Finite Group Databasebeta

← Group #213078

Character table — Group #213078

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444444444448888888888888888444488888888888888888888888888888888888888882222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1011111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1
χ1211111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ17111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−ii−ii−i1-11-1
χ18111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii−ii−ii-11-11
χ19111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1-11i−ii−i−ii−ii1-1-11
χ20111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-111-1−ii−iii−ii−i-111-1
χ21111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-1i−i−iii−i−ii-11-11
χ22111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-11−iii−i−iii−i1-11-1
χ23111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i1-1-11i−i−ii−iii−i-111-1
χ24111-1-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-111-1−iii−ii−i−ii1-1-11
χ25111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii−ii−ii1-11-1
χ26111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−ii−ii−i-11-11
χ27111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1-11−ii−iii−ii−i1-1-11
χ28111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-111-1i−ii−i−ii−ii-111-1
χ29111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-1−iii−i−iii−i-11-11
χ30111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-11i−i−iii−i−ii1-11-1
χ31111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii1-1-11−iii−ii−i−ii-111-1
χ32111-1-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-111-1i−i−ii−iii−i1-1-11
χ33222222222222222222-2-222-2-2-2-2-2-20000000000000000-2-2-2-200000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ34222222222222222222-2-222-2-2-2-2-2-20000000000000000-2-2-2-2000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ352222222222-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22-22-222-2-222-2-2000000000000000000000000000000000000000000000000
χ362222222222-2-222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-222222-22-2-2-222-2-222000000000000000000000000000000000000000000000000
χ372222222222-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000-22-220000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000-22-2200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-222-2-222-2-222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-22-2222-2-222-2-2000000000000000000000000000000000000000000000000
χ4122222222-2-222-2-222-2-2-2-2-2-2-2-2222200000000000000002-22-20000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4222222222-2-222-2-222-2-2-2-2-2-2-2-2222200000000000000002-22-200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-20000000000000000222200000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4422222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-200000000000000002222000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
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χ48222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-22i−2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ49222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-2-2-2222222-2-20000000000000000−2i2i2i−2i0000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
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χ52222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-2−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ53222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2222222-2-200000000000000002i−2i−2i2i0000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ54222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2222222-2-200000000000000002i−2i−2i2i00000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ55222-2-2-2-22−2i−2i−2i−2i2i2i2i2i22-2-2-2-222-2-22200000000000000002i2i−2i−2i00000000000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000
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χ5722-222-2-2-22-22-22-22-22-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−2002i−2i002i−2i002i−2i002i−2i0000000000000000
χ5822-222-2-2-22-22-22-22-22-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−2200−2i2i00−2i2i00−2i2i00−2i2i0000000000000000
χ5922-222-2-2-22-22-22-22-22-2002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−200−2i2i00−2i2i00−2i2i00−2i2i0000000000000000
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χ6222-222-2-2-22-2-222-2-22-2200-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i2i2−i2−i2i2−222−2−222−2−222−2−222−2−2i2i00−2i2i00−2i2i00−2i2i000000000000000000
χ6322-222-2-2-22-2-222-2-22-2200-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2−i2i2i2−i22−2−222−2−222−2−222−2−22−2i2i00−2i2i00−2i2i00−2i2i000000000000000000
χ6422-222-2-2-22-2-222-2-22-2200-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2−i2i2i2−i2−222−2−222−2−222−2−222−22i−2i002i−2i002i−2i002i−2i000000000000000000
