Finite Group Databasebeta

← Group #13170801

Character table — Group #13170801

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order122233366666666633346666666661212222244366612121212121212121212121244442446666666666121212121212224412121212666666612121212121212121244466121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-1-1-1-11-111-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-111111111111111111111111-11-1-1111111-1-1111111-1-1-1-111111-1-11111-1-11-1-11111-1-11-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-111111111111111111111-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-111-1-1-1-1-1-11-1-111-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1111111-1-11111111111-11111-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1111-111111-1-1-1-1-111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-111-1-111-11111-1-111-1-1-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-111111-1-111-111-1-11111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-11111-1-111-1-111-1-1-1-1111-1-111-1-1-1-1-111-1-1-111-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-111-1-111-1-1-1-1-1-11111111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-11111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1-11111-11111-1-11-111111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111-1-1111111111-1-1-1-11111111-1-111-1-1-111-1-111-1-1-1-11
χ17222222-122-1-12-12222-1-122-1-1-12-1-1-1222222200-1-1-1-1-1222-1-1-1-1-1-1-1-10000220222222-1-1-1-100000022000000-1-1-1-1-1-1-1-120-1-10000020-1-1000000-100
χ18222222-122-1-12-12222-1-122-1-1-12-1-1-122222-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-100002-20-2-22222-1-111000000-2-2000000-111-1-1-1-11-201100000-2011000000100
χ19222222-122-1-12-12222-1-122-1-1-12-1-1-1222-2-22200-1-1-1-1-1222-1-1-1-1-1-1-1-10000-22022-2-2-2-211-1-1000000-2-20000001-1-11111-120-1-100000-2011000000100
χ20222222-122-1-12-12222-1-122-1-1-12-1-1-1222-2-2-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-10000-2-20-2-2-2-2-2-211110000002200000011111111-20110000020-1-1000000-100
χ21222222-122-1-12-12222-1-1-22-1-1-12-1-1-12-2-2222200-1-1-1-11-2-2-2111111110000-2-202222-2-2-1-1-1-1000000220000001-1-1-1-1111-201100000-20-1-1000000100
χ22222222-122-1-12-12222-1-1-22-1-1-12-1-1-12-2-222-2-200-1-1-1-11-2-2-2111111110000-220-2-222-2-2-1-111000000-2-2000000111-1-111-120-1-1000002011000000-100
χ23222222-122-1-12-12222-1-1-22-1-1-12-1-1-12-2-2-2-22200-1-1-1-11-2-2-21111111100002-2022-2-22211-1-1000000-2-2000000-1-1-111-1-11-2011000002011000000-100
χ24222222-122-1-12-12222-1-1-22-1-1-12-1-1-12-2-2-2-2-2-200-1-1-1-11-2-2-2111111110000220-2-2-2-222111100000022000000-11111-1-1-120-1-100000-20-1-1000000100
χ2522222-122-122-122-12-12-12-12-1-1-12-12-1-1-1220022-1-1-1-122-1-122-1-1-1-1-1-1222220200-1-1-1-12200-1-1-1-1220000-1-1-1-1200-1-1-1-100200-1-1-1-100200-1-10000000
χ2622222-122-122-122-12-12-12-12-1-1-12-12-1-1-12200-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-220-200-1-1-1-122001111-2-200001111200-1-1-1-100-200111100-200110000000
χ2722222-122-122-122-12-12-12-12-1-1-12-12-1-1-1-2-20022-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-2-202001111-2-200-1-1-1-12200001111-200111100200-1-1-1-100-200110000000
χ2822222-122-122-122-12-12-12-12-1-1-12-12-1-1-1-2-200-2-2-1-1-1-122-1-122-1-1-1-1-1-12222-20-2001111-2-2001111-2-20000-1-1-1-1-200111100-200111100200-1-10000000
χ2922222-122-122-122-12-12-1-2-12-1-1-12-12-111220022-1-1-1-1-2-211-2-21111112222-20-200-1-1112200-1-111220000-1-1-1-1-200-1-11100-200-1-11100-200110000000
