Finite Group Databasebeta

← Group #13168677

Character table — Group #13168677

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222244444444444444444466668888888888888812121212121212121212121212121212121212121818181818181818181818181818242424242424242424242424242424243636363636363636363636108108
order122233344666666666333666666666121212121212444436661212121212121212121244441212121212121212121212121212121222444412121212121212121212121212121212121212121212121224466661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1-11111
χ5111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-111-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-1111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-11-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1111-1-111-1-1-1-111-111-1-1-1-11111-11
χ111111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-111-111-1-1-1-11111-1-111-111-1-1-1-111-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111-11111111-1-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-11-11111111-1-1-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1-11-1-11111-1-1-1-11111-111-1-1-1-1111-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-111-1-11111-1-1-111-1-1-1-111111-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-11111111111111111-11-11-1-111-1-111-1-111-1-1-1-1-111-1-1-1-1-11
χ17222222-12222-1-122-1222-1-122-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-1-122-1-1-1-12200-1-1-1-1-1-1-1-1000022220000220000-1-1-1-12200-1-1-1-1-1-1-1-10000200-1-100000000
χ18222222-12222-1-122-1222-1-122-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-2-200-1-1-1-11111000022220000-2-200001111-2-200-1-1-1-111110000-2001100000000
χ19222222-12222-1-122-1222-1-122-1-1-1-1-1-1222-1-122-2-2-2-2-1-1-1-1-1-1-1-122-1-1-1-122001111-1-1-1-10000-2-2-2-20000-2-20000111122001111-1-1-1-10000-2001100000000
χ20222222-12222-1-122-1222-1-122-1-1-1-1-1-1222-1-122-2-2-2-2-1-1-1-1-1-1-1-122-1-1-1-1-2-200111111110000-2-2-2-20000220000-1-1-1-1-2-200111111110000200-1-100000000
χ21222222-1-2-222-1-122-1222-1-122-1-1-1-1-1-12-2-211-2-222-2-2-1-1-1-11111-2-211112-200-1-111-1-111000022-2-20000220000-1-1-1-12-200-1-111-1-1110000-2001100000000
χ22222222-1-2-222-1-122-1222-1-122-1-1-1-1-1-12-2-211-2-222-2-2-1-1-1-11111-2-21111-2200-1-11111-1-1000022-2-20000-2-200001111-2200-1-11111-1-10000200-1-100000000
χ23222222-1-2-222-1-122-1222-1-122-1-1-1-1-1-12-2-211-2-2-2-222-1-1-1-11111-2-211112-20011-1-1-1-1110000-2-2220000-2-2000011112-20011-1-1-1-1110000200-1-100000000
χ24222222-1-2-222-1-122-1222-1-122-1-1-1-1-1-12-2-211-2-2-2-222-1-1-1-11111-2-21111-220011-1-111-1-10000-2-2220000220000-1-1-1-1-220011-1-111-1-10000-2001100000000
χ2522222-1222-1-1222222-1-12-1-1-12-12-12-1-12222-1-10000-1-1-1-122-1-1-1-1-1-1-1-12222000022222222000022000000000000-1-1-1-10000-1-1-1-1-1-1-1-102000-1-100-1-100
χ2622222-1222-1-1222222-1-12-1-1-12-12-12-1-12222-1-10000-1-1-1-122-1-1-1-1-1-1-1-122-2-200002222-2-2-2-20000-2-2000000000000-1-1110000-1-1-1-111110-200011001100
χ2722222-1222-1-1222222-1-12-1-1-12-12-12-1-12222-1-10000-1-1-1-122-1-1-1-1-1-1-1-1-2-2220000-2-2-2-222220000-2-200000000000011-1-100001111-1-1-1-10-200011001100
χ2822222-1222-1-1222222-1-12-1-1-12-12-12-1-12222-1-10000-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-2000022000000000000111100001111111102000-1-100-1-100
χ2922222-12-2-2-1-1222222-1-12-1-1-12-12-12-1-1-2-2-2-2110000-1-1-1-1-2-2111111112-22-2000022-2-222-2-2000022000000000000-11-110000-1-111-1-1110-2000-1-1001100
χ3022222-12-2-2-1-1222222-1-12-1-1-12-12-12-1-1-2-2-2-2110000-1-1-1-1-2-2111111112-2-22000022-2-2-2-2220000-2-2000000000000-111-10000-1-11111-1-1020001100-1-100