χ6522-222-2-2-2-222-2-222-2-2200-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i2−i2i2i2−i22−2−222−2−22−222−2−222−22i−2i002i−2i00−2i2i00−2i2i000000000000000000
χ6622-222-2-2-2-222-2-222-2-2200-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i2−i2i2i2−i2−222−2−222−22−2−222−2−22−2i2i00−2i2i002i−2i002i−2i000000000000000000
χ6722-222-2-2-2-222-2-222-2-2200-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i2i2−i2−i2i22−2−222−2−22−222−2−222−2−2i2i00−2i2i002i−2i002i−2i000000000000000000
χ6822-222-2-2-2-222-2-222-2-2200-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i2i2−i2−i2i2−222−2−222−22−2−222−2−222i−2i002i−2i00−2i2i00−2i2i000000000000000000
χ6922-222-2-2-2-22-22-22-222-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−22002i−2i002i−2i00−2i2i00−2i2i0000000000000000
χ7022-222-2-2-2-22-22-22-222-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−200−2i2i00−2i2i002i−2i002i−2i0000000000000000
χ7122-222-2-2-2-22-22-22-222-2002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−2200−2i2i00−2i2i002i−2i002i−2i0000000000000000
χ7222-222-2-2-2-22-22-22-222-2002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−2002i−2i002i−2i00−2i2i00−2i2i0000000000000000
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χ7722-2-2-222-22i−2i−2i2i−2i2i2i−2i-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000−222−22−2−222−2−22−222−2i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i00-22002-2000000000000000000
χ7822-2-2-222-22i−2i−2i2i−2i2i2i−2i-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000−222−22−2−22−222−22−2−22−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i002-200-22000000000000000000
χ7922-2-2-222-22i−2i−2i2i−2i2i2i−2i-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002−2−22−222−22−2−22−222−2i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i002-200-22000000000000000000
χ8022-2-2-222-22i−2i−2i2i−2i2i2i−2i-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002−2−22−222−2−222−22−2−22−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i00-22002-2000000000000000000
χ8122-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002−2−22−222−22−2−22−222−2−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i002-200-22000000000000000000
χ8222-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002−2−22−222−2−222−22−2−22i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i00-22002-2000000000000000000
χ8322-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000−222−22−2−222−2−22−222−2−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i00-22002-2000000000000000000
χ8422-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000−222−22−2−22−222−22−2−22i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i002-200-22000000000000000000
χ8522-2-2-222-2−2i2i−2i2i2i−2i2i−2i2-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i002-200-220000000000000000
χ8622-2-2-222-2−2i2i−2i2i2i−2i2i−2i2-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i00-22002-20000000000000000
χ8722-2-2-222-2−2i2i−2i2i2i−2i2i−2i2-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i00-22002-20000000000000000
χ8822-2-2-222-2−2i2i−2i2i2i−2i2i−2i2-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−22−222−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i002-200-220000000000000000
χ894-444-44-4-400000000004-4004-4000000004i−4i4i−4i00004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ904-444-44-4-400000000004-4004-400000000−4i4i−4i4i0000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ914-444-44-4-40000000000-4400-4400004i−4i4i−4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ924-444-44-4-40000000000-4400-440000−4i4i−4i4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-400000000004-400-44000000004i−4i4i−4i0000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-400000000004-400-4400000000−4i4i−4i4i00004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-40000000000-44004-400004i−4i4i−4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-40000000000-44004-40000−4i4i−4i4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ974-4-44-4-44400000000000000004-44-422−22−222222−22−222222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000
χ984-4-44-4-44400000000000000004-44-4−222222−22−222222−22−222222−22−222222−22000000000000000000000000000000000000000000000000000000000000
χ994-4-44-4-4440000000000000000-44-4422−22−2222−222222−2222−22−2222−222222−22000000000000000000000000000000000000000000000000000000000000
χ1004-4-44-4-4440000000000000000-44-44−222222−2222−22−2222−222222−2222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-444-4400000000000000004-4-4422−22−222222−22−2222−222222−22−222222−22000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-444-4400000000000000004-4-44−222222−22−222222−2222−22−222222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-440000000000000000-444-422−22−2222−222222−22−222222−2222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-440000000000000000-444-4−222222−2222−22−222222−22−2222−222222−22000000000000000000000000000000000000000000000000000000000000

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