Finite Group Databasebeta

← Group #13169315

Character table — Group #13169315

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212444424444466121212121212224444444412121212666121212121212121212121212121212121266121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-11-1111111111-1-1-1-1-1-111-1-111111111-11-1-11-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-11-1-1-1-111-1-111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11-11-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1111-1-111-1-11111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-11111-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1-1-111-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-111-1-1-1-111-1-111
χ91111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-11111-1-111-1-1-1-11111111-1-1-1111-1-1-111-1-1-1-11111-1-1-1-1-1-111-11
χ101111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-1-1-111-1-111-1-1-1-1111111111-11-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-11-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-11-1-11111-1-1-1-111-1-1-1-1111111-1-1-11-1111-1-111-1-1-1-11111-1-111-1-111-1-1-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-1111-1-1-1111-1-11111-1-111-1-1-1-1-1-1111-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-11
χ151111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-11-1-1111-11111-1-1-1-111-1-1-1-11111111-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1111111-1-1-1-1-11
χ17222222-122-1-122222-122-1-12-1-1-12-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-100002020222200220022220000000000-1-1-1-1-102-102-1-100-1-100-1-1-1-10000-1-10000
χ18222222-122-1-122222-122-1-12-1-1-12-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1000020-20-2222002200-2-2-2-20000000000-1-1-1-110-210-2-1-100110011110000110000
χ19222222-122-1-122222-122-1-12-1-1-12-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-20202-2-2-200-2-200-2-2-2-200000000001111-102-1021100-1-100-1-1110000110000
χ20222222-122-1-122222-122-1-12-1-1-12-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-20-20-2-2-2-200-2-20022220000000000111110-210-21100110011-1-10000-1-10000
χ21222222-1-2-2-1-122222-122-1-12-1-1-12-1-12-1-2-2-2-211-1-1-1-111-2-211111100002020-2-22200-2-20022-2-20000000000-1-1-11102-10-211001100-1-1-1-10000110000
χ22222222-1-2-2-1-122222-122-1-12-1-1-12-1-12-1-2-2-2-211-1-1-1-111-2-2111111000020-202-22200-2-200-2-2220000000000-1-1-11-10-21021100-1-10011110000-1-10000
χ23222222-1-2-2-1-122222-122-1-12-1-1-12-1-12-1-2-2-2-211-1-1-1-111-2-21111110000-2020-22-2-2002200-2-2220000000000111-1102-10-2-1-1001100-1-1110000-1-10000
χ24222222-1-2-2-1-122222-122-1-12-1-1-12-1-12-1-2-2-2-211-1-1-1-111-2-21111110000-20-2022-2-200220022-2-20000000000111-1-10-2102-1-100-1-10011-1-10000110000
χ2522222-122222-122-1-122-12-1-12-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222220202-1-1-1-1-1-1-1-10000002200-1-1-1-12-1-12020020-1-1-1-100-1-1000000-1-1000000
χ2622222-122222-122-1-122-12-1-12-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-2-20-20-2111111110000002200-1-1-1-1-211-20-200-2011110011000000-1-1000000
χ2722222-122222-122-1-122-12-1-12-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-22-20-202-1-111-1-111000000-2-20011112-1-120-200-20-1-111001100000011000000
χ2822222-122222-122-1-122-12-1-12-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-22020-211-1-111-1-1000000-2-2001111-211-202002011-1-100-1-100000011000000
