Finite Group Databasebeta

← Group #10823181

Character table — Group #10823181

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666666666668888888812121212121212122424242424242424242424242424242444444444121212121212121212121212121212122244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ1511111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1611111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002-22-2000000
χ182222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000-22-22000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-22-2-2-22222-222222-2-2-2-2-2-2-2-22200000000-2-2-22222-200000000000000000000000000000000000000000000002-2-22000000
χ2422222222-2-2-2-22-2-2-22222-222222-2-2-2-2-2-2-2-22200000000-2-2-22222-20000000000000000000000000000000000000000000000-222-2000000
χ2522222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-111111111-1-12222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-111111111-1-12222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-111111111-1-1-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-111111111-1-1-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ29222-2-2-2-2222-2-2222-222-2-2-22-2-2-2-22222-2-2-2-2220000000022-222-2-2-20000000000000000000000000000000000000000002i−2i2i−2i0000000000
χ30222-2-2-2-2222-2-2222-222-2-2-22-2-2-2-22222-2-2-2-2220000000022-222-2-2-2000000000000000000000000000000000000000000−2i2i−2i2i0000000000
χ31222-2-2-2-2222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-22200000000-2-22-2-2222000000000000000000002-22-20000000022-2-222-2-20000000000000000
χ32222-2-2-2-2222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-22200000000-2-22-2-222200000000000000000000-22-2200000000-2-222-2-2220000000000000000
χ33222-2-2-2-2222-2-2-1-2-22-2-2222-11111-1-1-1-11111-1-10000000011-111-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i300002-22-2−i3−i3i3i3−i3−i3i3i3-1-111-1-1110000000000000000
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χ35222-2-2-2-2222-2-2-1-2-22-2-2222-11111-1-1-1-11111-1-10000000011-111-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i300002-22-2i3i3−i3−i3i3i3−i3−i3-1-111-1-1110000000000000000
χ36222-2-2-2-2222-2-2-1-2-22-2-2222-11111-1-1-1-11111-1-10000000011-111-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i30000-22-22−i3−i3i3i3−i3−i3i3i311-1-111-1-10000000000000000
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χ38222-2-2-2-22-2-222222-2-2-222-22-2-2-2-2-2-2-2-22222220000000022-2-2-222-2000000000000000000000000000000000000000000−2i2i2i−2i0000000000
χ39222-2-2-2-22-2-2222-2-2222-2-222-2-2-2-2-2-2-2-222222200000000-2-2222-2-22000000000000000000002-2-220000000022-2-2-2-2220000000000000000
χ40222-2-2-2-22-2-2222-2-2222-2-222-2-2-2-2-2-2-2-222222200000000-2-2222-2-2200000000000000000000-222-200000000-2-22222-2-20000000000000000
χ41222-2-2-2-22-2-222-1-2-2222-2-22-111111111-1-1-1-1-1-10000000011-1-1-111-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300002-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ42222-2-2-2-22-2-222-1-2-2222-2-22-111111111-1-1-1-1-1-10000000011-1-1-111-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ43222-2-2-2-22-2-222-1-2-2222-2-22-111111111-1-1-1-1-1-10000000011-1-1-111-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300002-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ44222-2-2-2-22-2-222-1-2-2222-2-22-111111111-1-1-1-1-1-10000000011-1-1-111-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ452-2-222-2-222-22-222-222-22-2-2-222-2-222-2-222-2-2-22000000002-222-22-2-200000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-2-222-2-222-22-222-222-22-2-2-222-2-222-2-222-2-2-22000000002-222-22-2-20000000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ472-2-222-2-222-22-22-22-2-22-222-222-2-222-2-222-2-2-2200000000-22-2-22-22200000000000000000000000000000000000000002-2000000002-20000
χ482-2-222-2-222-22-22-22-2-22-222-222-2-222-2-222-2-2-2200000000-22-2-22-2220000000000000000000000000000000000000000-2200000000-220000
