Finite Group Databasebeta

← Group #13152460

Character table — Group #13152460

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size1111222222333333334444444466666666666666661212121212121212121212121212121212121212121218181818181818181818181836363636363611112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order1222344666336666664412121212121299912121212181818181818181818121212123636363636363636363636363636363636362244666612121212441212121222226446666666666644121212121212181818121212121818181818181818181212121236363636363636363636363636363636363622446666121212124412121212
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+i32111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−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+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+i32111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−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+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+i32111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−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+i32-1-1-1-11+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+i32111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−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+i32-1-1-1-11+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+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−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+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−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+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−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+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−i32-1-1-1-11−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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−i32-1-1-1-11−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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-111111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-1
χ1411111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-11-11-1111111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-11-11-11
χ1511111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-11-11-1111111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-11-11-11
χ1611111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-11-11-111111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-11-11-1
χ1711111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i3211111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ1811111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i3211111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ1911111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i3211111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ2011111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i3211111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ2111111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i3211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ2211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i3211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ2311111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i3211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ2411111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i3211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ2522222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ272222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i320000000000000000002222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000
χ282222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-222-2-2-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000000000002222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-222-2-2-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
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χ901111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−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−i3211-1-11111-11+i321−i321+i321+i321−i321−i32-11+i321−i32-11+i321−i32-11+i321−i32−1−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+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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−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+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i32-11−i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+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−i32111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+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−i32-1-1-1-11−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+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i32-11−i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+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+i3211-1-11111-11−i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i32-11−i321+i32−1+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−i32-1-1-1-11−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−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+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+i3211-1-11111-11−i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i32-11−i321+i32−1+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−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ9511111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111111-1-111-1-111-1-111-1-111-1-1-1-11111-11-11-11
χ9611111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-11-11-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111111-1-111-1-111-1-11111-1-11111-1-1-1-11-11-11-1
χ9711111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-11-11-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111111-1-111-1-111-1-1-1-111-1-1-1-111111-11-11-1
χ9811111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111111-1-111-1-111-1-111-1-11111-1-1-1-1-11-11-11
χ9911111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32-1-1-1-1-111-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1111-1-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i321+i32−1−i321−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ10011111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32-1-1-1-1-111-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1111-1-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i321+i32−1−i321−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ10111111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-1-1-1-1-111-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321-11111-1-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i32−1−i321+i32−1+i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ10211111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-1-1-1-1-111-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321-11111-1-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-11+i321−i32−1−i321+i32−1+i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ10311111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32-1-1-1-1-111-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1111-1-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i321−i32−1+i321+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ10411111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32-1-1-1-1-111-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1111-1-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i321−i32−1+i321+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ10511111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-1-1-1-1-111-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321-11111-1-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i32−1+i321−i32−1−i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ10611111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-1-1-1-1-111-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321-11111-1-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-11−i321+i32−1+i321−i32−1−i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ10722222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111-2-2-2-2111111111-2-2-2-2111111111111111111000000000000000000
χ108222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222111-2-2-2-21111111112222111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
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χ1524-44-4400-4-4444-4-444-4-400000000-2-2-20000222222-2-2-20000000000000000000000000000000000000000-44-44-40044-4-4-444-4-444000000002220000-2-2-2-2-2-22220000000000000000000000000000000000000000
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χ1616-6-66-3-663-3300000000003-333−33−333300000000000000000000000000000000000000000000000000000000-666-636-6-33-30000000000-33−333333−3300000000000000000000000000000000000000000000000000000000
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χ1631212-12-12-600-666000000000000000000000000000000000000000000000000000000000000000000000000-12-1212126006-6-6000000000000000000000000000000000000000000000000000000000000000000000000
χ16412-1212-12-60066-6000000000000000000000000000000000000000000000000000000000000000000000000-1212-1212600-6-66000000000000000000000000000000000000000000000000000000000000000000000000

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