Finite Group Databasebeta

← Group #13172351

Character table — Group #13172351

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666664444366666666666666624446612121212121212121212121212122266666661212121212121212121212121222444661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-1111111111111-1-1111111-1-1-11-1111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-1111-1111111-1-1-1-111-1-111-1-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-1-1-1111-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1111111-11-1-11-1-1-1-1111-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111111-1-111-1-111-1-1111111111-1-1-111-1-111-1-1-1-1-1-11-11-1-1-1-111-111-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-1-11111-1-111-1-11111111111-1-1-1-11-111-1-111-1-111-11-11-1-1-111-1-11-1-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-1-1-111-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111-111-1-1-1-111111-1-111111111-1-11-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11-1-111111111-1-1-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111-1-111-1-1-1-1111-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-11111111111-11-1-111-1-111-1-1-11-11-1-1-111-1-11-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-111111111-1-1-1111-1-111-1-11111-1-11-11-1-1-1-111-11-11
χ17222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-122222-122-1-1-1-122-1-1-1-1-1-1-102200022-1-1-1-1-1-1-1-1220022-1-1-1-1000202-1-1-1-1-1-1-1-10020000-1-100000000
χ18222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-1222-2-2-122-1-1-1-122-1-1-1-1-1-1-102-200022-1-1-1-11111-2-200-2-21111000-202-1-1-1-1111100-200001100000000
χ19222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-12-2-222-122-1-1-1-122-1-1-1-1-1-1-10-22000-2-21111-1-1-1-12200-2-2111100020-21111-1-1-1-100-200001100000000
χ20222222-12-122-1-12222-1-12-1-1-1-122-1-1-1-12-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-10-2-2000-2-211111111-2-20022-1-1-1-1000-20-2111111110020000-1-100000000
χ21222222-12-122-1-1222-2-1-1211-1-122-1-1-1-122222-1-2-21111-2-2-1-1-111110-2-200022-1-111-1-111220022-1-1-1-1000-20-2-1-111-1-11100-200001100000000
χ22222222-12-122-1-1222-2-1-1211-1-122-1-1-1-1222-2-2-1-2-21111-2-2-1-1-111110-2200022-1-11111-1-1-2-200-2-2111100020-2-1-11111-1-10020000-1-100000000
χ23222222-12-122-1-1222-2-1-1211-1-122-1-1-1-12-2-222-1-2-21111-2-2-1-1-1111102-2000-2-211-1-1-1-1112200-2-21111000-20211-1-1-1-1110020000-1-100000000
χ24222222-12-122-1-1222-2-1-1211-1-122-1-1-1-12-2-2-2-2-1-2-21111-2-2-1-1-11111022000-2-211-1-111-1-1-2-20022-1-1-1-100020211-1-111-1-100-200001100000000
χ2522222-12-122-1222-1222-1-1222-1-1-122-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-12022-1-10000002222-1-1220000002-1-1-1-100000-1-1-1-1-1-1020020000-1-1-1000
χ2622222-12-122-1222-1222-1-1222-1-1-122-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-1-202-2110000002222-1-1-2-2000000-211-1100000-1-1-1-1110-200-20000111000
χ2722222-12-122-1222-1222-1-1222-1-1-122-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-120-22-1-1000000-2-2-2-211220000002-1-11-1000001111-1-10-200-20000111000
χ2822222-12-122-1222-1222-1-1222-1-1-122-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-2-211000000-2-2-2-211-2-2000000-2111100000111111020020000-1-1-1000
χ2922222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-10022-1-21-2-21111-1-1-1111120-2-2-1-100000022-2-2-1-1-2-20000002-1-11100000-1-111110-20020000-1-11000
χ3022222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-10022-1-21-2-21111-1-1-11111-20-221100000022-2-2-1-122000000-2111-100000-1-111-1-10200-2000011-1000
