Finite Group Databasebeta

← Group #13169147

Character table — Group #13169147

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212122444661212121212121212121212121212121212121212226661212121212121212122224466661212661244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-111-1-1-11111111111111111111111-1-1-1-11-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-111-1-111111111-1-11111-1111-1-1-1-1-11-1-11-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-11-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1111111111111111-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-1-11-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-1111111-1-1-1-111111-1-1-1-1-111-1-1-1-1-11111-1-111-1-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-111-1-1-11-111111-1-1-111-1-111-1-1-1-111-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111-11-1-1-1-1-1111-11-11-1-111-1-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-11111-11-1-1-111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-11111-1-1-1-11111-1-1111-1-1-1-1-111-1-111-11-1-1-111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-111111-1-11-11-11-1-111-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1111111111-11-1-1-1-1-111-111-1-111-1-1-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-111111-1-111-1-1-11111-1-111-1-11-11
χ17222222-122-122-1-122-1-122-12-1-12-1-12-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-102200022-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200002000-1-1-1-120000-1-1-1-10000000
χ18222222-122-122-1-122-1-122-12-1-12-1-12-122-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-10-2200022-1-1111122-2-2-1-1-1-1-1-1-1-1-2-20000-20001111-2000011110000000
χ19222222-122-122-1-122-1-122-12-1-12-1-12-122-1-1-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-102-2000-2-211-1-1-1-1-2-22211111111-2-200002000-1-1-1-1-2000011110000000
χ20222222-122-122-1-122-1-122-12-1-12-1-12-122-1-1-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-2-2000-2-2111111-2-2-2-211111111220000-2000111120000-1-1-1-10000000
χ21222222-122-122-1-122-1-12-2-12-1-12-1-12-1-2-21111112222-1-1-1-1-1-1-1-1-2-2-21111110-2-20002211-1-111-2-222-1-1-1-11111220000-2000-1-111-20000-1-1110000000
χ22222222-122-122-1-122-1-12-2-12-1-12-1-12-1-2-211111122-2-2-1-1-1-1-1-1-1-1-2-2-211111102-2000221111-1-1-2-2-2-2-1-1-1-11111-2-20000200011-1-12000011-1-10000000
χ23222222-122-122-1-122-1-12-2-12-1-12-1-12-1-2-2111111-2-2221111-1-1-1-1-2-2-21111110-22000-2-2-1-1-1-11122221111-1-1-1-1-2-20000-2000-1-1112000011-1-10000000
χ24222222-122-122-1-122-1-12-2-12-1-12-1-12-1-2-2111111-2-2-2-21111-1-1-1-1-2-2-2111111022000-2-2-1-111-1-122-2-21111-1-1-1-1220000200011-1-1-20000-1-1110000000
χ2522222-122-122-1222-12-1-122-12-1-1-1-1-12-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1202222-1-1220000-1-100-1-1-1-1-1-1-1-100-1-1-120-1-1-1000002002000000-10-100
χ2622222-122-122-1222-12-1-122-12-1-1-1-1-12-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1-202-2-2-2-1-1220000-1-100-1-1-1-1-1-1-1-100111-2011100000-200-200000010100
χ2722222-122-122-1222-12-1-122-12-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-120-222211-2-2000011001111111100-1-1-120-1-1-100000-200-200000010100
χ2822222-122-122-1222-12-1-122-12-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1-20-2-2-2-211-2-2000011001111111100111-20111000002002000000-10-100