χ2922222-12-2-222-122-1-122-12-1-12-1-1-12-1-1211-2-2-2-2-1-1-1-11111-2-2111122222-2020-2-1-11111-1-1000000-2-200-1-1-1-12-1-1-20-2002011-1-1001100000011000000
χ3022222-12-2-222-122-1-122-12-1-12-1-1-12-1-1211-2-2-2-2-1-1-1-11111-2-211112222-220-20211-1-1-1-111000000-2-200-1-1-1-1-21120200-20-1-11100-1-100000011000000
χ3122222-12-2-222-122-1-122-12-1-12-1-1-12-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-2220-20-2-1-1-1-11111000000220011112-1-1-20200-20111100-1-1000000-1-1000000
χ3222222-12-2-222-122-1-122-12-1-12-1-1-12-1-1211-2-2-2-2-1-1-1-11111-2-21111-2-2-2-2-2-202021111-1-1-1-100000022001111-21120-20020-1-1-1-10011000000-1-1000000
χ332222-12222222-1-1222-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-10000022220002200220000220022000000002-1-12-1-100-1-1-1-1-1-1-1-100-1-10000-1-100
χ342222-12222222-1-1222-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1000002-22-20002200220000-2-200-2-200000000-2-11-2-1100-1-111-1-111001100001100
χ352222-12222222-1-1222-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100000-22-22000-2-200-2-20000-2-200-2-20000000021-121-10011-1-111-1-1001100001100
χ362222-12222222-1-1222-1-1-12-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-100000-2-2-2-2000-2-200-2-2000022002200000000-211-211001111111100-1-10000-1-100
χ372222-122-2-2222-1-1222-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-2111111110000022-2-20002200-2-20000-2-2002200000000-2-1-1211001111-1-1-1-100-1-100001100
χ382222-122-2-2222-1-1222-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-211111111000002-2-220002200-2-200002200-2-2000000002-11-21-10011-1-1-1-11100110000-1-100
χ392222-122-2-2222-1-1222-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000-222-2000-2-2002200002200-2-200000000-21-12-1100-1-11111-1-100110000-1-100
χ402222-122-2-2222-1-1222-1-1-12-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111100000-2-222000-2-200220000-2-2002200000000211-2-1-100-1-1-1-1111100-1-100001100
χ4122-2-222200-2-222-2-2-22-2222-2-2-22-2-2-2220000002-2-2200000000002i2i−2i−2i000000000000002-2002i−2i00002i2i−2i−2i000000000000000000002-20000002i−2i00
χ4222-2-222200-2-222-2-2-22-2222-2-2-22-2-2-2220000002-2-2200000000002i2i−2i−2i00000000000000-2200−2i2i00002i2i−2i−2i00000000000000000000-22000000−2i2i00
χ4322-2-222200-2-222-2-2-22-2222-2-2-22-2-2-2220000002-2-220000000000−2i−2i2i2i000000000000002-200−2i2i0000−2i−2i2i2i000000000000000000002-2000000−2i2i00
χ4422-2-222200-2-222-2-2-22-2222-2-2-22-2-2-2220000002-2-220000000000−2i−2i2i2i00000000000000-22002i−2i0000−2i−2i2i2i00000000000000000000-220000002i−2i00
χ452-22-22222i−2i2-2-2-2-22-2-22222-2-22-222-2-2-22i−2i2i−2i2i−2i22-2-22i−2i2i−2i2i−2i2i2i−2i−2i2-22-2000000000000000000002i−2i002-22-20000000000000000000000002i−2i000000
χ462-22-22222i−2i2-2-2-2-22-2-22222-2-22-222-2-2-22i−2i2i−2i2i−2i22-2-22i−2i2i−2i2i−2i2i2i−2i−2i-22-2200000000000000000000−2i2i00-22-22000000000000000000000000−2i2i000000
χ472-22-2222−2i2i2-2-2-2-22-2-22222-2-22-222-2-2-2−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i−2i2i−2i−2i2i2i2-22-200000000000000000000−2i2i002-22-2000000000000000000000000−2i2i000000
χ482-22-2222−2i2i2-2-2-2-22-2-22222-2-22-222-2-2-2−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i−2i2i−2i−2i2i2i-22-22000000000000000000002i−2i00-22-220000000000000000000000002i−2i000000
χ492-22-22-122i−2i2-21-2-2-11-22-12-11-2-11-1211-2−ii2i−2i2i−2i-1-111−ii−ii2i−2i−i−iii2-22-2000000−i3i33−33−3−i3i30000002i−2i00-11-110−i3i300000003−3−i3i3003−3000000−ii000000
