Finite Group Databasebeta

← Group #13167068

Character table — Group #13167068

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222444444444444444444444444444444448888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363636363636363636365454545454545454
order122244443666121212123333666666666666121212121212121212121212121212123666121212124444121212121212121212121212121212121212121212121212121212121212121222444444661212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-1-11i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1
χ1011-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-1-11−ii−ii1-11-1−i−iii−i−iii-1-111-1-111
χ1111-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-1-11i−ii−i1-11-1ii−i−iii−i−i-1-111-1-111
χ1211-1-111-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-1-11−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1
χ1311-1-1-1-1111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11i−i−ii-111-1ii−i−i−i−iii11-1-1-1-111
χ1411-1-1-1-1111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11−iii−i-111-1−i−iiiii−i−i-1-11111-1-1
χ1511-1-1-1-1111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1
χ1611-1-1-1-1111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11−iii−i-111-1−i−iiiii−i−i11-1-1-1-111
χ1722222222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-20000-2-2-2-20000000000000000
χ1822222222-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-2000011110000000000000000
χ1922222222-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-2000011110000000000000000
χ2022222222-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122220000-1-1-1-10000000000000000
χ2122222222-1-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-2111122220000-1-1-1-10000000000000000
χ222222-2-2-2-22222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000022-2-2000022-2-20000000000000000
χ232222-2-2-2-2-1-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-21111-2-2-2-21111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i322-2-20000-1-1110000000000000000
χ242222-2-2-2-2-1-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-21111-2-2-2-21111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i322-2-20000-1-1110000000000000000
χ252222-2-2-2-2-1-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-21111-2-2-2-21111-1-1-1-1111122-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-222000011-1-10000000000000000
χ262222-2-2-2-2-1-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-21111-2-2-2-21111-1-1-1-11111-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-222000011-1-10000000000000000
χ2722-2-222-2-22-2-2222-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22-2-2222-2-2000000000000000000000000000000000000-222-20000-22-220000000000000000
χ2822-2-222-2-2-111-1-1-11122-1-122-1-1-2-21111-2-22222-1-1-1-1-2-2-2-21111-111-1-1-11100003−3−333−3−330033−3−300−3−3330033−3−300−3−333-222-200001-11-10000000000000000
χ2922-2-222-2-2-111-1-1-11122-1-122-1-1-2-21111-2-22222-1-1-1-1-2-2-2-21111-111-1-1-1110000−333−3−333−300−3−3330033−3−300−3−3330033−3−3-222-200001-11-10000000000000000
χ3022-2-222-2-2-111-1-1-11122-1-122-1-1-2-21111-2-22222-1-1-1-1-2-2-2-21111-111-1-1-1112i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-2-220000-11-110000000000000000
χ3122-2-222-2-2-111-1-1-11122-1-122-1-1-2-21111-2-22222-1-1-1-1-2-2-2-21111-111-1-1-111−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-2-220000-11-110000000000000000
χ3222-2-2-2-2222-2-22-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-22-2-2220000000000000000000000000000000000002-22-200002-2-220000000000000000
χ3322-2-2-2-222-111-111-1-122-1-122-1-1-2-21111-2-2-2-2-2-211112222-1-1-1-1-111-111-1-100003−3−33−333−30033−3−300−3−33300−3−3330033−3−32-22-20000-111-10000000000000000
χ3422-2-2-2-222-111-111-1-122-1-122-1-1-2-21111-2-2-2-2-2-211112222-1-1-1-1-111-111-1-10000−333−33−3−3300−3−3330033−3−30033−3−300−3−3332-22-20000-111-10000000000000000
χ3522-2-2-2-222-111-111-1-122-1-122-1-1-2-21111-2-2-2-2-2-211112222-1-1-1-1-111-111-1-12i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-2200001-1-110000000000000000
χ3622-2-2-2-222-111-111-1-122-1-122-1-1-2-21111-2-2-2-2-2-211112222-1-1-1-1-111-111-1-1−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-2200001-1-110000000000000000
χ372-22-22i−2i2i−2i22-2-22i−2i2i−2i2222-2-2-2-22-222-2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000002−22−2−i2i2−i2i2
χ382-22-22i−2i2i−2i22-2-22i−2i2i−2i2222-2-2-2-22-222-2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000000000−22−22i2−i2i2−i2
χ392-22-2−2i2i−2i2i22-2-2−2i2i−2i2i2222-2-2-2-22-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000002−22−2i2−i2i2−i2
χ402-22-2−2i2i−2i2i22-2-2−2i2i−2i2i2222-2-2-2-22-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−22−22−i2i2−i2i2
χ412-2-222i−2i−2i2i2-22-22i−2i−2i2i2222-2-2-2-2-22-2-222-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-22-22i−2i−2i2i000000000000000000000000000000000000000000000000000000002−2−22−i2i2i2−i2
χ422-2-222i−2i−2i2i2-22-22i−2i−2i2i2222-2-2-2-2-22-2-222-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-22-22i−2i−2i2i00000000000000000000000000000000000000000000000000000000−222−2i2−i2−i2i2
