Finite Group Databasebeta

← Group #13153620

Character table — Group #13153620

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size1111222222333333334444444466666666666666661212121212121212121212121212121212121212121218181818181818181818181836363636363611112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order122222366633666666246666121266669991818181818181818186612121818181818181818181818183636363636364444121212121212121224661212222222666666666666246666121266661818181818181818181818186612121818181818181818181818183636363636364444121212121212121224661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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+i3211−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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+i3211−1−i32−1+i32−1−i32−1+i32
χ61111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32-1-11+i321−i321+i321−i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32-1-11+i321−i321+i321−i32
χ71111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ81111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ91111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i3211−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i3211−1+i32−1−i32−1+i32−1−i32
χ101111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-11−i321+i321−i321+i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-11−i321+i321−i321+i32
χ111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ121111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ131111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-11111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1
χ141111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-1111111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111
χ151111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-11-1-1111111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-11-1-111
χ161111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1111-111-1-11111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1111-111-1-1
χ171111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i321111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ181111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i321111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ191111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i321111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ201111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i321111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32
χ211111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i321111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ221111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i321111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ231111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i321111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ241111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i321111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32
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χ26222222222222222222-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000222222222222222222-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
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χ891111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211-1-111111+i321+i321−i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−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−i3211−1−i32−1+i32−1−i32−1+i32
χ901111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211-1-111111+i321+i321−i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−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+i32-1-11+i321−i321+i321−i32
χ911111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i3211−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-1-1-1-1-1-1-11−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ921111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-1-1-1-1-1-1-11−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ931111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211-1-111111−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+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+i3211−1+i32−1−i32−1+i32−1−i32
χ941111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211-1-111111−i321−i321+i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+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−i32-1-11−i321+i321−i321+i32
χ951111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-111-1-111-11-1-111
χ961111-1-11111111111111-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-111-1-111-1-11-111-1-1
χ971111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1111-111-1-1
χ981111-1-1111111111111-11-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-1-11-1-111
χ991111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32-1-1-1-111-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1111-1-111−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ1001111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32-1-1-1-111-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1111-1-111−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ1011111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i32-1-1-1-111-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321-11111-1-1−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32
χ1021111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321+i321−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+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32-1-1-1-111-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321-11111-1-1−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ1031111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32-1-1-1-111-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1111-1-111−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ1041111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32-1-1-1-111-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1111-1-111−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ1051111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i32-1-1-1-111-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321-11111-1-1−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32
χ1061111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−i321+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−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32-1-1-1-111-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321-11111-1-1−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i32
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χ1372-22-2-222-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-2200001+i3−1−i31−i3−1+i32−1−i3−1+i3-2-21+i31+i31−i31−i32−1−i3−1+i30000-221+i3−1−i31−i3−1+i3000000000000000000000000000000-22-222-2-222-21+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3002-20000−1−i31+i3−1+i31−i3-21+i31−i322−1−i3−1−i3−1+i3−1+i3-21+i31−i300002-2−1−i31+i3−1+i31−i3000000000000000000000000000000
χ1382-22-2-222-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-2200001+i3−1−i31−i3−1+i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i3200001-1−1−i321+i32−1+i321−i32−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000000000-22-222-2-222-21+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3002-20000−1−i31+i3−1+i31−i31−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i320000-111+i32−1−i321−i32−1+i32i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000000000
χ1392-22-2-222-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300-2200001+i3−1−i31−i3−1+i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i3200001-1−1−i321+i32−1+i321−i32i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000000000-22-222-2-222-21+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3002-20000−1−i31+i3−1+i31−i31−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i320000-111+i32−1−i321−i32−1+i32−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000000000
χ1402-22-2-222-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300-2200001−i3−1+i31+i3−1−i32−1+i3−1−i3-2-21−i31−i31+i31+i32−1+i3−1−i30000-221−i3−1+i31+i3−1−i3000000000000000000000000000000-22-222-2-222-21−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3002-20000−1+i31−i3−1−i31+i3-21−i31+i322−1+i3−1+i3−1−i3−1−i3-21−i31+i300002-2−1+i31−i3−1−i31+i3000000000000000000000000000000
χ1412-22-2-222-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300-2200001−i3−1+i31+i3−1−i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i3200001-1−1+i321−i32−1−i321+i32−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i32000000000000000000-22-222-2-222-21−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3002-20000−1+i31−i3−1−i31+i31−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i320000-111−i32−1+i321+i32−1−i32i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i32000000000000000000
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χ1432-2-22002-22-222-2-2-2-222000000000000222-22-22-22-2-2-200000000000000000000002-2002-2002-200000000-222-200-22-22-2-22222-2-2000000000000-2-2-22-22-22-22220000000000000000000000-2200-2200-2200000000
χ1442-2-22002-22-222-2-2-2-222000000000000222-22-22-22-2-2-20000000000000000000000-2200-2200-2200000000-222-200-22-22-2-22222-2-2000000000000-2-2-22-22-22-222200000000000000000000002-2002-2002-200000000
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χ14944-4-40044-4-44444-4-4-4-4000000000000-2-2-2-22-22-222220000000000000000000000000000000000000000-4-44400-4-444-4-4-4-444440000000000002222-22-22-2-2-2-20000000000000000000000000000000000000000
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χ15144-4-40044-4-4−2+2i3−2−2i3−2+2i3−2−2i32−2i32+2i32−2i32+2i3000000000000-21−i31+i3-221−i3−1+i31+i3−1−i32−1+i3−1−i30000000000000000000000000000000000000000-4-44400-4-4442−2i32+2i32−2i32+2i3−2+2i3−2−2i3−2+2i3−2−2i30000000000002−1+i3−1−i32-2−1+i31−i3−1−i31+i3-21−i31+i30000000000000000000000000000000000000000
χ1524-4-44004-44-444-4-4-4-444000000000000-2-2-22-22-22-22220000000000000000000000000000000000000000-444-400-44-44-4-44444-4-4000000000000222-22-22-22-2-2-20000000000000000000000000000000000000000
χ1534-4-44004-44-4−2−2i3−2+2i32+2i32−2i32+2i32−2i3−2−2i3−2+2i3000000000000-21+i31−i32-2−1−i31+i3−1+i31−i32−1−i3−1+i30000000000000000000000000000000000000000-444-400-44-442+2i32−2i3−2−2i3−2+2i3−2−2i3−2+2i32+2i32−2i30000000000002−1−i3−1+i3-221+i3−1−i31−i3−1+i3-21+i31−i30000000000000000000000000000000000000000
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χ155666666-3-3-3-30000000066-3-3-3-3-3-300000000000000000000000000000000000000000000000000000000-6-6-6-6-6-6333300000000-6-633333300000000000000000000000000000000000000000000000000000000
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χ1626-66-6-66-333-300000000003-33i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000-66-666-63-3-330000000000-33−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1631212-12-1200-6-666000000000000000000000000000000000000000000000000000000000000000000000000-12-1212120066-6-6000000000000000000000000000000000000000000000000000000000000000000000000
χ16412-12-121200-66-66000000000000000000000000000000000000000000000000000000000000000000000000-121212-12006-66-6000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.