Finite Group Databasebeta

← Group #72276910

Character table — Group #72276910

Order 8064.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112333333666666666667777141418181818181818181818181818181818181818182121212121212121212121213232323242424242424242424242424242429696969696969696168168168168168168168168168168168168168168168168168168168168168168168168224224224224224224224224
order12222222222222227141414336666141414141414141414141414141414141414141466666666666636666666666666666621214242424242422444444466121212121212121212121212121233666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ311111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111111111−1+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
χ411111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111-1-1-1-1-1-1-1-11−i321+i321−i321+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
χ511111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111111111−1−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
χ611111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111-1-1-1-1-1-1-1-11+i321−i321+i321−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
χ711-111111111-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-11-1111-1-1-111-1-1111-1-1-1111-1-1-1111-1-11-1-1
χ811-111111111-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-11-1-1-1111-1-111-1-1-1111-1-1-1111111-1-11-1-1
χ911-111111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321+i321111-1-1-1-11-1111-1-1-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ1011-111111111-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321+i321111-1-1-1-1-11-1-1-11111−i321+i32−1+i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ1111-111111111-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−i321111-1-1-1-11-1111-1-1-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ1211-111111111-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321−i321111-1-1-1-1-11-1-1-11111+i321−i32−1−i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ132222222222222222222222222222222222222222222222222222222222-1-1-1-122222222222222-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1
χ1422222222222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322222222222222222222−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-1-1-1-1−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-1-1-1-1-1-1-1-10000000000000000000000001−i321+i321−i321−i321−i321+i321+i321+i32
χ1522222222222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322222222222222222222−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-1-1-1-1−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-1-1-1-1-1-1-1-10000000000000000000000001+i321−i321+i321+i321+i321−i321−i321−i32
χ1622-222222222-2-2-2-2-222-2-22222-2-22222222222-2-2-2-2-2-2-2-2-2-2222222222222-1-11122-2-2-2-2-222-2-2-2-2-2-1-1-1-11111000000000000000000000000-1-1-111-111
χ1722-222222222-2-2-2-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i32222222222-2-2-2-2-2-2-2-2-2-2−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-1-111−1+i3−1+i31−i31−i31−i31−i31−i3−1−i3−1−i31+i31+i31+i31+i31+i3-1-1-1-111110000000000000000000000001−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1822-222222222-2-2-2-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i32222222222-2-2-2-2-2-2-2-2-2-2−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-1-111−1−i3−1−i31+i31+i31+i31+i31+i3−1+i3−1+i31−i31−i31−i31−i31−i3-1-1-1-111110000000000000000000000001+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ192-20222-2-2-22-2000002-20022-2-20022222-2-2-2-2-20000000000222-2-2-2222-2-2-22-2002-2000002-20000022-2-2000000000000000000000000000022-200-200
χ202-20222-2-2-22-2000002-20022-2-20022222-2-2-2-2-20000000000222-2-2-2222-2-2-2-11i3−i32-2000002-200000-1-111i3i3−i3−i3000000000000000000000000-1-11i3−i31i3−i3
χ212-20222-2-2-22-2000002-20022-2-20022222-2-2-2-2-20000000000222-2-2-2222-2-2-2-11−i3i32-2000002-200000-1-111−i3−i3i3i3000000000000000000000000-1-11−i3i31−i3i3
χ222-20222-2-2-22-2000002-200−1+i3−1−i31−i31+i30022222-2-2-2-2-20000000000−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i32-200−1+i31−i300000−1−i31+i30000022-2-20000000000000000000000000000−1+i3−1−i31−i3001+i300
