Finite Group Databasebeta

← Group #13164413

Character table — Group #13164413

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11222223333333333444666666666666666666666121212121212121212181818181818181818181818242424242424363636363636363636363636363636363636484848484848484848
order1234446223366666612121244466666612121212121212121212121212121212121212121244441212121212121212999181818222444666666121212121212363636363636363636
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ3111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−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+i321−1−i32−1+i321−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ5111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+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−i321−1+i32−1−i321−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ6111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ71111-1-1111111111111-1-11-1-111111111-1-1-1-111-1-1-1-11-1-11-1-11-1-11111111111111111111-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1-1
χ81111-1-1111111111111-1-11-1-111111111-1-1-1-111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-111-111-111-1111-1-11-1-11-1-1
χ91111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321-1-1−1−i321+i321+i32−1+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321-1-11-1-1−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ101111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i321-1-1−1−i321+i321+i32−1+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-111-1111+i32−1−i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ111111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321-1-1−1+i321−i321−i32−1−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321-1-11-1-1−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ121111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i321-1-1−1+i321−i321−i32−1−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-111-1111−i32−1+i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ13111-11-111111111111-11-1-11-1111111-1-111-1-1-1-111-1-1-11-1-11-1-11-1111111111111111111-11-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1
χ14111-11-111111111111-11-1-11-1111111-1-111-1-1-1-111-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-111-111-111-111-11-11-1-11-1-11-1
χ15111-11-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-11-111−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-11-11+i32−1−i321+i321−i32−1+i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-11-1-11-11+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ16111-11-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-11-111−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-11-11+i32−1−i321+i321−i32−1+i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321-111-11−1−i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ17111-11-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-11-111−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-11-11−i32−1+i321−i321+i32−1−i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-11-1-11-11−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ18111-11-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-11-111−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-11-11−i32−1+i321−i321+i32−1−i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321-111-11−1+i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ19111-1-1111111111111-1-11-1-11111111-1-1-1-111-1-1-1-111-1-11-1-11-1-11111111111111111111-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1-11-1-11
χ20111-1-1111111111111-1-11-1-11111111-1-1-1-111-1-1-1-111-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-111-111-111-1-1-11-1-11-1-11
χ21111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-1111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11-1-111+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ22111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-1111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i3211-111-1−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ23111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-1111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11-1-111−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ24111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-1111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i3211-111-1−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ2522222222222222222222222222222222222222222222222222000000000000-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-1-1
