Finite Group Databasebeta

← Group #13174729

Character table — Group #13174729

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ711111-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1-11-111-11-1-1-11111-1-1-1-111-111-11-1−1+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+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+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−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
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χ731111-1-111111111-111-1-1-1-1111-1-1-1-1-1-1111111-11-11-1-1-1-111-1-11111-1-111-1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+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−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ741111-1-111111111-111-1-1-1-1111-1-1-1-1-1-111111-1-111-1-11-1-11111-1-1-1-1111-1-11-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−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−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32
χ751111-1-111111111-111-1-1-1-1111-1-1-1-1-1-11111-111-1-111-111-1-1-1-111-1-111-111-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−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−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32
χ761111-1-111111111-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11111-1-111-1-111-1-1-1-1111-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+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−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32
χ772222222-12-12-12-12-1222-1-1-1-1-12-1-1-1-1-12-1-1-1020022020000-1-1-1-100000-10-100−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i320−1+i300−1+i3−1+i30−1+i300001−i321−i321−i321−i32000001−i3201−i3200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i320−1−i300−1−i3−1−i30−1−i300001+i321+i321+i321+i32000001+i3201+i3200
χ782222222-12-12-12-12-1222-1-1-1-1-12-1-1-1-1-12-1-1-10-200-2-20-2000011110000010100−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i3201−i3001−i31−i301−i30000−1+i32−1+i32−1+i32−1+i3200000−1+i320−1+i3200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i3201+i3001+i31+i301+i30000−1−i32−1−i32−1−i32−1−i3200000−1−i320−1−i3200
χ792222222-12-12-12-1-2-1-222-1-1-1-1-1-21-1-111-21110200-2-2020000111100000-10-100−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i321−i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i321−i32−1+i32−1+i321−i3−1+i32−1+i32−1+i320−1+i3001−i31−i30−1+i30000−1+i32−1+i32−1+i32−1+i32000001−i3201−i3200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i321+i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i321+i32−1−i32−1−i321+i3−1−i32−1−i32−1−i320−1−i3001+i31+i30−1−i30000−1−i32−1−i32−1−i32−1−i32000001+i3201+i3200
χ802222222-12-12-12-1-2-1-222-1-1-1-1-1-21-1-111-21110-200220-20000-1-1-1-10000010100−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i321−i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i321−i32−1+i32−1+i321−i3−1+i32−1+i32−1+i3201−i300−1+i3−1+i301−i300001−i321−i321−i321−i3200000−1+i320−1+i3200−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i321+i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i321+i32−1−i32−1−i321+i3−1−i32−1−i32−1−i3201+i300−1−i3−1−i301+i300001+i321+i321+i321+i3200000−1−i320−1−i3200
χ81222222-12-12-12-122-12-1-122-1-1-1-12-1-1-1-1-12-1-120220020-1-1-1-100000000-10-1000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i30−1+i3−1+i300−1+i301−i321−i321−i321−i32000000001−i3201−i32000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i30−1−i3−1−i300−1−i301+i321+i321+i321+i32000000001+i3201+i32000
χ82222222-12-12-12-122-12-1-122-1-1-1-12-1-1-1-1-12-1-1-20-2-200-20111100000000101000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i301−i31−i3001−i30−1+i32−1+i32−1+i32−1+i3200000000−1+i320−1+i32000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i301+i31+i3001+i30−1−i32−1−i32−1−i32−1−i3200000000−1−i320−1−i32000
χ83222222-12-12-12-12-2-1-2-1-122-1-1-11-2-1-1111-21120-2-20020111100000000-10-1000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i31−i321−i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i321−i31−i321−i32−1+i32−1+i32−1+i321−i3−1+i32−1+i32−1+i301−i31−i300−1+i30−1+i32−1+i32−1+i32−1+i32000000001−i3201−i32000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i31+i321+i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i321+i31+i321+i32−1−i32−1−i32−1−i321+i3−1−i32−1−i32−1−i301+i31+i300−1−i30−1−i32−1−i32−1−i32−1−i32000000001+i3201+i32000
χ84222222-12-12-12-12-2-1-2-1-122-1-1-11-2-1-1111-211-202200-20-1-1-1-100000000101000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i31−i321−i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i321−i31−i321−i32−1+i32−1+i32−1+i321−i3−1+i32−1+i321−i30−1+i3−1+i3001−i301−i321−i321−i321−i3200000000−1+i320−1+i32000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i31+i321+i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i321+i31+i321+i32−1−i32−1−i32−1−i321+i3−1−i32−1−i321+i30−1−i3−1−i3001+i301+i321+i321+i321+i3200000000−1−i320−1−i32000
