Finite Group Databasebeta

← Group #13168550

Character table — Group #13168550

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222244444444444444444444446666666666888888888888121212121212121212121212121212121212121212121212121212121218181818181824242424242424242424363636363636363636363654547272108
order122233344666666666333666666666121212121212121212124444441212121236661212121212121212444121212121212121212121212121212121212121212121212121244121212121212121212121212121222444666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-11111-1-111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111111-111-1-111-1-11-11-1-111-1-1-1-1111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-111-1-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1111111-1-111-1-111-1-1-1-1-1-111111111111-111-1-111-1-1-11-11-1-1-111-1-1-1-1-111
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-111-11-1-11111111-1-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-111-11-1-11111-1-11-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1111111-11-1-111-1-111-11-11-1-1-111-1-111-11-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-11-1-11111-1-11111-11-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-11111111111-11-1-111-1-1111-11-1-111-1-1-1-1-1-11-11
χ17222222-122-122-122-1222-1-122-1-1-1-1-1-12-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-10022222-1-10000-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1000022000-1-1-1-10000000
χ18222222-122-122-122-1222-1-122-1-1-1-1-1-12-1-12222-1-1-1-12222-2-21111-1-1-1-1-1-122-1-1-1-100-2-2-2-2-2110000-1-1-1-122221111111100000000-1-1-1-10000-2-200011110000000
χ19222222-122-122-122-1222-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-122-1-1-1-10022222-1-100001111-2-2-2-2-1-1-1-1-1-1-1-10000000011110000-2-200011110000000
χ20222222-122-122-122-1222-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-1-122-1-1-1-100-2-2-2-2-21100001111-2-2-2-211111111000000001111000022000-1-1-1-10000000
χ21222222-1-2-2-122-122-1222-1-122-1-1-1-1-1-1211-2-2-2-2111122-2-222-1-1-1-1-1-1-1-111-2-2111100-222-2-2110000-1-11122-2-2-1-1-1-1111100000000-1-11100002-2000-1-1110000000
χ22222222-1-2-2-122-122-1222-1-122-1-1-1-1-1-1211-2-2-2-2111122-2-2-2-21111-1-1-1-111-2-21111002-2-222-1-10000-1-11122-2-21111-1-1-1-100000000-1-1110000-2200011-1-10000000
χ23222222-1-2-2-122-122-1222-1-122-1-1-1-1-1-1211-2-2-2-21111-2-22222-1-1-1-1-1-1-1-111-2-2111100-222-2-211000011-1-1-2-222-1-1-1-111110000000011-1-10000-2200011-1-10000000
χ24222222-1-2-2-122-122-1222-1-122-1-1-1-1-1-1211-2-2-2-21111-2-222-2-21111-1-1-1-111-2-21111002-2-222-1-1000011-1-1-2-2221111-1-1-1-10000000011-1-100002-2000-1-1110000000
χ2522222-12222222-1-12-12-12-1-1-1-12-122-1-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1220000000-1-1-1-12222-1-1-1-10000000022-1-1-1-122-1-1-1-1-1-1-1-1000020000-1-100000
χ2622222-12222222-1-12-12-12-1-1-1-12-122-1-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000011112222-1-1-1-100000000-2-21111-2-2-1-1-1-111110000-200001100000
χ2722222-12222222-1-12-12-12-1-1-1-12-122-1-122-1-1222222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1220000000-1-1-1-1-2-2-2-2111100000000-2-21111221111-1-1-1-10000-200001100000
χ2822222-12222222-1-12-12-12-1-1-1-12-122-1-122-1-1222222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-2-200000001111-2-2-2-211110000000022-1-1-1-1-2-211111111000020000-1-100000
χ2922222-12-2-22222-1-12-12-12-1-1-1-12-122-1-1-2-211-2-2-2-2-2-222-2-2000000-1-1-1-1111111112-20000000-1-11122-2-2-1-1110000000022-1-1-1-12-2-1-111-1-1110000-200001100000
