Finite Group Databasebeta

← Group #13181075

Character table — Group #13181075

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112224444444444488888881212121212121818181824242424242436363636363636108108112224444444444488888881212121212121818181824242424242436363636363636108108
order123463333666612121236121212121244121212122466121212121212246612121288226466666666612121266121212121244121212122466121212121212246612121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111111111111111111111-1-1-1-11-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1
χ411111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111
χ5111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-1111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-1
χ6111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-1-11-1-1111-11111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-1-11-1-1111-11
χ7111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-11111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-11
χ8111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-1111-11-1-11111-1111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-1111-11-1-11111-1
χ922222222222222222222222000000-2-2-2-20000000000-2000022222222222222222222222000000-2-2-2-20000000000-20000
χ10222-2222222222-2-2-222-2-2-2-2-20000002-2220000000000-20000222-2222222222-2-2-222-2-2-2-2-20000002-2220000000000-20000
χ1122-12-12-1-122-1-12-122-1-12-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i300001000022-12-12-1-122-1-12-122-1-12-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i3000010000
χ1222-12-12-1-122-1-12-122-1-12-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i300001000022-12-12-1-122-1-12-122-1-12-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3000010000
χ1322-12-12-1-122-1-12-122-1-12-1-1-1-122-1-1-1-122-1-12-1-12-1-10000-1000022-12-12-1-122-1-12-122-1-12-1-1-1-122-1-1-1-122-1-12-1-12-1-10000-10000
χ1422-12-12-1-122-1-12-122-1-12-1-1-1-1-2-2111122-1-1-211-2110000-1000022-12-12-1-122-1-12-122-1-12-1-1-1-1-2-2111122-1-1-211-2110000-10000
χ1522-1-2-12-1-122-1-121-2-2-1-1-2111100−i3i3i3−i32-2-1-10−i3i30i3−i300001000022-1-2-12-1-122-1-121-2-2-1-1-2111100−i3i3i3−i32-2-1-10−i3i30i3−i3000010000
χ1622-1-2-12-1-122-1-121-2-2-1-1-2111100i3−i3−i3i32-2-1-10i3−i30−i3i300001000022-1-2-12-1-122-1-121-2-2-1-1-2111100i3−i3−i3i32-2-1-10i3−i30−i3i3000010000
χ1722-1-2-12-1-122-1-121-2-2-1-1-211112-2-1-111-22112-1-1-2110000-1000022-1-2-12-1-122-1-121-2-2-1-1-211112-2-1-111-22112-1-1-2110000-10000
χ1822-1-2-12-1-122-1-121-2-2-1-1-21111-2211-1-1-2211-2112-1-10000-1000022-1-2-12-1-122-1-121-2-2-1-1-21111-2211-1-1-2211-2112-1-10000-10000
χ1944444111-2111-24-2-2-2-2111-2-22222220000-1-1-1-1-1-100000000044444111-2111-24-2-2-2-2111-2-22222220000-1-1-1-1-1-1000000000
χ2044444111-2111-24-2-2-2-2111-2-2-2-2-2-2-2-2000011111100000000044444111-2111-24-2-2-2-2111-2-2-2-2-2-2-2-20000111111000000000
χ2144444-2-2-21-2-2-2141111-2-2-211000000000000000022-1-10-1-10044444-2-2-21-2-2-2141111-2-2-211000000000000000022-1-10-1-100
χ2244444-2-2-21-2-2-2141111-2-2-2110000000000000000-2-2110110044444-2-2-21-2-2-2141111-2-2-2110000000000000000-2-21101100
χ23444-44111-2111-2-422-2-2-1-1-1222-222-2-20000-1-1-1111000000000444-44111-2111-2-422-2-2-1-1-1222-222-2-20000-1-1-1111000000000
χ24444-44111-2111-2-422-2-2-1-1-122-22-2-2220000111-1-1-1000000000444-44111-2111-2-422-2-2-1-1-122-22-2-2220000111-1-1-1000000000