χ502-22-22-122i−2i2-21-2-2-11-22-12-11-2-11-1211-2−ii2i−2i2i−2i-1-111−ii−ii2i−2i−i−iii2-22-2000000i3−i3−33−33i3−i30000002i−2i00-11-110i3−i30000000−33i3−i300−33000000−ii000000
χ512-22-22-122i−2i2-21-2-2-11-22-12-11-2-11-1211-2−ii2i−2i2i−2i-1-111−ii−ii2i−2i−i−iii-22-22000000−i3i3−333−3i3−i3000000−2i2i001-11-10−i3i300000003−3i3−i300−33000000i−i000000
χ522-22-22-122i−2i2-21-2-2-11-22-12-11-2-11-1211-2−ii2i−2i2i−2i-1-111−ii−ii2i−2i−i−iii-22-22000000i3−i33−3−33−i3i3000000−2i2i001-11-10i3−i30000000−33−i3i3003−3000000i−i000000
χ532-22-22-12−2i2i2-21-2-2-11-22-12-11-2-11-1211-2i−i−2i2i−2i2i-1-111i−ii−i−2i2iii−i−i2-22-2000000−i3i3−33−33−i3i3000000−2i2i00-11-110−i3i30000000−33−i3i300−33000000i−i000000
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χ552-22-22-12−2i2i2-21-2-2-11-22-12-11-2-11-1211-2i−i−2i2i−2i2i-1-111i−ii−i−2i2iii−i−i-22-22000000−i3i33−3−33i3−i30000002i−2i001-11-10−i3i30000000−33i3−i3003−3000000−ii000000
χ562-22-22-12−2i2i2-21-2-2-11-22-12-11-2-11-1211-2i−i−2i2i−2i2i-1-111i−ii−i−2i2iii−i−i-22-22000000i3−i3−333−3−i3i30000002i−2i001-11-10i3−i300000003−3−i3i300−33000000−ii000000
χ572-2-2222200-22-2-22-22-2-222222-2-2-2-22-2-20000002-22-200000000002i−2i−2i2i00000000000000002i−2i00002-22i−2i−2i2i00000000000000000000002-2002i−2i0000
χ582-2-2222200-22-2-22-22-2-222222-2-2-2-22-2-20000002-22-200000000002i−2i−2i2i0000000000000000−2i2i0000-222i−2i−2i2i0000000000000000000000-2200−2i2i0000
χ592-2-2222200-22-2-22-22-2-222222-2-2-2-22-2-20000002-22-20000000000−2i2i2i−2i00000000000000002i−2i0000-22−2i2i2i−2i0000000000000000000000-22002i−2i0000
χ602-2-2222200-22-2-22-22-2-222222-2-2-2-22-2-20000002-22-20000000000−2i2i2i−2i0000000000000000−2i2i00002-2−2i2i2i−2i00000000000000000000002-200−2i2i0000
χ6144444-2-244-2-2-244-2-2-24-2-21-2-211-2-21-2-2-2-244-2-2111111-2-2-2-211110000400004-2-200-2-20000000000000000-211-20000001100000000000000000000
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χ684444-24-2-4-4-2-24-2-244-2-2-21-2-21-2-2-21-2-21-4-4222211112222-1-1-1-1-1-1000000-404000000000000000000000000000-20220-200001100-1-1000000000000
χ694444-2-244444-2-2-2-2-24-21-2-21-2-2-21-2-21-2-2-2-2-2441111-2-211-2-21111000004040000-2-200-2-20000000000000000000-200-200011001100000000000000
χ704444-2-244444-2-2-2-2-24-21-2-21-2-2-21-2-21-2-2-2-2-2441111-2-211-2-2111100000-40-4000022002200000000000000000002002000-1-100-1-100000000000000
χ714444-2-24-4-444-2-2-2-2-24-21-2-21-2-2-21-2-21-22222-4-4111122-1-122-1-1-1-10000040-40000-2-200220000000000000000000-2002000-1-1001100000000000000
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χ804-44-444-2−4i4i-22-4-4-44-4244-2-2-42-224-22-42−4i4i−4i4i2i−2i-2-2222i−2i−4i4i2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ814-44-44-2-24i−4i-222-4-4-2224-2-21221-1-2-2-122−2i2i4i−4i−2i2i11-1-1i−i−2i2i−2i2iii−i−i0000000000−2i32i30023−2300000000000000000i3−i30000000−3300000000000000000000
χ824-44-44-2-24i−4i-222-4-4-2224-2-21221-1-2-2-122−2i2i4i−4i−2i2i11-1-1i−i−2i2i−2i2iii−i−i00000000002i3−2i300−232300000000000000000−i3i300000003−300000000000000000000
χ834-44-44-2-2−4i4i-222-4-4-2224-2-21221-1-2-2-1222i−2i−4i4i2i−2i11-1-1−ii2i−2i2i−2i−i−iii0000000000−2i32i300−232300000000000000000i3−i300000003−300000000000000000000
χ844-44-44-2-2−4i4i-222-4-4-2224-2-21221-1-2-2-1222i−2i−4i4i2i−2i11-1-1−ii2i−2i2i−2i−i−iii00000000002i3−2i30023−2300000000000000000−i3i30000000−3300000000000000000000