χ3022222-122-122-122-12-12-1-2-12-1-1-12-12-1112200-2-2-1-1-1-1-2-211-2-2111111-2-2-2-2-20200-1-111220011-1-1-2-200001111-200-1-1110020011-1-100200-1-10000000
χ3122222-122-122-122-12-12-1-2-12-1-1-12-12-111-2-20022-1-1-1-1-2-211-2-2111111-2-2-2-220-20011-1-1-2-200-1-111220000111120011-1-100-200-1-11100200-1-10000000
χ3222222-122-122-122-12-12-1-2-12-1-1-12-12-111-2-200-2-2-1-1-1-1-2-211-2-211111122222020011-1-1-2-20011-1-1-2-20000-1-1-1-120011-1-10020011-1-100-200110000000
χ332222-122-122222-12-1-1-122-1-122-1-12-1-122002222-1-1-1-12-1-1-1-1-122-1-1-1-10000022-1-1000000222222-1-1002200000-1-100002-1-1-1-1-1-1-1-12000000-1-1000-10
χ342222-122-122222-12-1-1-122-1-122-1-12-1-1220022-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1000002-2-1-100000022-2-2-2-21100-2-200000-1-100002-11-1-11111-20000001100010
χ352222-122-122222-12-1-1-122-1-122-1-12-1-12200-2-222-1-1-1-12-1-1-1-1-122-1-1-1-100000-2211000000-2-22222-1-100-2-200000110000-21-111-1-1-1-1-20000001100010
χ362222-122-122222-12-1-1-122-1-122-1-12-1-12200-2-2-2-2-1-1-1-12-1-1-1-1-122-1-1-1-100000-2-211000000-2-2-2-2-2-211002200000110000-2111111112000000-1-1000-10
χ372222-122-122222-12-1-1-12-2-1-122-1-12-1-1-2-2002222-1-1-1-1-211111-2-2111100000-2-2-1-10000002222-2-2-1-1002200000-1-10000-21111-1-111-2000000-1-100010
χ382222-122-122222-12-1-1-12-2-1-122-1-12-1-1-2-20022-2-2-1-1-1-1-211111-2-2111100000-22-1-100000022-2-2221100-2-200000-1-10000-21-11111-1-1200000011000-10
χ392222-122-122222-12-1-1-12-2-1-122-1-12-1-1-2-200-2-222-1-1-1-1-211111-2-21111000002-211000000-2-222-2-2-1-100-2-2000001100002-11-1-1-1-111200000011000-10
χ402222-122-122222-12-1-1-12-2-1-122-1-12-1-1-2-200-2-2-2-2-1-1-1-1-211111-2-21111000002211000000-2-2-2-222110022000001100002-1-1-1-111-1-1-2000000-1-100010
χ4122-2-2222-222-2-2-22-2-22220-2-2-2-2222-2-2002-2002i−2i2-2-220000000000002i2i−2i−2i000002-2002-2002i−2i002i−2i00002i2i−2i−2i0002-200000002i−2i0000000000000000
χ4222-2-2222-222-2-2-22-2-22220-2-2-2-2222-2-2002-200−2i2i2-2-22000000000000−2i−2i2i2i000002-2002-200−2i2i00−2i2i0000−2i−2i2i2i0002-20000000−2i2i0000000000000000
χ4322-2-2222-222-2-2-22-2-22220-2-2-2-2222-2-200-22002i−2i2-2-22000000000000−2i−2i2i2i00000-2200-22002i−2i002i−2i0000−2i−2i2i2i000-2200000002i−2i0000000000000000
χ4422-2-2222-222-2-2-22-2-22220-2-2-2-2222-2-200-2200−2i2i2-2-220000000000002i2i−2i−2i00000-2200-2200−2i2i00−2i2i00002i2i−2i−2i000-220000000−2i2i0000000000000000
χ4522-2-22-12-2-12-21-221-2-12-101-211-12-1-21−i3i32-2002i−2i-111-100−i3i300−i3i3−i3−i3i3i32i2i−2i−2i00000-11−i3i32-200−ii3−32i−2i0000−i−iii000-11−i3i300000−ii3−3000003−30000000
χ4622-2-22-12-2-12-21-221-2-12-101-211-12-1-21−i3i32-200−2i2i-111-100−i3i300−i3i3−i3−i3i3i3−2i−2i2i2i00000-11−i3i32-200i−i−33−2i2i0000ii−i−i000-11−i3i300000i−i−3300000−330000000
χ4722-2-22-12-2-12-21-221-2-12-101-211-12-1-21−i3i3-22002i−2i-111-100−i3i300−i3i3−i3−i3i3i3−2i−2i2i2i000001-1i3−i3-2200−ii3−32i−2i0000ii−i−i0001-1i3−i300000−ii3−300000−330000000
χ4822-2-22-12-2-12-21-221-2-12-101-211-12-1-21−i3i3-2200−2i2i-111-100−i3i300−i3i3−i3−i3i3i32i2i−2i−2i000001-1i3−i3-2200i−i−33−2i2i0000−i−iii0001-1i3−i300000i−i−33000003−30000000
χ4922-2-22-12-2-12-21-221-2-12-101-211-12-1-21i3−i32-2002i−2i-111-100i3−i300i3−i3i3i3−i3−i32i2i−2i−2i00000-11i3−i32-200−ii−332i−2i0000−i−iii000-11i3−i300000−ii−3300000−330000000
χ5022-2-22-12-2-12-21-221-2-12-101-211-12-1-21i3−i32-200−2i2i-111-100i3−i300i3−i3i3i3−i3−i3−2i−2i2i2i00000-11i3−i32-200i−i3−3−2i2i0000ii−i−i000-11i3−i300000i−i3−3000003−30000000
