Finite Group Databasebeta

← Group #13156832

Character table — Group #13156832

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12222222333666666666666666666666333666666666666666666666444444441212121212121212121212121212121236666666441212121212121212121212121212121212121212121212121212121212121212121212121212121244441212121212121212224466661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ911-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1
χ1011-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−ii11-1-1ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11−ii-1-111−i−iii-11
χ1111-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1i−i11-1-1−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−i−i−iiiii-11i−i-1-111ii−i−i-11
χ1211-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−ii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1
χ1311-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1i−i-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii1-1−ii11-1-1−i−iii-11
χ1411-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−ii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iii−i−i−i−iiiii-11i−i-1-111ii−i−i1-1
χ1511-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−iiiii−i−i−i−i-11−ii-1-111−i−iii1-1
χ1611-11-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−ii-1-111−i−iii−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i-11
χ172222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-1000022220000000022222222-1-1-1-1-1-1-1-1220000-1-1-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002200-1-1-1-1000000
χ182222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-1000022220000000022222222-1-1-1-1-1-1-1-1-2-20000-1-1-1-1-2-211-2-21100000000-1-1-1-1-1-1-1-111111111000000000000-2-2001111000000
χ192222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1220000111122-1-122-1-10000000011111111-1-1-1-1-1-1-1-1000000000000-2-2001111000000
χ202222222222-122222222-1-1-1-1-12222-1-1222-1-122-1-1-1-1-1-12222-1-1-1-1-1-12-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-200001111-2-211-2-2110000000011111111111111110000000000002200-1-1-1-1000000
χ21222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-122-1-1-1-10000-1-122-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100
χ22222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-1-2-2-1-1-1-1000011-2-211-2-2-1-1-1-1-1-1-1-1000000001111111100000000000000-2-20000111100
χ23222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-12211110000-1-122-1-1221111111100000000-1-1-1-1-1-1-1-100000000000000-2-20000111100
χ24222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-2-21111000011-2-211-2-211111111000000001111111100000000000000220000-1-1-1-100
χ2522222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ2622222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-122222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1002222-2-2-2-200000000-1-1-1-1-1-1-1-11111111100000000-2-2-2-21111111100000000000000
χ2722222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-12-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-222220000000011111111-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ2822222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-1222-1-1-1-1-1-1-1222-1-12-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-100-2-2-2-2-2-2-2-2000000001111111111111111000000002222-1-1-1-1-1-1-1-100000000000000
χ29222-2-2-22-22222-22-22-22-22-2-22-2-2-22-22-2-222222-22-2-22-2-222-2-22-2-222-2-22-22i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-2002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000
χ30222-2-2-22-22222-22-22-22-22-2-22-2-2-22-22-2-222222-22-2-22-2-222-2-22-2-222-2-22-2−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-200−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000
χ31222-2-2-22-22-122-2-112-2-112-2-22-2-21212-2-2-1-12-1-112-2-2-111-1-1112-2-2-1-111212i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-1-111-1-11100−ii−ii00003−3003−300−i−iii−i−iii0000000033−3−333−3−300000000000000000000−i3i3−i3i300