χ852222-2-22-12-12-12-12-1-2-2-211-1-1-12-111-1-1-211102002-20-20000-1-11100000-10100−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i321−i32−1+i31−i32−1+i32−1+i321−i321−i321−i3−1+i32−1+i32−1+i320−1+i300−1+i31−i301−i300001−i321−i32−1+i32−1+i32000001−i320−1+i3200−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i321+i32−1−i31+i32−1−i32−1−i321+i321+i321+i3−1−i32−1−i32−1−i320−1−i300−1−i31+i301+i300001+i321+i32−1−i32−1−i32000001+i320−1−i3200
χ862222-2-22-12-12-12-12-1-2-2-211-1-1-12-111-1-1-21110-200-2202000011-1-10000010-100−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i321−i32−1+i31−i32−1+i32−1+i321−i321−i321−i3−1+i32−1+i32−1+i3201−i3001−i3−1+i30−1+i30000−1+i32−1+i321−i321−i3200000−1+i3201−i3200−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i321+i32−1−i31+i32−1−i32−1−i321+i321+i321+i3−1−i32−1−i32−1−i3201+i3001+i3−1−i30−1−i30000−1−i32−1−i321+i321+i3200000−1−i3201+i3200
χ872222-2-22-12-12-12-1-2-12-2-211-1-1-1-2111112-1-1-10200-220-2000011-1-100000-10100−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i32−1+i31−i31−i3−1+i32−1+i321−i321−i321−i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i321−i321−i320−1+i3001−i3−1+i301−i30000−1+i32−1+i321−i321−i32000001−i320−1+i3200−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i32−1−i31+i31+i3−1−i32−1−i321+i321+i321+i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i321+i321+i320−1−i3001+i3−1−i301+i30000−1−i32−1−i321+i321+i32000001+i320−1−i3200
χ882222-2-22-12-12-12-1-2-12-2-211-1-1-1-2111112-1-1-10-2002-2020000-1-1110000010-100−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i32−1+i31−i31−i3−1+i32−1+i321−i321−i321−i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i321−i321−i3201−i300−1+i31−i30−1+i300001−i321−i32−1+i32−1+i3200000−1+i3201−i3200−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i32−1−i31+i31+i3−1−i32−1−i321+i321+i321+i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i321+i321+i3201+i300−1−i31+i30−1−i300001+i321+i32−1−i32−1−i3200000−1−i3201+i3200
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χ1291111-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1111-11-1-1-111-1-111-1-111-1-111-1-1-11−1−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−i32−1−i321+i321+i321+i321+i321+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−i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−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+i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
χ1301111-1-11111111111-1-1-1-1-111111-1-111-1-1-1-11-11-1-11-1111-1-1-1-111-1-1111-1-111-1−1−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−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−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+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32
χ1311111-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1-11-111-11-1-1-11111-1-1-1-111-111-11-1−1−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−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−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+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ1321111-1-11111111111-1-1-1-1-111111-1-111-1-1-1-1-1-1-11-1111-1-111-1-11111-1-1-1-111-11−1−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−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+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+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ1331111-1-111111111-111-1-1-1-1111-1-1-1-1-1-1111111-11-11-1-1-1-111-1-11111-1-111-1-11-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−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+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ1341111-1-111111111-111-1-1-1-1111-1-1-1-1-1-111111-1-111-1-11-1-11111-1-1-1-1111-1-11-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+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+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32
χ1351111-1-111111111-111-1-1-1-1111-1-1-1-1-1-11111-111-1-111-111-1-1-1-111-1-111-111-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+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+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32
χ1361111-1-111111111-111-1-1-1-1111-1-1-1-1-1-11111-1-11-11-11111-1-111-1-111-1-1-1-1111-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−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+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32
χ1372222222-12-12-12-12-1222-1-1-1-1-12-1-1-1-1-12-1-1-1020022020000-1-1-1-100000-10-100−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i320−1−i300−1−i3−1−i30−1−i300001+i321+i321+i321+i32000001+i3201+i3200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i320−1+i300−1+i3−1+i30−1+i300001−i321−i321−i321−i32000001−i3201−i3200
