Finite Group Databasebeta

← Group #72316815

Character table — Group #72316815

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111111122222222222222222222444444444444444444448888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616
order1222444422224444444444444444222224444444444444442222444444444444444444448888888888888888888888888888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ91111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ101111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ111111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ121111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ131111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ141111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ161111111111-1-111111111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1111111-1-1-1-111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ181111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1111111-1-1-1-111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ191111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1111111-1-1-1-111-1-1-1-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii
χ201111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1111111-1-1-1-111-1-1-1-1-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i
χ211111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-11111-1-1111111-1-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ221111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-11111-1-1111111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ231111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-11111-1-11111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ241111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-11111-1-11111-1-111-1-111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ251111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-1111-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1
χ261111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-1111-1-111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-111
χ271111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-1111-1-111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i11-1-1-1-111
χ281111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-1111-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1
χ291111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-11-1-111-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111
χ301111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-11-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1
χ311111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-11-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1
χ321111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-111111-11-1-111-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111
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χ3422222222222222222222-2-22222-2-2-2-22-2-2-2-2-2-2-2-22-2222-2-22-2-2-2-2-222-2-22222-2-222000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222222222-2-22-2-22222-2-2-222-2-22-2-2-20000000000000000000000002-22-22-22-200000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-222222222-2-22-2-22222-2-2-222-2-22-2-2-2000000000000000000000000-22-22-22-2200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-22222-2-222222-2-2-2-222-2-22-2-2-22-22000000000000000000000000000000002-22-22-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-22222-2-222222-2-2-2-222-2-22-2-2-22-2200000000000000000000000000000000-22-22-22-22000000000000000000000000
χ392222222222-2-22222222222-2-22222-2-2-222-2-2-2-2-2-2-22-2-2-222-2222-2-2-2-222-2-222-2-222000000000000000000000000000000000000000000000000
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χ412222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-22222-2222-22-2000000000000000000000000000000002-22-2-22-22000000000000000000000000
χ422222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-22222-2222-22-200000000000000000000000000000000-22-222-22-2000000000000000000000000
χ432222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2222222-2-22-2-222-22220000000000000000000000002-22-2-22-2200000000000000000000000000000000
χ442222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2222222-2-22-2-222-2222000000000000000000000000-22-222-22-200000000000000000000000000000000
χ4522222222-2-22222-2-222-2-22222-2-2222-2-22-22-22-22-22-2-22-2-2-2-2200000000000000000000000000000000000000002-22-22-22-20000000000000000
χ4622222222-2-22222-2-222-2-22222-2-2222-2-22-22-22-22-22-2-22-2-2-2-220000000000000000000000000000000000000000-22-22-22-220000000000000000
χ4722222222-2-22222-2-222-2-2-2-222-2-2-2-2-22-2-22-22-22-2222-22-222-2-2000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ4822222222-2-22222-2-222-2-2-2-222-2-2-2-2-22-2-22-22-22-2222-22-222-2-200000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
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χ5022222222-2-222-2-222-2-2222222-2-222-22-2-222-22-2-22-2-2-2-22-222-20000000000000000-22-22-22-220000000000000000000000000000000000000000
χ5122222222-2-222-2-222-2-222-2-222-2-2-2-22-2-22-2-22-222-2-22-2-222-2220000000000000000000000000000000000000000000000002-22-22-22-200000000
χ5222222222-2-222-2-222-2-222-2-222-2-2-2-22-2-22-2-22-222-2-22-2-222-222000000000000000000000000000000000000000000000000-22-22-22-2200000000
χ5322222222-2-2-2-222-2-222-2-222-2-2-2-222-2222-2-22-22-22-2-22-22-2-222000000000000000000000000000000000000000000000000000000002-22-2-22-22
χ5422222222-2-2-2-222-2-222-2-222-2-2-2-222-2222-2-22-22-22-2-22-22-2-22200000000000000000000000000000000000000000000000000000000-22-222-22-2
χ5522222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-22-22-222-22-22-2-222-22222-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5622222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-22-22-222-22-22-2-222-22222-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5722222222-2-2-2-2-2-222-2-22222-2-2-2-2222-22-22-22-222-22-222-2-22-2-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ5822222222-2-2-2-2-2-222-2-22222-2-2-2-2222-22-22-22-222-22-222-2-22-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ5922222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2222-22-22-2-222222-22-2-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ6022222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2222-22-22-2-222222-22-2-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ612222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-22-2-2-2-222222-2-2-2-222222222-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ622222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-22-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000