χ25444-44-2-2-21-2-2-21-4-1-111222-1-100000000000000002-2-1-101100444-44-2-2-21-2-2-21-4-1-111222-1-100000000000000002-2-1-101100
χ26444-44-2-2-21-2-2-21-4-1-111222-1-10000000000000000-22110-1-100444-44-2-2-21-2-2-21-4-1-111222-1-10000000000000000-22110-1-100
χ2744-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i3200000000044-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000
χ2844-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i3211-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i3200000000044-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i3211-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000
χ2944-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i3200000000044-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000
χ3044-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i3211-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i3200000000044-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i3211-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000
χ3144-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i3200000000044-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000
χ3244-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i3200000000044-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000
χ3344-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i3200000000044-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000
χ3444-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i3200000000044-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000
χ354-440-44444-4-4-4-40004-40000000000000000000000000000004-440-44444-4-4-4-40004-4000000000000000000000000000000
χ364-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000−i3i303−3004-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000−i3i303−300
χ374-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000i3−i30−33004-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000i3−i30−3300
χ384-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000−i3i30−33004-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000−i3i30−3300
χ394-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000i3−i303−3004-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000i3−i303−300
χ404-4-2024-2-24-422-4000-220000000000000−2i32i30000000000000004-4-2024-2-24-422-4000-220000000000000−2i32i3000000000000000
χ414-4-2024-2-24-422-4000-2200000000000002i3−2i30000000000000004-4-2024-2-24-422-4000-2200000000000002i3−2i3000000000000000
χ4288-48-4-4222-4222-422-1-1-422-1-1000000000000000000000000088-48-4-4222-4222-422-1-1-422-1-10000000000000000000000000
χ4388-4-8-4-4222-42224-2-2-1-14-2-211000000000000000000000000088-4-8-4-4222-42224-2-2-1-14-2-2110000000000000000000000000
χ448-880-8222-4-2-2-24000-440000000000000000000000000000008-880-8222-4-2-2-24000-44000000000000000000000000000000
χ458-8-4042−1−3i3−1+3i3-4-21+3i31−3i340002-20000000000000000000000000000008-8-4042−1−3i3−1+3i3-4-21+3i31−3i340002-2000000000000000000000000000000
χ468-8-4042−1+3i3−1−3i3-4-21−3i31+3i340002-20000000000000000000000000000008-8-4042−1+3i3−1−3i3-4-21−3i31+3i340002-2000000000000000000000000000000
χ478-8-404-42224-2-2-206i−6i-11000−3i3i00000000000000000000000008-8-404-42224-2-2-206i−6i-11000−3i3i0000000000000000000000000
χ488-8-404-42224-2-2-20−6i6i-110003i−3i00000000000000000000000008-8-404-42224-2-2-20−6i6i-110003i−3i0000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-111
χ5211111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-111-1-1
