Finite Group Databasebeta

← Group #13168655

Character table — Group #13168655

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444121212121212121212121212121212122244121212121212121212121212121212121212121224446612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-1-1-1111111111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111111111-1-1-1-11-11-1-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-11-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-111111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-111-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11-1-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111-1-1-1-111-1-111-1-1111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111-111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11111-1-11111111-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-1-111-1-1-1-11111111-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1111-1-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-111-111111111-1-1-1
χ17222222-122-1-122-1222-1-122-1-1-1-122-1-1-1-1222200-1-1-1-122-1-1-1-122-1-1-1-12200022-1-1-1-1-1-1-1-122002222-1-1-1-122000000-1-1-1-1-1-1-1-10000-1-1000000000
χ18222222-122-1-122-1222-1-122-1-1-1-122-1-1-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-12-200022-1-1-1-11111-2-200-2-2-2-211112-2000000-1-1-1-11111000011000000000
χ19222222-122-1-122-1222-1-122-1-1-1-122-1-1-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-22000-2-21111-1-1-1-12200-2-2-2-21111-220000001111-1-1-1-1000011000000000
χ20222222-122-1-122-1222-1-122-1-1-1-122-1-1-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-2000-2-211111111-2-2002222-1-1-1-1-2-2000000111111110000-1-1000000000
χ21222222-122-1-122-1222-1-1-22-1-1-1-122-1-111222200-1-1-1-1-2-21111-2-21111-2-200022-1-111-1-111220022-2-21111-2-2000000-1-111-1-1110000-1-1000000000
χ22222222-122-1-122-1222-1-1-22-1-1-1-122-1-11122-2-200-1-1-1-1-2-21111-2-21111-2200022-1-11111-1-1-2-200-2-222-1-1-1-1-22000000-1-11111-1-1000011000000000
χ23222222-122-1-122-1222-1-1-22-1-1-1-122-1-111-2-22200-1-1-1-1-2-21111-2-211112-2000-2-211-1-1-1-1112200-2-222-1-1-1-12-200000011-1-1-1-111000011000000000
χ24222222-122-1-122-1222-1-1-22-1-1-1-122-1-111-2-2-2-200-1-1-1-1-2-21111-2-2111122000-2-211-1-111-1-1-2-20022-2-211112200000011-1-111-1-10000-1-1000000000
χ2522222-12-1-122222-12-12-12-12-12-1-1-12-122220022-1-1-1-1-1222-1-1-1-1-1-1-1-1202-1-1-1-122220000002200000000-102-1-1-1-1-1-1-1-1-1000020200000-1-100-100
χ2622222-12-1-122222-12-12-12-12-12-1-1-12-1222200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-120-211-1-12222000000-2-200000000-10-211111-1-1-1-10000-20-2000001100100
χ2722222-12-1-122222-12-12-12-12-12-1-1-12-122-2-20022-1-1-1-1-1222-1-1-1-1-1-1-1-1-202-1-111-2-2-2-20000002200000000102-1-1-1-1-111110000-20-2000001100100
χ2822222-12-1-122222-12-12-12-12-12-1-1-12-122-2-200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-20-21111-2-2-2-2000000-2-20000000010-2111111111000020200000-1-100-100
χ2922222-12-1-122222-12-12-1-2-12-12-1-1-12-1-2-2220022-1-1-1-11-2-2-211111111-20-2-1-1-1-122-2-2000000220000000010-2111-1-1-1-1110000-20200000-1-100100
χ3022222-12-1-122222-12-12-1-2-12-12-1-1-12-1-2-22200-2-2-1-1-1-11-2-2-211111111-20211-1-122-2-2000000-2-200000000102-1-1-111-1-111000020-2000001100-100
χ3122222-12-1-122222-12-12-1-2-12-12-1-1-12-1-2-2-2-20022-1-1-1-11-2-2-21111111120-2-1-111-2-2220000002200000000-10-2111-1-111-1-1000020-2000001100-100