χ492-2-222-2-222-22-2-12-222-22-2-21-1-111-1-111-1-1111-100000000-11-1-11-11133−3−333−3−333−3−333−3−32i−2i2i−2i0000−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-2-222-2-222-22-2-12-222-22-2-21-1-111-1-111-1-1111-100000000-11-1-11-11133−3−333−3−333−3−333−3−3−2i2i−2i2i0000i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i30000000000000000
χ512-2-222-2-222-22-2-12-222-22-2-21-1-111-1-111-1-1111-100000000-11-1-11-111−3−333−3−333−3−333−3−3332i−2i2i−2i0000−ii−ii−ii−iii3−i3i3−i3i3−i3i3−i30000000000000000
χ522-2-222-2-222-22-2-12-222-22-2-21-1-111-1-111-1-1111-100000000-11-1-11-111−3−333−3−333−3−333−3−333−2i2i−2i2i0000i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i30000000000000000
χ532-2-222-2-22-22-2222-22-22-22-2-222-2-2-2-222-2-222-22000000002-22-22-22-200000000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ542-2-222-2-22-22-2222-22-22-22-2-222-2-2-2-222-2-222-22000000002-22-22-22-20000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ552-2-222-2-22-22-222-22-22-22-22-222-2-2-2-222-2-222-2200000000-22-22-22-2200000000000000000000000000000000000000002-200000000-220000
χ562-2-222-2-22-22-222-22-22-22-22-222-2-2-2-222-2-222-2200000000-22-22-22-220000000000000000000000000000000000000000-22000000002-20000
χ572-2-222-2-22-22-22-12-22-22-22-21-1-11111-1-111-1-11-100000000-11-11-11-1133−3−333−3−3−3−333−3−3332i−2i−2i2i0000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i30000000000000000
χ582-2-222-2-22-22-22-12-22-22-22-21-1-11111-1-111-1-11-100000000-11-11-11-1133−3−333−3−3−3−333−3−333−2i2i2i−2i0000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i30000000000000000
χ592-2-222-2-22-22-22-12-22-22-22-21-1-11111-1-111-1-11-100000000-11-11-11-11−3−333−3−33333−3−333−3−32i−2i−2i2i0000−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i30000000000000000
χ602-2-222-2-22-22-22-12-22-22-22-21-1-11111-1-111-1-11-100000000-11-11-11-11−3−333−3−33333−3−333−3−3−2i2i2i−2i0000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-2-2-2-22222-2-2222-2-22-2-222-2-2-22222-2-2-2-222-22000000002-2-22-2-22200000000000000000000000000000000000000000000000000002-22-2
χ622-2-2-2-22222-2-2222-2-22-2-222-2-2-22222-2-2-2-222-22000000002-2-22-2-2220000000000000000000000000000000000000000000000000000-22-22
χ632-2-2-2-22222-2-222-222-222-2-2-2-2-22222-2-2-2-222-222i2i−2i−2i2i2i−2i−2i-222-222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ642-2-2-2-22222-2-222-222-222-2-2-2-2-22222-2-2-2-222-22−2i−2i2i2i−2i−2i2i2i-222-222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ652-2-2-2-22222-2-22-1-222-222-2-2111-1-1-1-11111-1-11-12i2i−2i−2i2i2i−2i−2i1-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i000000003−3−333−3−33−i3i3i3−i3−i3i3i3−i30000000000000000
χ662-2-2-2-22222-2-22-1-222-222-2-2111-1-1-1-11111-1-11-12i2i−2i−2i2i2i−2i−2i1-1-11-1-111−i−iiiii−i−i−i−iiiii−i−i00000000−333−3−333−3i3−i3−i3i3i3−i3−i3i30000000000000000
χ672-2-2-2-22222-2-22-1-222-222-2-2111-1-1-1-11111-1-11-1−2i−2i2i2i−2i−2i2i2i1-1-11-1-111ii−i−i−i−iiiii−i−i−i−iii000000003−3−333−3−33i3−i3−i3i3i3−i3−i3i30000000000000000
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χ712-2-2-2-2222-222-22-2222-2-22-2-2-2-222-2-22222-2-2-222i2i−2i−2i−2i−2i2i2i-2222-2-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ722-2-2-2-2222-222-22-2222-2-22-2-2-2-222-2-22222-2-2-22−2i−2i2i2i2i2i−2i−2i-2222-2-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ732-2-2-2-2222-222-2-1-2222-2-22-2111-1-111-1-1-1-1111-12i2i−2i−2i−2i−2i2i2i1-1-1-111-11−i−iiiii−i−iii−i−i−i−iii000000003−3−33−333−3−i3i3i3−i3i3−i3−i3i30000000000000000
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χ762-2-2-2-2222-222-2-1-2222-2-22-2111-1-111-1-1-1-1111-1−2i−2i2i2i2i2i−2i−2i1-1-1-111-11ii−i−i−i−iii−i−iiiii−i−i00000000−333−33−3−33−i3i3i3−i3i3−i3−i3i30000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000000000