χ32222-2-2-22-22-122-2-112-2-112-2-22-2-21212-2-2-1-12-1-112-2-2-111-1-1112-2-2-1-111212i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-1-111-1-11100−ii−ii0000−3300−3300−i−iii−i−iii00000000−3−333−3−33300000000000000000000i3−i3i3−i300
χ33222-2-2-22-22-122-2-112-2-112-2-22-2-21212-2-2-1-12-1-112-2-2-111-1-1112-2-2-1-11121−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-1-111-1-11100i−ii−i00003−3003−300ii−i−iii−i−i0000000033−3−333−3−300000000000000000000i3−i3i3−i300
χ34222-2-2-22-22-122-2-112-2-112-2-22-2-21212-2-2-1-12-1-112-2-2-111-1-1112-2-2-1-11121−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-1-111-1-11100i−ii−i0000−3300−3300ii−i−iii−i−i00000000−3−333−3−33300000000000000000000−i3i3−i3i300
χ35222-2-2-22-2-122-112-2-112-22-2-22-21-2-1-22-212-1-12-11-1112-2-2-1-111-11122-21-1-22i−2i2i−2i0000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i3-1-111-1-111002i−2i2i−2i000000000000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i300000000000033−3−333−3−300000000000000
χ36222-2-2-22-2-122-112-2-112-22-2-22-21-2-1-22-212-1-12-11-1112-2-2-1-111-11122-21-1-22i−2i2i−2i0000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3-1-111-1-111002i−2i2i−2i000000000000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3000000000000−3−333−3−33300000000000000
χ37222-2-2-22-2-122-112-2-112-22-2-22-21-2-1-22-212-1-12-11-1112-2-2-1-111-11122-21-1-2−2i2i−2i2i0000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−2i2i−2i2i000000000000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3000000000000−3−333−3−33300000000000000
χ38222-2-2-22-2-122-112-2-112-22-2-22-21-2-1-22-212-1-12-11-1112-2-2-1-111-11122-21-1-2−2i2i−2i2i0000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i3-1-111-1-11100−2i2i−2i2i000000000000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i300000000000033−3−333−3−300000000000000
χ3922-22-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-211111121100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-111112i−2i0000−i−iii2i2i−i−i−2i−2iii00000000−i−i−i−iiiii−i−i−i−iiiii0000000000002-200-1-111000000
χ4022-22-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-211111121100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-11111−2i2i0000−i−iii−2i−2iii2i2i−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i000000000000-220011-1-1000000
χ4122-22-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112i−2i0000ii−i−i2i2i−i−i−2i−2iii00000000iiii−i−i−i−i−i−i−i−iiiii000000000000-220011-1-1000000
χ4222-22-2-2-2222-12222-2-2-2-2-1-1-11122-2-211-2-22-1-122-1-1-1-1-1-1-2-2-2-21111112110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111−2i2i0000ii−i−i−2i−2iii2i2i−i−i00000000iiii−i−i−i−iiiii−i−i−i−i0000000000002-200-1-111000000
χ4322-22-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-2122-2-200002222-2-2-2-200000000-1-1-1-111112i−2i-1-1110000−i−i2i2iii−2i−2i-1-1-1-1111100000000−i−i−i−iiiii000000000000002i−2i0000−i−iii00
χ4422-22-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-2122-2-200002222-2-2-2-200000000-1-1-1-11111−2i2i-1-1110000ii−2i−2i−i−i2i2i-1-1-1-1111100000000iiii−i−i−i−i00000000000000−2i2i0000ii−i−i00
χ4522-22-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-21-2-2220000-2-2-2-2222200000000-1-1-1-111112i−2i11-1-10000−i−i2i2iii−2i−2i1111-1-1-1-100000000−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00
χ4622-22-2-2-222-1222-1-1-2-211222-2-22-1-21-2-2-21-12-1-1-1222-1-1-11111-2-2-2111-1-21-2-2220000-2-2-2-2222200000000-1-1-1-11111−2i2i11-1-10000ii−2i−2i−i−i2i2i1111-1-1-1-100000000iiii−i−i−i−i000000000000002i−2i0000−i−iii00
