Finite Group Databasebeta

← Group #134384

Character table — Group #134384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order1222222244444444444444448888888888888888444444448888888822444444888888881616161616161616161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−iζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iiiζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iiiζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−iζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i11-1-1-1-111−i−iii−i−iii11-1-1-1-111ii−i−i−i−iiiζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i11-1-1-1-111−i−iii−i−iii11-1-1-1-111ii−i−i−i−iii−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i11-1-1-1-111−i−iii−i−iii-1-11111-1-1−i−iiiii−i−iζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i11-1-1-1-111−i−iii−i−iii-1-11111-1-1−i−iiiii−i−i−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i11-1-1-1-111−i−iiiii−i−iζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i11-1-1-1-111−i−iiiii−i−i−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i-1-11111-1-1ii−i−i−i−iiiζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i-1-11111-1-1ii−i−i−i−iii−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2
χ332222222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-222-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-222-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ41222-2-22-2-222-2-222-2-20000000022222222-2-2-2-2-2-2-2-22-22-20000000000002-22-200002-22-2000000000000000000000000000000000000
χ42222-2-22-2-222-2-222-2-20000000022222222-2-2-2-2-2-2-2-22-22-2000000000000-22-220000-22-22000000000000000000000000000000000000
χ43222-2-22-2-222-2-222-2-2000000002222-2-2-2-2-2-2-2-22222-22-2200000000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000000000
χ44222-2-22-2-222-2-222-2-2000000002222-2-2-2-2-2-2-2-22222-22-220000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000
χ45222-2-22-2-222-2-222-2-200000000-2-2-2-222222222-2-2-2-2-22-2200000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000000000
χ46222-2-22-2-222-2-222-2-200000000-2-2-2-222222222-2-2-2-2-22-220000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000000000
χ47222-2-22-2-222-2-222-2-200000000-2-2-2-2-2-2-2-2222222222-22-20000000000002-22-20000-22-22000000000000000000000000000000000000
χ48222-2-22-2-222-2-222-2-200000000-2-2-2-2-2-2-2-2222222222-22-2000000000000-22-2200002-22-2000000000000000000000000000000000000
χ49222-2-22-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-220000000000002-2-2200002i−2i−2i2i000000000000000000000000000000000000
χ50222-2-22-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-22000000000000-222-20000−2i2i2i−2i000000000000000000000000000000000000
χ51222-2-22-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-200000000000000002i−2i−2i2i0000-222-200000000000000000000000000000000
χ52222-2-22-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-20000000000000000−2i2i2i−2i00002-2-2200000000000000000000000000000000
χ53222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-200000000000000002i−2i−2i2i00002-2-2200000000000000000000000000000000
χ54222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-20000000000000000−2i2i2i−2i0000-222-200000000000000000000000000000000
χ55222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-220000000000002-2-220000−2i2i2i−2i000000000000000000000000000000000000
χ56222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-22000000000000-222-200002i−2i−2i2i000000000000000000000000000000000000
χ5722-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i2ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ60000000000002ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5
χ5822-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i2ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ60000000000002ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5
χ5922-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i−2ζ22ζ2−2ζ62ζ60000−2ζ22ζ2−2ζ62ζ6000000000000−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5
χ6022-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i−2ζ22ζ2−2ζ62ζ60000−2ζ22ζ2−2ζ62ζ6000000000000−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5
χ6122-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i2ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ6000000000000−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5
χ6222-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i2ζ2−2ζ22ζ6−2ζ600002ζ2−2ζ22ζ6−2ζ6000000000000−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5
χ6322-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i−2ζ22ζ2−2ζ62ζ60000−2ζ22ζ2−2ζ62ζ60000000000002ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5
χ6422-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-222−2i−2i2i2i−2ζ22ζ2−2ζ62ζ60000−2ζ22ζ2−2ζ62ζ60000000000002ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.