χ3222222-12-1-122222-12-12-1-2-12-12-1-1-12-1-2-2-2-200-2-2-1-1-1-11-2-2-2111111112021111-2-222000000-2-200000000-102-1-1-11111-1-10000-20200000-1-100100
χ332222-1222222-1-122-1-1-122-1-12-12-1-1-1222002222-1-1-1-12-1-1-122-1-1-1-1-1-1022220000002222-1-1-1-1000000000-1-12-1-1-1-10000-1-1-1-1020200-1-100000-10
χ342222-1222222-1-122-1-1-122-1-12-12-1-1-12220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-102-2-2-20000002222-1-111000000000-11-211110000-1-1-1-10-20-200110000010
χ352222-1222222-1-122-1-1-122-1-12-12-1-1-122200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-10-2222000000-2-2-2-211-1-10000000001-12-1-1-1-1000011110-20-200110000010
χ362222-1222222-1-122-1-1-122-1-12-12-1-1-122200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-2-2000000-2-2-2-2111100000000011-2111100001111020200-1-100000-10
χ372222-1222222-1-122-1-1-12-2-1-12-12-1-1-12-2-2002222-1-1-1-1-2111-2-21111110-2-22200000022-2-2-1-1-1-100000000011-211-1-10000-1-111020-200-1-10000010
χ382222-1222222-1-122-1-1-12-2-1-12-12-1-1-12-2-20022-2-2-1-1-1-1-2111-2-21111110-22-2-200000022-2-2-1-1110000000001-12-1-1110000-1-1110-202001100000-10
χ392222-1222222-1-122-1-1-12-2-1-12-12-1-1-12-2-200-2-222-1-1-1-1-2111-2-211111102-222000000-2-22211-1-1000000000-11-211-1-1000011-1-10-202001100000-10
χ402222-1222222-1-122-1-1-12-2-1-12-12-1-1-12-2-200-2-2-2-2-1-1-1-1-2111-2-2111111022-2-2000000-2-2221111000000000-1-12-1-111000011-1-1020-200-1-10000010
χ412-22-2222-2-22-22-2-22-22220-2-22-2-22-22-20000002i−2i22-2-20000000000000002i−2i0000000000002i−2i002i−2i2i2i−2i−2i0000002i−2i0000000000000000002-2000
χ422-22-2222-2-22-22-2-22-22220-2-22-2-22-22-20000002i−2i22-2-20000000000000002i−2i0000000000002i−2i00−2i2i−2i−2i2i2i0000002i−2i000000000000000000-22000
χ432-22-2222-2-22-22-2-22-22220-2-22-2-22-22-2000000−2i2i22-2-2000000000000000−2i2i000000000000−2i2i002i−2i2i2i−2i−2i000000−2i2i000000000000000000-22000
χ442-22-2222-2-22-22-2-22-22220-2-22-2-22-22-2000000−2i2i22-2-2000000000000000−2i2i000000000000−2i2i00−2i2i−2i−2i2i2i000000−2i2i0000000000000000002-2000
χ452-2-222222-2-2-2-2-22-222220-2-2-222-22-2-2002i−2i2i−2i002-2-22000000000000000002i−2i2i−2i002i−2i002i−2i002-2000000000000002i−2i002i−2i0000002-2000000000
χ462-2-222222-2-2-2-2-22-222220-2-2-222-22-2-2002i−2i−2i2i002-2-22000000000000000002i−2i2i−2i00−2i2i00−2i2i00-22000000000000002i−2i00−2i2i000000-22000000000
χ472-2-222222-2-2-2-2-22-222220-2-2-222-22-2-200−2i2i2i−2i002-2-2200000000000000000−2i2i−2i2i002i−2i002i−2i00-2200000000000000−2i2i002i−2i000000-22000000000
χ482-2-222222-2-2-2-2-22-222220-2-2-222-22-2-200−2i2i−2i2i002-2-2200000000000000000−2i2i−2i2i00−2i2i00−2i2i002-200000000000000−2i2i00−2i2i0000002-2000000000
χ492-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211−i3i32i−2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i3000002i−2i−ii3−3−ii3−32i−2i002-200−i3i3−i3i300000000−ii3−3−ii3−30000-11000000000
χ502-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211−i3i32i−2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i3000002i−2i−ii3−3i−i−33−2i2i00-2200i3−i3i3−i300000000−ii3−3i−i−3300001-1000000000
χ512-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211−i3i3−2i2i2i−2i00-111-100−i3i3−i3i300−i3−i3i3i300000−2i2ii−i−33−ii3−32i−2i00-2200i3−i3i3−i300000000i−i−33−ii3−300001-1000000000
χ522-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211−i3i3−2i2i−2i2i00-111-100−i3i3−i3i300−i3−i3i3i300000−2i2ii−i−33i−i−33−2i2i002-200−i3i3−i3i300000000i−i−33i−i−330000-11000000000
