Finite Group Databasebeta

← Group #13157138

Character table — Group #13157138

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122444444444488888888888899991818181818181818181836363636363611112244444444448888888888889999181818181818181818183636363636361111224444444444888888888888999918181818181818181818363636363636
order12224422336666666666666612121212444444888888884488883666121266336666666666666612121212121212121212242424242424242412122424242436661212663366666666666666121212121212121212122424242424242424121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ5111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ6111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13i−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13i−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13i−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13
χ1011-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13i−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13i−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13i−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13
χ1111-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23
χ1211-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23
χ1311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ii−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ii−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ii−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13
χ1411-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−iiζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−iiζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−iiζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13
χ1511-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23i−i−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23i−i−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23i−i−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23i−iζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23i−iζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-1-1111-1-1-1-111-1-1-1-1111111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23i−iζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23
χ172222-2-2002222222200000000-2-2-2-22222-2-2000000000000002222-2-2002222222200000000-2-2-2-22222-2-2000000000000002222-2-2002222222200000000-2-2-2-22222-2-200000000000000
χ182222-2-2002222222200000000-2-2-2-2-2-2-2-222000000000000002222-2-2002222222200000000-2-2-2-2-2-2-2-222000000000000002222-2-2002222222200000000-2-2-2-2-2-2-2-22200000000000000
χ1922-2-2-220022-2-2-2-22200000000-2-2222i−2i2i−2i−2i2i0000000000000022-2-2-220022-2-2-2-22200000000-2-2222i−2i2i−2i−2i2i0000000000000022-2-2-220022-2-2-2-22200000000-2-2222i−2i2i−2i−2i2i00000000000000
χ2022-2-2-220022-2-2-2-22200000000-2-222−2i2i−2i2i2i−2i0000000000000022-2-2-220022-2-2-2-22200000000-2-222−2i2i−2i2i2i−2i0000000000000022-2-2-220022-2-2-2-22200000000-2-222−2i2i−2i2i2i−2i00000000000000
χ212-22-200002222-2-2-2-20000000000002i−2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000002-22-200002222-2-2-2-20000000000002i−2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000002-22-200002222-2-2-2-20000000000002i−2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
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χ232-22-200002222-2-2-2-2000000000000−2i2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000002-22-200002222-2-2-2-2000000000000−2i2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000002-22-200002222-2-2-2-2000000000000−2i2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ242-22-200002222-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-22-200002222-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-22-200002222-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ252-2-22000022-2-222-2-200000000000022-2-200i2−i2−i2i2i2−i2−i2i20000002-2-22000022-2-222-2-200000000000022-2-200i2−i2−i2i2i2−i2−i2i20000002-2-22000022-2-222-2-200000000000022-2-200i2−i2−i2i2i2−i2−i2i2000000
χ262-2-22000022-2-222-2-200000000000022-2-200−i2i2i2−i2−i2i2i2−i20000002-2-22000022-2-222-2-200000000000022-2-200−i2i2i2−i2−i2i2i2−i20000002-2-22000022-2-222-2-200000000000022-2-200−i2i2i2−i2−i2i2i2−i2000000
χ272-2-22000022-2-222-2-2000000000000-2-222002−2−22−222−20000002-2-22000022-2-222-2-2000000000000-2-222002−2−22−222−20000002-2-22000022-2-222-2-2000000000000-2-222002−2−22−222−2000000
χ282-2-22000022-2-222-2-2000000000000-2-22200−222−22−2−220000002-2-22000022-2-222-2-2000000000000-2-22200−222−22−2−220000002-2-22000022-2-222-2-2000000000000-2-22200−222−22−2−22000000
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χ4044-4-44-4-44-212-12-1-2122-1-1-2-211-212-10000000000000000000044-4-44-4-44-212-12-1-2122-1-1-2-211-212-10000000000000000000044-4-44-4-44-212-12-1-2122-1-1-2-211-212-100000000000000000000
χ4144-4-4-44001-2-12-121-23-300-3300-121-20000000000000000000044-4-4-44001-2-12-121-23-300-3300-121-20000000000000000000044-4-4-44001-2-12-121-23-300-3300-121-200000000000000000000
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χ488-8-880000-424-2-424-2000000000000000000000000000000008-8-880000-424-2-424-2000000000000000000000000000000008-8-880000-424-2-424-200000000000000000000000000000000
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χ501111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ511111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i−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−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ141−i321−i32ζ14ζ14−ζ14−ζ14−1−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+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ221+i321+i32ζ22ζ22−ζ22−ζ22
χ521111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii−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−i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ141−i321−i32−ζ14−ζ14ζ14ζ14−1−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+i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ221+i321+i32−ζ22−ζ22ζ22ζ22
χ53111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1−1+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+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+i321−i321−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−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−i321+i321+i321+i321+i321+i321+i32
χ54111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111−1+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+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+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−i321+i321+i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ55111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14−1+i32−1+i32−ζ14−ζ14ζ14ζ14−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22−1−i32−1−i32−ζ22−ζ22ζ22ζ22
χ56111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14−1+i32−1+i32ζ14ζ14−ζ14−ζ14−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22−1−i32−1−i32ζ22ζ22−ζ22−ζ22
χ5711-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13i−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14−ζ14ζ14−ζ14ζ14−ζ14−ζ23−ζ23ζ23ζ23−ζ5−ζ5ζ5ζ5ζ14−ζ14−ζ23ζ23−ζ5ζ5−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22−ζ22ζ22−ζ22ζ22−ζ22−ζ7−ζ7ζ7ζ7−ζ13−ζ13ζ13ζ13ζ22−ζ22−ζ7ζ7−ζ13ζ13
χ5811-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1i−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13i−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14−ζ14ζ14−ζ14ζ14−ζ14ζ23ζ23−ζ23−ζ23ζ5ζ5−ζ5−ζ5ζ14−ζ14ζ23−ζ23ζ5−ζ5−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22−ζ22ζ22−ζ22ζ22−ζ22ζ7ζ7−ζ7−ζ7ζ13ζ13−ζ13−ζ13ζ22−ζ22ζ7−ζ7ζ13−ζ13
χ5911-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14ζ14−ζ14ζ14−ζ14ζ14−ζ5−ζ5ζ5ζ5−ζ23−ζ23ζ23ζ23−ζ14ζ14−ζ5ζ5−ζ23ζ23−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22ζ22−ζ22ζ22−ζ22ζ22−ζ13−ζ13ζ13ζ13−ζ7−ζ7ζ7ζ7−ζ22ζ22−ζ13ζ13−ζ7ζ7
χ6011-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14ζ14−ζ14ζ14−ζ14ζ14ζ5ζ5−ζ5−ζ5ζ23ζ23−ζ23−ζ23−ζ14ζ14ζ5−ζ5ζ23−ζ23−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22ζ22−ζ22ζ22−ζ22ζ22ζ13ζ13−ζ13−ζ13ζ7ζ7−ζ7−ζ7−ζ22ζ22ζ13−ζ13ζ7−ζ7
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χ981111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1−1−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32
χ991111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i−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+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ221+i321+i32ζ22ζ22−ζ22−ζ22−1+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−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ141−i321−i32ζ14ζ14−ζ14−ζ14
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χ101111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1−1−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−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−i321+i321+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+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+i321−i321−i321−i321−i321−i321−i32
χ102111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111−1−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−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−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+i321−i321−i32−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ103111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22−1−i32−1−i32−ζ22−ζ22ζ22ζ22−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14−1+i32−1+i32−ζ14−ζ14ζ14ζ14
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.