χ632222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-22-2-222-2-222-22-222-22-220000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ642222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-22-2-222-2-222-22-222-22-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
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χ662222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222222-2-222-2-2-2-2-2222-2-2-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ672222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-222-2-22222-22222-2-2-2-222-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000000000000000
χ682222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-222-2-22222-22222-2-2-2-2-2-2222222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ692222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-222-2-2-2-2-222-2-2222-2-2-2222000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ702222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-222-2-2-2-2-222-2-2222-2-2-222200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ712222-2-2-2-222-2-2-2-2-2-22222-2-222-2-222-2-2-22222-2-2222-22-2-22-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ722222-2-2-2-222-2-2-2-2-2-22222-2-222-2-222-2-2-22222-2-2222-22-2-22-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ732222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-22-2-22-22-2-22-222-22-2222-2-200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ742222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-22-2-22-22-2-22-222-22-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ752222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-22-2-22-222-22-2222-22-2-2-22000000000000000000000000000000000000000000000000000000002-2-222-2-22
χ762222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-22-2-22-222-22-2222-22-2-2-2200000000000000000000000000000000000000000000000000000000-222-2-222-2
χ772222-2-2-2-2-2-222-2-22222-2-222-2-222-2-2-22-2-222-2-222-2-2-222-22-22200000000000000002-2-222-2-220000000000000000000000000000000000000000
χ782222-2-2-2-2-2-222-2-22222-2-222-2-222-2-2-22-2-222-2-222-2-2-222-22-2220000000000000000-222-2-222-20000000000000000000000000000000000000000
χ792222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2-22-2-222-2-22-2222-2-222-20000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ802222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2-22-2-222-2-22-2222-2-222-2000000000000000000000000000000000000000000000000-222-2-222-200000000
χ812222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2222-2-222-22-2-2-2-22-2222-2000000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ822222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2222-2-222-22-2-2-2-22-2222-200000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ832222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222222-22-222-2-22-22-22-22-2-2-22200000000000000000000000000000000000000002-2-22-222-20000000000000000
χ842222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222222-22-222-2-22-22-22-22-2-2-2220000000000000000000000000000000000000000-222-22-2-220000000000000000
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χ862222-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-22-22-22-222-2-222-2-2-222-2-22000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
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χ882222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2222-22-2-222-222-2-22-22-2-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000
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χ9244-4-44i−4i4i−4i4-400-44-44−4i4i−4i4i00004i−4i000000000000000000000000-4400000000−4i4i00000000000000000000000000000000000000000000000000
χ9344-4-44i−4i4i−4i-44004-4-444i−4i−4i4i0000−4i4i00000000000000000000004-400004i−4i00000000000000000000000000000000000000000000000000000000
χ9444-4-44i−4i4i−4i-44004-4-444i−4i−4i4i0000−4i4i0000000000000000000000-440000−4i4i00000000000000000000000000000000000000000000000000000000
χ9544-4-44i−4i4i−4i-4400-444-4−4i4i4i−4i0000−4i4i000000000000000000000000004-4004i−4i000000000000000000000000000000000000000000000000000000
χ9644-4-44i−4i4i−4i-4400-444-4−4i4i4i−4i0000−4i4i00000000000000000000000000-4400−4i4i000000000000000000000000000000000000000000000000000000
χ9744-4-4−4i4i−4i4i4-4004-44-4−4i4i−4i4i0000−4i4i000000000000000000000000000000004-400−4i4i000000000000000000000000000000000000000000000000
χ9844-4-4−4i4i−4i4i4-4004-44-4−4i4i−4i4i0000−4i4i00000000000000000000000000000000-44004i−4i000000000000000000000000000000000000000000000000
χ9944-4-4−4i4i−4i4i4-400-44-444i−4i4i−4i0000−4i4i0000000000000000000000004-400000000−4i4i00000000000000000000000000000000000000000000000000
χ10044-4-4−4i4i−4i4i4-400-44-444i−4i4i−4i0000−4i4i000000000000000000000000-44000000004i−4i00000000000000000000000000000000000000000000000000
χ10144-4-4−4i4i−4i4i-44004-4-44−4i4i4i−4i00004i−4i00000000000000000000004-40000−4i4i00000000000000000000000000000000000000000000000000000000
χ10244-4-4−4i4i−4i4i-44004-4-44−4i4i4i−4i00004i−4i0000000000000000000000-4400004i−4i00000000000000000000000000000000000000000000000000000000
χ10344-4-4−4i4i−4i4i-4400-444-44i−4i−4i4i00004i−4i000000000000000000000000004-400−4i4i000000000000000000000000000000000000000000000000000000
χ10444-4-4−4i4i−4i4i-4400-444-44i−4i−4i4i00004i−4i00000000000000000000000000-44004i−4i000000000000000000000000000000000000000000000000000000
χ1058-88-888-8-8008-800000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-888-8-800-880000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-8-888008-80000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-8-88800-8800000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-888i−8i−8i8i0000000000008i−8i00008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888i−8i−8i8i000000000000−8i8i0000-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88−8i8i8i−8i0000000000008i−8i0000-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88−8i8i8i−8i000000000000−8i8i00008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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