χ232-20222-2-2-22-2000002-200−1+i3−1−i31−i31+i30022222-2-2-2-2-20000000000−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i3-11i3−i3−1+i31−i300000−1−i31+i300000-1-111i3i3−i3−i30000000000000000000000001−i321+i32−1+i32−3−i323+i32−1−i323−i32−3+i32
χ242-20222-2-2-22-2000002-200−1+i3−1−i31−i31+i30022222-2-2-2-2-20000000000−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i3-11−i3i3−1+i31−i300000−1−i31+i300000-1-111−i3−i3i3i30000000000000000000000001−i321+i32−1+i323+i32−3−i32−1−i32−3+i323−i32
χ252-20222-2-2-22-2000002-200−1−i3−1+i31+i31−i30022222-2-2-2-2-20000000000−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i32-200−1−i31+i300000−1+i31−i30000022-2-20000000000000000000000000000−1−i3−1+i31+i3001−i300
χ262-20222-2-2-22-2000002-200−1−i3−1+i31+i31−i30022222-2-2-2-2-20000000000−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i3-11i3−i3−1−i31+i300000−1+i31−i300000-1-111i3i3−i3−i30000000000000000000000001+i321−i32−1−i323−i32−3+i32−1+i32−3−i323+i32
χ272-20222-2-2-22-2000002-200−1−i3−1+i31+i31−i30022222-2-2-2-2-20000000000−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i3-11−i3i3−1−i31+i300000−1+i31−i300000-1-111−i3−i3i3i30000000000000000000000001+i321−i32−1−i32−3+i323−i32−1+i323+i32−3−i32
χ283333-1-13-1-1-1-13-1-1-1-133333333333-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-13-1-13-1-13-1-13-1-10000-1-13-1-1-1-1-1-13-1-1-1-100000000111-1-11-1-111111-1-11-1-11-1-11-1-100000000
χ293333-1-13-1-1-1-13-1-1-1-133333333333-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-13-1-13-1-13-1-13-1-10000-1-13-1-1-1-1-1-13-1-1-1-100000000-1-1-111-111-1-1-1-1-111-111-111-11100000000
χ303333-1-13-1-1-1-13-1-1-1-13333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1−3+3i321−i321−i32−3+3i321−i321−i32−3−3i321+i321+i32−3−3i321+i321+i3200001−i321−i32−3+3i321−i321−i321−i321−i321+i321+i32−3−3i321+i321+i321+i321+i3200000000111-1-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1−i321+i321+i32−1−i321+i321+i3200000000
χ313333-1-13-1-1-1-13-1-1-1-13333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1−3+3i321−i321−i32−3+3i321−i321−i32−3−3i321+i321+i32−3−3i321+i321+i3200001−i321−i32−3+3i321−i321−i321−i321−i321+i321+i32−3−3i321+i321+i321+i321+i3200000000-1-1-111-1111−i321+i321−i321+i321−i32−1+i32−1+i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i32−1−i32−1−i3200000000
χ323333-1-13-1-1-1-13-1-1-1-13333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1−3−3i321+i321+i32−3−3i321+i321+i32−3+3i321−i321−i32−3+3i321−i321−i3200001+i321+i32−3−3i321+i321+i321+i321+i321−i321−i32−3+3i321−i321−i321−i321−i3200000000111-1-11-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1+i321−i321−i32−1+i321−i321−i3200000000
χ333333-1-13-1-1-1-13-1-1-1-13333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1−3−3i321+i321+i32−3−3i321+i321+i32−3+3i321−i321−i32−3+3i321−i321−i3200001+i321+i32−3−3i321+i321+i321+i321+i321−i321−i32−3+3i321−i321−i321−i321−i3200000000-1-1-111-1111+i321−i321+i321−i321+i32−1−i32−1−i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i32−1+i32−1+i3200000000
χ34333-13-1-13-1-1-1-13-1-1-13333333333-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-1-13-1-13-1-13-1-13-10000-1-1-13-1-1-1-1-1-13-1-1-10000000011-11-1-11-11111-11-1-11-1-11-1-11-100000000
χ35333-13-1-13-1-1-1-13-1-1-13333333333-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-1-13-1-13-1-13-1-13-10000-1-1-13-1-1-1-1-1-13-1-1-100000000-1-11-111-11-1-1-1-11-111-111-111-1100000000
χ36333-13-1-13-1-1-1-13-1-1-13333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-11−i32−3+3i321−i321−i32−3+3i321−i321+i32−3−3i321+i321+i32−3−3i321+i3200001−i321−i321−i32−3+3i321−i321−i321−i321+i321+i321+i32−3−3i321+i321+i321+i320000000011-11-1-11-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i321+i321+i32−1−i321+i3200000000
χ37333-13-1-13-1-1-1-13-1-1-13333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-11−i32−3+3i321−i321−i32−3+3i321−i321+i32−3−3i321+i321+i32−3−3i321+i3200001−i321−i321−i32−3+3i321−i321−i321−i321+i321+i321+i32−3−3i321+i321+i321+i3200000000-1-11-111-111−i321+i321−i321+i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1−i321+i32−1−i3200000000
