Finite Group Databasebeta

← Group #14415313

Character table — Group #14415313

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222444444444444555555555555666688888810101010101010101010101010101010101012121616161616161616202020202020202020202020202020202020202020202020242424243030303030303030303030304848606060606060
order1222344666445101010121212121212444488888888444415202030303044888812121212242424242424242444202060606060606022666688881212242424242424242424242424202020202244888888882020228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111-1-1-1-1iiii−i−i−i−i1111111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1-1ii−i−i-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i
χ61111111111111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-111111111-1-1-1-1-1-1ii−i−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111−i−iii
χ71111111111111111111111-1-1-1-1−i−i−i−iiiii1111111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii1111111111-1-1-1-1-1-1−i−iii-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1−i−iii
χ81111111111111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-111111111-1-1-1-1-1-1−i−iii-1-1−i−iii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111ii−i−i
χ91111111111-1-1111111-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ101111111111-1-1111111-1-1-1-1111111111111-1-1-1-111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ121111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ131111111111-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111-1-1-1-1111111−i−iii-1-1ii−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i-1-111−i−iii
χ141111111111-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−i11-1-111-1-1-1-1111111−i−iii-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii11-1-1ii−i−i
χ151111111111-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-111-1-1-1-1111111ii−i−i-1-1−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−iii−i−iii-1-111ii−i−i
χ161111111111-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii11-1-111-1-1-1-1111111ii−i−i-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−iii−i−i11-1-1−i−iii
χ1711111-1-11111-11111-1-111-1-111111111111111-1-11-1-1111-1-1-1-1-1-11111111111111-11-1-1-111-1-11-111-1-11-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1811111-1-11111-11111-1-111-1-1111111111111-1-1111-1-1111-1-1-1-1-1-1111111111111-111-1-1-111-1-11-111-1-11-11-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-11-11-11-11
χ1911111-1-11111-11111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11-111-1-1-11-11-1-11111-1-111-1-11111-1-1-1-111-1-1-1-111111-11-1-11-11
χ2011111-1-11111-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11-111-1-1-11-11-1-11111-1-111-1-111-1-11111-1-11111-1-1-1-1-11-111-11-1
χ2111111-1-11111-11111-1-111-1-1-1-1-1-1iiii−i−i−i−i11-1-11-1-111111−i−iii-1-1-1-1iiii−i−i−i−i1-11-1-1-111-1-1-11-1-111i−i−ii11−i−iiiii−i−i−i−iii11-1-111-1-1ii−i−i−i−iii1-1-11i−i−ii
χ2211111-1-11111-11111-1-111-1-1-1-1-1-1iiii−i−i−i−i-1-1111-1-111111−i−iii-1-1-1-1iiii−i−i−i−i-111-1-1-111-1-1-11-1-111i−i−ii11−i−iiiii−i−i−i−iii-1-111-1-111−i−iiiii−i−i-111-1−iii−i
χ2311111-1-11111-11111-1-111-1-1-1-1-1-1−i−i−i−iiiii11-1-11-1-111111ii−i−i-1-1-1-1−i−i−i−iiiii1-11-1-1-111-1-1-11-1-111−iii−i11ii−i−i−i−iiiii−i−i11-1-111-1-1−i−iiiii−i−i1-1-11−iii−i
χ2411111-1-11111-11111-1-111-1-1-1-1-1-1−i−i−i−iiiii-1-1111-1-111111ii−i−i-1-1-1-1−i−i−i−iiiii-111-1-1-111-1-1-11-1-111−iii−i11ii−i−i−i−iiiii−i−i-1-111-1-111ii−i−i−i−iii-111-1i−i−ii
χ2511111-1-1111-111111-1-1-1-11111111111111111-1-11-1-1111-1-1-1-1-1-1111111111111-11-11-1-1-1-111-11-1-111-11-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-11-11-11-11
χ2611111-1-1111-111111-1-1-1-111111111111111-1-1111-1-1111-1-1-1-1-1-11111111111111-1-11-1-1-1-111-11-1-111-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111-11-11-11-1
χ2711111-1-1111-111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-11-1-1111-11-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11111-11-111-11-1