χ532-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211i3−i32i−2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i3000002i−2i−ii−33−ii−332i−2i002-200i3−i3i3−i300000000−ii−33−ii−330000-11000000000
χ542-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211i3−i32i−2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i3000002i−2i−ii−33i−i3−3−2i2i00-2200−i3i3−i3i300000000−ii−33i−i3−300001-1000000000
χ552-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211i3−i3−2i2i2i−2i00-111-100i3−i3i3−i300i3i3−i3−i300000−2i2ii−i3−3−ii−332i−2i00-2200−i3i3−i3i300000000i−i3−3−ii−3300001-1000000000
χ562-2-2222-12-211-2-2-1-222-1-10-211-1-1-2211i3−i3−2i2i−2i2i00-111-100i3−i3i3−i300i3i3−i3−i300000−2i2ii−i3−3i−i3−3−2i2i002-200i3−i3i3−i300000000i−i3−3i−i3−30000-11000000000
χ5744444-2-2-2-2-2-244-2-24-2-214-2-21-21-2-2-21-2-24400001111-24-2-211-2-2111140000-2-2-2-2-2-20000000000000000-2000000011110000000000000000000
χ5844444-2-2-2-2-2-244-2-24-2-214-2-21-21-2-2-21-2-2-4-400001111-24-2-211-2-21111-40000222222000000000000000020000000-1-1-1-10000000000000000000
χ5944444-2-2-2-2-2-244-2-24-2-21-4-2-21-21-2-2-212244000011112-422-1-122-1-1-1-1-40000-2-2-2-22200000000000000002000000011-1-10000000000000000000
χ6044444-2-2-2-2-2-244-2-24-2-21-4-2-21-21-2-2-2122-4-4000011112-422-1-122-1-1-1-1400002222-2-20000000000000000-20000000-1-1110000000000000000000
χ614444-24-244-2-2-2-2-24-2-21-24-21-21-2-2-21-2-2-200440011114-211-2-2-2-2111104000000000-2-2-2-2-2-200000000000-200000000001111000000000000000
χ624444-24-244-2-2-2-2-24-2-21-24-21-21-2-2-21-2-2-200-4-40011114-211-2-2-2-211110-40000000002222220000000000020000000000-1-1-1-1000000000000000
χ634444-24-244-2-2-2-2-24-2-21-2-4-21-21-2-2-21-2220044001111-42-1-12222-1-1-1-10-4000000000-2-222-2-2000000000002000000000011-1-1000000000000000
χ644444-24-244-2-2-2-2-24-2-21-2-4-21-21-2-2-21-22200-4-4001111-42-1-12222-1-1-1-10400000000022-2-22200000000000-20000000000-1-111000000000000000
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χ674444-2-24-2-244-2-24-2-21-2-2-41-2-2-2-211-2-2-4-40000441111222222-1-1-1-1-1-100-4-2-2000000000000-2-2000000000022-1-11100000000000000000000000
χ684444-2-24-2-244-2-24-2-21-2-2-41-2-2-2-211-2-2-4-40000-4-41111222222-1-1-1-1-1-100422000000000000220000000000-2-211-1-100000000000000000000000
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χ7444-4-4-244-44-442-2-4-42-2-240-2-2-42-4222400000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ7544-4-4-244-44-442-2-4-42-2-240-2-2-42-4222400000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
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χ784-44-44-24224-44-4-4-2-4-24-202-4-2-42-22420000004i−4i-2-222000000000000000−2i2i0000000000004i−4i00000000000000−2i2i00000000000000000000000
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χ804-44-4-244-4-44-4-22-442-2-2402242-4-22-2-40000004i−4i-2-2220000000000000004i−4i000000000000−2i2i00000000000000−2i2i00000000000000000000000
χ814-44-4-244-4-44-4-22-442-2-2402242-4-22-2-4000000−4i4i-2-222000000000000000−4i4i0000000000002i−2i000000000000002i−2i00000000000000000000000
χ824-44-4-2-24224-4-22-4-221-2-20-12-2221-1-220000004i−4i11-1-10000003i−3i3i−3i3i−3i000−2i2i000000000000−2i2i0000000000003-3i−i00000000000000000000000
χ834-44-4-2-24224-4-22-4-221-2-20-12-2221-1-220000004i−4i11-1-1000000−3i3i−3i3i−3i3i000−2i2i000000000000−2i2i000000000000-33i−i00000000000000000000000
