Finite Group Databasebeta

← Group #13167297

Character table — Group #13167297

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11222224444444444444466666666666688888991212121212121212121212121818181818363672721081081122222444444444444446666666666668888899121212121212121212121212181818181836367272108108
order12236663333666666666644441212121212121212366664412121212121212121212121241212121224612882226666666666666666664444121212121212121266666441212121212121212121212124121212122461288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111
χ511-11-1-111111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-11-1-1-1-1iiiiii−i−i−i−i−i−i111-1-11-11-1i−i11-11-1-111111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-11-1-1-1-1iiiiii−i−i−i−i−i−i111-1-11-11-1i−i
χ611-11-1-111111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-11-1-1-1-1iiiiii−i−i−i−i−i−i111-1-1-11-11−ii11-11-1-111111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-11-1-1-1-1iiiiii−i−i−i−i−i−i111-1-1-11-11−ii
χ711-11-1-111111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-11-1-1-1-1−i−i−i−i−i−iiiiiii111-1-11-11-1−ii11-11-1-111111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-11-1-1-1-1−i−i−i−i−i−iiiiiii111-1-11-11-1−ii
χ811-11-1-111111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-11-1-1-1-1−i−i−i−i−i−iiiiiii111-1-1-11-11i−i11-11-1-111111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-11-1-1-1-1−i−i−i−i−i−iiiiiii111-1-1-11-11i−i
χ922222222222222222222200000000000022222-2-2000000000000-2-2-2-2-200000022222222222222222222200000000000022222-2-2000000000000-2-2-2-2-2000000
χ10222-1-1-1-12-1-122-1-12-1-12-1-120000−i3−i3i3i3−i3−i3i3i3-12-1-1-1-2-200−i3−i3i3i300−i3−i3i3i3-21111000000222-1-1-1-12-1-122-1-12-1-12-1-120000−i3−i3i3i3−i3−i3i3i3-12-1-1-1-2-200−i3−i3i3i300−i3−i3i3i3-21111000000
χ11222-1-1-1-12-1-122-1-12-1-12-1-120000i3i3−i3−i3i3i3−i3−i3-12-1-1-1-2-200i3i3−i3−i300i3i3−i3−i3-21111000000222-1-1-1-12-1-122-1-12-1-12-1-120000i3i3−i3−i3i3i3−i3−i3-12-1-1-1-2-200i3i3−i3−i300i3i3−i3−i3-21111000000
χ12222-1-1-1-12-1-122-1-12-1-12-1-122222-1-1-1-1-1-1-1-1-12-1-1-12222-1-1-1-122-1-1-1-12-1-1-1-1000000222-1-1-1-12-1-122-1-12-1-12-1-122222-1-1-1-1-1-1-1-1-12-1-1-12222-1-1-1-122-1-1-1-12-1-1-1-1000000
χ13222-1-1-1-12-1-122-1-12-1-12-1-12-2-2-2-211111111-12-1-1-122-2-21111-2-211112-1-1-1-1000000222-1-1-1-12-1-122-1-12-1-12-1-12-2-2-2-211111111-12-1-1-122-2-21111-2-211112-1-1-1-1000000
χ1422-22-2-222222222-2-2-2-2-2-220000000000002-22-2-222000000000000-2-2-22200000022-22-2-222222222-2-2-2-2-2-220000000000002-22-2-222000000000000-2-2-222000000
χ1522-2-111-12-1-122-1-1-211-2112000033−3−3−3−333-1-2-111220033−3−300−3−333-211-1-100000022-2-111-12-1-122-1-1-211-2112000033−3−3−3−333-1-2-111220033−3−300−3−333-211-1-1000000
χ1622-2-111-12-1-122-1-1-211-21120000−3−33333−3−3-1-2-1112200−3−3330033−3−3-211-1-100000022-2-111-12-1-122-1-1-211-21120000−3−33333−3−3-1-2-1112200−3−3330033−3−3-211-1-1000000
χ1722-2-111-12-1-122-1-1-211-21122i2i−2i−2i−i−i−i−iiiii-1-2-111-2-22i2i−i−i−i−i−2i−2iiiii2-1-11100000022-2-111-12-1-122-1-1-211-21122i2i−2i−2i−i−i−i−iiiii-1-2-111-2-22i2i−i−i−i−i−2i−2iiiii2-1-111000000
χ1822-2-111-12-1-122-1-1-211-2112−2i−2i2i2iiiii−i−i−i−i-1-2-111-2-2−2i−2iiiii2i2i−i−i−i−i2-1-11100000022-2-111-12-1-122-1-1-211-2112−2i−2i2i2iiiii−i−i−i−i-1-2-111-2-2−2i−2iiiii2i2i−i−i−i−i2-1-111000000
χ192-20200-22222-2-2-2000000-21+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i20-2002i−2i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i0002i−2i0000002-20200-22222-2-2-2000000-21+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i20-2002i−2i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i0002i−2i000000
χ202-20200-22222-2-2-2000000-21−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i20-200−2i2i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i000−2i2i0000002-20200-22222-2-2-2000000-21−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i20-200−2i2i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i000−2i2i000000
χ212-20200-22222-2-2-2000000-2−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i20-200−2i2i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i000−2i2i0000002-20200-22222-2-2-2000000-2−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i20-200−2i2i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i000−2i2i000000