χ3122222-12-2-2-1-1222222-1-12-1-1-12-12-12-1-1-2-2-2-2110000-1-1-1-1-2-211111111-222-20000-2-22222-2-20000-2-20000000000001-1-11000011-1-1-1-111020001100-1-100
χ3222222-12-2-2-1-1222222-1-12-1-1-12-12-12-1-1-2-2-2-2110000-1-1-1-1-2-211111111-22-220000-2-222-2-2220000220000000000001-11-1000011-1-111-1-10-2000-1-1001100
χ332222-122222222-1-12-12-1-12-1-1-12-12-12-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1002222220000-1-1-1-1-1-1-1-1002200-1-1-1-100000022-1-1-1-10000-1-1-1-10020000-1-10000
χ342222-122222222-1-12-12-1-12-1-1-12-12-12-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-100-2-2222200001111-1-1-1-100-2-2001111000000-2-2-1-1-1-10000111100-20000110000
χ352222-122222222-1-12-12-1-12-1-1-12-12-12-1-1-12222-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-10022-2-2-2-20000-1-1-1-1111100-2-20011110000002211110000-1-1-1-100-20000110000
χ362222-122222222-1-12-12-1-12-1-1-12-12-12-1-1-12222-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2000011111111002200-1-1-1-1000000-2-21111000011110020000-1-10000
χ372222-122-2-22222-1-12-12-1-12-1-1-12-12-12-111-2-2-2-222-2-2-1-1-1-111-2-2111111002-222-2-20000-1-111-1-111002200-1-1-1-10000002-2-1-1110000-1-11100-20000110000
χ382222-122-2-22222-1-12-12-1-12-1-1-12-12-12-111-2-2-2-222-2-2-1-1-1-111-2-211111100-2222-2-2000011-1-1-1-11100-2-2001111000000-22-1-111000011-1-10020000-1-10000
χ392222-122-2-22222-1-12-12-1-12-1-1-12-12-12-111-2-2-2-2-2-222-1-1-1-111-2-2111111002-2-2-2220000-1-11111-1-100-2-20011110000002-211-1-10000-1-1110020000-1-10000
χ402222-122-2-22222-1-12-12-1-12-1-1-12-12-12-111-2-2-2-2-2-222-1-1-1-111-2-211111100-22-2-222000011-1-111-1-1002200-1-1-1-1000000-2211-1-1000011-1-100-20000110000
χ412-22-22222-2-2-2-2-22-22-22222-2-2-2-222-2-222-22-22-22i−2i2i−2i2-2-222-22-22-222-2-200002i−2i2i−2i000000002i−2i2i−2i0000000000000000002i−2i2i−2i000000000000000000000
χ422-22-22222-2-2-2-2-22-22-22222-2-2-2-222-2-222-22-22-2−2i2i−2i2i2-2-222-22-22-222-2-20000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000−2i2i−2i2i000000000000000000000
χ432-22-2222-22-2-2-2-22-22-22222-2-2-2-222-2-22-22-22-222i−2i−2i2i2-2-22-22-22-22-2-22200002i−2i−2i2i000000002i−2i−2i2i0000000000000000002i−2i−2i2i000000000000000000000
χ442-22-2222-22-2-2-2-22-22-22222-2-2-2-222-2-22-22-22-22−2i2i2i−2i2-2-22-22-22-22-2-2220000−2i2i2i−2i00000000−2i2i2i−2i000000000000000000−2i2i2i−2i000000000000000000000
χ452-22-222-12-2-2-2112-2-1-222-1-1-2-211-1-11122-2-112-22i−2i2i−2i-111-1-11-112-2-1-1110000−ii−ii3−33−300002i−2i2i−2i0000000000−i3−i3i3i30000−ii−ii3−33−30000000−i3i300000000
χ462-22-222-12-2-2-2112-2-1-222-1-1-2-211-1-11122-2-112-22i−2i2i−2i-111-1-11-112-2-1-1110000−ii−ii−33−3300002i−2i2i−2i0000000000i3i3−i3−i30000−ii−ii−33−330000000i3−i300000000
χ472-22-222-12-2-2-2112-2-1-222-1-1-2-211-1-11122-2-112-2−2i2i−2i2i-111-1-11-112-2-1-1110000i−ii−i3−33−30000−2i2i−2i2i0000000000i3i3−i3−i30000i−ii−i3−33−30000000i3−i300000000
χ482-22-222-12-2-2-2112-2-1-222-1-1-2-211-1-11122-2-112-2−2i2i−2i2i-111-1-11-112-2-1-1110000i−ii−i−33−330000−2i2i−2i2i0000000000−i3−i3i3i30000i−ii−i−33−330000000−i3i300000000
χ492-22-222-1-22-2-2112-2-1-222-1-1-2-211-1-1112-221-1-222i−2i−2i2i-111-11-11-1-2211-1-10000−iii−i3−3−3300002i−2i−2i2i0000000000−i3−i3i3i30000−iii−i3−3−330000000i3−i300000000
χ502-22-222-1-22-2-2112-2-1-222-1-1-2-211-1-1112-221-1-222i−2i−2i2i-111-11-11-1-2211-1-10000−iii−i−333−300002i−2i−2i2i0000000000i3i3−i3−i30000−iii−i−333−30000000−i3i300000000