χ2811111-1-1111-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-11-1-1111-11-1-1-1111111-1-111-1-1-1-11111-1-11111-1-1-1-11-11-1-11-11
χ2911111-1-1111-111111-1-1-1-111-1-1-1-1iiii−i−i−i−i11-1-11-1-111111−i−iii-1-1-1-1iiii−i−i−i−i-11-11-1-1-1-1111-111-1-1−iii−i11−i−iii−i−iiiii−i−i11-1-111-1-1ii−i−i−i−iii-111-1−iii−i
χ3011111-1-1111-111111-1-1-1-111-1-1-1-1iiii−i−i−i−i-1-1111-1-111111−i−iii-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-1111-111-1-1−iii−i11−i−iii−i−iiiii−i−i-1-111-1-111−i−iiiii−i−i1-1-11i−i−ii
χ3111111-1-1111-111111-1-1-1-111-1-1-1-1−i−i−i−iiiii11-1-11-1-111111ii−i−i-1-1-1-1−i−i−i−iiiii-11-11-1-1-1-1111-111-1-1i−i−ii11ii−i−iii−i−i−i−iii11-1-111-1-1−i−iiiii−i−i-111-1i−i−ii
χ3211111-1-1111-111111-1-1-1-111-1-1-1-1−i−i−i−iiiii-1-1111-1-111111ii−i−i-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-1111-111-1-1i−i−ii11ii−i−iii−i−i−i−iii-1-111-1-111ii−i−i−i−iii1-1-11−iii−i
χ332222-122-1-1-1222222-1-1-1-1-1-12222222222220000-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ342222-122-1-1-1222222-1-1-1-1-1-12222-2-2-2-2-2-2-2-20000-122-1-1-122-2-2-2-2-1-1-1-1111111110022-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1111111111111000000000000000000000000
χ352222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-22i2i2i2i−2i−2i−2i−2i0000-122-1-1-1-2-22i2i−2i−2i1111−i−i−i−iiiii0022-1-1-1-1-1-1-2-211112i2i−2i−2i11−i−iii−i−i−i−iiiii000000000000000000000000
χ362222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-122-1-1-1-2-2−2i−2i2i2i1111iiii−i−i−i−i0022-1-1-1-1-1-1-2-21111−2i−2i2i2i11ii−i−iiiii−i−i−i−i000000000000000000000000
χ372222-122-1-1-1-2-22222-1-111112222222222220000-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-1-11111-2-21111-2-2-2-2-1-1-1-1-1-111111111000000000000000000000000
χ382222-122-1-1-1-2-22222-1-111112222-2-2-2-2-2-2-2-20000-122-1-1-122-2-2-2-2-1-1-1-11111111100-2-2-1-11111-2-211112222-1-11111-1-1-1-1-1-1-1-1000000000000000000000000
χ392222-122-1-1-1-2-22222-1-11111-2-2-2-22i2i2i2i−2i−2i−2i−2i0000-122-1-1-1-2-22i2i−2i−2i1111−i−i−i−iiiii00-2-2-1-1111122-1-1-1-1−2i−2i2i2i11−i−iiiiiii−i−i−i−i000000000000000000000000
χ402222-122-1-1-1-2-22222-1-11111-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-122-1-1-1-2-2−2i−2i2i2i1111iiii−i−i−i−i00-2-2-1-1111122-1-1-1-12i2i−2i−2i11ii−i−i−i−i−i−iiiii000000000000000000000000
χ412222-1-2-2-1-1-12-2222211-1-1112222222222220000-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1002-211-1-1112-2-1-1112-22-2111111-1-111-1-111000000000000000000000000
χ422222-1-2-2-1-1-12-2222211-1-1112222-2-2-2-2-2-2-2-20000-1-2-2-1-1-1-2-22222-1-1-1-111111111002-211-1-1112-2-1-111-22-2211-1-1-1-111-1-111-1-1000000000000000000000000
χ432222-1-2-2-1-1-12-2222211-1-111-2-2-2-22i2i2i2i−2i−2i−2i−2i0000-1-2-2-1-1-122−2i−2i2i2i1111−i−i−i−iiiii002-211-1-111-2211-1-12i−2i−2i2i-1-1ii−i−i−i−iiiii−i−i000000000000000000000000
χ442222-1-2-2-1-1-12-2222211-1-111-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-1-2-2-1-1-1222i2i−2i−2i1111iiii−i−i−i−i002-211-1-111-2211-1-1−2i2i2i−2i-1-1−i−iiiii−i−i−i−iii000000000000000000000000
χ452222-1-2-2-1-1-1-2222221111-1-12222222222220000-1-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-100-221111-1-1-2211-1-1-22-2211111111-1-111-1-1000000000000000000000000
χ462222-1-2-2-1-1-1-2222221111-1-12222-2-2-2-2-2-2-2-20000-1-2-2-1-1-1-2-22222-1-1-1-11111111100-221111-1-1-2211-1-12-22-211-1-1-1-1-1-111-1-111000000000000000000000000
χ472222-1-2-2-1-1-1-2222221111-1-1-2-2-2-22i2i2i2i−2i−2i−2i−2i0000-1-2-2-1-1-122−2i−2i2i2i1111−i−i−i−iiiii00-221111-1-12-2-1-111−2i2i2i−2i-1-1ii−i−iii−i−i−i−iii000000000000000000000000
χ482222-1-2-2-1-1-1-2222221111-1-1-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-1-2-2-1-1-1222i2i−2i−2i1111iiii−i−i−i−i00-221111-1-12-2-1-1112i−2i−2i2i-1-1−i−iii−i−iiiii−i−i000000000000000000000000
