Finite Group Databasebeta

← Group #13168414

Character table — Group #13168414

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order122233366666666633346666666661212121212121212224444121212123666121212121212121212444666612121212121212121212121212121212121244446612121212121212121212244412121212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-11111111111-1-111111-1-1-111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1111
χ51111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11111-11-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-111-11-1-1-1-111-1-1-111-1-1-1111111-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-1-1-11-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111111111-11-1-1-1-111-1-1-1-1-1111-1-111-1-1-1-111
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1111-11-111-1-1-1-11111-1-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-11-11-111-1-1-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-111-1-1-1111-1-11111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-11-1-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11-11111-1-111-111-1-1-11111-1-1-11-11
χ17222222-12-1-12222-122-1-12-1-12-1-122-1-1222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1220000-1-100000000002200-1-1-122-1-1-1-1-1-1-120000000-1-100-1000
χ18222222-12-1-12222-122-1-12-1-12-1-122-1-1222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2222-1-1220000110000000000-2-200-1-1-1-2-21-1-11111-2000000011001000
χ19222222-12-1-12222-122-1-12-1-12-1-122-1-122222222-2-200000000-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-211-2-20000-1-10000000000-2-20011122-111-1-1-1-1-2000000011001000
χ20222222-12-1-12222-122-1-12-1-12-1-122-1-122222222-2-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211-2-200001100000000002200111-2-2111111120000000-1-100-1000
χ21222222-12-1-12222-122-1-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-22200000000-1-1-1-11111111112-2-222-1-1-2-20000-1-100000000002200-1-112-2111-1-111-20000000-1-1001000
χ22222222-12-1-12222-122-1-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-22200000000-1-1-1-1111111111-22-222-1-1-2-20000110000000000-2-200-1-11-22-11111-1-1200000001100-1000
χ23222222-12-1-12222-122-1-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-2-2-200000000-1-1-1-11111111112-22-2-211220000-1-10000000000-2-20011-12-21-1-1-1-111200000001100-1000
χ24222222-12-1-12222-122-1-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-2-2-200000000-1-1-1-1111111111-222-2-211220000110000000000220011-1-22-1-1-111-1-1-20000000-1-1001000
χ2522222-12222-12-1-122-12-122-1-12-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002-1-122-1-1-1-1220022-1-1-1-1-1-1-1-10022-1-12000-1-100000200-1-1-1-100000000
χ2622222-12222-12-1-122-12-122-1-12-1-1-1-1222-1-1-1-1-1-122-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1002-1-122-1-111-2-200-2-21111111100-2-2-1-12000-1-100000-200111100000000
χ2722222-12222-12-1-122-12-122-1-12-1-1-1-1222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-211-2-211-1-1220022-1-1-1-1-1-1-1-100-2-211-20001100000-200111100000000
χ2822222-12222-12-1-122-12-122-1-12-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1222-1-1-1-1-1-100-211-2-21111-2-200-2-211111111002211-20001100000200-1-1-1-100000000
χ2922222-12222-12-1-122-12-1-22-1-12-1-1-1-12-2-21111112222-2-2-1-1-1-1-1-1-1-1-2-2-211111100-2-1-12211112200-2-2-1-1-1-1111100-2-2-1-1-2000110000020011-1-100000000