χ512-22-222-1-22-2-2112-2-1-222-1-1-2-211-1-1112-221-1-22−2i2i2i−2i-111-11-11-1-2211-1-10000i−i−ii3−3−330000−2i2i2i−2i0000000000i3i3−i3−i30000i−i−ii3−3−330000000−i3i300000000
χ522-22-222-1-22-2-2112-2-1-222-1-1-2-211-1-1112-221-1-22−2i2i2i−2i-111-11-11-1-2211-1-10000i−i−ii−333−30000−2i2i2i−2i0000000000−i3−i3i3i30000i−i−ii−333−30000000i3−i300000000
χ532-22-2-1222-2-2-2-2-2-11212-1-12111-2-121-2-1-112-22-22i−2i2i−2i-111-1-112-2-11-1-11100002i−2i2i−2i0000−i3i3−i3i3−ii−ii00000033−3−300000000−ii−ii0000−i3i3−i3i300000003−30000
χ542-22-2-1222-2-2-2-2-2-11212-1-12111-2-121-2-1-112-22-22i−2i2i−2i-111-1-112-2-11-1-11100002i−2i2i−2i0000i3−i3i3−i3−ii−ii000000−3−33300000000−ii−ii0000i3−i3i3−i30000000−330000
χ552-22-2-1222-2-2-2-2-2-11212-1-12111-2-121-2-1-112-22-2−2i2i−2i2i-111-1-112-2-11-1-1110000−2i2i−2i2i0000−i3i3−i3i3i−ii−i000000−3−33300000000i−ii−i0000−i3i3−i3i30000000−330000
χ562-22-2-1222-2-2-2-2-2-11212-1-12111-2-121-2-1-112-22-2−2i2i−2i2i-111-1-112-2-11-1-1110000−2i2i−2i2i0000i3−i3i3−i3i−ii−i00000033−3−300000000i−ii−i0000i3−i3i3−i300000003−30000
χ572-22-2-122-22-2-2-2-2-11212-1-12111-2-121-2-11-1-22-222i−2i−2i2i-111-11-1-221-111-1-100002i−2i−2i2i0000−i3i3i3−i3−iii−i00000033−3−300000000−iii−i0000−i3i3i3−i30000000−330000
χ582-22-2-122-22-2-2-2-2-11212-1-12111-2-121-2-11-1-22-222i−2i−2i2i-111-11-1-221-111-1-100002i−2i−2i2i0000i3−i3−i3i3−iii−i000000−3−33300000000−iii−i0000i3−i3−i3i300000003−30000
χ592-22-2-122-22-2-2-2-2-11212-1-12111-2-121-2-11-1-22-22−2i2i2i−2i-111-11-1-221-111-1-10000−2i2i2i−2i0000−i3i3i3−i3i−i−ii000000−3−33300000000i−i−ii0000−i3i3i3−i300000003−30000
χ602-22-2-122-22-2-2-2-2-11212-1-12111-2-121-2-11-1-22-22−2i2i2i−2i-111-11-1-221-111-1-10000−2i2i2i−2i0000i3−i3−i3i3i−i−ii00000033−3−300000000i−i−ii0000i3−i3−i3i30000000−330000
χ612-2-22222002-22-2-2-2-22-22222-2-22-2-22-2-2000000000022-2-20000000000000000000000000000002-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000002-2000000
χ622-2-22222002-22-2-2-2-22-22222-2-22-2-22-2-2000000000022-2-20000000000000000000000000000002-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000002-2000000
χ632-2-22222002-22-2-2-2-22-22222-2-22-2-22-2-2000000000022-2-2000000000000000000000000000000-222i−2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000-22000000
χ642-2-22222002-22-2-2-2-22-22222-2-22-2-22-2-2000000000022-2-2000000000000000000000000000000-22−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000-22000000
χ6544444-2-244-2-2-2-244-24-2-2-21-2-2-21-21-21-244-2-2-2-200001111-2-211-2-2111144000000-2-2-2-20000000000000000000000-2-2000000111100000000000000000
χ6644444-2-244-2-2-2-244-24-2-2-21-2-2-21-21-21-244-2-2-2-200001111-2-211-2-21111-4-40000002222000000000000000000000022000000-1-1-1-100000000000000000
χ6744444-2-2-4-4-2-2-2-244-24-2-2-21-2-2-21-21-21-2-4-422220000111122-1-122-1-1-1-14-4000000-2-2220000000000000000000000-2200000011-1-100000000000000000
χ6844444-2-2-4-4-2-2-2-244-24-2-2-21-2-2-21-21-21-2-4-422220000111122-1-122-1-1-1-1-4400000022-2-200000000000000000000002-2000000-1-11100000000000000000
χ694444-24-24444-2-2-2-2-2-24-21-2-2-21-21-21-2-2-2-2-2-2444444111111-2-2-2-211110000-2-2-2-200000000-2-2-2-20000000000000000001111000000000000000000000
χ704444-24-24444-2-2-2-2-2-24-21-2-2-21-21-21-2-2-2-2-2-244-4-4-4-4111111-2-2-2-2111100002222000000002222000000000000000000-1-1-1-1000000000000000000000
χ714444-24-2-4-444-2-2-2-2-2-24-21-2-2-21-21-21-2-22222-4-444-4-41111-1-12222-1-1-1-10000-2-22200000000-2-22200000000000000000011-1-1000000000000000000000
χ724444-24-2-4-444-2-2-2-2-2-24-21-2-2-21-21-21-2-22222-4-4-4-4441111-1-12222-1-1-1-1000022-2-20000000022-2-2000000000000000000-1-111000000000000000000000
