20000-1-1-1-11111000000000000001-111-1-10-22000000001-100
χ23222222-1-2-2222-1-122-12-2-2-2-22-1-1-1-12-1-122-1-1-2-211-2-2-2-21111-2-2000000-1-1-1-11111112-20222-2-211-1-100-2-22200001111-1-1-1-100000000000000-11-1-1110-22000000001-100
χ24222222-1-2-2222-1-122-12-2-2-2-22-1-1-1-12-1-122-1-1-2-211-2-2-2-21111-2-2000000-1-1-1-1111111-2202-2-22211-1-100-2-22200001111-1-1-1-1000000000000001-111-1-102-200000000-1100
χ2522222-12222-1-122222-12222-12-1-1-1-12-1-1-122-1-122-1-1-1-122220022-1-1-1-1-1-1-1-1-1-1-1-1-1-12220-1-1-1-10000-1-10000222200000000-1-1-1-1-1-1-1-100222222-1-1-1-10000000-1-1-1-10000
χ2622222-12222-1-122222-12222-12-1-1-1-12-1-1-122-1-122-1-1-1-122220022-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22011110000-1-10000222200000000-1-1-1-1-1-1-1-100-2-2-2-2-2-21111000000011110000
χ2722222-12222-1-122222-12222-12-1-1-1-12-1-1-122-1-122-1-1-1-1222200-2-21111-1-1-1-1-1-1-1-1-1-122-20-1-1-1-10000110000-2-2-2-2000000001111111100-2-2-2-222-1-1-1-1000000011110000
χ2822222-12222-1-122222-12222-12-1-1-1-12-1-1-122-1-122-1-1-1-1222200-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2011110000110000-2-2-2-20000000011111111002222-2-211110000000-1-1-1-10000
χ2922222-12-2-22-1-122222-1-2-2-2-2-12-1-1-1-12-1-1-12211-2-21111-2-2-2-20022-1-1-1-1-1-1-1-11111112-2-20-1-111000011000022-2-200000000-1-1-1-111110022-2-22-2-1-1110000000-1-1110000
χ3022222-12-2-22-1-122222-1-2-2-2-2-12-1-1-1-12-1-1-12211-2-21111-2-2-2-20022-1-1-1-1-1-1-1-1111111-22-2011-1-1000011000022-2-200000000-1-1-1-1111100-2-222-2211-1-1000000011-1-10000
χ3122222-12-2-22-1-122222-1-2-2-2-2-12-1-1-1-12-1-1-12211-2-21111-2-2-2-200-2-21111-1-1-1-11111112-220-1-1110000-1-10000-2-222000000001111-1-1-1-100-2-2222-2-1-111000000011-1-10000
χ3222222-12-2-22-1-122222-1-2-2-2-2-12-1-1-1-12-1-1-12211-2-21111-2-2-2-200-2-21111-1-1-1-1111111-222011-1-10000-1-10000-2-222000000001111-1-1-1-10022-2-2-2211-1-10000000-1-1110000
χ332222-12222-12222-1-122-1-1-1-1-1-1222-1-12-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-100220000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000000200-1-1-1-100000000
χ342222-12222-12222-1-122-1-1-1-1-1-1222-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2200002222-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-20000000000-200111100000000
χ352222-12222-12222-1-122-1-1-1-1-1-1222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-2222222-1-1-1-122-1-1-1-1002-20000-2-2-2-2221111-1-1-1-111111111-1-1-1-1-1-1-1-1-2-20000000000-200111100000000
χ362222-12222-12222-1-122-1-1-1-1-1-1222-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-20000-2-2-2-2-2-2111111111111111111111111220000000000200-1-1-1-100000000
χ372222-122-2-2-12222-1-1221111-1-1222-1-12-1-1-1-1-2-2-2-21111111122222222-1-1-1-1-2-2111100-2-2000022-2-2-2-2-1-111-1-111-1-1-1-11111-1-1-1-11111220000000000-200-1-11100000000
