Finite Group Databasebeta

← Group #13153058

Character table — Group #13153058

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size11112222223333333344444444444466666666666666668888121212121212121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424242424363636363636363636363636363636363636
order122234466633666666224444661212121299912121212181818181818181818612121266661212121212121212181818181818363636363636363636363636444412121212121212121818183636363636363636362444446612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-11-1-1-1-1-111-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111-11-1-1-1-1-111-1-1111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11111-1-111-1-11111
χ5111111111111111111-11-1-11-11111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111-1-1-1-1-1-111-1-1
χ6111111111111111111-11-1-11-11111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111-1-111
χ7111111111111111111-1-1-11-11-1-111-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-11-1-11-1-1-1-111-1-1-1-111
χ8111111111111111111-1-1-11-11-1-111-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-11111-1-1
χ91111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ101111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-11-1-1-1-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32-11-11-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32
χ121111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-11-1-1-1-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i321-11-111−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ131111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-11-11111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i321-1-1-11-1−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32
χ141111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-11-11111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-11+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32-1111-111+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ151111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-11-11-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32-1-11-1-111+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ161111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-11-11-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3211-111-1−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ171111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ181111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ191111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-11-1-1-1-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32-11-11-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32
χ201111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-11-1-1-1-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i321-11-111−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ211111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-11-11111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i321-1-1-11-1−1+i32−1−i321−i321+i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32
χ221111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-11-11111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-11−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32-1111-111−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ231111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-11-11-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1111−i321+i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32-1-11-1-111−i321+i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ241111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-11-11-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1111−i321+i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3211-111-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ2511111-1-11111111111111-1-1-1111-1-1-1-1111-1-1-1-11111111111-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1111-1-1111-1-1-1-1-1111111-1-1
χ2611111-1-11111111111111-1-1-1111-1-1-1-1111-1-1-1-11111111111-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-111111-1-1-111111-1-1-1-1-1-111
χ2711111-1-1111111111111-1-111-1-1-1-1-111111-1-1-1-11111111111-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111-1-1-1111-1-1-11-1-11-1111-1-1-1-111-1-111
χ2811111-1-1111111111111-1-111-1-1-1-1-111111-1-1-1-11111111111-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-111-11-1-1-11111-1-111-1-1
χ2911111-1-111111111111-1111-1-111-1-1-1-1111-1-1-1-1111111111-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-111-1-1-1-11111
χ3011111-1-111111111111-1111-1-111-1-1-1-1111-1-1-1-1111111111-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-11-111-1-111-1-11111-1-1-1-1
χ3111111-1-111111111111-1-11-111-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1111-1-1-1111111-1-1-1111111-1-1-1-1-1-1
χ3211111-1-111111111111-1-11-111-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1111-1-1-1111-1-1-1111-1-1-1-1-1-1111111
χ3311111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i32-1-1111-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ3411111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3211-1-1-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32
χ3511111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-11-1−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i321-1-11-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ3611111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-11-1−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i32-111-11-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ3711111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1111-1-111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-111-11+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11-1-1111+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ3811111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1111-1-111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-111-11+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i321-111-1-1−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ3911111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-111-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-111+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32111-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32
χ4011111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11-111-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-111+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4111111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i32-1-1111-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ4211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3211-1-1-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32
χ4311111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-11-1−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i321-1-11-11−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ4411111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-11-1−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i32-111-11-11−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ4511111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1111-1-111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-111-11−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11-1-1111−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ4611111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1111-1-111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-111-11−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i321-111-1-1−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ4711111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-111-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-111−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32111-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i32
χ4811111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11-111-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-111−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32-1-1-11111−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ49222222222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ502222222222222222222-22-2-2-2-2-222-2-2-1-1-12222-1-1-1-1-1-1-1-1-122-2-222-2-222-2-2-2-2-2-2111111-1-1-1-1-1-1111111000000000000-1-1-1-1-1-1111111000000000000000000
χ51222222222222222222-22-2-22-2222222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000000000
χ52222222222222222222-2-2-22-22-2-222-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-222-2-222111111-1-1-1-1-1-1111111000000000000111111-1-1-1-1-1-1000000000000000000
χ532222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3222222222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i322222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ542222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-22-2-2-2-2-222-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i3222-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ552222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-22-2-22-2222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-2-2-2-21+i31−i3−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ562222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-2-22-22-2-222-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-2-2221+i31−i31+i31−i31+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i320000000000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ572222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3222222222222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i322222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ582222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-22-2-2-2-2-222-2-2-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i3222-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ592222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-22-2-22-2222222-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-2-2-2-21−i31+i3−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ602222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-2-22-22-2-222-2-2-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-2-2221−i31+i31−i31+i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i320000000000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ6122222-2-22222222222222-2-2-2222-2-2-2-2-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-12-2-222222-2-2-2-2-2-222-1-1-1-1-1-1111111111111000000000000-1-1-1111111-1-1-1000000000000000000
χ6222222-2-2222222222222-2-222-2-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-12-22-222-2-2-2-22222-2-2111111111111-1-1-1-1-1-1000000000000-1-1-1111-1-1-1111000000000000000000
χ6322222-2-222222222222-2222-2-222-2-2-2-2-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-222-2-2-2222222-2-2-2-2-1-1-1-1-1-1111111111111000000000000111-1-1-1-1-1-1111000000000000000000
χ6422222-2-222222222222-2-22-222-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-22-22-2-2-2-222-2-22222111111111111-1-1-1-1-1-1000000000000111-1-1-1111-1-1-1000000000000000000
χ6522222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-2-2222-2-2-2-2-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i322-2-22−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32000000000000000000
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χ6722222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2222-2-222-2-2-2-2-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i32-222-21+i31−i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i32000000000000000000
χ6822222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-22-222-2-2-2-222-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i32-22-221+i31−i31+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i320000000000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i32000000000000000000
χ6922222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-2-2222-2-2-2-2-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i322-2-22−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32000000000000000000
χ7022222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-2-222-2-2-2-2-222-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i322-22-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32000000000000000000
χ7122222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2222-2-222-2-2-2-2-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i32-222-21−i31+i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i32000000000000000000
χ7222222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-22-222-2-2-2-222-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i32-22-221−i31+i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i320000000000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i32000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.