χ3022222-12222-12-1-122-12-1-22-1-12-1-1-1-12-2-211111122-2-2221111-1-1-1-1-2-2-211111100-2-1-12211-1-1-2-200221111-1-1-1-10022-1-1-20001100000-200-1-11100000000
χ3122222-12222-12-1-122-12-1-22-1-12-1-1-1-12-2-2111111-2-222-2-2-1-1-1-1-1-1-1-1-2-2-211111100211-2-2-1-1112200-2-2-1-1-1-111110022112000-1-100000-200-1-11100000000
χ3222222-12222-12-1-122-12-1-22-1-12-1-1-1-12-2-2111111-2-2-2-2221111-1-1-1-1-2-2-211111100211-2-2-1-1-1-1-2-200221111-1-1-1-100-2-2112000-1-10000020011-1-100000000
χ332222-122-1222-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-10022222222-1-1-1-12-1-122-1-1-1-122000000022-1-122-1-1-1-1-1-1-1-1-1-10000000-1-1200-1-1-1-10022000000000-1-10
χ342222-122-1222-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-10022222222-1-1-1-12-1-122-1-1-1-1-2-2000000022-1-1-2-2-1-1-1-1-1-1-1-1-1-1000000011-200111100-2-2000000000110
χ352222-122-1222-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1220000000-2-2112211111111110000000-1-1200-1-1-1-100-2-2000000000110
χ362222-122-1222-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-20000000-2-211-2-21111111111000000011-20011110022000000000-1-10
χ372222-122-1222-1222-1-1-12-2-12-1-12-1-12-111-2-211110022-2-22222-1-1-1-1-211-2-211112-20000000-2-2-1-12211-1-1-1-111110000000-11-200-1-111002-2000000000-110
χ382222-122-1222-1222-1-1-12-2-12-1-12-1-12-111-2-211110022-2-22222-1-1-1-1-211-2-21111-220000000-2-2-1-1-2-211-1-1-1-1111100000001-120011-1-100-220000000001-10
χ392222-122-1222-1222-1-1-12-2-12-1-12-1-12-111-2-2111100-2-222-2-2-2-2-1-1-1-1-211-2-211112-20000000221122-1-11111-1-1-1-10000000-11-200-1-11100-220000000001-10
χ402222-122-1222-1222-1-1-12-2-12-1-12-1-12-111-2-2111100-2-222-2-2-2-2-1-1-1-1-211-2-21111-2200000002211-2-2-1-11111-1-1-1-100000001-120011-1-1002-2000000000-110
χ4122-2-2222-2-2-2-22-222-22220-22-2-2-22-2-22000000002-2002i−2i000022-2-20000000000002-22-2002i−2i00002i−2i00002i2i−2i−2i002i−2i2-2000000000000002i−2i0000000000
χ4222-2-2222-2-2-2-22-222-22220-22-2-2-22-2-22000000002-200−2i2i000022-2-20000000000002-22-200−2i2i0000−2i2i0000−2i−2i2i2i00−2i2i2-200000000000000−2i2i0000000000
χ4322-2-2222-2-2-2-22-222-22220-22-2-2-22-2-2200000000-22002i−2i000022-2-2000000000000-22-22002i−2i00002i−2i00002i2i−2i−2i00−2i2i-2200000000000000−2i2i0000000000
χ4422-2-2222-2-2-2-22-222-22220-22-2-2-22-2-2200000000-2200−2i2i000022-2-2000000000000-22-2200−2i2i0000−2i2i0000−2i−2i2i2i002i−2i-22000000000000002i−2i0000000000
χ4522-2-22-12-2-2-2121-12-2-12-10-2-11-21-1112003−333−3−32-2002i−2i−i3−i3i3i3-1-1110003−333−3−3000-112-23−3−ii00002i−2i−i3−i3i3i3−i−iii002i−2i-1100003−300000000−ii−i3i300000000
χ4622-2-22-12-2-2-2121-12-2-12-10-2-11-21-1112003−333−3−32-200−2i2ii3i3−i3−i3-1-1110003−333−3−3000-112-23−3i−i0000−2i2ii3i3−i3−i3ii−i−i00−2i2i-1100003−300000000i−ii3−i300000000
χ4722-2-22-12-2-2-2121-12-2-12-10-2-11-21-1112003−333−3−3-22002i−2i−i3−i3i3i3-1-1110003−333−3−30001-1-22−33−ii00002i−2i−i3−i3i3i3−i−iii00−2i2i1-10000−3300000000i−ii3−i300000000
χ4822-2-22-12-2-2-2121-12-2-12-10-2-11-21-1112003−333−3−3-2200−2i2ii3i3−i3−i3-1-1110003−333−3−30001-1-22−33i−i0000−2i2ii3i3−i3−i3ii−i−i002i−2i1-10000−3300000000−ii−i3i300000000
χ4922-2-22-12-2-2-2121-12-2-12-10-2-11-21-111200−33−3−3332-2002i−2ii3i3−i3−i3-1-111000−33−3−333000-112-2−33−ii00002i−2ii3i3−i3−i3−i−iii002i−2i-110000−3300000000−iii3−i300000000
χ5022-2-22-12-2-2-2121-12-2-12-10-2-11-21-111200−33−3−3332-200−2i2i−i3−i3i3i3-1-111000−33−3−333000-112-2−33i−i0000−2i2i−i3−i3i3i3ii−i−i00−2i2i-110000−3300000000i−i−i3i300000000