χ382222-122-2-2-12222-1-1221111-1-1222-1-12-1-1-1-1-2-2-2-21111111122-2-2-2-2-2-2-1-1-1-1-2-21111002-2000022-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-1-2-2000000000020011-1-100000000
χ392222-122-2-2-12222-1-1221111-1-1222-1-12-1-1-1-1-2-2-2-211111111-2-2222222-1-1-1-1-2-2111100-220000-2-222-2-211-1-1-1-1111111-1-1-1-1-1-1-1-11111-2-2000000000020011-1-100000000
χ402222-122-2-2-12222-1-1221111-1-1222-1-12-1-1-1-1-2-2-2-211111111-2-2-2-2-2-2-2-2-1-1-1-1-2-2111100220000-2-2222211-1-111-1-11111-1-1-1-11111-1-1-1-1220000000000-200-1-11100000000
χ412-22-222200-2-2-22-22-2-2200002222-2-2-2-22-22-20000000000002i−2i2-222-2-222-2-2000000000000002i−2i00002i−2i002-2002i2i−2i−2i000022-2-200002i−2i00000000000002i−2i0000000000
χ422-22-222200-2-2-22-22-2-2200002222-2-2-2-22-22-20000000000002i−2i-22-2-22222-2-2000000000000002i−2i00002i−2i00-22002i2i−2i−2i0000-2-2220000−2i2i0000000000000−2i2i0000000000
χ432-22-222200-2-2-22-22-2-2200002222-2-2-2-22-22-2000000000000−2i2i2-222-2-222-2-200000000000000−2i2i0000−2i2i002-200−2i−2i2i2i000022-2-20000−2i2i0000000000000−2i2i0000000000
χ442-22-222200-2-2-22-22-2-2200002222-2-2-2-22-22-2000000000000−2i2i-22-2-22222-2-200000000000000−2i2i0000−2i2i00-2200−2i−2i2i2i0000-2-22200002i−2i00000000000002i−2i0000000000
χ452-22-2-122001-2-22-2-11-2233−3−3-1-122-211-2-11-11000033−3−333−3−32i−2i2-222-2-2-1-1110033−3−3000000002i−2i0000−ii−i3i3-113−3−i−iii−i3−i3i3i3-1-11133−3−32i−2i0000000000000−ii−i3i300000000
χ462-22-2-122001-2-22-2-11-2233−3−3-1-122-211-2-11-11000033−3−333−3−32i−2i-22-2-222-1-1110033−3−3000000002i−2i0000−ii−i3i31-1−33−i−iii−i3−i3i3i311-1-1−3−333−2i2i0000000000000i−ii3−i300000000
χ472-22-2-122001-2-22-2-11-2233−3−3-1-122-211-2-11-11000033−3−333−3−3−2i2i2-222-2-2-1-1110033−3−300000000−2i2i0000i−ii3−i3-113−3ii−i−ii3i3−i3−i3-1-11133−3−3−2i2i0000000000000i−ii3−i300000000
χ482-22-2-122001-2-22-2-11-2233−3−3-1-122-211-2-11-11000033−3−333−3−3−2i2i-22-2-222-1-1110033−3−300000000−2i2i0000i−ii3−i31-1−33ii−i−ii3i3−i3−i311-1-1−3−3332i−2i0000000000000−ii−i3i300000000
χ492-22-2-122001-2-22-2-11-22−3−333-1-122-211-2-11-110000−3−333−3−3332i−2i2-222-2-2-1-11100−3−333000000002i−2i0000−iii3−i3-11−33−i−iiii3i3−i3−i3-1-111−3−3332i−2i0000000000000−iii3−i300000000
χ502-22-2-122001-2-22-2-11-22−3−333-1-122-211-2-11-110000−3−333−3−3332i−2i-22-2-222-1-11100−3−333000000002i−2i0000−iii3−i31-13−3−i−iiii3i3−i3−i311-1-133−3−3−2i2i0000000000000i−i−i3i300000000
χ512-22-2-122001-2-22-2-11-22−3−333-1-122-211-2-11-110000−3−333−3−333−2i2i2-222-2-2-1-11100−3−33300000000−2i2i0000i−i−i3i3-11−33ii−i−i−i3−i3i3i3-1-111−3−333−2i2i0000000000000i−i−i3i300000000
χ522-22-2-122001-2-22-2-11-22−3−333-1-122-211-2-11-110000−3−333−3−333−2i2i-22-2-222-1-11100−3−33300000000−2i2i0000i−i−i3i31-13−3ii−i−i−i3−i3i3i311-1-133−3−32i−2i0000000000000−iii3−i300000000
