Finite Group Databasebeta

← Group #10823482

Character table — Group #10823482

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222234444444444446666666121212121212121288888888121212121212121224242424242424242424242424242424222244446666666612121212121212122444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-11111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ9111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1-1-11111-1-1
χ10111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1111-1-1-1-111
χ11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-111111-1-1-111-1-1
χ12111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1111-1-111
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-1111-1-1-1-1-111
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-1-111111-1-1
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-111-1-111
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000000000000000000000000000000002-20000-2002000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000000000000000-220000200-2000000
χ19222222222-2-2-2-22222-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000220000-200-2000000
χ20222222222-2-2-2-22222-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-200002002000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ3522-2-22-22-22−2i−2i2i2i−2i−2i2i2i2-22-222-2-22-2-2−2i−2i−2i−2i2i2i2i2i000000002-2−2i−2i2i2i2-200000000000000002-200−2i2i0022-2-20000−2i−2i2i2i00000000000000000000
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χ4022-2-22-22-2-12i2i−2i−2i2i2i−2i−2i2-22-2-1-111-111−i−i−i−iiiii00000000-11−i−iii-11i3i3i3i3−i3−i3−i3−i3−3−3−3−33333-2200−2i2i0011-1-1−i3−i3i3i3ii−i−i33−3−30000000000000000
χ4122-2-22-22-2-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-111-111iiii−i−i−i−i00000000-11ii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−333332-200−2i2i00-1-111−i3−i3i3i3ii−i−i−3−3330000000000000000
χ4222-2-22-22-2-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-111-111iiii−i−i−i−i00000000-11ii−i−i-11−i3−i3−i3−i3i3i3i3i3−3−3−3−33333-22002i−2i0011-1-1i3i3−i3−i3−i−iii33−3−30000000000000000
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χ4422-2-22-22-2-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-111-111iiii−i−i−i−i00000000-11ii−i−i-11i3i3i3i3−i3−i3−i3−i33333−3−3−3−3-22002i−2i0011-1-1−i3−i3i3i3−i−iii−3−3330000000000000000
χ452-22-2-222-222i−2i2i−2i2i−2i2i−2i2-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i22-2-22i2i−2i−2i-222i−2i2i−2i2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462-22-2-222-222i−2i2i−2i2i−2i2i−2i2-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i-222i−2i2i−2i2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472-22-2-222-222i−2i2i−2i−2i2i−2i2i-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i000000002-22i−2i2i−2i-2200000000000000000000000000000000000000000000000000002i−2i2-2
χ482-22-2-222-222i−2i2i−2i−2i2i−2i2i-222-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i000000002-22i−2i2i−2i-220000000000000000000000000000000000000000000000000000−2i2i-22
χ492-22-2-222-22−2i2i−2i2i2i−2i2i−2i-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i000000002-2−2i2i−2i2i-2200000000000000000000000000000000000000000000000000002i−2i-22
χ502-22-2-222-22−2i2i−2i2i2i−2i2i−2i-222-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i000000002-2−2i2i−2i2i-220000000000000000000000000000000000000000000000000000−2i2i2-2
χ512-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i−2i2i2i-22−2i2i−2i2i2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ522-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i-22−2i2i−2i2i2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ532-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-2-2211-1-1-111−i−iii−i−iii22-2-22i2i−2i−2i1-1−ii−ii-11-1-111-1-111−i−iii−i−iii00000000−i3i3−i3i3−i3i3−i3i33−33−33−33−30000000000000000
χ542-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-2-2211-1-1-111−i−iii−i−iii22-2-22i2i−2i−2i1-1−ii−ii-11-1-111-1-111−i−iii−i−iii00000000i3−i3i3−i3i3−i3i3−i3−33−33−33−330000000000000000