χ3022222-12-2-22222-1-12-12-12-1-1-1-12-122-1-1-2-211-2-2-2-2-2-222-2-2000000-1-1-1-111111111-22000000011-1-122-2-2-1-11100000000-2-21111-22-1-11111-1-1000020000-1-100000
χ3122222-12-2-22222-1-12-12-12-1-1-1-12-122-1-1-2-211-2-2-2-2-2-2-2-222000000-1-1-1-1111111112-20000000-1-111-2-22211-1-100000000-2-211112-211-1-1-1-111000020000-1-100000
χ3222222-12-2-22222-1-12-12-12-1-1-1-12-122-1-1-2-211-2-2-2-2-2-2-2-222000000-1-1-1-111111111-22000000011-1-1-2-22211-1-10000000022-1-1-1-1-2211-1-111-1-10000-200001100000
χ332222-122222-1-122222-1-1-12-1-12-12-1-12-12222-1-1-1-1-1-10000222222-1-1-1-122-1-1-1-1-1-1222-1-1-1-122222200000000-1-1-1-1-1-1-1-1000000-1-10000-1-1-1-10022000000000-1-10
χ342222-122222-1-122222-1-1-12-1-12-12-1-12-12222-1-1-1-1-1-10000222222-1-1-1-122-1-1-1-1-1-1-2-22-1-1-1-122-2-2-2-200000000-1-1-1-1-1-1-1-1000000110000111100-2-2000000000110
χ352222-122222-1-122222-1-1-12-1-12-12-1-12-12222-1-1-1-1-1-10000-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-122-21111-2-222220000000011111111000000-1-10000-1-1-1-100-2-2000000000110
χ362222-122222-1-122222-1-1-12-1-12-12-1-12-12222-1-1-1-1-1-10000-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-21111-2-2-2-2-2-2000000001111111100000011000011110022000000000-1-10
χ372222-122-2-22-1-122222-1-1-12-1-12-12-1-12-1-2-2-2-21111110000222222-1-1-1-1-2-21111112-2-2-1-111-2-222-2-200000000-1-1-1-11111000000-110000-1-111002-2000000000-110
χ382222-122-2-22-1-122222-1-1-12-1-12-12-1-12-1-2-2-2-21111110000222222-1-1-1-1-2-2111111-22-2-1-111-2-2-2-22200000000-1-1-1-111110000001-1000011-1-100-220000000001-10
χ392222-122-2-22-1-122222-1-1-12-1-12-12-1-12-1-2-2-2-21111110000-2-2-2-2-2-2-1-1-1-1-2-21111112-2211-1-12222-2-2000000001111-1-1-1-1000000-110000-1-11100-220000000001-10
χ402222-122-2-22-1-122222-1-1-12-1-12-12-1-12-1-2-2-2-21111110000-2-2-2-2-2-2-1-1-1-1-2-2111111-22211-1-122-2-222000000001111-1-1-1-10000001-1000011-1-1002-2000000000-110
χ4122-2-22222-22-2-2-22-2-2-22222-2-2-222-2-2-222-22-22-222-2-22i−2i2i−2i0000002-2-222-22-222-2-200000000000002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i00000000000000000000
χ4222-2-22222-22-2-2-22-2-2-22222-2-2-222-2-2-222-22-22-222-2-2−2i2i−2i2i0000002-2-222-22-222-2-20000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000000000
χ4322-2-2222-222-2-2-22-2-2-22222-2-2-222-2-2-22-22-22-22-2-2222i−2i−2i2i0000002-2-22-22-22-2-22200000000000002i−2i−2i2i2i−2i−2i2i00000000000000002i−2i−2i2i00000000000000000000
χ4422-2-2222-222-2-2-22-2-2-22222-2-2-222-2-2-22-22-22-22-2-222−2i2i2i−2i0000002-2-22-22-22-2-2220000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i2i−2i00000000000000000000
χ4522-2-222-12-2-1-2-212-21-222-1-1-2-21-1-11112-112-22-2-1-1112i−2i2i−2i0033−3−3-111-1-112-2-1-11100000003−30000−ii−ii2i−2i2i−2i33−3−333−3−300000000−ii−ii000000000−i3i3−i3i30000000
χ4622-2-222-12-2-1-2-212-21-222-1-1-2-21-1-11112-112-22-2-1-1112i−2i2i−2i00−3−333-111-1-112-2-1-1110000000−330000−ii−ii2i−2i2i−2i−3−333−3−33300000000−ii−ii000000000i3−i3i3−i30000000
χ4722-2-222-12-2-1-2-212-21-222-1-1-2-21-1-11112-112-22-2-1-111−2i2i−2i2i0033−3−3-111-1-112-2-1-11100000003−30000i−ii−i−2i2i−2i2i33−3−333−3−300000000i−ii−i000000000i3−i3i3−i30000000
χ4822-2-222-12-2-1-2-212-21-222-1-1-2-21-1-11112-112-22-2-1-111−2i2i−2i2i00−3−333-111-1-112-2-1-1110000000−330000i−ii−i−2i2i−2i2i−3−333−3−33300000000i−ii−i000000000−i3i3−i3i30000000