χ26222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322222222−1−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+i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3000000000000-11+i321−i32-11+i321−i32000000000000000000-1-1-11+i321+i321+i321−i321−i321−i32
χ27222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322222222−1+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−i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3000000000000-11−i321+i32-11−i321+i32000000000000000000-1-1-11−i321−i321−i321+i321+i321+i32
χ282222-2-2222222222222-2-22-2-222222222-2-2-2-222-2-2-2-22-2-22-2-22-2-2000000000000-1-1-1-1-1-1000000000000000000-111-111-111
χ292222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32-2-22-2-222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i31+i31+i31+i31+i3−1+i3−1+i31−i31−i31−i31−i32-2-2−1−i31+i31+i3−1+i31−i31−i3000000000000-11+i321−i32-11+i321−i32000000000000000000-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ302222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32-2-22-2-222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i31−i31−i31−i31−i3−1−i3−1−i31+i31+i31+i31+i32-2-2−1+i31−i31−i3−1−i31+i31+i3000000000000-11−i321+i32-11−i321+i32000000000000000000-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ31222-22-222222222222-22-2-22-2222222-2-222-2-2-2-222-2-2-22-2-22-2-22-2000000000000-1-1-1-1-1-10000000000000000001-111-111-11
χ32222-22-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-22-2-22-222−1−i3−1−i3−1+i3−1+i31+i31+i3−1−i3−1−i31+i31+i31−i31−i3−1+i3−1+i31−i31−i3-22-21+i3−1−i31+i31−i3−1+i31−i3000000000000-11+i321−i32-11+i321−i320000000000000000001-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ33222-22-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-22-2-22-222−1+i3−1+i3−1−i3−1−i31−i31−i3−1+i3−1+i31−i31−i31+i31+i3−1−i3−1−i31+i31+i3-22-21−i3−1+i31−i31+i3−1−i31+i3000000000000-11−i321+i32-11−i321+i320000000000000000001-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ34222-2-2222222222222-2-22-2-22222222-2-2-2-222-2-2-2-222-2-22-2-22-2-22000000000000-1-1-1-1-1-100000000000000000011-111-111-1
χ35222-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-22-2-2222−1−i3−1−i3−1+i3−1+i31+i31+i31+i31+i3−1−i3−1−i31−i31−i31−i31−i3−1+i3−1+i3-2-221+i31+i3−1−i31−i31−i3−1+i3000000000000-11+i321−i32-11+i321−i3200000000000000000011-1−1−i32−1−i321+i32−1+i32−1+i321−i32
χ36222-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-2-22-2-2222−1+i3−1+i3−1−i3−1−i31−i31−i31−i31−i3−1+i3−1+i31+i31+i31+i31+i3−1−i3−1−i3-2-221−i31−i3−1+i31+i31+i3−1−i3000000000000-11−i321+i32-11−i321+i3200000000000000000011-1−1+i32−1+i321−i32−1−i32−1−i321+i32
χ372-22000-2-2222-2-22-22-20000002-22-22-20000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i222-2-2-2000000000000000000000000000
χ382-22000-2-2222-2-22-22-20000002-22-22-2000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i222-2-2-2000000000000000000000000000
χ392-22000-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000002-2−1−i31+i3−1+i31−i30000000000000000000002i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72−1−i3−1+i3-21+i31−i3000000000000000000000000000
χ402-22000-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000002-2−1−i31+i3−1+i31−i3000000000000000000000−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ72−1−i3−1+i3-21+i31−i3000000000000000000000000000
χ412-22000-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000002-2−1+i31−i3−1−i31+i30000000000000000000002i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112−1+i3−1−i3-21−i31+i3000000000000000000000000000
χ422-22000-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000002-2−1+i31−i3−1−i31+i3000000000000000000000−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ112−1+i3−1−i3-21−i31+i3000000000000000000000000000
χ433333333-1-133-1-1-13-13333-1-1-1-1-1-1-1-1-13-13-13-13-13-13-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111000000111-1-1-1111111-1-1-1-1-1-1000000000
χ443333333-1-133-1-1-13-13333-1-1-1-1-1-1-1-1-13-13-13-13-13-13-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1000000-1-1-1111-1-1-1-1-1-1111111000000000
χ453333333-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i32333-1-1-1-1-11+i321+i321−i321−i32−3−3i321+i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3+3i321−i32-1-1-11+i321+i321+i321−i321−i321−i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32000000000
χ463333333-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i32333-1-1-1-1-11+i321+i321−i321−i32−3−3i321+i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3+3i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32000000-1-1-11111+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000