χ3122222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-100-2-2-1-21-2-21111-1-1-11111202-2-1-1000000-2-22211-2-20000002-1-1-110000011-1-1110200-2000011-1000
χ3222222-12-122-1222-12-22-1-1-2-22-1-1-122-1-1-100-2-2-1-21-2-21111-1-1-11111-202211000000-2-2221122000000-211-1-10000011-1-1-1-10-20020000-1-11000
χ332222-12222-1222-12-12-12-122-12-1-1-1-122-12200-1-12-1-122-1-1-1-1-1-1-1-1-1220222-1-12222000000-1-1000000-1-1-102-1-1-1-1-10000-1-10022000-1-1000-100
χ342222-12222-1222-12-12-12-122-12-1-1-1-122-12200-1-12-1-122-1-1-1-1-1-1-1-1-1-220-2-2-2-1-12222000000110000001110-2-1-1-1-1-100001100-2-200011000100
χ352222-12222-1222-12-12-12-122-12-1-1-1-122-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-12-2022211-2-2-2-2000000-1-1000000-1-1-102111110000-1-100-2-200011000100
χ362222-12222-1222-12-12-12-122-12-1-1-1-122-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-1-2-20-2-2-211-2-2-2-2000000110000001110-2111110000110022000-1-1000-100
χ372222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-12200-11-211-2-211-1-1-111112-20-222-1-122-2-200000011000000-1-1-10-21-1-111000011002-200011000-100
χ382222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-12200-11-211-2-211-1-1-11111-2-202-2-2-1-122-2-2000000-1-1000000111021-1-1110000-1-100-22000-1-1000100
χ392222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-1-2-200-11-211-2-211-1-1-11111220-22211-2-22200000011000000-1-1-10-2-111-1-100001100-22000-1-1000100
χ402222-12222-1222-12-1-2-12-1-2-2-12-1-1-1-122-1-2-200-11-211-2-211-1-1-11111-2202-2-211-2-222000000-1-100000011102-111-1-10000-1-1002-200011000-100
χ412-22-222222-2-2-2-22-2-2022200222-2-2-2-2-2-22i−2i2i−2i2000000002-2-200000000002i−2i2i−2i002i−2i002i−2i002-222-2-20000002i−2i002i−2i0000000000000000000
χ422-22-222222-2-2-2-22-2-2022200222-2-2-2-2-2-22i−2i−2i2i2000000002-2-200000000002i−2i2i−2i00−2i2i00−2i2i00-22-2-2220000002i−2i00−2i2i0000000000000000000
χ432-22-222222-2-2-2-22-2-2022200222-2-2-2-2-2-2−2i2i2i−2i2000000002-2-20000000000−2i2i−2i2i002i−2i002i−2i00-22-2-222000000−2i2i002i−2i0000000000000000000
χ442-22-222222-2-2-2-22-2-2022200222-2-2-2-2-2-2−2i2i−2i2i2000000002-2-20000000000−2i2i−2i2i00−2i2i00−2i2i002-222-2-2000000−2i2i00−2i2i0000000000000000000
χ452-22-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-22i−2i2i−2i-100−i3i3−i3i300-111−i3−i3i3i30000002i−2i−ii3−3−ii3−32i−2i002-2-1-111000000−ii3−3−ii3−30000000−i3i300000000
χ462-22-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-22i−2i−2i2i-100−i3i3−i3i300-111−i3−i3i3i30000002i−2i−ii3−3i−i−33−2i2i00-2211-1-1000000−ii3−3i−i−330000000i3−i300000000
χ472-22-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-2−2i2i2i−2i-100−i3i3−i3i300-111−i3−i3i3i3000000−2i2ii−i−33−ii3−32i−2i00-2211-1-1000000i−i−33−ii3−30000000i3−i300000000
χ482-22-222-12-1-2-2112-2-20-1-12−i3i3-1-12-21111-2−2i2i−2i2i-100−i3i3−i3i300-111−i3−i3i3i3000000−2i2ii−i−33i−i−33−2i2i002-2-1-111000000i−i−33i−i−330000000−i3i300000000
χ492-22-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-22i−2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i30000002i−2i−ii−33−ii−332i−2i002-2-1-111000000−ii−33−ii−330000000i3−i300000000
χ502-22-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-22i−2i−2i2i-100i3−i3i3−i300-111i3i3−i3−i30000002i−2i−ii−33i−i3−3−2i2i00-2211-1-1000000−ii−33i−i3−30000000−i3i300000000
χ512-22-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-2−2i2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i3000000−2i2ii−i3−3−ii−332i−2i00-2211-1-1000000i−i3−3−ii−330000000−i3i300000000
χ522-22-222-12-1-2-2112-2-20-1-12i3−i3-1-12-21111-2−2i2i−2i2i-100i3−i3i3−i300-111i3i3−i3−i3000000−2i2ii−i3−3i−i3−3−2i2i002-2-1-111000000i−i3−3i−i3−30000000i3−i300000000