χ2922222-122-122-1222-12-1-1-22-12-1-1-1-1-1211-2-2111122002222-1-1-1-1-211-2-2111120-2-222-1-1-2-200001100-1-1-1-1111100-1-1-1-2011100000-200200000010-100
χ3022222-122-122-1222-12-1-1-22-12-1-1-1-1-1211-2-2111122002222-1-1-1-1-211-2-21111-20-22-2-2-1-1-2-200001100-1-1-1-111110011120-1-1-100000200-2000000-10100
χ3122222-122-122-1222-12-1-1-22-12-1-1-1-1-1211-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-21111202-22211220000-1-1001111-1-1-1-100-1-1-1-2011100000200-2000000-10100
χ3222222-122-122-1222-12-1-1-22-12-1-1-1-1-1211-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-21111-2022-2-211220000-1-1001111-1-1-1-10011120-1-1-100000-200200000010-100
χ332222-122-122-1222-12-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12202-1-10000222200-1-100000000002-1-1-1-12-1-1-1-1-1-1002200000-1-10-1000
χ342222-122-122-1222-12-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-220-2110000222200-1-10000000000-2111-1-211-1-1-1-100-2-2000001101000
χ352222-122-122-1222-12-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-12-202-1-10000-2-2-2-2001100000000002-1-1-112-1-1111100-2-2000001101000
χ362222-122-122-1222-12-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2110000-2-2-2-200110000000000-21111-2111111002200000-1-10-1000
χ372222-122-122-1222-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111112-20-2-1-1000022-2-200-1-100000000002-1-111-211-1-11100-2200000-1-101000
χ382222-122-122-1222-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-2-20211000022-2-200-1-10000000000-211-112-1-1-1-111002-200000110-1000
χ392222-122-122-1222-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111220-2-1-10000-2-222001100000000002-1-11-1-21111-1-1002-200000110-1000
χ402222-122-122-1222-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-2202110000-2-22200110000000000-211-1-12-1-111-1-100-2200000-1-101000
χ412-22-2222222-2-2-2-2-2-22220-2-2222-2-2-2-2000000002i−2i2i−2i2i2i−2i−2i2-2-220000000000000002i−2i002i−2i00002i−2i2i2i−2i−2i00002-2000000002i−2i00000002-2000000000
χ422-22-2222222-2-2-2-2-2-22220-2-2222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i2-2-220000000000000002i−2i00−2i2i0000−2i2i2i2i−2i−2i0000-2200000000−2i2i0000000-22000000000
χ432-22-2222222-2-2-2-2-2-22220-2-2222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i2-2-22000000000000000−2i2i002i−2i00002i−2i−2i−2i2i2i0000-22000000002i−2i0000000-22000000000
χ442-22-2222222-2-2-2-2-2-22220-2-2222-2-2-2-200000000−2i2i−2i2i−2i−2i2i2i2-2-22000000000000000−2i2i00−2i2i0000−2i2i−2i−2i2i2i00002-200000000−2i2i00000002-2000000000
χ452-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100−i3i3−i3−i3i3i32i−2i2i−2i−i−iii-111-1000−i3i3−i3−i3i3i30000002i−2i3−3−ii3−3002i−2i−i−iii33−3−32-200000000−ii3−300000-11−i3i30000000
χ462-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100−i3i3−i3−i3i3i32i−2i−2i2i−i−iii-111-1000−i3i3−i3−i3i3i30000002i−2i3−3i−i−3300−2i2i−i−iii33−3−3-2200000000i−i−33000001-1i3−i30000000
χ472-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100−i3i3−i3−i3i3i3−2i2i2i−2iii−i−i-111-1000−i3i3−i3−i3i3i3000000−2i2i−33−ii3−3002i−2iii−i−i−3−333-2200000000−ii3−3000001-1i3−i30000000
χ482-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100−i3i3−i3−i3i3i3−2i2i−2i2iii−i−i-111-1000−i3i3−i3−i3i3i3000000−2i2i−33i−i−3300−2i2iii−i−i−3−3332-200000000i−i−3300000-11−i3i30000000
χ492-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100i3−i3i3i3−i3−i32i−2i2i−2i−i−iii-111-1000i3−i3i3i3−i3−i30000002i−2i−33−ii−33002i−2i−i−iii−3−3332-200000000−ii−3300000-11i3−i30000000