χ222-20200-22222-2-2-2000000-2−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i20-2002i−2i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i0002i−2i0000002-20200-22222-2-2-2000000-2−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i20-2002i−2i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i0002i−2i000000
χ232-20-1−i3i312-1-12-2110−i3i30−i3i3-21+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11-101−i3i32i−2i1+i−1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ111−i−1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1103−3−ii0000002-20-1−i3i312-1-12-2110−i3i30−i3i3-21+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11-101−i3i32i−2i1+i−1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ111−i−1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1103−3−ii000000
χ242-20-1−i3i312-1-12-2110−i3i30−i3i3-21−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11-101−i3i3−2i2i1−i−1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ111+i−1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110−33i−i0000002-20-1−i3i312-1-12-2110−i3i30−i3i3-21−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11-101−i3i3−2i2i1−i−1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ111+i−1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110−33i−i000000
χ252-20-1−i3i312-1-12-2110−i3i30−i3i3-2−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11-101−i3i3−2i2i−1+i1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−1−i1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110−33i−i0000002-20-1−i3i312-1-12-2110−i3i30−i3i3-2−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11-101−i3i3−2i2i−1+i1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−1−i1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110−33i−i000000
χ262-20-1−i3i312-1-12-2110−i3i30−i3i3-2−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11-101−i3i32i−2i−1−i1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−1+i1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1103−3−ii0000002-20-1−i3i312-1-12-2110−i3i30−i3i3-2−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11-101−i3i32i−2i−1−i1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−1+i1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1103−3−ii000000
χ272-20-1i3−i312-1-12-2110i3−i30i3−i3-21+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7-101i3−i32i−2i1+i−1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ71−i−1+i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70−33−ii0000002-20-1i3−i312-1-12-2110i3−i30i3−i3-21+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7-101i3−i32i−2i1+i−1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ71−i−1+i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70−33−ii000000
χ282-20-1i3−i312-1-12-2110i3−i30i3−i3-21−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7-101i3−i3−2i2i1−i−1+i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ71+i−1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ703−3i−i0000002-20-1i3−i312-1-12-2110i3−i30i3−i3-21−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7-101i3−i3−2i2i1−i−1+i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ71+i−1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ703−3i−i000000
χ292-20-1i3−i312-1-12-2110i3−i30i3−i3-2−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7-101i3−i3−2i2i−1+i1−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−1−i1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ703−3i−i0000002-20-1i3−i312-1-12-2110i3−i30i3−i3-2−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7-101i3−i3−2i2i−1+i1−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−1−i1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ703−3i−i000000
χ302-20-1i3−i312-1-12-2110i3−i30i3−i3-2−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7-101i3−i32i−2i−1−i1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−1+i1−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70−33−ii0000002-20-1i3−i312-1-12-2110i3−i30i3−i3-2−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7-101i3−i32i−2i−1−i1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−1+i1−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70−33−ii000000
χ314444444111-2111111111-2222222222222-2-2-2-2-200-1-1-1-1-1-1-1-1-1-1-1-1000000000004444444111-2111111111-2222222222222-2-2-2-2-200-1-1-1-1-1-1-1-1-1-1-1-100000000000
