Finite Group Databasebeta

← Group #13175111

Character table — Group #13175111

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216C217C218C219C220C221C222C223C224C225C226C227C228C229C230C231C232C233C234C235C236C237C238C239C240C241C242C243C244C245C246C247C248C249C250C251C252
size111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818
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χ441111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ4511111111111111111111111111-1-111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211111111111111111111111111-1-111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ4611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i3211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ471111-1-1111111111-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321111-1-1111111111-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ481111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ491111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
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χ512222222-12-1-122-1-122-1-1-1-1-1-1-1-1-12200-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i32000000002222222-12-1-122-1-122-1-1-1-1-1-1-1-1-12200-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i3200000000
χ522222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-200111100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i31−i300−1+i32−1+i32−1+i32−1+i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i31+i300−1−i32−1−i32−1−i32−1−i32000000002222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-200111100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i31−i300−1+i32−1+i32−1+i32−1+i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i31+i300−1−i32−1−i32−1−i32−1−i3200000000
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χ179222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100220000-1-1-1-10000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i320000-2-2-2-2-2-21-21-2-211-2111-2-2111111100-2-20000111100001−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32001−i31−i30000−1+i32−1+i32−1+i32−1+i3200001+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32001+i31+i30000−1−i32−1−i32−1−i32−1−i320000
χ180222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100-2-2000011110000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32001+i31+i30000−1−i32−1−i32−1−i32−1−i320000-2-2-2-2-2-21-21-2-211-2111-2-2111111100220000-1-1-1-100001−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200−1+i3−1+i300001−i321−i321−i321−i3200001+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200−1−i3−1−i300001+i321+i321+i321+i320000
χ1812222-2-22-12-1-122-1-1-2-211-1-1-111112-200-1-11100000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i31−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i31−i3001−i321−i32−1+i32−1+i3200000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i31+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i31+i3001+i321+i32−1−i32−1−i3200000000-2-2-2-222-21-211-2-21122-1-1111-1-1-1-1-220011-1-1000000001−i31−i31−i31−i3−1+i3−1+i31−i3−1+i321−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i3−1+i300−1+i32−1+i321−i321−i32000000001+i31+i31+i31+i3−1−i3−1−i31+i3−1−i321+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i3−1−i300−1−i32−1−i321+i321+i3200000000
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χ1832222-2-2-12-122-1-12-111-2-2-1-1-11111002-20000-1-1110000−1+i3−1+i3−1+i3−1+i31−i31−i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i32−1+i32−1+i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i3200−1+i31−i300001−i321−i32−1+i32−1+i320000−1−i3−1−i3−1−i3−1−i31+i31+i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i32−1−i32−1−i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i3200−1−i31+i300001+i321+i32−1−i32−1−i320000-2-2-2-2221-21-2-211-21-1-122111-1-1-1-100-22000011-1-100001−i31−i31−i31−i3−1+i3−1+i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i321−i321−i32−1+i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i321−i32001−i3−1+i30000−1+i32−1+i321−i321−i3200001+i31+i31+i31+i3−1−i3−1−i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i321+i321+i32−1−i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i321+i32001+i3−1−i30000−1−i32−1−i321+i321+i320000
χ1842222-2-2-12-122-1-12-111-2-2-1-1-1111100-22000011-1-10000−1+i3−1+i3−1+i3−1+i31−i31−i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i32−1+i32−1+i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i32001−i3−1+i30000−1+i32−1+i321−i321−i320000−1−i3−1−i3−1−i3−1−i31+i31+i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i32−1−i32−1−i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i32001+i3−1−i30000−1−i32−1−i321+i321+i320000-2-2-2-2221-21-2-211-21-1-122111-1-1-1-1002-20000-1-11100001−i31−i31−i31−i3−1+i3−1+i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i321−i321−i32−1+i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i321−i3200−1+i31−i300001−i321−i32−1+i32−1+i3200001+i31+i31+i31+i3−1−i3−1−i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i321+i321+i32−1−i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i321+i3200−1−i31+i300001+i321+i32−1−i32−1−i320000