χ4722-22-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-222-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-1-1-1-111110022-2-22i2i−2i−2i00000000-1-1-1-11111−i−i−i−iiiii000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ4822-22-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-222-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-1-1-1-111110022-2-2−2i−2i2i2i00000000-1-1-1-11111iiii−i−i−i−i00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ4922-22-2-2-22-122-1-12211-2-2222-2-2-121-2-2-21-2-1-12-1-1-1-1-12221111111-2-2-2-11-2-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii-1-1-1-1111100-2-2222i2i−2i−2i000000001111-1-1-1-1−i−i−i−iiiii00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
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χ1204-4444-4-4-44-24-4-42244-22-44-44-44-2-4-2-44-42-24-222-44-42-22-22-2244-4-222-2-4-2000000000000000000000000-22-22-22-2200000000000000000000000000000000000000000000000000000000000000000000
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χ1224-4444-4-4-44-2-2-4-42244-222-22-224-2-4-22-2-42-2-21222-22-11-1-22-22-2-221-1-1-2210000000000000000000000001-11-11-11-10000000000000000000000000000000000-333-3-333-300000000000000000000000000
χ1234-4444-4-4-4-24-222-4-4-2-24-42-22-22-24242-22-4-21-222-11-12-22-22-2211-1-222-2-1-2000000000000000023−2323−2323−2323−231-11-11-11-100000000000000000000000000−33−33−33−330000000000000000000000000000000000
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χ1274-44-4-44-444-24-442-24-4-2-2-4-4444-42-42-4-442-24-22-2-4-4422-2-222-24-44-22-22-42000000000000000000000000-222-2-222-200000000000000000000000000000000000000000000000000000000000000000000
χ1284-44-4-44-444-2-2-442-24-4-2-222-2-2-2-42-422242-2-212-222-2-1-11-222-2-22-21-1122-10000000000000000000000001-1-111-1-1100000000000023−230023−230000000000000000−33−33−33−3300000000000000000000000000
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χ1374-4-44-444-44-2-2-4-422-4-42-22-222-24-242-224-2-2-21222-22-11-12-22-222-2-111-2-2-10000000000000000000000001-11-1-11-110000000000000000000000000000000000−3i3i3i−3i3i−3i−3i3i00000000000000000000000000
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χ1414-4-44-444-4-2-242222222-2-44-4-44-2-2-224-4-2-21-2-2-1-12-222-22-11-1122-22-2-21-22000000002i3−2i32i3−2i3−2i32i3−2i32i3000000001-11-1-11-11000000000000000000−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
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χ1464-4-4-44-444-24-22-2-442-2-4-422-2222-4-24-2-224-21-22-2-1-1122-22-2-22-11-12-2221-20000-444-4000000002-2-22-222-21-1-11-111-10000002-2-220000000000000000-111-11-1-110000000000000000000000000000000000
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χ14988888888-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222222222222222000000000000000000000000-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000000000000000
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χ15188-88-8-8-88-4-4-4-4-4-4-44444-4-4-444-4-444444422222222222-2-2-2-2-2-2-2-2-2-22-2-2000000000000000000000000-1-1-1-1111100000000000000000000000000000000000000000000000000000000000000000000
χ15288-8-888-8-8-4-4-4-44-444-44-4-4444-4444-44-4-442222-22-2-22-2-2-2-222-222-2-22-2-22000000000000000000000000-1-11111-1-100000000000000000000000000000000000000000000000000000000000000000000
χ1538-8888-8-8-8-4-4-44444-4-4-444-44-44-4-44-44-444222-2-2-22-2-22-22-22-222-22-2-22-22000000000000000000000000-11-11-11-1100000000000000000000000000000000000000000000000000000000000000000000
χ1548-88-8-88-88-4-4-44-44-4-44-4-444-4-4-4444444-44222-22-2-22-2-222-2-222-222-22-2-2-2000000000000000000000000-111-1-111-100000000000000000000000000000000000000000000000000000000000000000000
χ1558-8-88-888-8-4-4-44444444-44-444-4-4-4-44-44-4-4222-2-2-22-2-22-2-22-22-2-22-22222-2000000000000000000000000-11-111-11-100000000000000000000000000000000000000000000000000000000000000000000
χ1568-8-8-88-888-4-4-44-44-44-44444-44444-4-4-4-44-4222-22-2-22-2-22-222-2-22-2-22-2-222000000000000000000000000-111-11-1-1100000000000000000000000000000000000000000000000000000000000000000000

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