χ5122-2-22-12-2-2-2121-12-2-12-10-2-11-21-111200−33−3−333-22002i−2ii3i3−i3−i3-1-111000−33−3−3330001-1-223−3−ii00002i−2ii3i3−i3−i3−i−iii00−2i2i1-100003−300000000i−i−i3i300000000
χ5222-2-22-12-2-2-2121-12-2-12-10-2-11-21-111200−33−3−333-2200−2i2i−i3−i3i3i3-1-111000−33−3−3330001-1-223−3i−i0000−2i2i−i3−i3i3i3ii−i−i002i−2i1-100003−300000000−iii3−i300000000
χ532-2-22222-2-222-2-2-2-2222202-2-2-2-2-222-200000000002i−2i002i−2i2i−2i2-22-2000000000000000000002i−2i00002i−2i2i−2i00002i−2i00000000000000000000002i−2i2-20000
χ542-2-22222-2-222-2-2-2-2222202-2-2-2-2-222-200000000002i−2i002i−2i2i−2i2-22-2000000000000000000002i−2i00002i−2i2i−2i0000−2i2i0000000000000000000000−2i2i-220000
χ552-2-22222-2-222-2-2-2-2222202-2-2-2-2-222-20000000000−2i2i00−2i2i−2i2i2-22-200000000000000000000−2i2i0000−2i2i−2i2i00002i−2i00000000000000000000002i−2i-220000
χ562-2-22222-2-222-2-2-2-2222202-2-2-2-2-222-20000000000−2i2i00−2i2i−2i2i2-22-200000000000000000000−2i2i0000−2i2i−2i2i0000−2i2i0000000000000000000000−2i2i2-20000
χ5744444-2-24-2-2-24-2-2-24-2-214-21-2-21-2-21-244-2-2-2-2-2-244000000001111-2-2-2111111004-2-2-2-2-2-20000000000000000000011-20001100000000000000000000
χ5844444-2-24-2-2-24-2-2-24-2-214-21-2-21-2-21-244-2-2-2-2-2-2-4-4000000001111-2-2-211111100-422222200000000000000000000-1-12000-1-100000000000000000000
χ5944444-2-24-2-2-24-2-2-24-2-21-4-21-2-21-2-21-2-4-422222244000000001111222-1-1-1-1-1-100-4-2-2-2-22200000000000000000000112000-1-100000000000000000000
χ6044444-2-24-2-2-24-2-2-24-2-21-4-21-2-21-2-21-2-4-4222222-4-4000000001111222-1-1-1-1-1-10042222-2-200000000000000000000-1-1-20001100000000000000000000
χ614444-24-2-2-2-24-244-2-2-21-241-2-21-2-2-2-21-2-244-2-2-2-200000000001111-211-2-211114400000000000-2-200000000000000000-2-2-20011110000000000000000
χ624444-24-2-2-2-24-244-2-2-21-241-2-21-2-2-2-21-2-244-2-2-2-200000000001111-211-2-21111-4-400000000000220000000000000000022200-1-1-1-10000000000000000
χ634444-24-2-2-2-24-244-2-2-21-2-41-2-21-2-2-2-2122-4-42222000000000011112-1-122-1-1-1-14-400000000000-2-200000000000000000-2220011-1-10000000000000000
χ644444-24-2-2-2-24-244-2-2-21-2-41-2-21-2-2-2-2122-4-42222000000000011112-1-122-1-1-1-1-440000000000022000000000000000002-2-200-1-1110000000000000000
χ654444-2-24-244-2-2-2-24-21-2-24-2-21-2-211-2-2-2-2-2-21111004444-2-2-2-211114-2-2-2-21111000000000-2-2-2-200-2-21111111100000000000000000000000000000000
χ664444-2-24-244-2-2-2-24-21-2-24-2-21-2-211-2-2-2-2-2-2111100-4-4-4-4222211114-2-2-2-2111100000000022220022-1-1-1-1-1-1-1-100000000000000000000000000000000
χ674444-2-24-244-2-2-2-24-21-2-2-4-2-21-2-211-2-22222-1-1-1-10044-4-4-2-2-2-21111-42222-1-1-1-100000000022-2-200221111-1-1-1-100000000000000000000000000000000
χ684444-2-24-244-2-2-2-24-21-2-2-4-2-21-2-211-2-22222-1-1-1-100-4-44422221111-42222-1-1-1-1000000000-2-22200-2-2-1-1-1-1111100000000000000000000000000000000
χ6944-4-444-2-422-44-44-2-44-2-202-2-4224-42-2000000004-400000000-2-2220000000000004-4-220000000000000000000000-2200000000000000000000000000
χ7044-4-444-2-422-44-44-2-44-2-202-2-4224-42-200000000-4400000000-2-222000000000000-442-200000000000000000000002-200000000000000000000000000
χ7144-4-44-2-2-422242-2-2-4-2-2102122-1-22-1-20023−232323−23−234-40000000011-1-1000−33−3−333000-22-2223−23000000000000000000001-10000−3300000000000000000000
χ7244-4-44-2-2-422242-2-2-4-2-2102122-1-22-1-20023−232323−23−23-440000000011-1-1000−33−3−3330002-22-2−232300000000000000000000-1100003−300000000000000000000
χ7344-4-44-2-2-422242-2-2-4-2-2102122-1-22-1-200−2323−23−2323234-40000000011-1-10003−333−3−3000-22-22−2323000000000000000000001-100003−300000000000000000000