χ473333333-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32333-1-1-1-1-11−i321−i321+i321+i32−3+3i321−i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3−3i321+i32-1-1-11−i321−i321−i321+i321+i321+i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32000000000
χ483333333-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32333-1-1-1-1-11−i321−i321+i321+i32−3+3i321−i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3−3i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32000000-1-1-11111−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000
χ493333-3-33-1-133-1-1-13-133-3-3-111-1-1-1-1-1-13-1-31-313-1-31-31-111-111-11111-1-1-1-1-1-111110000001-1-1-1111-1-11-1-1-111-111000000000
χ503333-3-33-1-133-1-1-13-133-3-3-111-1-1-1-1-1-13-1-31-313-1-31-31-111-111-111-1-1111111-1-1-1-1000000-1111-1-1-111-1111-1-11-1-1000000000
χ513333-3-33-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i323-3-3-111-1-11+i321+i321−i321−i32−3−3i321+i323+3i32−1−i323+3i32−1−i32−3+3i321−i323−3i32−1+i323−3i32−1+i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i320000001-1-1-111−1−i321+i321+i32−1+i321−i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32000000000
χ523333-3-33-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i323-3-3-111-1-11+i321+i321−i321−i32−3−3i321+i323+3i32−1−i323+3i32−1−i32−3+3i321−i323−3i32−1+i323−3i32−1+i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32000000-1111-1-11+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i321+i321+i32−1+i321−i321−i32000000000
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χ543333-3-33-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i323-3-3-111-1-11−i321−i321+i321+i32−3+3i321−i323−3i32−1+i323−3i32−1+i32−3−3i321+i323+3i32−1−i323+3i32−1−i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32000000-1111-1-11−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i321−i321−i32−1−i321+i321+i32000000000
χ55333-33-33-1-133-1-1-13-13-33-31-11-1-1-1-1-1-1-313-1-31-313-1-311-111-111-1111-1-1-1-1-1-11111000000-11-11-11-11-1-11-11-111-11000000000
χ56333-33-33-1-133-1-1-13-13-33-31-11-1-1-1-1-1-1-313-1-31-313-1-311-111-111-11-1-1111111-1-1-1-10000001-11-11-11-111-11-11-1-11-1000000000
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χ58333-33-33-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i32-33-31-11-1-11+i321+i321−i321−i323+3i32−1−i32−3−3i321+i323+3i32−1−i323−3i32−1+i32−3+3i321−i323−3i32−1+i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i320000001-11-11-1−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32000000000
χ59333-33-33-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32-33-31-11-1-11−i321−i321+i321+i323−3i32−1+i32−3+3i321−i323−3i32−1+i323+3i32−1−i32−3−3i321+i323+3i32−1−i321-11−1+i321−i32−1+i32−1−i321+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000-11-11-111−i32−1+i321−i321+i32−1−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32000000000
χ60333-33-33-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32-33-31-11-1-11−i321−i321+i321+i323−3i32−1+i32−3+3i321−i323−3i32−1+i323+3i32−1−i32−3−3i321+i323+3i32−1−i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i320000001-11-11-1−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32000000000
χ61333-3-333-1-133-1-1-13-13-3-3311-1-1-1-1-1-1-1-31-313-1-31-313-111-111-111-111-1-1-1-1-1-11111000000-1-1111-1-1-11-1-1111-111-1000000000
χ62333-3-333-1-133-1-1-13-13-3-3311-1-1-1-1-1-1-1-31-313-1-31-313-111-111-111-1-1-1111111-1-1-1-100000011-1-1-1111-111-1-1-11-1-11000000000
χ63333-3-333-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i32-3-3311-1-1-11+i321+i321−i321−i323+3i32−1−i323+3i32−1−i32−3−3i321+i323−3i32−1+i323−3i32−1+i32−3+3i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000-1-1111-11+i321+i32−1−i321−i321−i32−1+i32−1−i32−1−i321+i32−1+i32−1+i321−i32000000000
χ64333-3-333-1-1−3−3i32−3+3i321+i321−i321+i32−3−3i321−i32−3+3i32-3-3311-1-1-11+i321+i321−i321−i323+3i32−1−i323+3i32−1−i32−3−3i321+i323−3i32−1+i323−3i32−1+i32−3+3i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3200000011-1-1-11−1−i32−1−i321+i32−1+i32−1+i321−i321+i321+i32−1−i321−i321−i32−1+i32000000000
χ65333-3-333-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32-3-3311-1-1-11−i321−i321+i321+i323−3i32−1+i323−3i32−1+i32−3+3i321−i323+3i32−1−i323+3i32−1−i32−3−3i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000-1-1111-11−i321−i32−1+i321+i321+i32−1−i32−1+i32−1+i321−i32−1−i32−1−i321+i32000000000
χ66333-3-333-1-1−3+3i32−3−3i321−i321+i321−i32−3+3i321+i32−3−3i32-3-3311-1-1-11−i321−i321+i321+i323−3i32−1+i323−3i32−1+i32−3+3i321−i323+3i32−1−i323+3i32−1−i32−3−3i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3200000011-1-1-11−1+i32−1+i321−i32−1−i32−1−i321+i321−i321−i32−1+i321+i321+i32−1−i32000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.