χ53111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-11-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1111-1-111111-11-1-1111-111-1-1-1111-11-1-1-111-11
χ54111-1111111111-1-1-111-1-1-1-1-11-111-1-1-11-1-1111-1-1-1-11-1-1111-11-1-1-11-1-1-1-1-1-1-1-1-1111-1-111111-11-1-1111-111-1-1-11111-111-1-1-11-1
χ55111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-11111-1111-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1111-1-1111111-111-1-11-111111-1-1-1-11-1-1-1111-1
χ56111-1111111111-1-1-111-1-1-1-1-1-11-1-111-11-1-1-1-1-1111-11-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1111-1-1111111-111-1-11-111111-1-1-11-111-1-1-1-11
χ5722222222222222222222222000000-2-2-2-20000000000-20000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000002222000000000020000
χ58222-2222222222-2-2-222-2-2-2-2-20000002-2220000000000-20000-2-2-22-2-2-2-2-2-2-2-2-2222-2-222222000000-22-2-2000000000020000
χ5922-12-12-1-122-1-12-122-1-12-1-1-1-100−i3i3−i3i3-2-2110−i3i30−i3i3000010000-2-21-21-211-2-211-21-2-211-2111100i3−i3i3−i322-1-10i3−i30i3−i30000-10000
χ6022-12-12-1-122-1-12-122-1-12-1-1-1-100i3−i3i3−i3-2-2110i3−i30i3−i3000010000-2-21-21-211-2-211-21-2-211-2111100−i3i3−i3i322-1-10−i3i30−i3i30000-10000
χ6122-12-12-1-122-1-12-122-1-12-1-1-1-122-1-1-1-122-1-12-1-12-1-10000-10000-2-21-21-211-2-211-21-2-211-21111-2-21111-2-211-211-211000010000
χ6222-12-12-1-122-1-12-122-1-12-1-1-1-1-2-2111122-1-1-211-2110000-10000-2-21-21-211-2-211-21-2-211-2111122-1-1-1-1-2-2112-1-12-1-1000010000
χ6322-1-2-12-1-122-1-121-2-2-1-1-2111100−i3i3i3−i32-2-1-10−i3i30i3−i3000010000-2-2121-211-2-211-2-122112-1-1-1-100i3−i3−i3i3-22110i3−i30−i3i30000-10000
χ6422-1-2-12-1-122-1-121-2-2-1-1-2111100i3−i3−i3i32-2-1-10i3−i30−i3i3000010000-2-2121-211-2-211-2-122112-1-1-1-100−i3i3i3−i3-22110−i3i30i3−i30000-10000
χ6522-1-2-12-1-122-1-121-2-2-1-1-211112-2-1-111-22112-1-1-2110000-10000-2-2121-211-2-211-2-122112-1-1-1-1-2211-1-12-2-1-1-2112-1-1000010000
χ6622-1-2-12-1-122-1-121-2-2-1-1-21111-2211-1-1-2211-2112-1-10000-10000-2-2121-211-2-211-2-122112-1-1-1-12-2-1-1112-2-1-12-1-1-211000010000
χ6744444111-2111-24-2-2-2-2111-2-22222220000-1-1-1-1-1-1000000000-4-4-4-4-4-1-1-12-1-1-12-42222-1-1-122-2-2-2-2-2-20000111111000000000
χ6844444111-2111-24-2-2-2-2111-2-2-2-2-2-2-2-20000111111000000000-4-4-4-4-4-1-1-12-1-1-12-42222-1-1-1222222220000-1-1-1-1-1-1000000000
χ6944444-2-2-21-2-2-2141111-2-2-211000000000000000022-1-10-1-100-4-4-4-4-4222-1222-1-4-1-1-1-1222-1-10000000000000000-2-21101100
χ7044444-2-2-21-2-2-2141111-2-2-2110000000000000000-2-21101100-4-4-4-4-4222-1222-1-4-1-1-1-1222-1-1000000000000000022-1-10-1-100
χ71444-44111-2111-2-422-2-2-1-1-1222-222-2-20000-1-1-1111000000000-4-4-44-4-1-1-12-1-1-124-2-222111-2-2-22-2-2220000111-1-1-1000000000
χ72444-44111-2111-2-422-2-2-1-1-122-22-2-2220000111-1-1-1000000000-4-4-44-4-1-1-12-1-1-124-2-222111-2-22-222-2-20000-1-1-1111000000000
χ73444-44-2-2-21-2-2-21-4-1-111222-1-100000000000000002-2-1-101100-4-4-44-4222-1222-1411-1-1-2-2-2110000000000000000-22110-1-100
χ74444-44-2-2-21-2-2-21-4-1-111222-1-10000000000000000-22110-1-100-4-4-44-4222-1222-1411-1-1-2-2-21100000000000000002-2-1-101100
χ7544-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000-4-42-42-11+3i321−3i322-11+3i321−3i322222-1-1-11+3i321−3i32-1-1-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000