χ432-2-22−2i2i2i−2i2-22-2−2i2i2i−2i2222-2-2-2-2-22-2-222-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-22-2−2i2i2i−2i000000000000000000000000000000000000000000000000000000002−2−22i2−i2−i2i2
χ442-2-22−2i2i2i−2i2-22-2−2i2i2i−2i2222-2-2-2-2-22-2-222-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-22-2−2i2i2i−2i00000000000000000000000000000000000000000000000000000000−222−2−i2i2i2−i2
χ4544444444444444441-2111-211111111-2-21-21-211111-21-21111-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ4644444444444444441-2111-211111111-2-21-21-211111-21-21111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111111111110000000000000000000000000000
χ474444444444444444-21-2-2-21-2-2-2-2-2-2-2-211-21-21-2-2-2-2-21-21-2-2-2-211111111000000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ484444444444444444-21-2-2-21-2-2-2-2-2-2-2-211-21-21-2-2-2-2-21-21-2-2-2-2111111110000000000000000000000000000000000000000-2-2-2-200001111111100000000
χ4944444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21-21-2−1−3i32−1+3i32−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i32111111112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000000000000000
χ5044444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21-21-2−1−3i32−1+3i32−1−3i32−1+3i321-21-2−1−3i32−1+3i32−1−3i32−1+3i3211111111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000000000000000
χ5144444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21-21-2−1+3i32−1−3i32−1+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i32111111112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000000000000000
χ5244444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21-21-2−1+3i32−1−3i32−1+3i32−1−3i321-21-2−1+3i32−1−3i32−1+3i32−1−3i3211111111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000000000000000
χ534444-4-4-4-44444-4-4-4-41-2111-211111111-2-2-12-12-1-1-1-1-12-12-1-1-1-1-2-2-2-2222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000000
χ544444-4-4-4-44444-4-4-4-41-2111-211111111-2-2-12-12-1-1-1-1-12-12-1-1-1-1-2-2-2-22222-2-222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ554444-4-4-4-44444-4-4-4-4-21-2-2-21-2-2-2-2-2-2-2-2112-12-122222-12-122221111-1-1-1-1000000000000000000000000000000000000000022-2-20000-1-1-1-1111100000000
χ564444-4-4-4-44444-4-4-4-4-21-2-2-21-2-2-2-2-2-2-2-2112-12-122222-12-122221111-1-1-1-10000000000000000000000000000000000000000-2-22200001111-1-1-1-100000000
χ574444-4-4-4-4-2-2-2-222221-2−1−3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2-12-121+3i321−3i321+3i321−3i32-12-121+3i321−3i321+3i321−3i321111-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000000000000000
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χ1054-4-44−4i4i4i−4i4-44-4−4i4i4i−4i1-211-12-1-1-11-1-1112-2−i2ii−2i−i−iiii−2i−i2iii−i−i-22-222i−2i−2i2i000000000000−33−33−333−33−33−3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i30000000000000000000000000000
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χ1084-4-44−4i4i4i−4i-22-222i−2i−2i2i1-2−1−3i32−1+3i32-121+3i321−3i32-111+3i321−3i32−1−3i32−1+3i322-2−i2ii−2iζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ22i−2i−i2i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ221-11-1−iii−i0000000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i320000000000000000000000000000
χ1094-4-44−4i4i4i−4i-22-222i−2i−2i2i1-2−1−3i32−1+3i32-121+3i321−3i32-111+3i321−3i32−1−3i32−1+3i322-2−i2ii−2iζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ22i−2i−i2i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ221-11-1−iii−i000000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i320000000000000000000000000000
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χ1114-4-44−4i4i4i−4i-22-222i−2i−2i2i1-2−1+3i32−1−3i32-121−3i321+3i32-111−3i321+3i32−1+3i32−1−3i322-2−i2ii−2i−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22i−2i−i2i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ221-11-1−iii−i000000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i320000000000000000000000000000
χ1124-4-44−4i4i4i−4i-22-222i−2i−2i2i44-2-2-4-422-4422-2-2-44−4i−4i4i4i2i2i−2i−2i4i4i−4i−4i−2i−2i2i2i-22-222i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ11388888888-4-4-4-4-4-4-4-4-4222-4222-4-4222222-42-422222-42-422222-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1148888-8-8-8-8-4-4-4-44444-4222-4222-4-42222224-24-2-2-2-2-24-24-2-2-2-2-2-1-1-1-111110000000000000000000000000000000000000000000000000000000000000000
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χ1178-88-88i−8i8i−8i-4-444−4i4i−4i4i-42224-2-2-2-4422-2-22-2−4i2i4i−2i2i2i−2i−2i−4i2i4i−2i2i2i−2i−2i-1-111−ii−ii0000000000000000000000000000000000000000000000000000000000000000
χ1188-88-8−8i8i−8i8i-4-4444i−4i4i−4i-42224-2-2-2-4422-2-22-24i−2i−4i2i−2i−2i2i2i4i−2i−4i2i−2i−2i2i2i-1-111i−ii−i0000000000000000000000000000000000000000000000000000000000000000
χ1198-8-888i−8i−8i8i-44-44−4i4i4i−4i-42224-2-2-24-4-2-222-22−4i2i4i−2i2i2i−2i−2i4i−2i−4i2i−2i−2i2i2i-11-11−iii−i0000000000000000000000000000000000000000000000000000000000000000
χ1208-8-88−8i8i8i−8i-44-444i−4i−4i4i-42224-2-2-24-4-2-222-224i−2i−4i2i−2i−2i2i2i−4i2i4i−2i2i2i−2i−2i-11-11i−i−ii0000000000000000000000000000000000000000000000000000000000000000

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