χ4922-2-222-1-22-1-2-212-21-222-1-1-2-21-1-111121-1-22-2211-1-12i−2i−2i2i0033−3−3-111-11-1-2211-1-10000000−330000−iii−i2i−2i−2i2i33−3−3−3−33300000000−iii−i000000000−i3i3i3−i30000000
χ5022-2-222-1-22-1-2-212-21-222-1-1-2-21-1-111121-1-22-2211-1-12i−2i−2i2i00−3−333-111-11-1-2211-1-100000003−30000−iii−i2i−2i−2i2i−3−33333−3−300000000−iii−i000000000i3−i3−i3i30000000
χ5122-2-222-1-22-1-2-212-21-222-1-1-2-21-1-111121-1-22-2211-1-1−2i2i2i−2i0033−3−3-111-11-1-2211-1-10000000−330000i−i−ii−2i2i2i−2i33−3−3−3−33300000000i−i−ii000000000i3−i3−i3i30000000
χ5222-2-222-1-22-1-2-212-21-222-1-1-2-21-1-111121-1-22-2211-1-1−2i2i2i−2i00−3−333-111-11-1-2211-1-100000003−30000i−i−ii−2i2i2i−2i−3−33333−3−300000000i−i−ii000000000−i3i3i3−i30000000
χ5322-2-22-122-22-2-2-2-11-212-12-11112-1-2-21-12-2-112-222-2-22i−2i2i−2i000000-111-1-11-11-1-111000000000−i3i3−i3i32i−2i2i−2i−ii−ii000000000033−3−300−ii−ii−i3i3−i3i30000000003−300000
χ5422-2-22-122-22-2-2-2-11-212-12-11112-1-2-21-12-2-112-222-2-22i−2i2i−2i000000-111-1-11-11-1-111000000000i3−i3i3−i32i−2i2i−2i−ii−ii0000000000−3−33300−ii−iii3−i3i3−i3000000000−3300000
χ5522-2-22-122-22-2-2-2-11-212-12-11112-1-2-21-12-2-112-222-2-2−2i2i−2i2i000000-111-1-11-11-1-111000000000−i3i3−i3i3−2i2i−2i2ii−ii−i0000000000−3−33300i−ii−i−i3i3−i3i3000000000−3300000
χ5622-2-22-122-22-2-2-2-11-212-12-11112-1-2-21-12-2-112-222-2-2−2i2i−2i2i000000-111-1-11-11-1-111000000000i3−i3i3−i3−2i2i−2i2ii−ii−i000000000033−3−300i−ii−ii3−i3i3−i30000000003−300000
χ5722-2-22-12-222-2-2-2-11-212-12-11112-1-2-21-1-221-1-22-2-2222i−2i−2i2i000000-111-11-11-111-1-1000000000−i3i3i3−i32i−2i−2i2i−iii−i000000000033−3−300−iii−i−i3i3i3−i3000000000−3300000
χ5822-2-22-12-222-2-2-2-11-212-12-11112-1-2-21-1-221-1-22-2-2222i−2i−2i2i000000-111-11-11-111-1-1000000000i3−i3−i3i32i−2i−2i2i−iii−i0000000000−3−33300−iii−ii3−i3−i3i30000000003−300000
χ5922-2-22-12-222-2-2-2-11-212-12-11112-1-2-21-1-221-1-22-2-222−2i2i2i−2i000000-111-11-11-111-1-1000000000−i3i3i3−i3−2i2i2i−2ii−i−ii0000000000−3−33300i−i−ii−i3i3i3−i30000000003−300000
χ6022-2-22-12-222-2-2-2-11-212-12-11112-1-2-21-1-221-1-22-2-222−2i2i2i−2i000000-111-11-11-111-1-1000000000i3−i3−i3i3−2i2i2i−2ii−i−ii000000000033−3−300i−i−iii3−i3−i3i3000000000−3300000
χ612-2-2222200-22-2-2-2-222-22222-2-2-2-22-22-2000000000000002-22-22-222-2-2000000000002-200000000000000002-22-200002i−2i2i−2i2i−2i0000000000000000000002i−2i000
χ622-2-2222200-22-2-2-2-222-22222-2-2-2-22-22-2000000000000002-22-22-222-2-2000000000002-200000000000000002-22-20000−2i2i−2i2i−2i2i000000000000000000000−2i2i000
χ632-2-2222200-22-2-2-2-222-22222-2-2-2-22-22-200000000000000-22-22-2222-2-200000000000-220000000000000000-22-2200002i−2i2i−2i2i−2i000000000000000000000−2i2i000
χ642-2-2222200-22-2-2-2-222-22222-2-2-2-22-22-200000000000000-22-22-2222-2-200000000000-220000000000000000-22-220000−2i2i−2i2i−2i2i0000000000000000000002i−2i000
χ6544444-2-244-244-2-2-2-2-24-2-21-2-21-21-2-21-2-2-2-2-244-2-2-2-24444000000111111-2-211110000000000000-2-2-2-2-2-2-2-20000000000000000111100000000000000000000
χ6644444-2-244-244-2-2-2-2-24-2-21-2-21-21-2-21-2-2-2-2-244-2-2-2-2-4-4-4-4000000111111-2-211110000000000000222222220000000000000000-1-1-1-100000000000000000000
χ6744444-2-2-4-4-244-2-2-2-2-24-2-21-2-21-21-2-21-22222-4-4222244-4-40000001111-1-122-1-1-1-10000000000000-2-222-2-222000000000000000011-1-100000000000000000000
χ6844444-2-2-4-4-244-2-2-2-2-24-2-21-2-21-21-2-21-22222-4-42222-4-4440000001111-1-122-1-1-1-1000000000000022-2-222-2-20000000000000000-1-11100000000000000000000
χ694444-24-244-2-2-2-244-24-2-21-2-2-2-21-211-2-2-2-244-2-21111000044-2-2-2-21111-2-2-2-21111004-2-2-2-2-2-20000000000001111111100000000000000000000000000000000
