Finite Group Databasebeta

← Group #13145728

Character table — Group #13145728

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order12222233344446666666666666121212121212121233333666666666666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444488888888121212121212121224242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-11-1111ii−i−i1111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101-11-11-1111ii−i−i1111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111-11-11-1111ii−i−i1111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ121-11-11-1111ii−i−i1111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ131-11-11-1111−i−iii1111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ141-11-11-1111−i−iii1111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ151-11-11-1111−i−iii1111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii-11i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161-11-11-1111−i−iii1111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii-11i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1722222222-12222222-12222-12-12222-1-122-1-12-1-1-1-12-12-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12-12-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1822222222-12222222-12222-12-12222-1-122-1-12-1-1-1-12-12-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12-12-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ1922222222-1-2-2-2-2222-12222-12-122-2-211-2-2112-1-1-1-12-12-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-2-2-2-2-21111111111111111-2-2-2-21111111111111111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ2022222222-1-2-2-2-2222-12222-12-122-2-211-2-2112-1-1-1-12-12-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-21-21-2-2-2-2-2-2-2-21111111111111111-2-2-2-2111111111111111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ212222222-12222222-12222-12-1222-1-122-1-122-12-1-1-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-12-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ222222222-12222222-12222-12-1222-1-122-1-122-12-1-1-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-12-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ232222222-12-2-2-2-222-12222-12-122211-2-211-2-2-12-1-1-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-11-21-2-2-2-2-21111-2-2-2-21111111111111111-2-2-2-211111111111100002i2i−2i−2i000000000000−i−i−i−iiiii00000000
χ242222222-12-2-2-2-222-12222-12-122211-2-211-2-2-12-1-1-1-12-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-11-21-2-2-2-2-21111-2-2-2-21111111111111111-2-2-2-21111111111110000−2i−2i2i2i000000000000iiii−i−i−i−i00000000
χ25222222-1222222-1-122-1-1-12222-1-122222222-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ26222222-1222222-1-122-1-1-12222-1-122222222-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ27222222-122-2-2-2-2-1-122-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-1-2-2-2-2111111111111-2-2-2-21111111111111111-2-2-2-21111111122-2-200000000-1-1-1-111110000000000000000
χ28222222-122-2-2-2-2-1-122-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12-1-1-2-2-2-2111111111111-2-2-2-21111111111111111-2-2-2-211111111-2-222000000001111-1-1-1-10000000000000000
χ292222-2-22222-22-2-2-2222-2-222222222-2-222-2-222222-2-2-2-22-2-22-2-22-2-222-2-2-2-22-2-22-2-22-2-222-2-2-2-222222-22-222-22-222-2-222-2-222-2-22222-2-2-2-222-2-222-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ302222-2-2222-22-22-2-2222-2-2222222-2-222-2-22222222-2-2-2-22-2-22-2-22-2-222-2-2-2-22-2-22-2-22-2-222-2-2-2-2222222-22-2-22-22-2-222-2-222-2-222-2-2-2-22222-2-222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000
χ312222-2-222-12-22-2-2-22-12-2-22-12-122221122112-1-1-1-1-21-212-2-2-111-111-1-111112-2-2-111-111-1-111112-1-1-1-1-2-1-2-12-22-222-2-2-1-111-1-111-1-1-1-1111122-2-2-1-111-1-111-1-1-1-1111100000000000000000000000000003−33−33−33−3