χ38333-13-1-13-1-1-1-13-1-1-13333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-11+i32−3−3i321+i321+i32−3−3i321+i321−i32−3+3i321−i321−i32−3+3i321−i3200001+i321+i321+i32−3−3i321+i321+i321+i321−i321−i321−i32−3+3i321−i321−i321−i320000000011-11-1-11-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i321−i321−i32−1+i321−i3200000000
χ39333-13-1-13-1-1-1-13-1-1-13333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-13-1-1-1-13-1-1-1-1-133-1-1-1-1-1-11+i32−3−3i321+i321+i32−3−3i321+i321−i32−3+3i321−i321−i32−3+3i321−i3200001+i321+i321+i32−3−3i321+i321+i321+i321−i321−i321−i32−3+3i321−i321−i321−i3200000000-1-11-111-111+i321−i321+i321−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1+i321−i32−1+i3200000000
χ40333-1-13-1-13-1-1-1-13-1-13333333333-1-13-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-13-1-13-1-13-1-130000-1-1-1-13-1-1-1-1-1-13-1-10000000011-1-11-1-111111-1-11-1-11-1-11-1-1100000000
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χ956-60-2-2-22222-2000-446-600−3+3i3−3−3i33−3i33+3i300-2-2-222222-2-2000000-44-441−i31−i31−i3−1+i3−1+i3−1+i31+i31+i31+i3−1−i3−1−i3−1−i30000−1+i31−i30002−2i3−2+2i3−1−i31+i30002+2i3−2−2i30000000000000000000000000000000000000000
χ966-60-2-2-22222-2000-446-600−3−3i3−3+3i33+3i33−3i300-2-2-222222-2-2000000-44-441+i31+i31+i3−1−i3−1−i3−1−i31−i31−i31−i3−1+i3−1+i3−1+i30000−1−i31+i30002+2i3−2−2i3−1+i31−i30002−2i3−2+2i30000000000000000000000000000000000000000
χ9718181818-6-618-6-6-6-618-6-6-6-6-3-3-3-3000000-31111-31111-3-3111111110000000000000000000000000000000000000000000000000000000000000000000000
χ98181818-618-6-618-6-6-6-618-6-6-6-3-3-3-30000001-31111-311111-3-31111110000000000000000000000000000000000000000000000000000000000000000000000
χ99181818-6-618-6-618-6-6-6-618-6-6-3-3-3-300000011-31111-3111111-3-311110000000000000000000000000000000000000000000000000000000000000000000000
χ100181818-6-6-6-6-6-666-6-6-666-3-3-3-3000000111−1−2i7−1+2i7111−1−2i7−1+2i7111111−1−2i7−1+2i7−1+2i7−1−2i70000000000000000000000000000000000000000000000000000000000000000000000
χ101181818-6-6-6-6-6-666-6-6-666-3-3-3-3000000111−1+2i7−1−2i7111−1+2i7−1−2i7111111−1+2i7−1−2i7−1−2i7−1+2i70000000000000000000000000000000000000000000000000000000000000000000000
χ1021818-1818-6-618-6-6-6-6-186666-3-333000000-31111-3111133-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000000000000
χ1031818-18-618-6-618-6-6-66-18666-3-3330000001-31111-3111-1-133-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000000000000
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χ1051818-18-6-6-6-6-6-666666-6-6-3-333000000111−1−2i7−1+2i7111−1−2i7−1+2i7-1-1-1-1-1-11+2i71−2i71−2i71+2i70000000000000000000000000000000000000000000000000000000000000000000000
χ1061818-18-6-6-6-6-6-666666-6-6-3-333000000111−1+2i7−1−2i7111−1+2i7−1−2i7-1-1-1-1-1-11−2i71+2i71+2i71−2i70000000000000000000000000000000000000000000000000000000000000000000000
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χ10818-18018-6-6-1866-6600000-333i7−3i7000000-311113-1-1-1-13i7−3i7−i7i7−i7i7−i7−i7i7i70000000000000000000000000000000000000000000000000000000000000000000000
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χ11018-180-618-66-186-6600000-333i7−3i70000001-3111-13-1-1-1−i7i73i7−3i7−i7i7−i7−i7i7i70000000000000000000000000000000000000000000000000000000000000000000000
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χ11318-180-6-6-66666-600012-12-33−3i73i7000000111−1−2i7−1+2i7-1-1-11+2i71−2i7i7−i7i7−i7i7−i7−2−i72−i7−2+i72+i70000000000000000000000000000000000000000000000000000000000000000000000
χ11418-180-6-6-66666-600012-12-333i7−3i7000000111−1+2i7−1−2i7-1-1-11−2i71+2i7−i7i7−i7i7−i7i7−2+i72+i7−2−i72−i70000000000000000000000000000000000000000000000000000000000000000000000
χ11518-180-6-6-66666-6000-1212-33−3i73i7000000111−1+2i7−1−2i7-1-1-11−2i71+2i7i7−i7i7−i7i7−i72−i7−2−i72+i7−2+i70000000000000000000000000000000000000000000000000000000000000000000000
χ11618-180-6-6-66666-6000-1212-333i7−3i7000000111−1−2i7−1+2i7-1-1-11+2i71−2i7−i7i7−i7i7−i7i72+i7−2+i72−i7−2−i70000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 21 (ζ21 = 1); i = ζ5.