χ5344444-2-2-2-24-2-2-24-244-21-2-2-2-21-2-2-2-211-2004414-2-2-211-2-21111111004000000000-2-2-2-2-2-200000000000-2000000111100000000000000000
χ5444444-2-2-2-24-2-2-24-244-21-2-2-2-21-2-2-2-211-200-4-414-2-2-211-2-2111111100-4000000000222222000000000002000000-1-1-1-100000000000000000
χ5544444-2-2-2-24-2-2-24-24-4-21-222-21-2-2-2-211-200441-4222-1-122111-1-1-1-100-4000000000-2-222-2-200000000000200000011-1-100000000000000000
χ5644444-2-2-2-24-2-2-24-24-4-21-222-21-2-2-2-211-200-4-41-4222-1-122111-1-1-1-100400000000022-2-22200000000000-2000000-1-11100000000000000000
χ574444-24-24-2-24-2-2-24-241-2-2-2-21-2-2-211-2-2-244001-2411-2-2-2-21111111040000-2-2-2-2-2-20000000000000000000-21111000000000000000000000
χ584444-24-24-2-24-2-2-24-241-2-2-2-21-2-2-211-2-2-2-4-4001-2411-2-2-2-211111110-4000022222200000000000000000002-1-1-1-1000000000000000000000
χ594444-24-24-2-24-2-2-24-2-41-2-2221-2-2-211-2-2-2440012-4-1-12222111-1-1-1-10-40000-2-2-2-2220000000000000000000211-1-1000000000000000000000
χ604444-24-24-2-24-2-2-24-2-41-2-2221-2-2-211-2-2-2-4-40012-4-1-12222111-1-1-1-10400002222-2-20000000000000000000-2-1-111000000000000000000000
χ614444-2-24-24-2-244-2-2-24-2-2144-2-211-2-2-2-2100001-2-2-2-2-2-21111111114004-2-2000000000000-2-2000000-2110-200000000011000000000000000
χ624444-2-24-24-2-244-2-2-24-2-2144-2-211-2-2-2-2100001-2-2-2-2-2-2111111111-400-422000000000000220000002-1-102000000000-1-1000000000000000
χ634444-2-24-24-2-244-2-2-2-4-2-21-4-4-2-211-2-2-2-2100001222222-1-1111-1-1-1-1400-4-2-200000000000022000000-21102000000000-1-1000000000000000
χ644444-2-24-24-2-244-2-2-2-4-2-21-4-4-2-211-2-2-2-2100001222222-1-1111-1-1-1-1-400422000000000000-2-20000002-1-10-200000000011000000000000000
χ6544-4-4444-4-4-444-4-4-44044400-4-4-4-44-44-440000400000000-44-40000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-2-42-44-22-4-440-2-240022-4-4-22-2240000-2000000002-2200000000000000000000000000−2i32i3−2i32i30000000000000000000000000000000
χ6744-4-444-2-42-44-22-4-440-2-240022-4-4-22-2240000-2000000002-22000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000000
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χ6944-4-44-242-4-4-24-4-42404-2-200-42224-4-22-20000-2000000002-22000000002i3−2i30000000000000000000002i3−2i30000000000000000000000000000
χ7044-4-4-244-4-4244-42-4-20-24-2002-422-224-4-20000-2000000002-220000000000000000000000−2i32i300000000000000000000−2i32i3000000000000000
χ7144-4-4-244-4-4244-42-4-20-24-2002-422-224-4-20000-2000000002-2200000000000000000000002i3−2i3000000000000000000002i3−2i3000000000000000
χ7244-4-4-2-242-42-24-422-20-2-210022-1-1-22-221000010000003-3-11-13-33-30000−2i32i3000000000000−2i32i30000000i3−i300000000000i3−i3000000000000000
χ7344-4-4-2-242-42-24-422-20-2-210022-1-1-22-221000010000003-3-11-13-33-300002i3−2i30000000000002i3−2i30000000−i3i300000000000−i3i3000000000000000
χ7444-4-4-2-242-42-24-422-20-2-210022-1-1-22-22100001000000-33-11-1-33-330000−2i32i30000000000002i3−2i30000000i3−i300000000000−i3i3000000000000000
χ7544-4-4-2-242-42-24-422-20-2-210022-1-1-22-22100001000000-33-11-1-33-3300002i3−2i3000000000000−2i32i30000000−i3i300000000000i3−i3000000000000000
χ764-44-44-24-24-42-4-442-404-2-2004-2-22-4-4222004i−4i-200000000-22200000000000000004i−4i00−2i2i000000000000000000−2i2i0000000000000000000
χ774-44-44-24-24-42-4-442-404-2-2004-2-22-4-422200−4i4i-200000000-2220000000000000000−4i4i002i−2i0000000000000000002i−2i0000000000000000000
χ784-44-44-2-2-2-2-422242-40-21-2−2i32i3-21-2222-1-12004i−4i100−2i32i3i3−i3001-1-1i3i3−i3−i3000000000000−2i2i23−23−2i2i000000000000000000i−i−3300000000000000000
