Finite Group Databasebeta

← Group #13034872

Character table — Group #13034872

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222444445555888888881010101016161616202020202020202020202020202020202040401111222244444555588888888101010101616161620202020202020202020202020202020204040
order12224444251010104444441010202020202222202020204444444448888888824222244442101010104444441010202020202222202020204444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111-1-11111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111111111111-1-11111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111111111111111111-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111-1-1-1-111111111-1-1-1-11111-1iiii−i−i−i−iiiii−i−i−i−i-1-11111111111111-1-1-1-111111111-1-1-1-11111-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111-1-1-1-111111111-1-1-1-11111-1−i−i−i−iiiii−i−i−i−iiiii-1-11111111111111-1-1-1-111111111-1-1-1-11111-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-111-1-111-1-111-1-111-1-1-11111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-111-1-111-1-111-1-111-1-1-11
χ10111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-11111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-11
χ11111111-1-1-111111111-11-1-111-1-1-1-111-1-111-111-1-111-1-1-1-111-1-1111-1111111-1-1-111111111-11-1-111-1-1-1-111-1-111-111-1-111-1-1-1-111-1-1111-1
χ12111111-1-1-111111111-11-1-111-1-1-1-111-1-111-1-1-111-1-11111-1-111-1-11-1111111-1-1-111111111-11-1-111-1-1-1-111-1-111-1-1-111-1-11111-1-111-1-11-1
χ13111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1
χ14111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1
χ15111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i-11111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i-11
χ16111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii-11111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii-11
χ172222-2-222-22222222200-2-2-2-22222-2-20000-20000000000000000002222-2-222-22222222200-2-2-2-22222-2-20000-2000000000000000000
χ182222-2-222-22222-2-2-2-200-2-2-2-222-2-222000020000000000000000002222-2-222-22222-2-2-2-200-2-2-2-222-2-22200002000000000000000000
χ192222-2-2-2-22222222220022-2-2-2-2-2-2-2-2000020000000000000000002222-2-2-2-22222222220022-2-2-2-2-2-2-2-200002000000000000000000
χ202222-2-2-2-222222-2-2-2-20022-2-2-2-222220000-20000000000000000002222-2-2-2-222222-2-2-2-20022-2-2-2-222220000-2000000000000000000
χ2122-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000022-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ2222-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-20000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000022-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-20000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ2322-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-2200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000022-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-2200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ2422-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-220000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000022-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-220000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ2522-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-2200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000022-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-2200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ2622-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-220000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000022-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-220000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ2722-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000022-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ2822-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-20000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000022-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-20000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ292-2-222-20002-2-2222-2-200002-200002-200000000000002i−2i002i−2i00002-2-222-20002-2-2222-2-200002-200002-200000000000002i−2i002i−2i0000
χ302-2-222-20002-2-2222-2-200002-200002-20000000000000−2i2i00−2i2i00002-2-222-20002-2-2222-2-200002-200002-20000000000000−2i2i00−2i2i0000
χ312-2-222-20002-2-22-2-22200002-20000-2200000000000002-200-2200002-2-222-20002-2-22-2-22200002-20000-2200000000000002-200-220000
χ322-2-222-20002-2-22-2-22200002-20000-220000000000000-22002-200002-2-222-20002-2-22-2-22200002-20000-220000000000000-22002-20000
χ332-2-22-220002-2-2222-2-20000-220000-220000000000000002i−2i002i−2i002-2-22-220002-2-2222-2-20000-220000-220000000000000002i−2i002i−2i00