χ7444-4-44-2-2-422242-2-2-4-2-2102122-1-22-1-200−2323−23−232323-440000000011-1-10003−333−3−30002-22-223−2300000000000000000000-110000−3300000000000000000000
χ7544-4-4-2442-4-4-4-2-4442-2-2402422-4-22-4-20000000000004i−4i0000-2-2220000000000000000004i−4i0000−2i2i0000−2i−2i2i2i00000000000000000000000000000000
χ7644-4-4-2442-4-4-4-2-4442-2-2402422-4-22-4-2000000000000−4i4i0000-2-222000000000000000000−4i4i00002i−2i00002i2i−2i−2i00000000000000000000000000000000
χ7744-4-4-2-242-4-42-22-2421-2-202-2-1221-12-20023−23−3−33300004i−4i−2i3−2i32i32i311-1-100023−23−3−333000000000−2i2i0000−2i2ii3i3−i3−i3ii−i−i00000000000000000000000000000000
χ7844-4-4-2-242-4-42-22-2421-2-202-2-1221-12-20023−23−3−3330000−4i4i2i32i3−2i3−2i311-1-100023−23−3−3330000000002i−2i00002i−2i−i3−i3i3i3−i−iii00000000000000000000000000000000
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χ904-44-4-24-2-2-22-424-422-21-20-12-21-2222-12i3−2i3002i3−2i32i3−2i300000000001-1-110−i3i300−i3i3−i3i3000000000000023−230000000000000000000000−33−3i3i0000000000000000
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χ934-44-4-2-24-24-422-22-421-2-20221-2-2-1-122−2i32i300i3−i3i3−i3000000−232323−231-1-110−2i32i300i3−i3i3−i3000000000000000003−3−33−3i3i−3i3i00000000000000000000000000000000
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χ974-4-4444-2-42-24-4-4-4244-2-20-22-422-44-22000000000000000000-22-220000000000000000000000000000000000−4i4i00000000000000000000002i−2i000000
χ984-4-444-24-4-44-2-422-44-24-20422-422-2-2-400000000004i−4i00−2i2i−2i2i-22-22000000000000000000004i−4i0000−2i2i−2i2i000000000000000000000000000000000000
χ994-4-444-24-4-44-2-422-44-24-20422-422-2-2-40000000000−4i4i002i−2i2i−2i-22-2200000000000000000000−4i4i00002i−2i2i−2i000000000000000000000000000000000000
χ1004-4-44-2442-4442-4-4-4-2-2-240-2-422-42-24200000000004i−4i004i−4i4i−4i-22-2200000000000000000000−2i2i0000−2i2i−2i2i000000000000000000000000000000000000
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χ1024-4-44-2-242-44-2222-4-21-2-20-22-122-11-2200003i−3i−3i3i004i−4i00−2i2i−2i2i1-11-1000003i−3i−3i3i00000000000−2i2i0000i−ii−i3-3-3300000000000000000000000000000000
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χ1044-4-44-2-242-44-2222-4-21-2-20-22-122-11-220000−3i3i3i−3i004i−4i00−2i2i−2i2i1-11-100000−3i3i3i−3i00000000000−2i2i0000i−ii−i-333-300000000000000000000000000000000
χ1054-4-44-2-242-44-2222-4-21-2-20-22-122-11-220000−3i3i3i−3i00−4i4i002i−2i2i−2i1-11-100000−3i3i3i−3i000000000002i−2i0000−ii−ii3-3-3300000000000000000000000000000000
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χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
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χ10988-8-8-4-4-44444-44-4-442220-22-2-2-22-2-220043−43−23−2323230000000000-1-111000−232333−3−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44444-44-4-442220-22-2-2-22-2-2200−43432323−23−230000000000-1-11100023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1118-88-88-4-48-444-8-444-8-4-4204-2-4-4244-240000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-4-4-4444-44442220-2-2222-2-2-2-2−4i34i3002i3−2i32i3−2i30000000000-111-102i3−2i300−i3i3−i3i3000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4-4-4444-44442220-2-2222-2-2-2-24i3−4i300−2i32i3−2i32i30000000000-111-10−2i32i300i3−i3i3−i3000000000000000000000000000000000000000000000000000000000
χ1148-8-888-4-4-84-4-4-84448-4-420-4-244-24-4240000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).