χ794-44-44-2-2-2-2-422242-40-21-2−2i32i3-21-2222-1-1200−4i4i100−2i32i3i3−i3001-1-1i3i3−i3−i30000000000002i−2i−23232i−2i000000000000000000−ii3−300000000000000000
χ804-44-44-2-2-2-2-422242-40-21-22i3−2i3-21-2222-1-12004i−4i1002i3−2i3−i3i3001-1-1−i3−i3i3i3000000000000−2i2i−2323−2i2i000000000000000000i−i3−300000000000000000
χ814-44-44-2-2-2-2-422242-40-21-22i3−2i3-21-2222-1-1200−4i4i1002i3−2i3−i3i3001-1-1−i3−i3i3i30000000000002i−2i23−232i−2i000000000000000000−ii−3300000000000000000
χ824-44-4-244442-4-4-4-2-420-24-200-24-2222-4-424i−4i00-200000000-2220000000000−2i2i4i−4i0000000000000000000000−2i2i00000000000000000000000
χ834-44-4-244442-4-4-4-2-420-24-200-24-2222-4-42−4i4i00-200000000-22200000000002i−2i−4i4i00000000000000000000002i−2i00000000000000000000000
χ844-44-4-24-24-22-422-2-4201-2-2−2i32i31-2-22-1-12224i−4i00100i3−i3−2i32i3001-1-1i3i3−i3−i3000000−2i2i−2i2i23−2300000000000000000000i−i−33000000000000000000000
χ854-44-4-24-24-22-422-2-4201-2-2−2i32i31-2-22-1-1222−4i4i00100i3−i3−2i32i3001-1-1i3i3−i3−i30000002i−2i2i−2i−232300000000000000000000−ii3−3000000000000000000000
χ864-44-4-24-24-22-422-2-4201-2-22i3−2i31-2-22-1-12224i−4i00100−i3i32i3−2i3001-1-1−i3−i3i3i3000000−2i2i−2i2i−232300000000000000000000i−i3−3000000000000000000000
χ874-44-4-24-24-22-422-2-4201-2-22i3−2i31-2-22-1-1222−4i4i00100−i3i32i3−2i3001-1-1−i3−i3i3i30000002i−2i2i−2i23−2300000000000000000000−ii−33000000000000000000000
χ884-4-44444-4-44-4-44-44-4044400-4-4-44-44-44-40000400000000-4-440000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-424-42-2-44-40-2-240022-442-22-2-40000-20000000022-200000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ904-4-4444-2-424-42-2-44-40-2-240022-442-22-2-40000-20000000022-2000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ914-4-444-242-442-44-4-2-404-2-200-422-2-442-220000-20000000022-20000000000000000000000000000000000000000000000000000000−2i32i30000
χ924-4-444-242-442-44-4-2-404-2-200-422-2-442-220000-20000000022-200000000000000000000000000000000000000000000000000000002i3−2i30000
χ934-4-44-244-4-4-2-4-442420-24-2002-42-22-2-4420000-20000000022-20000000000000000000000000000000000000000000000000000023−23000000
χ944-4-44-244-4-4-2-4-442420-24-2002-42-22-2-4420000-20000000022-200000000000000000000000000000000000000000000000000000−2323000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-444-8-4-44-8480-42-4004-244-442-2-40000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-8448-444-8-402-4-400-24442-2-44-40000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4444-4-4444-4022200-2-2-2-22-22-220000-10000006-61-11-33-33000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4444-4-4444-4022200-2-2-2-22-22-220000-1000000-661-113-33-3000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48-4844-8-8-4440-4-4200-4-42-24444-200002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-4-44444-4440222−4i34i3222-2-2-2-2-2-20000-1002i3−2i32i3−2i300-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4-44444-44402224i3−4i3222-2-2-2-2-2-20000-100−2i32i3−2i32i300-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-444844-4-8-4-80-42-4004-24-44-4-2240000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-84-4-84-448402-4-400-244-4-224-440000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-8-44-884-440-4-420044-224-44-4-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-444-44-44022200-2-2-22-22-22-20000-10000000011-1−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-444-44-44022200-2-2-22-22-22-20000-10000000011-13i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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