χ502-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100i3−i3i3i3−i3−i32i−2i−2i2i−i−iii-111-1000i3−i3i3i3−i3−i30000002i−2i−33i−i3−300−2i2i−i−iii−3−333-2200000000i−i3−3000001-1−i3i30000000
χ512-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100i3−i3i3i3−i3−i3−2i2i2i−2iii−i−i-111-1000i3−i3i3i3−i3−i3000000−2i2i3−3−ii−33002i−2iii−i−i33−3−3-2200000000−ii−33000001-1−i3i30000000
χ522-22-222-122-1-2-211-2-2-1-1201-2-1-1211-2100i3−i3i3i3−i3−i3−2i2i−2i2iii−i−i-111-1000i3−i3i3i3−i3−i3000000−2i2i3−3i−i3−300−2i2iii−i−i33−3−32-200000000i−i3−300000-11i3−i30000000
χ5344444-2-24-2-24-2-2-24-2-21-24-2-2-21-211-2-2-2-2-2-211114400-2-2-2-211114-2-2-2-21111004000-2-2-2-20000-2-20011111111000000000000000000000000000000
χ5444444-2-24-2-24-2-2-24-2-21-24-2-2-21-211-2-2-2-2-2-21111-4-400222211114-2-2-2-2111100-4000222200002200-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5544444-2-24-2-24-2-2-24-2-21-2-4-2-2-21-211-2-22222-1-1-1-14400-2-2-2-21111-42222-1-1-1-100-4000-2-222000022001111-1-1-1-1000000000000000000000000000000
χ5644444-2-24-2-24-2-2-24-2-21-2-4-2-2-21-211-2-22222-1-1-1-1-4-40022221111-42222-1-1-1-100400022-2-20000-2-200-1-1-1-11111000000000000000000000000000000
χ574444-24-2-24-2-24-2-2-241-2-241-21-2-2-2-2-2144-2-2-2-2-2-2004400001111-2-2-21111110400000000-2-2-2-200-2-200000000000000-200011110000000000000000
χ584444-24-2-24-2-24-2-2-241-2-241-21-2-2-2-2-2144-2-2-2-2-2-200-4-400001111-2-2-21111110-40000000022220022000000000000002000-1-1-1-10000000000000000
χ594444-24-2-24-2-24-2-2-241-2-2-41-21-2-2-2-2-21-4-4222222004400001111222-1-1-1-1-1-10-400000000-2-22200-2-200000000000000200011-1-10000000000000000
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χ7344-4-44-2-2-422-4-22-242-21-202-22-121-12-2−2323003−33−300002i3−2i32i3−2i311-1-10−2323003−33−3000000000000000000−i3i3−i3i33i−3i3i−3i000000000000000000000000000000
χ7444-4-4-2442-4-424-44-2-4-24-202-22-424-42-20000000000000000-2-2220000000000000−2i32i300000000000000000000000−2i32i30000000000000000000000000
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χ7644-4-4-2-2422-42-2-44-22-2-2102122-1-22-1-223−230023−2323−230000000011-1-10−3300−33−330000−2i32i300000000000000000000000i3−i30003i−3i00000000000000000000
χ7744-4-4-2-2422-42-2-44-22-2-2102122-1-22-1-223−230023−2323−230000000011-1-10−3300−33−3300002i3−2i300000000000000000000000−i3i3000−3i3i00000000000000000000
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χ7944-4-4-2-2422-42-2-44-22-2-2102122-1-22-1-2−232300−2323−23230000000011-1-103−3003−33−300002i3−2i300000000000000000000000−i3i30003i−3i00000000000000000000
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χ824-44-44-2-24-2-2-4222-42-21-2022-21-2-1-12200−2i32i3i3i3−i3−i34i−4i00−2i−2i2i2i1-1-11000−2i32i3i3i3−i3−i3000000−2i2i23−2300000000ii−i−i−3−333000000000000000000000000000000
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χ844-44-44-2-24-2-2-4222-42-21-2022-21-2-1-122002i3−2i3−i3−i3i3i34i−4i00−2i−2i2i2i1-1-110002i3−2i3−i3−i3i3i3000000−2i2i−232300000000ii−i−i33−3−3000000000000000000000000000000
χ854-44-44-2-24-2-2-4222-42-21-2022-21-2-1-122002i3−2i3−i3−i3i3i3−4i4i002i2i−2i−2i1-1-110002i3−2i3−i3−i3i3i30000002i−2i23−2300000000−i−iii−3−333000000000000000000000000000000
χ864-44-4-244-2442-4-4-42-4-24-2022-24-2-4-42200000000004i−4i0000-222-200000000000000000004i−4i0000−2i2i000000000000000000−2i2i000000000000000000
