Finite Group Databasebeta

← Group #13147380

Character table — Group #13147380

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152
size1111111111112222229999999999991212121212121212121212121212121218181818181818181818181818181818181818181818181818181818181811111111111122222299999999999912121212121212121212121212121212181818181818181818181818181818181818181818181818181818181818
order1222336666664412121212444412121212121212123366666612121212121212124488888888121212122424242424242424242424242424242422226666666644121212124444121212121212121266666666121212121212121244888888881212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-111-1-111-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i1-1i−i1-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-11-111-1-111-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i1-1i−i1-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-11-111-1-111-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i-11−ii-11−iiii−i−i-1-111−i−iii-1-111−i−iii1-11-111-1-111-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−ii−i-11−ii-11−iiii−i−i-1-111−i−iii-1-111−i−iii
χ111-11-111-1-111-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−iii−i-11−ii1-1−i−iiiii−i−i-1-111−i−iii11-1-11-11-111-1-111-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−iii−i-11−ii1-1−i−iiiii−i−i-1-111−i−iii11-1-1
χ121-11-111-1-111-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−ii−ii1-1i−i-11−i−iii−i−iii11-1-1ii−i−i-1-1111-11-111-1-111-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−ii−ii1-1i−i-11−i−iii−i−iii11-1-1ii−i−i-1-111
χ131-11-111-1-111-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii1-1−ii1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-11-111-1-111-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii1-1−ii1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-11-111-1-111-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii-11i−i-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i1-11-111-1-111-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−ii-11i−i-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-11-111-1-111-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−ii−i1-1−ii-11ii−i−iii−i−i11-1-1−i−iii-1-1111-11-111-1-111-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−ii−i1-1−ii-11ii−i−iii−i−i11-1-1−i−iii-1-111
χ161-11-111-1-111-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−i−ii-11i−i1-1ii−i−i−i−iii-1-111ii−i−i11-1-11-11-111-1-111-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−i−ii-11i−i1-1ii−i−i−i−iii-1-111ii−i−i11-1-1
χ1722-2-22222-2-2-2-20000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i22-2-2-2-2220000000000000000000000000000000000000022-2-22222-2-2-2-20000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i22-2-2-2-22200000000000000000000000000000000000000
χ1822-2-22222-2-2-2-2000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i22-2-2-2-2220000000000000000000000000000000000000022-2-22222-2-2-2-2000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i22-2-2-2-22200000000000000000000000000000000000000
χ192-2-2222-2-2-2-2220000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i22-2-222-2-2000000000000000000000000000000000000002-2-2222-2-2-2-2220000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i22-2-222-2-200000000000000000000000000000000000000
χ202-2-2222-2-2-2-222000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i22-2-222-2-2000000000000000000000000000000000000002-2-2222-2-2-2-222000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i22-2-222-2-200000000000000000000000000000000000000
χ213333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011iiii−i−i−i−i−1−i32−1+i32−1−i32−1+i32ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ113333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011iiii−i−i−i−i−1−i32−1+i32−1−i32−1+i32ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11
χ223333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011−i−i−i−iiiii−1−i32−1+i32−1−i32−1+i32−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ113333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011−i−i−i−iiiii−1−i32−1+i32−1−i32−1+i32−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11
χ233333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1111111111+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−i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1111111111+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
χ243333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ253333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1ii−i−i−i−iii1+i321−i321+i321−i32ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ113333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1ii−i−i−i−iii1+i321−i321+i321−i32ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ263333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1−i−iiiii−i−i1+i321−i321+i321−i32−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ113333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1−i−iiiii−i−i1+i321−i321+i321−i32−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ273333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001111-1-111-1-1−1−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−i321−i321+i321−i321+i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001111-1-111-1-1−1−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−i321−i321+i321−i321+i32
χ283333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000011-1-111-1-111−1−i32−1+i32−1−i32−1+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000011-1-111-1-111−1−i32−1+i32−1−i32−1+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ293333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011iiii−i−i−i−i−1+i32−1−i32−1+i32−1−i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ73333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011iiii−i−i−i−i−1+i32−1−i32−1+i32−1−i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7
χ303333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ73333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7
χ313333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1111111111−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+i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1111111111−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
χ323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
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χ1033333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001111-1-111-1-1−1−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−i321−i321+i321−i321+i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1-1-111-1-1111+i321−i321+i321−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ1043333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000011-1-111-1-111−1−i32−1+i32−1−i32−1+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-111-1-111-1-11+i321−i321+i321−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ1053333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011iiii−i−i−i−i−1+i32−1−i32−1+i32−1−i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1−i−i−i−iiiii1−i321+i321−i321+i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7
χ1063333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1iiii−i−i−i−i1−i321+i321−i321+i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7
χ1073333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1111111111−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+i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000000011-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ1083333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i320000000000000000-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000000001111111111−1+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
χ1093333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000-1-1ii−i−i−i−iii1−i321+i321−i321+i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000000011−i−iiiii−i−i−1+i32−1−i32−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ1103333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000-1-1−i−iiiii−i−i1−i321+i321−i321+i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000000011ii−i−i−i−iii−1+i32−1−i32−1+i32−1−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ1113333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000000001111-1-111-1-1−1+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+i321+i321−i321+i321−i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000-1-1-1-111-1-1111−i321+i321−i321+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ1123333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000000011-1-111-1-111−1+i32−1−i32−1+i32−1−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000-1-111-1-111-1-11−i321+i321−i321+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ1133-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−ii−i-11−ii1-1ζ11ζ7−ζ11−ζ7ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ11−3ζ73ζ113ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000−ii−ii1-1i−i-11−ζ11−ζ7ζ11ζ7−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32
χ1143-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−i−ii1-1i−i-11ζ11ζ7−ζ11−ζ7−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ11−3ζ73ζ113ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000−iii−i-11−ii1-1−ζ11−ζ7ζ11ζ7ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32
χ1153-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000−ii1-1i−i1-1i−i−ζ11−ζ7ζ11ζ7−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ11−3ζ73ζ113ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−i-11−ii-11−iiζ11ζ7−ζ11−ζ71−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11
χ1163-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000−ii-11−ii-11−ii−ζ11−ζ7ζ11ζ71−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i32−3i3i−3ζ11−3ζ73ζ113ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−i1-1i−i1-1i−iζ11ζ7−ζ11−ζ7−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11
χ1173-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−iii−i1-1−ii-11−ζ11−ζ7ζ11ζ7ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323i−3i3ζ113ζ7−3ζ11−3ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000i−i−ii-11i−i1-1ζ11ζ7−ζ11−ζ7−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32
χ1183-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−ii−ii-11i−i1-1−ζ11−ζ7ζ11ζ7−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323i−3i3ζ113ζ7−3ζ11−3ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000i−ii−i1-1−ii-11ζ11ζ7−ζ11−ζ7ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32
χ1193-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000i−i1-1−ii1-1−iiζ11ζ7−ζ11−ζ7−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323i−3i3ζ113ζ7−3ζ11−3ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−ii-11i−i-11i−i−ζ11−ζ7ζ11ζ71−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11
χ1203-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ7-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000i−i-11i−i-11i−iζ11ζ7−ζ11−ζ71−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11-33-333+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323i−3i3ζ113ζ7−3ζ11−3ζ711-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−ii1-1−ii1-1−ii−ζ11−ζ7ζ11ζ7−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.