χ7644-24-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i3211-2-21+i31−i31+i31−i300001−1−i32−1+i321−1−i32−1+i32000000000-4-42-42-11+3i321−3i322-11+3i321−3i322222-1-1-11+3i321−3i32-1-122−1−i3−1+i3−1−i3−1+i30000-11+i321−i32-11+i321−i32000000000
χ7744-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000-4-42-42-11−3i321+3i322-11−3i321+3i322222-1-1-11−3i321+3i32-1-1-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000
χ7844-24-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i3211-2-21−i31+i31−i31+i300001−1+i32−1−i321−1+i32−1−i32000000000-4-42-42-11−3i321+3i322-11−3i321+3i322222-1-1-11−3i321+3i32-1-122−1+i3−1−i3−1+i3−1−i30000-11−i321+i32-11−i321+i32000000000
χ7944-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-12-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000-4-4242-11+3i321−3i322-11+3i321−3i322-2-2-2-1-11−1−3i32−1+3i3211-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000
χ8044-2-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222211-11+3i321−3i32-1-1-221+i31−i3−1−i3−1+i300001−1−i32−1+i32-11+i321−i32000000000-4-4242-11+3i321−3i322-11+3i321−3i322-2-2-2-1-11−1−3i32−1+3i32112-2−1−i3−1+i31+i31−i30000-11+i321−i321−1−i32−1+i32000000000
χ8144-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-12-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000-4-4242-11−3i321+3i322-11−3i321+3i322-2-2-2-1-11−1+3i32−1−3i3211-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000
χ8244-2-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222211-11−3i321+3i32-1-1-221−i31+i3−1+i3−1−i300001−1+i32−1−i32-11−i321+i32000000000-4-4242-11−3i321+3i322-11−3i321+3i322-2-2-2-1-11−1+3i32−1−3i32112-2−1+i3−1−i31−i31+i30000-11−i321+i321−1+i32−1−i32000000000
χ834-440-44444-4-4-4-40004-4000000000000000000000000000000-44-404-4-4-4-44444000-44000000000000000000000000000000
χ844-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000−i3i303−300-44-404222-1-2-2-210−3i3i-11000−3i3i000000000000000000i3−i30−3300
χ854-440-4-2-2-21222-103i−3i1-10003i−3i000000000000000000i3−i30−3300-44-404222-1-2-2-210−3i3i-11000−3i3i000000000000000000−i3i303−300
χ864-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000−i3i30−3300-44-404222-1-2-2-2103i−3i-110003i−3i000000000000000000i3−i303−300
χ874-440-4-2-2-21222-10−3i3i1-1000−3i3i000000000000000000i3−i303−300-44-404222-1-2-2-2103i−3i-110003i−3i000000000000000000−i3i30−3300
χ884-4-2024-2-24-422-4000-220000000000000−2i32i3000000000000000-4420-2-422-44-2-240002-200000000000002i3−2i3000000000000000
χ894-4-2024-2-24-422-4000-2200000000000002i3−2i3000000000000000-4420-2-422-44-2-240002-20000000000000−2i32i3000000000000000
χ9088-48-4-4222-4222-422-1-1-422-1-10000000000000000000000000-8-84-844-2-2-24-2-2-24-2-2114-2-2110000000000000000000000000
χ9188-4-8-4-4222-42224-2-2-1-14-2-2110000000000000000000000000-8-84844-2-2-24-2-2-2-42211-422-1-10000000000000000000000000
χ928-880-8222-4-2-2-24000-44000000000000000000000000000000-88-808-2-2-24222-40004-4000000000000000000000000000000
χ938-8-4042−1−3i3−1+3i3-4-21+3i31−3i340002-2000000000000000000000000000000-8840-4-21+3i31−3i342−1−3i3−1+3i3-4000-22000000000000000000000000000000
χ948-8-4042−1+3i3−1−3i3-4-21−3i31+3i340002-2000000000000000000000000000000-8840-4-21−3i31+3i342−1+3i3−1−3i3-4000-22000000000000000000000000000000
χ958-8-404-42224-2-2-206i−6i-11000−3i3i0000000000000000000000000-8840-44-2-2-2-42220−6i6i1-10003i−3i0000000000000000000000000
χ968-8-404-42224-2-2-20−6i6i-110003i−3i0000000000000000000000000-8840-44-2-2-2-422206i−6i1-1000−3i3i0000000000000000000000000

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