χ704444-24-244-2-2-2-244-24-2-21-2-2-2-21-211-2-2-2-244-2-211110000-4-422221111-2-2-2-2111100-4222222000000000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ714444-24-2-4-4-2-2-2-244-24-2-21-2-2-2-21-211-2-222-4-422-1-1-1-1000044-2-2-2-211112222-1-1-1-100-4-2-222220000000000001111-1-1-1-100000000000000000000000000000000
χ724444-24-2-4-4-2-2-2-244-24-2-21-2-2-2-21-211-2-222-4-422-1-1-1-10000-4-4222211112222-1-1-1-100422-2-2-2-2000000000000-1-1-1-1111100000000000000000000000000000000
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χ754444-2-24-4-44-2-24-2-24-2-21-2-211-2-2-2-2-2-21-4-4222222220000000000111122-1-1-1-1-1-14-40000000-2-2220000000000000000000000-22000011-1-10000000000000000
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χ7944-4-44-2-2-44-2-4-42-22224-2-2122-1-2122-1-22-22-2-4422-2-24i−4i−4i4i0000001-1-11-112-2-1-1110000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000i−i−ii00000000000000000000
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χ8544-4-4-24-2-44-22224-42-4-2-21-22221-2-1-12-22-2-442-2-1-1110000002323−23−231-1-112-22-2-1-1110000000−2323000000000000−3−33333−3−300000000000000000000000000000000
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χ8744-4-4-2-244-4422-4-22-42-21-2-2-1-12-2-222214-4-22-22-2-22200000000001-1-11-221-111-1-1000000000−2i32i3−2i32i30000000000000000000000000000i3−i3i3−i30000000000000000
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χ974-44-4-24400-42-24-44-4-42-2-242-242-42-2-4200000000000000000000-22-2200000000000002i3−2i30000000000000000002i3−2i32i3−2i300000000000000000000000000000000
χ984-44-4-24-20022-2-2-442-42-21-22-2-2-12-11220000003i−3i3i−3i00000023−23−23231-11-100003i−3i3i−3i00000−2i32i300000000000000−333−3i3−i3i3−i300000000000000000000000000000000
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χ1094-4-44-24-2002-222-4-4-242-21-2-222-121-1-220000003i−3i−3i3i0000-442-22-211-1-100003i−3i−3i3i0002-20000000000000000-11-11−3i3i3i−3i00000000000000000000000000000000
χ1104-4-44-24-2002-222-4-4-242-21-2-222-121-1-22000000−3i3i3i−3i00004-4-22-2211-1-10000−3i3i3i−3i000-2200000000000000001-11-1−3i3i3i−3i00000000000000000000000000000000
χ1114-4-44-24-2002-222-4-4-242-21-2-222-121-1-22000000−3i3i3i−3i0000-442-22-211-1-10000−3i3i3i−3i0002-20000000000000000-11-113i−3i−3i3i00000000000000000000000000000000
χ1128888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-422220000000000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1138888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-20000000000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
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χ1168-88-88-4-4004-88-44-444-8-4-424-424-24-4-24000000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
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χ1188-88-8-4-4-40044-4-44-4444222-222-2-2-22-2-20000006i−6i6i−6i0000000000-11-110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
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χ1208-8-888-4-40048-8444-4-4-8-4-42-44-24-2-44240000000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1218-8-88-4-4800-8-44-8448-442-4-42-2444-44-4-20000000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
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χ1238-8-88-4-4-4004-44444-4-442222-2-2-2-22-22-2000000−6i6i6i−6i0000000000-1-11100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000000

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