χ532-2-222222-222-2-2-2-2-22-22-22-2222-2-2222-2-2-2-22-22-22-22-22-22-2000000002-2-222-22-22-200000000000000000000000000000000000000002i−2i2i−2i00000000000002i−2i2i−2i0000
χ542-2-222222-222-2-2-2-2-22-22-22-2222-2-2222-2-2-2-22-22-22-22-22-22-2000000002-2-222-22-22-20000000000000000000000000000000000000000−2i2i−2i2i0000000000000−2i2i−2i2i0000
χ552-2-22222-2222-2-2-2-2-22-2-22-22222-2-2222-2-2-2-2-22-22-22-22-22-22000000002-2-22-22-22-2200000000000000000000000000000000000000002i−2i−2i2i00000000000002i−2i−2i2i0000
χ562-2-22222-2222-2-2-2-2-22-2-22-22222-2-2222-2-2-2-2-22-22-22-22-22-22000000002-2-22-22-22-220000000000000000000000000000000000000000−2i2i2i−2i0000000000000−2i2i2i−2i0000
χ572-2-222-122-22-11-2-2-2-2212-22-2-12-111-12-111-2-2-112-2-11-112-22-200003−33−3-111-1-11-11-110000−i3i3−i3i300003−300000000000000003−33−33−33−3002i−2i2i−2i00−i3i3−i3i30000000−ii−ii0000
χ582-2-222-122-22-11-2-2-2-2212-22-2-12-111-12-111-2-2-112-2-11-112-22-200003−33−3-111-1-11-11-110000i3−i3i3−i300003−300000000000000003−33−33−33−300−2i2i−2i2i00i3−i3i3−i30000000i−ii−i0000
χ592-2-222-122-22-11-2-2-2-2212-22-2-12-111-12-111-2-2-112-2-11-112-22-20000−33−33-111-1-11-11-110000−i3i3−i3i30000−330000000000000000−33−33−33−3300−2i2i−2i2i00−i3i3−i3i30000000i−ii−i0000
χ602-2-222-122-22-11-2-2-2-2212-22-2-12-111-12-111-2-2-112-2-11-112-22-20000−33−33-111-1-11-11-110000i3−i3i3−i30000−330000000000000000−33−33−33−33002i−2i2i−2i00i3−i3i3−i30000000−ii−ii0000
χ612-2-222-12-222-11-2-2-2-221-22-22-12-111-12-111-2-21-1-221-11-1-22-2200003−33−3-111-11-11-11-10000−i3i3i3−i30000−3300000000000000003−33−3−33−33002i−2i−2i2i00−i3i3i3−i30000000−iii−i0000
χ622-2-222-12-222-11-2-2-2-221-22-22-12-111-12-111-2-21-1-221-11-1-22-2200003−33−3-111-11-11-11-10000i3−i3−i3i30000−3300000000000000003−33−3−33−3300−2i2i2i−2i00i3−i3−i3i30000000i−i−ii0000
χ632-2-222-12-222-11-2-2-2-221-22-22-12-111-12-111-2-21-1-221-11-1-22-220000−33−33-111-11-11-11-10000−i3i3i3−i300003−30000000000000000−33−333−33−300−2i2i2i−2i00−i3i3i3−i30000000i−i−ii0000
χ642-2-222-12-222-11-2-2-2-221-22-22-12-111-12-111-2-21-1-221-11-1-22-220000−33−33-111-11-11-11-10000i3−i3−i3i300003−30000000000000000−33−333−33−3002i−2i−2i2i00i3−i3−i3i30000000−iii−i0000
χ6544444-2-2444-2-2-2-244-2-24444-2-2111-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000011111111114400-2-2-2-2000000000000000000000000000000000000-2-21111000000000000000
χ6644444-2-2444-2-2-2-244-2-24444-2-2111-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000001111111111-4-400222200000000000000000000000000000000000022-1-1-1-1000000000000000
χ6744444-2-2-4-44-2-2-2-244-2-2-4-4-4-4-2-2111-2-21-2-2-2-2222222222222000000001111-1-1-1-1-1-14-400-2-222000000000000000000000000000000000000-2211-1-1000000000000000
χ6844444-2-2-4-44-2-2-2-244-2-2-4-4-4-4-2-2111-2-21-2-2-2-2222222222222000000001111-1-1-1-1-1-1-440022-2-20000000000000000000000000000000000002-2-1-111000000000000000
