Finite Group Databasebeta

← Group #13157132

Character table — Group #13157132

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216
size111111112222444444444444444444444444444444449999999918181818181818181818181818181818181818181111111122224444444444444444444444444444444499999999181818181818181818181818181818181818181811111111222244444444444444444444444444444444999999991818181818181818181818181818181818181818
order1222222244443366666666666666121212121212121212121212121212124444444444448888888888888888366666661212121233666666666666661212121212121212121212121212121212121212121212121212121224242424242424242424242424242424366666661212121233666666666666661212121212121212121212121212121212121212121212121212121224242424242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ10111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ11111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ12111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ13111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ14111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ15111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ16111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1711-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i1-11-1i−ii−i1-11-1i−ii−i11-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i1-11-1i−ii−i1-11-1i−ii−i11-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i1-11-1i−ii−i1-11-1i−ii−i
χ1811-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i-11-11−ii−ii-11-11−ii−ii11-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i-11-11−ii−ii-11-11−ii−ii11-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i-11-11−ii−ii-11-11−ii−ii
χ1911-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−iii−ii−i-11-11−ii−ii1-11-111-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−iii−ii−i-11-11−ii−ii1-11-111-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−iii−ii−i-11-11−ii−ii1-11-1
χ2011-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii1-11-1i−ii−i-11-1111-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii1-11-1i−ii−i-11-1111-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii1-11-1i−ii−i-11-11
χ2111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii1-11-1−ii−ii1-11-1−ii−ii11-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii1-11-1−ii−ii1-11-1−ii−ii11-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii1-11-1−ii−ii1-11-1−ii−ii
χ2211-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii-11-11i−ii−i-11-11i−ii−i11-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii-11-11i−ii−i-11-11i−ii−i11-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii-11-11i−ii−i-11-11i−ii−i
χ2311-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i1-11-1−ii−ii-11-1111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i1-11-1−ii−ii-11-1111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i1-11-1−ii−ii-11-11
χ2411-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i−ii−ii-11-11i−ii−i1-11-111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i−ii−ii-11-11i−ii−i1-11-111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i−ii−ii-11-11i−ii−i1-11-1
χ2511-1-11-1-11i−i−ii1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-1-11-1-11i−i−ii1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-1-11-1-11i−i−ii1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
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χ15111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−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−i32−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14
χ15211111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−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−i32−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14
χ153111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+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+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ13−ζ13ζ13ζ13−ζ13−ζ13ζ13ζ13−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−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−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−ζ23−ζ23ζ23ζ23−ζ23−ζ23ζ23ζ23−ζ5−ζ5ζ5ζ5−ζ5−ζ5ζ5ζ5
χ154111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+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+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ13ζ13−ζ13−ζ13ζ13ζ13−ζ13−ζ13−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−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−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ23ζ23−ζ23−ζ23ζ23ζ23−ζ23−ζ23ζ5ζ5−ζ5−ζ5ζ5ζ5−ζ5−ζ5
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.