χ552-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-2-2211-1-1-111−i−iii−i−iii-2-222−2i−2i2i2i1-1−ii−ii-1111-1-111-1-1ii−i−iii−i−i00000000−i3i3−i3i3i3−i3i3−i33−33−3−33−330000000000000000
χ562-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-2-2211-1-1-111−i−iii−i−iii-2-222−2i−2i2i2i1-1−ii−ii-1111-1-111-1-1ii−i−iii−i−i00000000i3−i3i3−i3−i3i3−i3i3−33−333−33−30000000000000000
χ572-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-2-2211-1-1-111ii−i−iii−i−i22-2-2−2i−2i2i2i1-1i−ii−i-11-1-111-1-111ii−i−iii−i−i00000000−i3i3−i3i3−i3i3−i3i3−33−33−33−330000000000000000
χ582-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-2-2211-1-1-111ii−i−iii−i−i22-2-2−2i−2i2i2i1-1i−ii−i-11-1-111-1-111ii−i−iii−i−i00000000i3−i3i3−i3i3−i3i3−i33−33−33−33−30000000000000000
χ592-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-2-2211-1-1-111ii−i−iii−i−i-2-2222i2i−2i−2i1-1i−ii−i-1111-1-111-1-1−i−iii−i−iii00000000−i3i3−i3i3i3−i3i3−i3−33−333−33−30000000000000000
χ602-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-2-2211-1-1-111ii−i−iii−i−i-2-2222i2i−2i−2i1-1i−ii−i-1111-1-111-1-1−i−iii−i−iii00000000i3−i3i3−i3−i3i3−i3i33−33−3−33−330000000000000000
χ612-2-22-2-22222-2-222-2-2222-2-2-2-2-2-222222-2-2-2-22200000000-2-22-2-22220000000000000000002-2002-200002-2-2200002-2-220000000000000000
χ622-2-22-2-22222-2-222-2-2222-2-2-2-2-2-222222-2-2-2-22200000000-2-22-2-2222000000000000000000-2200-220000-222-20000-222-20000000000000000
χ632-2-22-2-22222-2-22-222-2-2-222-2-2-2-2222-2-22222-2-200000000222-2-22-2-2000000000000000000000000000000000000000000000002-202-20000
χ642-2-22-2-22222-2-22-222-2-2-222-2-2-2-2222-2-22222-2-200000000222-2-22-2-200000000000000000000000000000000000000000000000-220-220000
χ652-2-22-2-2222-222-22-2-22-2-222-2-2-2-222222-2-2-2-2220000000022-222-2-2-2000000000000000000000000000000000000000000000002-20-220000
χ662-2-22-2-2222-222-22-2-22-2-222-2-2-2-222222-2-2-2-2220000000022-222-2-2-200000000000000000000000000000000000000000000000-2202-20000
χ672-2-22-2-2222-222-2-222-222-2-2-2-2-2-2222-2-22222-2-200000000-2-2-222-2220000000000000000002-200-2200002-2-220000-222-20000000000000000
χ682-2-22-2-2222-222-2-222-222-2-2-2-2-2-2222-2-22222-2-200000000-2-2-222-222000000000000000000-22002-20000-222-200002-2-220000000000000000
χ692-2-22-2-222-12-2-222-2-2222-2-21111-1-1-1-1-11111-1-10000000011-111-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3002-2002-2−i3i3i3−i3-111-1−i3i3i3−i3-111-10000000000000000
χ702-2-22-2-222-12-2-222-2-2222-2-21111-1-1-1-1-11111-1-10000000011-111-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300-2200-22i3−i3−i3i31-1-11i3−i3−i3i31-1-110000000000000000
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χ722-2-22-2-222-12-2-222-2-2222-2-21111-1-1-1-1-11111-1-10000000011-111-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300-2200-22−i3i3i3−i31-1-11−i3i3i3−i31-1-110000000000000000
χ732-2-22-2-222-1-222-2-222-222-2-21111-1-1-111-1-1-1-11100000000111-1-11-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3002-200-22−i3i3i3−i3-111-1i3−i3−i3i31-1-110000000000000000
χ742-2-22-2-222-1-222-2-222-222-2-21111-1-1-111-1-1-1-11100000000111-1-11-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300-22002-2i3−i3−i3i31-1-11−i3i3i3−i3-111-10000000000000000
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χ7744444444-24444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2222222220000000022-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-440000000000004-44-4-44-40000000022−2222−2200000000000022−2222−2222−2222−22000000000000000000000000000000000000000000000000
χ804444-4-4-4-440000000000004-44-4-44-400000000−2222−2222000000000000−2222−2222−2222−2222000000000000000000000000000000000000000000000000
χ814444-4-4-4-4-2000000000000-22-222-2223−2323−2323−2323−2322−2222−22000000000000−22−22−22−226−66−66−66−60000000000000000000000000000000000000000
χ824444-4-4-4-4-2000000000000-22-222-2223−2323−2323−2323−23−2222−22220000000000002−22−22−22−2−66−66−66−660000000000000000000000000000000000000000