χ874-44-4-244-2442-4-4-42-4-24-2022-24-2-4-4220000000000−4i4i0000-222-20000000000000000000−4i4i00002i−2i0000000000000000002i−2i000000000000000000
χ884-44-4-24-2-24-22-4222-41-2-20-121-2-2222-100−2i32i3−2i3−2i32i32i3004i−4i00001-1-11000i3−i3i3i3−i3−i30000000000−2i2i23−2300−2i2i000000000000000000i−i−330000000000000000
χ894-44-4-24-2-24-22-4222-41-2-20-121-2-2222-100−2i32i3−2i3−2i32i32i300−4i4i00001-1-11000i3−i3i3i3−i3−i300000000002i−2i−2323002i−2i000000000000000000−ii3−30000000000000000
χ904-44-4-24-2-24-22-4222-41-2-20-121-2-2222-1002i3−2i32i32i3−2i3−2i3004i−4i00001-1-11000−i3i3−i3−i3i3i30000000000−2i2i−232300−2i2i000000000000000000i−i3−30000000000000000
χ914-44-4-24-2-24-22-4222-41-2-20-121-2-2222-1002i3−2i32i32i3−2i3−2i300−4i4i00001-1-11000−i3i3−i3−i3i3i300000000002i−2i23−23002i−2i000000000000000000−ii−330000000000000000
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χ934-4-4444-2-4-424-4-22-44-2-240-2-422-42-24200000000000023−23−2323-22-2200000000000000000000000000023−23−23230000000000000000000000000000000000
χ944-4-4444-2-4-424-4-22-44-2-240-2-422-42-242000000000000−232323−23-22-22000000000000000000000000000−232323−230000000000000000000000000000000000
χ954-4-444-24-42-4424-4-4-24-2-2042-4222-2-2-40000000000000000-22-2200000000000000000000000−2i32i3000000−2i32i32i3−2i3000000000000000000000000000000
χ964-4-444-24-42-4424-4-4-24-2-2042-4222-2-2-40000000000000000-22-22000000000000000000000002i3−2i30000002i3−2i3−2i32i3000000000000000000000000000000
χ974-4-444-2-2-42242-22-4-2-21-20-222-12-11-2200003i−3i−3i3i000023−23−23231-11-1000003i−3i−3i3i000000000000002i3−2i300−333−3−i3i3i3−i3000000000000000000000000000000
χ984-4-444-2-2-42242-22-4-2-21-20-222-12-11-2200003i−3i−3i3i0000−232323−231-11-1000003i−3i−3i3i00000000000000−2i32i3003−3−33i3−i3−i3i3000000000000000000000000000000
χ994-4-444-2-2-42242-22-4-2-21-20-222-12-11-220000−3i3i3i−3i000023−23−23231-11-100000−3i3i3i−3i00000000000000−2i32i300−333−3i3−i3−i3i3000000000000000000000000000000
χ1004-4-444-2-2-42242-22-4-2-21-20-222-12-11-220000−3i3i3i−3i0000−232323−231-11-100000−3i3i3i−3i000000000000002i3−2i3003−3−33−i3i3i3−i3000000000000000000000000000000
χ1014-4-44-2442-4-4-2-44-424-24-20-222-42-44-220000000000000000-22-22000000000000000000000000000000000000000000000000000000000023−2300000
χ1024-4-44-2442-4-4-2-44-424-24-20-222-42-44-220000000000000000-22-220000000000000000000000000000000000000000000000000000000000−232300000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-48-44-84484-4-4-82-4-40-2-4-244-4442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44444-44-4-442220-22-2-2-22-2-2243−4300−2323−232300000000-1-1110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44444-44-4-442220-22-2-2-22-2-22−43430023−2323−2300000000-1-111023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-48-4-4844-8-844-4-4204-2-4-4244-2400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-4-4-44444442220-2-2222-2-2-2-200−4i34i32i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-4-4-44444442220-2-2222-2-2-2-2004i3−4i3−2i3−2i32i32i300000000-111-1000−2i32i3i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-44-84-4-8-44482-4-4024-2444-4-4-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4844-8-448-84-4-4-420-4-244-24-42400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-44-444-422202-2-2-2-2-222-200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-44-444-422202-2-2-2-2-222-20000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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