χ694444-24-244-244-2-2-2-2-24-2-2-2-2-21-2-2-2-21-2-2-21144-2-2-2-2-2-21111440000001111-2-2111100040000-2-2-2-200-2-2-2-200001111111100000000000000000000000000000000000
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χ1054-4-4444-2-4444-422-4-4-2-4-44-444-2-2224-2-2-4-422-442-2-44-442-22-200000000-222-22-22-22-200000000000000000000000000000000000000000000000000000000000000000
χ1064-4-444-2-24-44-2222-4-4-224-44-4-2-21-1-1-2-212222-22-22-22-22-22-22000000001-1-111-11-11-10000−2i32i3−2i32i300000000000000000000000000000000000000i3−i3i3−i3000000000000000
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χ1104-4-44-2444-4-24-4-4-4224-4-22-22-2-24-4-4-2-2422224-44-4-22-22-22-2200000000-222-24-4-22-2200000000000000000000000000000000000000000000000000000000000000000
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χ1154-4-44-24-2-44-24-42222-2-42-22-2-21-222-21-222-1-1-442-22-22-2-11-11000000001-1-112-2-11-110000000000000000000000−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000000000
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χ1174-4-44-2-244-4-2-22-4-42242-22-221-2-2221-2-2-1-122-224-41-11-1-22-220000−2323−23231-1-11-221-11-1000000000000−232300000000000000003−33−33−33−3000000000000000000000000000
χ1184-4-44-2-24-44-2-22-4-422422-22-21-2-2221-2-2-1-1222-2-44-11-112-22-2000023−2323−231-1-112-2-11-11000000000000−23230000000000000000−33−333−33−3000000000000000000000000000
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χ1208888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4-42222222200000000-1-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000000000000
χ1218888-4-4-4-8-8-4-4-4-4-4-4-4-4-444442222222222224444-2-2-2-2-2-2-2-200000000-1-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000000000000
χ12288-8-88-4-400-84-44-4-88440000-4-42-2244-24-44-4000000000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000000000
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χ12488-8-8-4-4-40044-44-44-444−434343−43222-22-2-2-2-22-22000023−23−232323−23−232300000000-11-1100−333−300000000000000000000000000000000000000000000000000000000000000000
χ1258-88-88-4-400-844-448-84-40000-4-422-244-2-44-440000000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000000000
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χ1278-88-8-4-4-400444-44-444-4−43−4343432222-2-2-2-22-22-200002323−23−232323−23−2300000000-1-11100−3−33300000000000000000000000000000000000000000000000000000000000000000
χ1288-8-88-4-4-48-8-4-444444-44-44-44222-2-2222-2-2-2-2-44-442-22-22-22-200000000-111-12-2-11-1100000000000000000000000000000000000000000000000000000000000000000
χ1298-8-88-4-4-4-88-4-444444-444-44-4222-2-2222-2-2-2-24-44-4-22-22-22-2200000000-111-1-221-11-100000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).