χ4922-2-2200-22-2002-22-20000002i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-2002002-2-20000002i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000002-200002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ5022-2-2200-22-2002-22-20000002i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13-22002002-2-20000002i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000000000000000000000-220000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ5122-2-2200-22-2002-22-20000002i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132-2002002-2-20000002i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000002-200002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ5222-2-2200-22-2002-22-20000002i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13-22002002-2-20000002i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000000000000000000000000000000000-220000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ5322-2-2200-22-2002-22-2000000−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232-2002002-2-2000000−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000002-20000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ5422-2-2200-22-2002-22-2000000−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23-22002002-2-2000000−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000000000000000000000-2200002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5522-2-2200-22-2002-22-2000000−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232-2002002-2-2000000−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000002-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ5622-2-2200-22-2002-22-2000000−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23-22002002-2-2000000−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000000000000000000000000000000000-2200002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ572-22-2200-2-22002-2-2200000022-2-22i−2i2i−2i2i−2i2i−2i002-2200-2-2200000022-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002-22-20000002i−2i2i−2i00000000
χ582-22-2200-2-22002-2-2200000022-2-22i−2i2i−2i2i−2i2i−2i00-22200-2-2200000022-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000-22-22000000−2i2i−2i2i00000000
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χ1068888-488-4-4-4-8-8-2-2-2-2-4-4444400000000000000001-2-2111000000000000000000002211-1-1-1-1000000000000000000000000000000000000000000000000
χ1078888-4-8-8-4-4-48-8-2-2-2-244-4-444000000000000000012211100000000000000000000-22-1-111-1-1000000000000000000000000000000000000000000000000
χ1088888-4-8-8-4-4-4-88-2-2-2-24444-4-40000000000000000122111000000000000000000002-2-1-1-1-111000000000000000000000000000000000000000000000000
χ10988-8-8800-88-800-22-220000000000000000008-800-200-2220000000000000000000000000000000000000000000000000000-220000000000000000000000
χ11088-8-8800-88-800-22-22000000000000000000-8800-200-22200000000000000000000000000000000000000000000000000002-20000000000000000000000
χ1118-88-8800-8-8800-222-2000000000000000000008-8-20022-2000000000000000000000000000000000000000000000000000000-2200000000000000000000
χ1128-88-8800-8-8800-222-200000000000000000000-88-20022-20000000000000000000000000000000000000000000000000000002-200000000000000000000
χ1138-8-8888-88-8-800-2-2228-800000000000000000000-2-222-220000000000000000000000-220000000000000000000000000000000000000000000000000000
χ1148-8-888-888-8-800-2-222-8800000000000000000000-22-22-2200000000000000000000002-20000000000000000000000000000000000000000000000000000
χ1158-8-88-48-8-44400-2-222-4443−4343−4300000000000000001-22-11-100000000000000000000001-1−33−33000000000000000000000000000000000000000000000000
χ1168-8-88-48-8-44400-2-222-44−4343−434300000000000000001-22-11-100000000000000000000001-13−33−3000000000000000000000000000000000000000000000000
χ1178-8-88-4-88-44400-2-2224-443−43−4343000000000000000012-2-11-10000000000000000000000-11−333−3000000000000000000000000000000000000000000000000
χ1188-8-88-4-88-44400-2-2224-4−434343−43000000000000000012-2-11-10000000000000000000000-113−3−33000000000000000000000000000000000000000000000000
χ1191616-16-16-8008-8800-44-4400000000000000000000002002-2-20000000000000000000000000000000000000000000000000000000000000000000000000000
χ12016-1616-16-80088-800-444-40000000000000000000000200-2-220000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.