χ5122-2-22-12-2-12-21-221-2-12-101-211-12-1-21i3−i3-22002i−2i-111-100i3−i300i3−i3i3i3−i3−i3−2i−2i2i2i000001-1−i3i3-2200−ii−332i−2i0000ii−i−i0001-1−i3i300000−ii−33000003−30000000
χ5222-2-22-12-2-12-21-221-2-12-101-211-12-1-21i3−i3-2200−2i2i-111-100i3−i300i3−i3i3i3−i3−i32i2i−2i−2i000001-1−i3i3-2200i−i3−3−2i2i0000−i−iii0001-1−i3i300000i−i3−300000−330000000
χ532-22-22222-2-2-222-2-2-22220222-2-2-2-2-2-200002-20022-2-20000000000002i−2i2i−2i0002-20000002-200000000002i−2i2i−2i02-200000000000000000000002i−2i000
χ542-22-22222-2-2-222-2-2-22220222-2-2-2-2-2-200002-20022-2-2000000000000−2i2i−2i2i0002-20000002-20000000000−2i2i−2i2i02-20000000000000000000000−2i2i000
χ552-22-22222-2-2-222-2-2-22220222-2-2-2-2-2-20000-220022-2-20000000000002i−2i2i−2i000-22000000-2200000000002i−2i2i−2i0-220000000000000000000000−2i2i000
χ562-22-22222-2-2-222-2-2-22220222-2-2-2-2-2-20000-220022-2-2000000000000−2i2i−2i2i000-22000000-220000000000−2i2i−2i2i0-2200000000000000000000002i−2i000
χ572-2-22222-2-2-22-2-2-2222220-2-2-22-2-2-222000000002-22-20000000000002-2-2200000000000000000002-22-22-2-2200000000000000000002-2002-200000
χ582-2-22222-2-2-22-2-2-2222220-2-2-22-2-2-222000000002-22-20000000000002-2-220000000000000000000-22-222-2-220000000000000000000-2200-2200000
χ592-2-22222-2-2-22-2-2-2222220-2-2-22-2-2-222000000002-22-2000000000000-222-200000000000000000002-2-22-222-200000000000000000002-200-2200000
χ602-2-22222-2-2-22-2-2-2222220-2-2-22-2-2-222000000002-22-2000000000000-222-20000000000000000000-222-2-222-20000000000000000000-22002-200000
χ6144444-2-24-2-2-2-2-24-24-2-214-2-211-2-21-2-2-2-24400001111-24-2-2-2-2111111000040000-2-2-2-2-2-20000000000000000-200111100000000000000000000000
χ6244444-2-24-2-2-2-2-24-24-2-214-2-211-2-21-2-2-2-2-4-400001111-24-2-2-2-21111110000-400002222220000000000000000200-1-1-1-100000000000000000000000
χ6344444-2-24-2-2-2-2-24-24-2-21-4-2-211-2-21-2-22244000011112-42222-1-1-1-1-1-10000-40000-2-222-2-2000000000000000020011-1-100000000000000000000000
χ6444444-2-24-2-2-2-2-24-24-2-21-4-2-211-2-21-2-222-4-4000011112-42222-1-1-1-1-1-100004000022-2-2220000000000000000-200-1-11100000000000000000000000
χ654444-24-2-24-2-24-2-24-2-21-24-21-2-2-21-21-2440044001111-2-2-2-211-2-211110000040-2-2000000-2-2000000000000000110000-2-2011000000000000000000
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χ684444-24-2-24-2-24-2-24-2-21-2-4-21-2-2-21-21-2-4-400-4-40011112222-1-122-1-1-1-100000402200000022000000000000000-1-10000-2-2011000000000000000000
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χ704444-2-24-2-244-24-2-2-21-2-241-2-2-21-2-2-21-2-20000-4-411114-211-2-2-2-21111000000-4000000000022222200000000000000000200-1-1-1-100000000000000
χ714444-2-24-2-244-24-2-2-21-2-2-41-2-2-21-2-2-21220000441111-42-1-12222-1-1-1-1000000-40000000000-2-222-2-20000000000000000020011-1-100000000000000
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χ7744-4-44-2-2-4-2-222242-4-2-21022-1-1-2-21222i3−2i34-400001-1-11002i3−2i300−i3i3−i3−i3i3i3000000000-222i3−2i3-2200000000000000000001-1−i3i300000000000000000000000
χ7844-4-44-2-2-4-2-222242-4-2-21022-1-1-2-21222i3−2i3-4400001-1-11002i3−2i300−i3i3−i3−i3i3i30000000002-2−2i32i32-20000000000000000000-11i3−i300000000000000000000000
χ7944-4-4-244244-4-4-4-2-42-2-24022-4-4-2-24220000004i−4i-222-2000000000000000000000000000004i−4i00−2i2i00000000000000000000−2i2i0000000000000000
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χ8344-4-4-2-242-24-42-4-2221-2-20-12221-2-22-12i3−2i300004i−4i1-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000000000−2i2i−2323−2i2i00000000000000000000i−i3−300000000000000