χ734444-2-2444-2-244-2-24-2-21-2-211-2-2-2-2-2-21-2-244-2-200001111-2-2-2-2111111004400000000-2-2-2-200000000000000000000-2-20000000011110000000000000
χ744444-2-2444-2-244-2-24-2-21-2-211-2-2-2-2-2-21-2-244-2-200001111-2-2-2-211111100-4-4000000002222000000000000000000002200000000-1-1-1-10000000000000
χ754444-2-24-4-4-2-244-2-24-2-21-2-211-2-2-2-2-2-2122-4-422000011112222-1-1-1-1-1-1004-400000000-2-22200000000000000000000-220000000011-1-10000000000000
χ764444-2-24-4-4-2-244-2-24-2-21-2-211-2-2-2-2-2-2122-4-422000011112222-1-1-1-1-1-100-440000000022-2-2000000000000000000002-200000000-1-1110000000000000
χ7744-4-444400-44-44-44-4-4-4444-444-4-4-4-44-400000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000000
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χ904-44-4-24-24-4-4-422-22-224-21-222-121-2-12-2-22-224-44i−4i4i−4i1-1-111-1-22-2211-1-10000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000i−ii−i000000000000000000000
χ914-44-4-24-24-4-4-422-22-224-21-222-121-2-12-2-22-224-4−4i4i−4i4i1-1-111-1-22-2211-1-100002i−2i2i−2i000000002i−2i2i−2i000000000000000000−ii−ii000000000000000000000
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χ954-44-4-2-244-422-4-4-2242-21-2-2-1-122-2-2221-224-4-2200001-1-11-22-221-111-1-10000000000002i3−2i32i3−2i3000000000000000000000000000000−i3i3−i3i30000000000000
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χ974-44-4-2-24-4422-4-4-2242-21-2-2-1-122-2-22212-2-442-200001-1-112-22-2-11-1-1110000000000002i3−2i3−2i32i3000000000000000000000000000000−i3i3i3−i30000000000000
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χ1004-4-444-2400-224-4-4-4-442-24-2-22-4-2-424220000000000-2-2220000000000000000000000000000004-4000000000000000000000000000000000-22000000
χ1014-4-444-2400-224-4-4-4-442-24-2-22-4-2-424220000000000-2-222000000000000000000000000000000-440000000000000000000000000000000002-2000000
χ1024-4-44-244004-44-422-4-2-4-2-24-22242-4-2-420000000000-2-222000000000000000000000000000000004i−4i00−2i2i−2i2i000000000000000000000000000000000
χ1034-4-44-244004-44-422-4-2-4-2-24-22242-4-2-420000000000-2-22200000000000000000000000000000000−4i4i002i−2i2i−2i000000000000000000000000000000000
χ1048888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-40000-1-1-1-1222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000000
χ1058888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444440000-1-1-1-1-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000000
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χ10988-8-8-4-4-4004-44-44-4444222-222-2-2-2-22-20000000000-11-1100000033−3333−33000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4004-44-44-4444222-222-2-2-2-22-20000000000-11-11000000−3333−3333000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-48-84444-44-44-4222-2-2-2-222-2-22-44-44-440000-111-12-22-22-2-1-111000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-4-884444-44-44-4222-2-2-2-222-2-224-44-44-40000-111-1-22-22-2211-1-1000000000000000000000000000000000000000000000000000000000000000
χ1138-8-888-4-400-44-44-8-8484-4-42-44424-2-4-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-4008-8-44444-4-8-42-4-44-2-4-24244000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-4800-448-844-8-442-4-42-24-444-44-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-400-44-44444-442222-2-22-2-22-2-20000000000-1-11100000033−33−3333000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-400-44-44444-442222-2-22-2-22-2-20000000000-1-111000000−333333−33000000000000000000000000000000000000000000000000000000000000000

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