χ342-2-22-220002-2-2222-2-20000-220000-22000000000000000−2i2i00−2i2i002-2-22-220002-2-2222-2-20000-220000-22000000000000000−2i2i00−2i2i00
χ352-2-22-220002-2-22-2-2220000-2200002-20000000000000002-200-22002-2-22-220002-2-22-2-2220000-2200002-20000000000000002-200-2200
χ362-2-22-220002-2-22-2-2220000-2200002-2000000000000000-22002-2002-2-22-220002-2-22-2-2220000-2200002-2000000000000000-22002-200
χ37444444444-1-1-1-1000044-1-1-1-1-1-10000-1-1-1-10000000000000000000444444444-1-1-1-1000044-1-1-1-1-1-10000-1-1-1-10000000000000000000
χ38444444444-1-1-1-10000-4-4-1-1-1-1-1-1000011110000000000000000000444444444-1-1-1-10000-4-4-1-1-1-1-1-1000011110000000000000000000
χ39444444-4-4-4-1-1-1-100004-411-1-1110000-1-1110000000000000000000444444-4-4-4-1-1-1-100004-411-1-1110000-1-1110000000000000000000
χ40444444-4-4-4-1-1-1-10000-4411-1-111000011-1-10000000000000000000444444-4-4-4-1-1-1-10000-4411-1-111000011-1-10000000000000000000
χ414444-4-444-4-1-1-1-10000001111-1-100005−55−500000000000000000004444-4-444-4-1-1-1-10000001111-1-100005−55−50000000000000000000
χ424444-4-444-4-1-1-1-10000001111-1-10000−55−5500000000000000000004444-4-444-4-1-1-1-10000001111-1-10000−55−550000000000000000000
χ434444-4-4-4-44-1-1-1-1000000-1-1111100005−5−5500000000000000000004444-4-4-4-44-1-1-1-1000000-1-1111100005−5−550000000000000000000
χ444444-4-4-4-44-1-1-1-1000000-1-111110000−555−500000000000000000004444-4-4-4-44-1-1-1-1000000-1-111110000−555−50000000000000000000
χ454-44-40000044-4-44i−4i−4i4i000000000000000000000000000000000004-44-40000044-4-44i−4i−4i4i00000000000000000000000000000000000
χ464-44-40000044-4-4−4i4i4i−4i000000000000000000000000000000000004-44-40000044-4-4−4i4i4i−4i00000000000000000000000000000000000
χ4788-8-8008i−8i0-22-220000000000−2i2i00000000000000000000000000088-8-8008i−8i0-22-220000000000−2i2i000000000000000000000000000
χ4888-8-800−8i8i0-22-2200000000002i−2i00000000000000000000000000088-8-800−8i8i0-22-2200000000002i−2i000000000000000000000000000
χ498-88-800000-2-22200000025−2500000000000000000000000000000008-88-800000-2-22200000025−250000000000000000000000000000000
χ508-88-800000-2-222000000−252500000000000000000000000000000008-88-800000-2-222000000−25250000000000000000000000000000000
χ518-8-888-8000-222-200000000-22000000000000000000000000000008-8-888-8000-222-200000000-2200000000000000000000000000000
χ528-8-88-88000-222-2000000002-2000000000000000000000000000008-8-88-88000-222-2000000002-200000000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ541111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ5511111111111111111-1-11111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111111111
χ5611111111111111111-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-1-1-1-1-111
χ571111111111111-1-1-1-111111111-1-1-1-11111-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11
χ581111111111111-1-1-1-111111111-1-1-1-11111-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11
χ591111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1
χ601111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111iiii−i−i−i−i−i−i−i−iiiii-1-1
χ61111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-111-1-111-1-111-1-111-1-1-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-111-1-111-1-111-1-1111-1
χ62111111-1-1-1111111111-1-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111-1-111-1-111-1-111-1-11-1
χ63111111-1-1-111111111-11-1-111-1-1-1-111-1-111-111-1-111-1-1-1-111-1-1111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-11-1-111-1-11111-1-111-1-1-11
χ64111111-1-1-111111111-11-1-111-1-1-1-111-1-111-1-1-111-1-11111-1-111-1-11-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1111-1-111-1-1-1-111-1-111-11
χ65111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-1-1-1-1-1-1111-1-1-1-11111-1111-1-111-1-111-1-111-1−i−iiiii−i−i−i−iiiii−i−i-11
χ66111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-1-1-1-1-1-1111-1-1-1-11111-1111-1-111-1-111-1-111-1ii−i−i−i−iiiii−i−i−i−iii-11
χ67111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i-11-1-1-1-1-1-1111-1-1-1-111111-111-1-111-1-11111-1-1-1−i−iiiii−i−iii−i−i−i−iii1-1
χ68111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii-11-1-1-1-1-1-1111-1-1-1-111111-111-1-111-1-11111-1-1-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ692222-2-222-22222222200-2-2-2-22222-2-20000-2000000000000000000-2-2-2-222-2-22-2-2-2-2-2-2-2-2002222-2-2-2-22200002000000000000000000
χ702222-2-222-22222-2-2-2-200-2-2-2-222-2-22200002000000000000000000-2-2-2-222-2-22-2-2-2-22222002222-2-222-2-20000-2000000000000000000
χ712222-2-2-2-22222222220022-2-2-2-2-2-2-2-200002000000000000000000-2-2-2-22222-2-2-2-2-2-2-2-2-200-2-2222222220000-2000000000000000000
χ722222-2-2-2-222222-2-2-2-20022-2-2-2-222220000-2000000000000000000-2-2-2-22222-2-2-2-2-2222200-2-22222-2-2-2-200002000000000000000000