χ8444-4-4-2-242-24-42-4-2221-2-20-12221-2-22-12i3−2i30000−4i4i1-1-1100−i3i3002i3−2i3−i3−i3i3i3000000000000000002i−2i23−232i−2i00000000000000000000−ii−3300000000000000
χ854-44-444-24-4224-2-4-4-44-2-204-2-22-4222-400004-400-2-22200000000000000000004-4000000-22000000000000000-22000000000000000000000000000
χ864-44-444-24-4224-2-4-4-44-2-204-2-22-4222-40000-4400-2-2220000000000000000000-440000002-20000000000000002-2000000000000000000000000000
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χ884-44-44-2442-4-4-24-42-4-24-20-24-222-42-4200000000-2-222000000000000−4i4i−4i4i000000000000000000000002i−2i2i−2i000000000000000000000000000000
χ894-44-4-244-2-4-4-4442-42-2-240-2-24-422-42200004-400-2-2220000000000000000000-220000004-4000000000000000-22000000000000000000000000000
χ904-44-4-244-2-4-4-4442-42-2-240-2-24-422-4220000-4400-2-22200000000000000000002-2000000-440000000000000002-2000000000000000000000000000
χ914-44-4-24-2-2-4224-22-42-21-20-21-222-12-1200004-40011-1-100003i−3i003i−3i3i−3i0000000-22000000-220000000000000001-100000003i−3i000000000000000000
χ924-44-4-24-2-2-4224-22-42-21-20-21-222-12-1200004-40011-1-10000−3i3i00−3i3i−3i3i0000000-22000000-220000000000000001-10000000−3i3i000000000000000000
χ934-44-4-24-2-2-4224-22-42-21-20-21-222-12-120000-440011-1-100003i−3i003i−3i3i−3i00000002-20000002-2000000000000000-110000000−3i3i000000000000000000
χ944-44-4-24-2-2-4224-22-42-21-20-21-222-12-120000-440011-1-10000−3i3i00−3i3i−3i3i00000002-20000002-2000000000000000-1100000003i−3i000000000000000000
χ954-4-4444-2-4-42-2-42-4444-2-20-422-2-422-2400000000-22-22000000000000000000000000000000000004-40000000000000000000000000-22000000000
χ964-4-4444-2-4-42-2-42-4444-2-20-422-2-422-2400000000-22-2200000000000000000000000000000000000-4400000000000000000000000002-2000000000
χ974-4-444-24-42-442-4-4-24-24-202-42-22-424-200000000-22-220000000000004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ984-4-444-24-42-442-4-4-24-24-202-42-22-424-200000000-22-22000000000000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ994-4-44-2442-4-44-4-424-2-2-24022-4422-4-2-200000000-22-2200000000000000000000000000000000000004-4000000000000000000000000000-2200000
χ1004-4-44-2442-4-44-4-424-2-2-24022-4422-4-2-200000000-22-220000000000000000000000000000000000000-440000000000000000000000000002-200000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-448-44-84-4-84-42-404-244-42-4-24000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-4-4444-4442220-2-2-2-2222-2-2−4i34i3000000-111-1002i3−2i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-44-4-4444-4442220-2-2-2-2222-2-24i3−4i3000000-111-100−2i32i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-48444-4-4-84-8-4-420-4-42-244-2440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-48-44-8-8-484442-4-402-4-44-2444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-4444-4-44442220222-2-2-2-2-2-200000000-1-11100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-4444-4-44442220222-2-2-2-2-2-200000000-1-1110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-4-844-444-8-48-4-42044-2244-2-4-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-44-84-4-8448-4-42-404-24-44-242-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4844-884-84-4-42-4-40-244-4-244-42000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4444-4-42220-2-2-22-2-2-22200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4444-4-42220-2-2-22-2-2-22200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000000

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