Finite Group Databasebeta

← Group #13153713

Character table — Group #13153713

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size1111222222333333334444444466666666666666661212121212121212121212121212121212121212121218181818181818181818181836363636363611112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order124423461212336612121212246661212123336666612121212121212126666666666612121212121212121212128888242424242424242424661212224426461212666612121212246661212126666666612121212121212126666666666612121212121212121212128888242424242424242424661212
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
χ3111111111111111111-1-11-1-11-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111111111-1-11-1-11-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-11-1-11-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-11-1-11-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−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+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−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+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−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+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−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+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ81111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+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+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ121111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−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−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−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
χ1311-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-111-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1
χ1411-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-11111-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111
χ1511-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-11-1-11111-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-11-1-111
χ1611-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-1111-111-1-111-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-1111-111-1-1
χ1711-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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−i3211-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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
χ1811-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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+i3211-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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
χ1911-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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+i3211-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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
χ2011-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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−i3211-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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
χ2111-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+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+i3211-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+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
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χ2411-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1-11111−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−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+i3211-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1-11111−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−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
χ2522222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-100000000000000000022222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222-2-22-2-22-2-2-1-1-122-1-1-1-1-1-1-1-1-122-2-2-1-1-1111111-2-2-1-1-1111111000000000000000000222222222222222222-2-22-2-22-2-2-1-1-122-1-1-1-1-1-1-1-1-122-2-2-1-1-1111111-2-2-1-1-1111111000000000000000000
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χ881111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−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−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321+i321−i32-11+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
χ891111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i3211-111-111-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11+i321−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+i32-1-11-1-11-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321+i321−i321−1−i32−1+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−i3211-111-111-11+i321−i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11+i321−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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i32-11−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−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+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+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i32-11−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−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i3211-111-111-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11−i321+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−i32-1-11-1-11-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−i321+i321−1+i32−1−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+i3211-111-111-11−i321+i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11−i321+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
χ9511-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1-1-1111-1-1-111-1-1-1-11111-111-1-1-111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1-1-111-1-1-1111111-1-111-1-111-1-111-11-1-111
χ9611-1-1-1111-1-11111-1-1-1-11-1-1111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111-1-1111-1-1-111-1-1-1-11111-111-1-1-111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1-1-111-1-1-111111111-1-111-1-111-1-11-111-1-1
χ9711-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-11-1-111-1-1111-1-1-111-1-1-1-111111-1111-1-1-1-1-1-111-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-111-1-1
χ9811-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-1111-111-1-1-1-1111-1-1-111-1-1-1-111111-1111-1-1-1-1-1-111-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11-1-111
χ9911-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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−i32-1-1111-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32-111-1-1-111-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32-11+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
χ10011-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1111-1-11−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321−1−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+i32-1-1111-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32-111-1-1-111-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i32-11+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
χ10111-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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+i32-1-1111-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1111-1-1-1-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−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
χ10211-1-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1-11111−1−i32−1+i321+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i321−1−i32−1+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−i32-1-1111-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1111-1-1-1-11+i321−i32−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-11+i321−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
χ10311-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+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+i32-1-1111-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32-111-1-1-111-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32-11−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
χ10411-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-1-1111-1-11−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−1+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−i32-1-1111-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32-111-1-1-111-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i32-11−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
χ10511-1-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1-11111−1+i32−1−i321−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i321−1+i32−1−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−i32-1-1111-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1111-1-1-1-11−i321+i32−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-11−i321+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
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χ10722222222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111-2-2111111111-2-2-2-2111111111-2-2111111111000000000000000000
χ108222222222222222222-2-22-2-22-2-2-1-1-122-1-1-1-1-1-1-1-1-122-2-2-1-1-1111111-2-2-1-1-1111111000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-222-222111-2-2111111111-2-222111-1-1-1-1-1-122111-1-1-1-1-1-1000000000000000000
χ1092222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322222222-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000000000000-2-2-2-2-2-2-2-2-2-21+i31−i31+i31−i31+i31+i31−i31−i3-2-2-2-2-2-2-2-21−1−i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i31−i31+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ1102222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-22-2-22-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i321+i31−i3-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000-2-2-2-2-2-2-2-2-2-21+i31−i31+i31−i31+i31+i31−i31−i322-222-2221−1−i32−1+i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i31−i3−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i3−1+i31−1−i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
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χ1122222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-22-2-22-2-2-11−i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i321−i31+i3-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000-2-2-2-2-2-2-2-2-2-21−i31+i31−i31+i31−i31−i31+i31+i322-222-2221−1+i32−1−i321−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i31+i3−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i3−1−i31−1+i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
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χ1142222-22-22222222222200-200-200-1-1-1-2-2-1-1-1-1-1-1-1-1-1-2-200111−i3i3−i3i3−i3i300111−i3i3−i3i3−i3i3000000000000000000-2-2-2-22-22-2-2-2-2-2-2-2-2-2-2-200200200111221111111112200-1-1-1i3−i3i3−i3i3−i300-1-1-1i3−i3i3−i3i3−i3000000000000000000
χ1152222-22-22222222222200-200-200-1-1-1-2-2-1-1-1-1-1-1-1-1-1-2-200111i3−i3i3−i3i3−i300111i3−i3i3−i3i3−i3000000000000000000-2-2-2-22-22-2-2-2-2-2-2-2-2-2-2-200200200111221111111112200-1-1-1−i3i3−i3i3−i3i300-1-1-1−i3i3−i3i3−i3i3000000000000000000
χ1162222-22-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300-200-2002−1−i3−1+i31+i31−i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i31+i31−i300-21+i31−i300000000-21+i31−i3000000000000000000000000-2-2-2-22-22-2-2-21+i31−i31+i31−i31+i31+i31−i31−i300200200-21+i31−i3−1−i3−1+i3-21+i31−i3-2-21+i31+i31−i31−i3−1−i3−1+i3002−1−i3−1+i3000000002−1−i3−1+i3000000000000000000000000
χ1172222-22-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300-200-200-11+i321−i321+i31−i3-11+i321−i32-1-11+i321+i321−i321−i321+i31−i3001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32001−1−i32−1+i32−i3i3−3+i323−i323+i32−3−i32000000000000000000-2-2-2-22-22-2-2-21+i31−i31+i31−i31+i31+i31−i31−i3002002001−1−i32−1+i32−1−i3−1+i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i300-11+i321−i32i3−i33−i32−3+i32−3−i323+i3200-11+i321−i32i3−i33−i32−3+i32−3−i323+i32000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.