χ324444444111-2111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200111111111111000000000004444444111-2111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20011111111111100000000000
χ334444444-2-2-21-2-2-2-2-2-2-2-2-2100000000000011111000000000000000000022-1-1004444444-2-2-21-2-2-2-2-2-2-2-2-2100000000000011111000000000000000000022-1-100
χ344444444-2-2-21-2-2-2-2-2-2-2-2-21000000000000111110000000000000000000-2-211004444444-2-2-21-2-2-2-2-2-2-2-2-21000000000000111110000000000000000000-2-21100
χ35444-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i321−1+3i32−1−3i32-22222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i31-211100-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000444-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i321−1+3i32−1−3i32-22222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i31-211100-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000
χ36444-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i321−1+3i32−1−3i32-2-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i31-21110011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000444-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i321−1+3i32−1−3i32-2-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i31-21110011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000
χ37444-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i321−1−3i32−1+3i32-22222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i31-211100-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000444-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i321−1−3i32−1+3i32-22222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i31-211100-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000
χ38444-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i321−1−3i32−1+3i32-2-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i31-21110011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000444-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i321−1−3i32−1+3i32-2-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i31-21110011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000
χ3944-44-4-44111-2111-1-1-1-1-1-1-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-22-22200−i−i−i−i−i−iiiiiii0000000000044-44-4-44111-2111-1-1-1-1-1-1-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-22-22200−i−i−i−i−i−iiiiiii00000000000
χ4044-44-4-44111-2111-1-1-1-1-1-1-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-22-22200iiiiii−i−i−i−i−i−i0000000000044-44-4-44111-2111-1-1-1-1-1-1-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-22-22200iiiiii−i−i−i−i−i−i00000000000
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χ1204-40-22i3−2i321−1+3i32−1−3i32-2-11−3i321+3i323−3+i32−3−i32-33+i323−i3222-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i310-1−i3i300-111−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i3200000000000-4402−2i32i3-2-11−3i321+3i3221−1+3i32−1−3i32-33−i323+i323−3−i32−3+i32-2-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3-101i3−i3001-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i3200000000000
χ1214-40-22i3−2i321−1+3i32−1−3i32-2-11−3i321+3i323−3+i32−3−i32-33+i323−i322-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i310-1−i3i3001-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i3200000000000-4402−2i32i3-2-11−3i321+3i3221−1+3i32−1−3i32-33−i323+i323−3−i32−3+i32-22-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3-101i3−i300-111−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i3200000000000
χ122888-4-4-4-4-4222-422-422-4222000000000000-12-1-1-10000000000000000000000000-8-8-844444-2-2-24-2-24-2-24-2-2-20000000000001-21110000000000000000000000000
χ12388-8-444-4-4222-4224-2-24-2-22000000000000-1-2-1110000000000000000000000000-8-884-4-444-2-2-24-2-2-422-422-2000000000000121-1-10000000000000000000000000
χ1248-80800-8-4-4-42444000000-200000000000020-2000000000000000000000000000-880-8008444-2-4-4-40000002000000000000-202000000000000000000000000000
χ1258-80-4−4i34i34-42224-2-202i3−2i302i3−2i3-2000000000000-101−i3i30000000000000000000000000-88044i3−4i3-44-2-2-2-4220−2i32i30−2i32i3200000000000010-1i3−i30000000000000000000000000
χ1268-80-44i3−4i34-42224-2-20−2i32i30−2i32i3-2000000000000-101i3−i30000000000000000000000000-8804−4i34i3-44-2-2-2-42202i3−2i302i3−2i3200000000000010-1−i3i30000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.