χ844-44-4-2-24224-4-22-4-221-2-20-12-2221-1-22000000−4i4i11-1-10000003i−3i3i−3i3i−3i0002i−2i0000000000002i−2i000000000000-33−ii00000000000000000000000
χ854-44-4-2-24224-4-22-4-221-2-20-12-2221-1-22000000−4i4i11-1-1000000−3i3i−3i3i−3i3i0002i−2i0000000000002i−2i0000000000003-3−ii00000000000000000000000
χ864-4-444-24-22-4-4-4-4424-24-202-424-22-2-42004i−4i0000-222-200000000000000000−2i2i4i−4i00000000000000000000000000−2i2i000000000000000000000
χ874-4-444-24-22-4-4-4-4424-24-202-424-22-2-4200−4i4i0000-222-2000000000000000002i−2i−4i4i000000000000000000000000002i−2i000000000000000000000
χ884-4-444-2-2-2222-4-4-224-2-21022-1-212-22-1−2i32i34i−4i00001-1-1100−2i32i3i3−i300i3i3−i3−i300000−2i2i−2i2i23−23000000000000000000000000i−i−330000000000000000000
χ894-4-444-2-2-2222-4-4-224-2-21022-1-212-22-1−2i32i3−4i4i00001-1-1100−2i32i3i3−i300i3i3−i3−i3000002i−2i2i−2i−2323000000000000000000000000−ii3−30000000000000000000
χ904-4-444-2-2-2222-4-4-224-2-21022-1-212-22-12i3−2i34i−4i00001-1-11002i3−2i3−i3i300−i3−i3i3i300000−2i2i−2i2i−2323000000000000000000000000i−i3−30000000000000000000
χ914-4-444-2-2-2222-4-4-224-2-21022-1-212-22-12i3−2i3−4i4i00001-1-11002i3−2i3−i3i300−i3−i3i3i3000002i−2i2i−2i23−23000000000000000000000000−ii−330000000000000000000
χ924-4-44-2444-4-4-4224-4-2-2-24022-4-242-22-400004i−4i00-222-2000000000000000000000004i−4i00−2i2i0000000000000000000000−2i2i00000000000000000
χ934-4-44-2444-4-4-4224-4-2-2-24022-4-242-22-40000−4i4i00-222-200000000000000000000000−4i4i002i−2i00000000000000000000002i−2i00000000000000000
χ944-4-44-24-24-42222-2-4-2-21-202-121-22-2-12−2i32i3004i−4i001-1-1100i3−i3−2i32i300i3i3−i3−i300000000000−2i2i23−23−2i2i0000000000000000000000i−i−33000000000000000
χ954-4-44-24-24-42222-2-4-2-21-202-121-22-2-12−2i32i300−4i4i001-1-1100i3−i3−2i32i300i3i3−i3−i3000000000002i−2i−23232i−2i0000000000000000000000−ii3−3000000000000000
χ964-4-44-24-24-42222-2-4-2-21-202-121-22-2-122i3−2i3004i−4i001-1-1100−i3i32i3−2i300−i3−i3i3i300000000000−2i2i−2323−2i2i0000000000000000000000i−i3−3000000000000000
χ974-4-44-24-24-42222-2-4-2-21-202-121-22-2-122i3−2i300−4i4i001-1-1100−i3i32i3−2i300−i3−i3i3i3000000000002i−2i23−232i−2i0000000000000000000000−ii−33000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-44-44-4-8844-8-4-420-4-4-24-24442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-884-44-44-84-42-40-424-2444-2-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-484-4-884-4-8442-4-402-4444-2-24-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-44-44-4444222022-2-2-2-2-2-2200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-44-44-4444222022-2-2-2-2-2-2200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-444-448-84-4-8-4-4204424-2-44-4-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-8-8-44-44484-42-404-2-4-24-44240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-44-444-442220-2-22-2-22-22-200000000-1-1110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-444-44-444-442220-2-22-2-22-22-200000000-1-111000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-44-8-84484-42-4-40-244-4-4-2244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444444-44-42220-2-2-222-22-2-2−4i34i3000000-111-1002i3−2i32i3−2i300−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444444-44-42220-2-2-222-22-2-24i3−4i3000000-111-100−2i32i3−2i32i300i3i3−i3−i30000000000000000000000000000000000000000000000000000000000

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