χ7322-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000-2-22200−2i2i0-22-22−2i2i−2i2i000000−2i2i-220000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ7422-2-2002i−2i02-22-22i−2i2i−2i0000002i−2i2-20000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000-2-22200−2i2i0-22-22−2i2i−2i2i000000−2i2i-2200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ7522-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-2200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000-2-22200−2i2i0-22-222i−2i2i−2i000000−2i2i2-20000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ7622-2-2002i−2i02-22-2−2i2i−2i2i0000002i−2i-220000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000-2-22200−2i2i0-22-222i−2i2i−2i000000−2i2i2-200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ7722-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-2200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000-2-222002i−2i0-22-22−2i2i−2i2i0000002i−2i2-20000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ7822-2-200−2i2i02-22-22i−2i2i−2i000000−2i2i-220000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000-2-222002i−2i0-22-22−2i2i−2i2i0000002i−2i2-200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ7922-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000-2-222002i−2i0-22-222i−2i2i−2i0000002i−2i-220000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ8022-2-200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-20000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000-2-222002i−2i0-22-222i−2i2i−2i0000002i−2i-2200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ812-2-222-20002-2-2222-2-200002-200002-200000000000002i−2i002i−2i0000-222-2-22000-222-2-2-2220000-220000-220000000000000−2i2i00−2i2i0000
χ822-2-222-20002-2-2222-2-200002-200002-20000000000000−2i2i00−2i2i0000-222-2-22000-222-2-2-2220000-220000-2200000000000002i−2i002i−2i0000
χ832-2-222-20002-2-22-2-22200002-20000-2200000000000002-200-220000-222-2-22000-222-222-2-20000-2200002-20000000000000-22002-20000
χ842-2-222-20002-2-22-2-22200002-20000-220000000000000-22002-20000-222-2-22000-222-222-2-20000-2200002-200000000000002-200-220000
χ852-2-22-220002-2-2222-2-20000-220000-220000000000000002i−2i002i−2i00-222-22-2000-222-2-2-22200002-200002-2000000000000000−2i2i00−2i2i00
χ862-2-22-220002-2-2222-2-20000-220000-22000000000000000−2i2i00−2i2i00-222-22-2000-222-2-2-22200002-200002-20000000000000002i−2i002i−2i00
χ872-2-22-220002-2-22-2-2220000-2200002-20000000000000002-200-2200-222-22-2000-222-222-2-200002-20000-22000000000000000-22002-200
χ882-2-22-220002-2-22-2-2220000-2200002-2000000000000000-22002-200-222-22-2000-222-222-2-200002-20000-220000000000000002-200-2200
χ89444444444-1-1-1-1000044-1-1-1-1-1-10000-1-1-1-10000000000000000000-4-4-4-4-4-4-4-4-411110000-4-4111111000011110000000000000000000
χ90444444444-1-1-1-10000-4-4-1-1-1-1-1-1000011110000000000000000000-4-4-4-4-4-4-4-4-411110000441111110000-1-1-1-10000000000000000000
χ91444444-4-4-4-1-1-1-100004-411-1-1110000-1-1110000000000000000000-4-4-4-4-4-444411110000-44-1-111-1-1000011-1-10000000000000000000
χ92444444-4-4-4-1-1-1-10000-4411-1-111000011-1-10000000000000000000-4-4-4-4-4-4444111100004-4-1-111-1-10000-1-1110000000000000000000
χ934444-4-444-4-1-1-1-10000001111-1-100005−55−50000000000000000000-4-4-4-444-4-441111000000-1-1-1-1110000−55−550000000000000000000
χ944444-4-444-4-1-1-1-10000001111-1-10000−55−550000000000000000000-4-4-4-444-4-441111000000-1-1-1-11100005−55−50000000000000000000
χ954444-4-4-4-44-1-1-1-1000000-1-1111100005−5−550000000000000000000-4-4-4-44444-4111100000011-1-1-1-10000−555−50000000000000000000
χ964444-4-4-4-44-1-1-1-1000000-1-111110000−555−50000000000000000000-4-4-4-44444-4111100000011-1-1-1-100005−5−550000000000000000000
χ974-44-40000044-4-44i−4i−4i4i00000000000000000000000000000000000-44-4400000-4-444−4i4i4i−4i00000000000000000000000000000000000
χ984-44-40000044-4-4−4i4i4i−4i00000000000000000000000000000000000-44-4400000-4-4444i−4i−4i4i00000000000000000000000000000000000
χ9988-8-8008i−8i0-22-220000000000−2i2i000000000000000000000000000-8-88800−8i8i02-22-200000000002i−2i000000000000000000000000000
χ10088-8-800−8i8i0-22-2200000000002i−2i000000000000000000000000000-8-888008i−8i02-22-20000000000−2i2i000000000000000000000000000
χ1018-88-800000-2-22200000025−250000000000000000000000000000000-88-880000022-2-2000000−25250000000000000000000000000000000
χ1028-88-800000-2-222000000−25250000000000000000000000000000000-88-880000022-2-200000025−250000000000000000000000000000000
χ1038-8-888-8000-222-200000000-2200000000000000000000000000000-888-8-880002-2-22000000002-200000000000000000000000000000
χ1048-8-88-88000-222-2000000002-200000000000000000000000000000-888-88-80002-2-2200000000-2200000000000000000000000000000

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