χ322222-2-222-12-22-2-2-22-12-2-22-12-122221122112-1-1-1-1-21-212-2-2-111-111-1-111112-2-2-111-111-1-111112-1-1-1-1-2-1-2-12-22-222-2-2-1-111-1-111-1-1-1-1111122-2-2-1-111-1-111-1-1-1-111110000000000000000000000000000−33−33−33−33
χ332222-2-222-1-22-22-2-22-12-2-22-12-122-2-2-1-1-2-2-1-12-1-1-1-1-21-212-2-2-111-111-1-111112-2-2-111-111-1-111112-1-1-1-12121-22-22-2-22211-1-111-1-11111-1-1-1-1-2-22211-1-111-1-11111-1-1-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ342222-2-222-1-22-22-2-22-12-2-22-12-122-2-2-1-1-2-2-1-12-1-1-1-1-21-212-2-2-111-111-1-111112-2-2-111-111-1-111112-1-1-1-12121-22-22-2-22211-1-111-1-11111-1-1-1-1-2-22211-1-111-1-11111-1-1-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ352222-2-22-122-22-2-2-2-122-2-2-12-1222-1-1-2-2-1-1-2-2-12-1-1-11-21-2-1112-2-2-111-1-11111-1112-2-2-111-1-11111-12-1-1-112122-22-2-1-11122-2-2-1-111-1-1-1-11111-1-11122-2-2-1-111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ362222-2-22-122-22-2-2-2-122-2-2-12-1222-1-1-2-2-1-1-2-2-12-1-1-11-21-2-1112-2-2-111-1-11111-1112-2-2-111-1-11111-12-1-1-112122-22-2-1-11122-2-2-1-111-1-1-1-11111-1-11122-2-2-1-111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ372222-2-22-12-22-22-2-2-122-2-2-12-122211221122-12-1-1-11-21-2-1112-2-2-111-1-11111-1112-2-2-111-1-11111-12-1-1-1-1-2-1-2-22-2211-1-1-2-22211-1-11111-1-1-1-111-1-1-2-22211-1-11111-1-1-1-1000000000000000000003−33−3−33−3300000000
χ382222-2-22-12-22-22-2-2-122-2-2-12-122211221122-12-1-1-11-21-2-1112-2-2-111-1-11111-1112-2-2-111-1-11111-12-1-1-1-1-2-1-2-22-2211-1-1-2-22211-1-11111-1-1-1-111-1-1-2-22211-1-11111-1-1-1-100000000000000000000−33−333−33−300000000
χ392222-2-2-1222-22-21122-1112222-1-122-2-222-2-2-1-12-1-1-2-2-2-2-111-1112-2-2-1-11111-111-1112-2-2-1-11111-1-12-1-1-22-22-11-11-1-111-1-11122-2-2-1-1-1-11111-1-111-1-11122-2-2-1-1-1-11111000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ402222-2-2-1222-22-21122-1112222-1-122-2-222-2-2-1-12-1-1-2-2-2-2-111-1112-2-2-1-11111-111-1112-2-2-1-11111-1-12-1-1-22-22-11-11-1-111-1-11122-2-2-1-1-1-11111-1-111-1-11122-2-2-1-1-1-11111000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
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χ1594-4-4400-2-2-200002i3−2i3222−2i32i322-2-22-2−2i32i3−2i32i32i3−2i32i3−2i3111−1+3i32−1−3i320000-1−i3i3-1−i3i3-13-31−3i321+3i32−3+i323−i32−3−i323+i32-1i3−i3-1i3−i3-1-331−3i321+3i323−i32−3+i323+i32−3−i32111−1+3i32−1−3i3200000000i3−i3-33-33i3−i3i3−i3i3−i33−i32−3+i32−3−i323+i323−i32−3+i32−3−i323+i32−i3i33-33-3−i3i3−i3i3−i3i3−3+i323−i323+i32−3−i32−3+i323−i323+i32−3−i32000000000000000000000000000000000000
χ1604-4-4400-2-2-200002i3−2i3222−2i32i322-2-22-2−2i32i32i3−2i32i3−2i3−2i32i3111−1−3i32−1+3i320000-1−i3i3-1−i3i3-1-331+3i321−3i323+i32−3−i323−i32−3+i32-1i3−i3-1i3−i3-13-31+3i321−3i32−3−i323+i32−3+i323−i32111−1−3i32−1+3i3200000000i3−i3-333-3−i3i3i3−i3−i3i3−3−i323+i323−i32−3+i323+i32−3−i32−3+i323−i32−i3i33-3-33i3−i3−i3i3i3−i33+i32−3−i32−3+i323−i32−3−i323+i323−i32−3+i32000000000000000000000000000000000000
χ1614-4-4400-2-2-200002i3−2i3222−2i32i322-2-22-22i3−2i3−2i32i3−2i32i32i3−2i3111−1−3i32−1+3i320000-1−i3i3-1−i3i3-1-331+3i321−3i323+i32−3−i323−i32−3+i32-1i3−i3-1i3−i3-13-31+3i321−3i32−3−i323+i32−3+i323−i32111−1−3i32−1+3i3200000000−i3i33-3-33i3−i3−i3i3i3−i33+i32−3−i32−3+i323−i32−3−i323+i323−i32−3+i32i3−i3-333-3−i3i3i3−i3−i3i3−3−i323+i323−i32−3+i323+i32−3−i32−3+i323−i32000000000000000000000000000000000000
χ1624-4-4400-2-2-200002i3−2i3222−2i32i322-2-22-22i3−2i32i3−2i3−2i32i3−2i32i3111−1+3i32−1−3i320000-1−i3i3-1−i3i3-13-31−3i321+3i32−3+i323−i32−3−i323+i32-1i3−i3-1i3−i3-1-331−3i321+3i323−i32−3+i323+i32−3−i32111−1+3i32−1−3i3200000000−i3i33-33-3−i3i3−i3i3−i3i3−3+i323−i323+i32−3−i32−3+i323−i323+i32−3−i32i3−i3-33-33i3−i3i3−i3i3−i33−i32−3+i32−3−i323+i323−i32−3+i32−3−i323+i32000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.