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χ2171111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1111-1-1-1-11111-1-11+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ2181111-1-1111111111-1-1-1-1111-1-1-1-1-11-11-1-111-1-11111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-111111-11-111-1-111-1-1-1-1111+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ2192222222-12-1-122-1-122-1-1-1-1-1-1-1-1-12200-1-1-1-100000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3001+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3001−i321−i321−i321−i3200000000-2-2-2-2-2-2-21-211-2-211-2-2111111111-2-2001111000000001+i31+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i32−1−i321+i31+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i31+i300−1−i32−1−i32−1−i32−1−i32000000001−i31−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i32−1+i321−i31−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i31−i300−1+i32−1+i32−1+i32−1+i3200000000
χ2202222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-200111100000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i31+i300−1−i32−1−i32−1−i32−1−i3200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i31−i300−1+i32−1+i32−1+i32−1+i3200000000-2-2-2-2-2-2-21-211-2-211-2-21111111112200-1-1-1-1000000001+i31+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i32−1−i321+i31+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3−1−i3001+i321+i321+i321+i32000000001−i31−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i32−1+i321−i31−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3−1+i3001−i321−i321−i321−i3200000000
χ221222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100220000-1-1-1-10000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i320000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i320000-2-2-2-2-2-21-21-2-211-2111-2-2111111100-2-20000111100001+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32001+i31+i30000−1−i32−1−i32−1−i32−1−i3200001−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320000
χ222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100-2-2000011110000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32001+i31+i30000−1−i32−1−i32−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320000-2-2-2-2-2-21-21-2-211-2111-2-2111111100220000-1-1-1-100001+i31+i31+i31+i31+i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200−1−i3−1−i300001+i321+i321+i321+i3200001−i31−i31−i31−i31−i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200−1+i3−1+i300001−i321−i321−i321−i320000
χ2232222-2-22-12-1-122-1-1-2-211-1-1-111112-200-1-11100000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i31+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i31+i3001+i321+i32−1−i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i31−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i31−i3001−i321−i32−1+i32−1+i3200000000-2-2-2-222-21-211-2-21122-1-1111-1-1-1-1-220011-1-1000000001+i31+i31+i31+i3−1−i3−1−i31+i3−1−i321+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i3−1−i300−1−i32−1−i321+i321+i32000000001−i31−i31−i31−i3−1+i3−1+i31−i3−1+i321−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i3−1+i300−1+i32−1+i321−i321−i3200000000
χ2242222-2-22-12-1-122-1-1-2-211-1-1-11111-220011-1-100000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i31+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i3−1−i300−1−i32−1−i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i31−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i3−1+i300−1+i32−1+i321−i321−i3200000000-2-2-2-222-21-211-2-21122-1-1111-1-1-1-12-200-1-111000000001+i31+i31+i31+i3−1−i3−1−i31+i3−1−i321+i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i31+i3001+i321+i32−1−i32−1−i32000000001−i31−i31−i31−i3−1+i3−1+i31−i3−1+i321−i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i31−i3001−i321−i32−1+i32−1+i3200000000
χ2252222-2-2-12-122-1-12-111-2-2-1-1-11111002-20000-1-1110000−1−i3−1−i3−1−i3−1−i31+i31+i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i32−1−i32−1−i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i3200−1−i31+i300001+i321+i32−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i31−i31−i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i32−1+i32−1+i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i3200−1+i31−i300001−i321−i32−1+i32−1+i320000-2-2-2-2221-21-2-211-21-1-122111-1-1-1-100-22000011-1-100001+i31+i31+i31+i3−1−i3−1−i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i321+i321+i32−1−i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i321+i32001+i3−1−i30000−1−i32−1−i321+i321+i3200001−i31−i31−i31−i3−1+i3−1+i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i321−i321−i32−1+i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i321−i32001−i3−1+i30000−1+i32−1+i321−i321−i320000
χ2262222-2-2-12-122-1-12-111-2-2-1-1-1111100-22000011-1-10000−1−i3−1−i3−1−i3−1−i31+i31+i31+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i31+i32−1−i32−1−i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i32001+i3−1−i30000−1−i32−1−i321+i321+i320000−1+i3−1+i3−1+i3−1+i31−i31−i31−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i31−i32−1+i32−1+i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i32001−i3−1+i30000−1+i32−1+i321−i321−i320000-2-2-2-2221-21-2-211-21-1-122111-1-1-1-1002-20000-1-11100001+i31+i31+i31+i3−1−i3−1−i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i321+i3−1−i321+i321+i32−1−i3−1−i3−1−i32−1−i32−1−i321+i321+i321+i321+i3200−1−i31+i300001+i321+i32−1−i32−1−i3200001−i31−i31−i31−i3−1+i3−1+i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i321−i3−1+i321−i321−i32−1+i3−1+i3−1+i32−1+i32−1+i321−i321−i321−i321−i3200−1+i31−i300001−i321−i32−1+i32−1+i320000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.