χ834444-4-4-4-4-2000000000000-22-222-22−2323−2323−2323−232322−2222−22000000000000−22−22−22−22−66−66−66−660000000000000000000000000000000000000000
χ844444-4-4-4-4-2000000000000-22-222-22−2323−2323−2323−2323−2222−22220000000000002−22−22−22−26−66−66−66−60000000000000000000000000000000000000000
χ8544-4-44-44-4-24i4i−4i−4i−4i−4i4i4i-44-44-2-222-2222i2i2i2i−2i−2i−2i−2i000000002-2−2i−2i2i2i2-200000000000000000000000000000000000000000000000000000000
χ8644-4-44-44-4-2−4i−4i4i4i4i4i−4i−4i-44-44-2-222-222−2i−2i−2i−2i2i2i2i2i000000002-22i2i−2i−2i2-200000000000000000000000000000000000000000000000000000000
χ8744-4-4-44-4440000000000004-4-44-4-4400000000000022−2222−22000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ8844-4-4-44-4440000000000004-4-44-4-44000000000000−2222−22220000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ8944-4-4-44-44-2000000000000-222-222-2−2i32i3−2i32i32i3−2i32i3−2i3000022−2222−2200000000−i6i6−i6i6i6−i6i6−i6−22−222−22−20000000000000000000000000000000000000000
χ9044-4-4-44-44-2000000000000-222-222-2−2i32i3−2i32i32i3−2i32i3−2i30000−2222−222200000000i6−i6i6−i6−i6i6−i6i62−22−2−22−220000000000000000000000000000000000000000
χ9144-4-4-44-44-2000000000000-222-222-22i3−2i32i3−2i3−2i32i3−2i32i3000022−2222−2200000000i6−i6i6−i6−i6i6−i6i6−22−222−22−20000000000000000000000000000000000000000
χ9244-4-4-44-44-2000000000000-222-222-22i3−2i32i3−2i3−2i32i3−2i32i30000−2222−222200000000−i6i6−i6i6i6−i6i6−i62−22−2−22−220000000000000000000000000000000000000000
χ934-44-44-4-444000000000000-444-4-4-440000000022−22−222200000000000022−22−222222−22−2222000000000000000000000000000000000000000000000000
χ944-44-44-4-444000000000000-444-4-4-4400000000−222222−22000000000000−222222−22−222222−22000000000000000000000000000000000000000000000000
χ954-44-44-4-44-20000000000002-2-2222-2−2i32i32i3−2i3−2i32i32i3−2i322−22−2222000000000000−222−2−222−2−i6i6i6−i6−i6i6i6−i60000000000000000000000000000000000000000
χ964-44-44-4-44-20000000000002-2-2222-2−2i32i32i3−2i3−2i32i32i3−2i3−222222−220000000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i60000000000000000000000000000000000000000
χ974-44-44-4-44-20000000000002-2-2222-22i3−2i3−2i32i32i3−2i3−2i32i322−22−2222000000000000−222−2−222−2i6−i6−i6i6i6−i6−i6i60000000000000000000000000000000000000000
χ984-44-44-4-44-20000000000002-2-2222-22i3−2i3−2i32i32i3−2i3−2i32i3−222222−220000000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i60000000000000000000000000000000000000000
χ994-44-4-444-4-24i−4i4i−4i−4i4i−4i4i-444-422-2-2-2222i2i−2i−2i2i2i−2i−2i00000000-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ1004-44-4-444-4-2−4i4i−4i4i4i−4i4i−4i-444-422-2-2-222−2i−2i2i2i−2i−2i2i2i00000000-222i−2i2i−2i2-200000000000000000000000000000000000000000000000000000000
χ1014-4-4444-4-44000000000000-44-44-44-4000000000000−2i22i22i2−2i20000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ1024-4-4444-4-44000000000000-44-44-44-40000000000002i2−2i2−2i22i200000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ1034-4-4444-4-4-20000000000002-22-22-2223−23−2323−232323−230000−2i22i22i2−2i200000000i6−i6−i6i6−i6i6i6−i6i2−i2−i2i2−i2i2i2−i20000000000000000000000000000000000000000
χ1044-4-4444-4-4-20000000000002-22-22-2223−23−2323−232323−2300002i2−2i2−2i22i200000000−i6i6i6−i6i6−i6−i6i6−i2i2i2−i2i2−i2−i2i20000000000000000000000000000000000000000
χ1054-4-4444-4-4-20000000000002-22-22-22−232323−2323−23−23230000−2i22i22i2−2i200000000−i6i6i6−i6i6−i6−i6i6i2−i2−i2i2−i2i2i2−i20000000000000000000000000000000000000000
χ1064-4-4444-4-4-20000000000002-22-22-22−232323−2323−23−232300002i2−2i2−2i22i200000000i6−i6−i6i6−i6i6i6−i6−i2i2i2−i2i2−i2−i2i20000000000000000000000000000000000000000
χ1074-4-44-4-444-24-4-44-444-4-4-4442222-2-2-222-2-2-2-22200000000-2-2-222-22200000000000000000000000000000000000000000000000000000000
χ1084-4-44-4-444-2-444-44-4-44-4-4442222-2-2-2-2-22222-2-200000000-2-22-2-222200000000000000000000000000000000000000000000000000000000

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