χ1382222222-12-12-12-12-1222-1-1-1-1-12-1-1-1-1-12-1-1-10-200-2-20-2000011110000010100−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i3201+i3001+i31+i301+i30000−1−i32−1−i32−1−i32−1−i3200000−1−i320−1−i3200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i3201−i3001−i31−i301−i30000−1+i32−1+i32−1+i32−1+i3200000−1+i320−1+i3200
χ1392222222-12-12-12-1-2-1-222-1-1-1-1-1-21-1-111-21110200-2-2020000111100000-10-100−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i321+i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i321+i32−1−i32−1−i321+i3−1−i32−1−i32−1−i320−1−i3001+i31+i30−1−i30000−1−i32−1−i32−1−i32−1−i32000001+i3201+i3200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i321−i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i321−i32−1+i32−1+i321−i3−1+i32−1+i32−1+i320−1+i3001−i31−i30−1+i30000−1+i32−1+i32−1+i32−1+i32000001−i3201−i3200
χ1402222222-12-12-12-1-2-1-222-1-1-1-1-1-21-1-111-21110-200220-20000-1-1-1-10000010100−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i321+i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i321+i32−1−i32−1−i321+i3−1−i32−1−i32−1−i3201+i300−1−i3−1−i301+i300001+i321+i321+i321+i3200000−1−i320−1−i3200−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i321−i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i321−i32−1+i32−1+i321−i3−1+i32−1+i32−1+i3201−i300−1+i3−1+i301−i300001−i321−i321−i321−i3200000−1+i320−1+i3200
χ141222222-12-12-12-122-12-1-122-1-1-1-12-1-1-1-1-12-1-120220020-1-1-1-100000000-10-1000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i30−1−i3−1−i300−1−i301+i321+i321+i321+i32000000001+i3201+i32000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i30−1+i3−1+i300−1+i301−i321−i321−i321−i32000000001−i3201−i32000
χ142222222-12-12-12-122-12-1-122-1-1-1-12-1-1-1-1-12-1-1-20-2-200-20111100000000101000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i321+i301+i31+i3001+i30−1−i32−1−i32−1−i32−1−i3200000000−1−i320−1−i32000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i321−i301−i31−i3001−i30−1+i32−1+i32−1+i32−1+i3200000000−1+i320−1+i32000
χ143222222-12-12-12-12-2-1-2-1-122-1-1-11-2-1-1111-21120-2-20020111100000000-10-1000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i31+i321+i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i321+i31+i321+i32−1−i32−1−i32−1−i321+i3−1−i32−1−i32−1−i301+i31+i300−1−i30−1−i32−1−i32−1−i32−1−i32000000001+i3201+i32000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i31−i321−i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i321−i31−i321−i32−1+i32−1+i32−1+i321−i3−1+i32−1+i32−1+i301−i31−i300−1+i30−1+i32−1+i32−1+i32−1+i32000000001−i3201−i32000
χ144222222-12-12-12-12-2-1-2-1-122-1-1-11-2-1-1111-211-202200-20-1-1-1-100000000101000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i31+i321+i31+i321+i32−1−i3−1−i31+i321+i321+i32−1−i321+i31+i321+i32−1−i32−1−i32−1−i321+i3−1−i32−1−i321+i30−1−i3−1−i3001+i301+i321+i321+i321+i3200000000−1−i320−1−i32000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i31−i321−i31−i321−i32−1+i3−1+i31−i321−i321−i32−1+i321−i31−i321−i32−1+i32−1+i32−1+i321−i3−1+i32−1+i321−i30−1+i3−1+i3001−i301−i321−i321−i321−i3200000000−1+i320−1+i32000
χ1452222-2-22-12-12-12-12-1-2-2-211-1-1-12-111-1-1-211102002-20-20000-1-11100000-10100−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i321+i32−1−i31+i32−1−i32−1−i321+i321+i321+i3−1−i32−1−i32−1−i320−1−i300−1−i31+i301+i300001+i321+i32−1−i32−1−i32000001+i320−1−i3200−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i321−i32−1+i31−i32−1+i32−1+i321−i321−i321−i3−1+i32−1+i32−1+i320−1+i300−1+i31−i301−i300001−i321−i32−1+i32−1+i32000001−i320−1+i3200
χ1462222-2-22-12-12-12-12-1-2-2-211-1-1-12-111-1-1-21110-200-2202000011-1-10000010-100−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i321+i32−1−i31+i32−1−i32−1−i321+i321+i321+i3−1−i32−1−i32−1−i3201+i3001+i3−1−i30−1−i30000−1−i32−1−i321+i321+i3200000−1−i3201+i3200−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i321−i32−1+i31−i32−1+i32−1+i321−i321−i321−i3−1+i32−1+i32−1+i3201−i3001−i3−1+i30−1+i30000−1+i32−1+i321−i321−i3200000−1+i3201−i3200
χ1472222-2-22-12-12-12-1-2-12-2-211-1-1-1-2111112-1-1-10200-220-2000011-1-100000-10100−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i31+i32−1−i31+i31+i3−1−i32−1−i321+i321+i321+i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i321+i321+i320−1−i3001+i3−1−i301+i30000−1−i32−1−i321+i321+i32000001+i320−1−i3200−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i31−i32−1+i31−i31−i3−1+i32−1+i321−i321−i321−i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i321−i321−i320−1+i3001−i3−1+i301−i30000−1+i32−1+i321−i321−i32000001−i320−1+i3200
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.