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χ8344-44-44-4-40000-200000000-2-22-22−2i32i3−2i32i3−2i32i3−2i32i322000022−2222−2200000000i6−i6i6−i6i6−i6i6−i6−22−22−22−220000000000000000000000000000000000000000
χ8444-44-44-4-40000-200000000-2-22-22−2i32i3−2i32i3−2i32i3−2i32i3220000−2222−222200000000−i6i6−i6i6−i6i6−i6i62−22−22−22−20000000000000000000000000000000000000000
χ8544-44-44-4-40000-200000000-2-22-222i3−2i32i3−2i32i3−2i32i3−2i322000022−2222−2200000000−i6i6−i6i6−i6i6−i6i6−22−22−22−220000000000000000000000000000000000000000
χ8644-44-44-4-40000-200000000-2-22-222i3−2i32i3−2i32i3−2i32i3−2i3220000−2222−222200000000i6−i6i6−i6i6−i6i6−i62−22−22−22−20000000000000000000000000000000000000000
χ8744-4-44-44-400004000000004-44-4400000000-4-422−2222−2200000000000022−2222−22−2222−2222000000000000000000000000000000000000000000000000
χ8844-4-44-44-400004000000004-44-4400000000-4-4−2222−2222000000000000−2222−222222−2222−22000000000000000000000000000000000000000000000000
χ8944-4-44-44-40000-200000000-22-22-2−2i32i3−2i32i32i3−2i32i3−2i32222−2222−22000000000000−22−222−22−2i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000000000
χ9044-4-44-44-40000-200000000-22-22-2−2i32i3−2i32i32i3−2i32i3−2i322−2222−22220000000000002−22−2−22−22−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000000000
χ9144-4-44-44-40000-200000000-22-22-22i3−2i32i3−2i3−2i32i3−2i32i32222−2222−22000000000000−22−222−22−2−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000000000
χ9244-4-44-44-40000-200000000-22-22-22i3−2i32i3−2i3−2i32i3−2i32i322−2222−22220000000000002−22−2−22−22i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000000000
χ934-444-4-44-40000400000000-44-4-44000000004-4−2i22i22i2−2i2000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ944-444-4-44-40000400000000-44-4-44000000004-42i2−2i2−2i22i20000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ954-444-4-44-40000-2000000002-222-2−2i32i32i3−2i3−2i32i32i3−2i3-22−2i22i22i2−2i2000000000000i2−i2−i2i2i2−i2−i2i26−6−666−6−660000000000000000000000000000000000000000
χ964-444-4-44-40000-2000000002-222-2−2i32i32i3−2i3−2i32i32i3−2i3-222i2−2i2−2i22i2000000000000−i2i2i2−i2−i2i2i2−i2−666−6−666−60000000000000000000000000000000000000000
χ974-444-4-44-40000-2000000002-222-22i3−2i3−2i32i32i3−2i3−2i32i3-22−2i22i22i2−2i2000000000000i2−i2−i2i2i2−i2−i2i2−666−6−666−60000000000000000000000000000000000000000
χ984-444-4-44-40000-2000000002-222-22i3−2i3−2i32i32i3−2i3−2i32i3-222i2−2i2−2i22i2000000000000−i2i2i2−i2−i2i2i2−i26−6−666−6−660000000000000000000000000000000000000000
χ994-44-444-4-40000400000000-4-444-4000000004-40000−2i22i22i2−2i20000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ1004-44-444-4-40000400000000-4-444-4000000004-400002i2−2i2−2i22i200000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ1014-44-444-4-40000-20000000022-2-22−2i32i32i3−2i32i3−2i3−2i32i3-220000−2i22i22i2−2i2000000006−6−66−666−6i2−i2−i2i2−i2i2i2−i20000000000000000000000000000000000000000
χ1024-44-444-4-40000-20000000022-2-22−2i32i32i3−2i32i3−2i3−2i32i3-2200002i2−2i2−2i22i200000000−666−66−6−66−i2i2i2−i2i2−i2−i2i20000000000000000000000000000000000000000
χ1034-44-444-4-40000-20000000022-2-222i3−2i3−2i32i3−2i32i32i3−2i3-220000−2i22i22i2−2i200000000−666−66−6−66i2−i2−i2i2−i2i2i2−i20000000000000000000000000000000000000000
χ1044-44-444-4-40000-20000000022-2-222i3−2i3−2i32i3−2i32i32i3−2i3-2200002i2−2i2−2i22i2000000006−6−66−666−6−i2i2i2−i2i2−i2−i2i20000000000000000000000000000000000000000
χ1054-4-444-4-444-44-4-2-44-4-44-4442-2-222-2-222-2-2222-2000000002-222-22-2-200000000000000000000000000000000000000000000000000000000
χ1064-4-444-4-44-44-44-2-44-44-44-442-2-22222-2-222-2-22-2000000002-22-22-22-200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-44444-4-44-24-4-44-4-444222-2-2-2-22222-2-22-200000000-222-222-2-200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4-4444-444-4-24-4-4-444-44222-2-222-2-2-2-2222-200000000-2222-2-22-200000000000000000000000000000000000000000000000000000000

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