χ854-44-4-2444i−4i4-4-4224-4-4-2-2-24224-4-2-2-4224i−4i−2i2i4i−4i-2-2224i−4i−2i2i−2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ864-44-4-244−4i4i4-4-4224-4-4-2-2-24224-4-2-2-422−4i4i2i−2i−4i4i-2-222−4i4i2i−2i2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ874-44-4-24-24i−4i-22-4224-42-2-21-22-1-22-2122-14i−4i−2i2i−2i2i11-1-1−2i2i−2i2ii−iii−i−i00000000000000000000000000000000000000000000003-3003i−3i000000000000
χ884-44-4-24-24i−4i-22-4224-42-2-21-22-1-22-2122-14i−4i−2i2i−2i2i11-1-1−2i2i−2i2ii−iii−i−i0000000000000000000000000000000000000000000000-3300−3i3i000000000000
χ894-44-4-24-2−4i4i-22-4224-42-2-21-22-1-22-2122-1−4i4i2i−2i2i−2i11-1-12i−2i2i−2i−ii−i−iii00000000000000000000000000000000000000000000003-300−3i3i000000000000
χ904-44-4-24-2−4i4i-22-4224-42-2-21-22-1-22-2122-1−4i4i2i−2i2i−2i11-1-12i−2i2i−2i−ii−i−iii0000000000000000000000000000000000000000000000-33003i−3i000000000000
χ914-44-4-2-244i−4i4-4222-22-4-21-2-2-12-221-22-12−2i2i−2i2i4i−4i11-1-1−2i2ii−i−2i2iii−i−i00000000000023−2300−2i32i300000000000000000000000000i3−i300−3300000000000000
χ924-44-4-2-244i−4i4-4222-22-4-21-2-2-12-221-22-12−2i2i−2i2i4i−4i11-1-1−2i2ii−i−2i2iii−i−i000000000000−2323002i3−2i300000000000000000000000000−i3i3003−300000000000000
χ934-44-4-2-24−4i4i4-4222-22-4-21-2-2-12-221-22-122i−2i2i−2i−4i4i11-1-12i−2i−ii2i−2i−i−iii00000000000023−23002i3−2i300000000000000000000000000−i3i300−3300000000000000
χ944-44-4-2-24−4i4i4-4222-22-4-21-2-2-12-221-22-122i−2i2i−2i−4i4i11-1-12i−2i−ii2i−2i−i−iii000000000000−232300−2i32i300000000000000000000000000i3−i3003−300000000000000
χ954-4-4444-2002-2-4-44-442-44-2-24-222-42-2-42000000-22-220000000000000000000000000000004i−4i000000000000000000000000000000000000−2i2i0000
χ964-4-4444-2002-2-4-44-442-44-2-24-222-42-2-42000000-22-22000000000000000000000000000000−4i4i0000000000000000000000000000000000002i−2i0000
χ974-4-444-2400-442-442-2-4-4-24-2-24222-4-22-4000000-22-2200000000004i−4i−4i4i000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ984-4-444-2400-442-442-2-4-4-24-2-24222-4-22-4000000-22-220000000000−4i4i4i−4i0000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ994-4-44-24400-44-42-2-44-42-2-24-2-2-4-422422000000-22-220000000000000000000000000000000000004-400000000000000000000000000-2200000000
χ1004-4-44-24400-44-42-2-44-42-2-24-2-2-4-422422000000-22-22000000000000000000000000000000000000-44000000000000000000000000002-200000000
χ1018888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-40044-48-844-4-8-4-4244-2244-2-4-40000002-2-2200000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-400448-44-8-8-44-42-44-24-44-24-420000002-2-2200000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4800-8-8-4-4444842-4-4-244-4-2442-40000002-2-2200000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-40044-4-4444-44222-2-2-22-2-2-222000000-111-1000000−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-40044-4-4444-44222-2-2-22-2-2-222000000-111-10000003i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-48i−8i-44444-444-4222-2-22-222-2-2-2−4i4i−4i4i−4i4i-1-1112i−2i2i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4−8i8i-44444-444-4222-2-22-222-2-2-24i−4i4i−4i4i−4i-1-111−2i2i−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-4004-44-884-44-8-4-42-4-4-2-2442440000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4004-4-84-4-8844-42-4-42444-2-44-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4800-8844-44-4-842-4-42-444-24-4-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004-444-44-44422222-2-2-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004-444-44-44422222-2-2-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000000000

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