Finite Group Databasebeta

← Group #359014

Character table — Group #359014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12224444888888882222224444448888888888882222444488888888222244444444444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1011111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1211111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ171-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-11-1ii−i−i1-11-111-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ181-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1-11−i−iii1-1-1111-1-1-1-111−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii-1-111
χ191-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-111-1−i−iii-111-1-1-11111-1-1−i−iii-1-111−i−iiiii−i−i−i−iiiii−i−i-1-111
χ201-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11-11ii−i−i-11-11-1-111-1-111ii−i−i11-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ211-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii1-11-1−i−iii1-11-1-1-111-1-111ii−i−i-1-111ii−i−iii−i−i−i−iii−i−iii11-1-1
χ221-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii1-1-11ii−i−i1-1-11-1-11111-1-1−i−iii11-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111
χ231-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-111-1ii−i−i-111-111-1-1-1-111−i−iii11-1-1−i−iiiii−i−iii−i−i−i−iii-1-111
χ241-1-1111-1-1iiii−i−i−i−i1-1-111-111-11-1-1iiiiii−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-11-11−i−iii-11-1111-1-111-1-1ii−i−i-1-111−i−iii−i−iiiii−i−iii−i−i11-1-1
χ251-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii11-1-111-1-1−i−i−i−iiiii1-11-1−i−iii1-11-111-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ261-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii11-1-111-1-1−i−i−i−iiiii1-1-11ii−i−i1-1-1111-1-1-1-111ii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i-1-111
χ271-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii11-1-111-1-1−i−i−i−iiiii-111-1ii−i−i-111-1-1-11111-1-1ii−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii-1-111
χ281-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii11-1-111-1-1−i−i−i−iiiii-11-11−i−iii-11-11-1-111-1-111−i−iii11-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ291-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii-1-111-1-111iiii−i−i−i−i1-11-1ii−i−i1-11-1-1-111-1-111−i−iii-1-111−i−iii−i−iiiii−i−iii−i−i11-1-1
χ301-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii-1-111-1-111iiii−i−i−i−i1-1-11−i−iii1-1-11-1-11111-1-1ii−i−i11-1-1−i−iiiii−i−iii−i−i−i−iii-1-111
χ311-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii-1-111-1-111iiii−i−i−i−i-111-1−i−iii-111-111-1-1-1-111ii−i−i11-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111
χ321-1-1111-1-1−i−i−i−iiiii1-1-111-111-11-1-1−i−i−i−i−i−iiiiiii-1-111-1-111iiii−i−i−i−i-11-11ii−i−i-11-1111-1-111-1-1−i−iii-1-111ii−i−iii−i−i−i−iii−i−iii11-1-1
χ3322222222222222222-2-2-2-22-2-222-2-222-2-2-2-222-2-2-2-20000000000000000000000000000000000002-22-2000000000000000000002-22-2
χ3422222222222222222-2-2-2-22-2-222-2-222-2-2-2-222-2-2-2-2000000000000000000000000000000000000-22-2200000000000000000000-22-22
χ352222222222222222-22-22-2-22-2-2-22-2-2-222-2-2-2-222-2-2000000000000000000000000000000002-22-2000000000000000000002-22-20000
χ362222222222222222-22-22-2-22-2-2-22-2-2-222-2-2-2-222-2-200000000000000000000000000000000-22-2200000000000000000000-22-220000
χ372222222222222222-2-22-22-2-22-2-2-22-2-2-2-222-2-2-2-22200000000000000000000000000002-22-2000000000000000000002-22-200000000
χ382222222222222222-2-22-22-2-22-2-2-22-2-2-2-222-2-2-2-2220000000000000000000000000000-22-2200000000000000000000-22-2200000000
χ3922222222-2-2-2-2-2-2-2-22-2-2-2-22-2-222-2-2-2-22222-2-222220000000000000000000000000000000000002-22-200000000000000000000-22-22
χ4022222222-2-2-2-2-2-2-2-22-2-2-2-22-2-222-2-2-2-22222-2-22222000000000000000000000000000000000000-22-22000000000000000000002-22-2
χ4122222222-2-2-2-2-2-2-2-2-22-22-2-22-2-2-22-222-2-22222-2-222000000000000000000000000000000002-22-200000000000000000000-22-220000
χ4222222222-2-2-2-2-2-2-2-2-22-22-2-22-2-2-22-222-2-22222-2-22200000000000000000000000000000000-22-22000000000000000000002-22-20000
χ4322222222-2-2-2-2-2-2-2-2-2-22-22-2-22-2-2-222222-2-22222-2-200000000000000000000000000002-22-200000000000000000000-22-2200000000
χ4422222222-2-2-2-2-2-2-2-2-2-22-22-2-22-2-2-222222-2-22222-2-20000000000000000000000000000-22-22000000000000000000002-22-200000000
χ452222-2-2-2-22i2i−2i−2i2i2i−2i−2i222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ462222-2-2-2-22i2i−2i−2i2i2i−2i−2i222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-2-2-2-22222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ472222-2-2-2-22i2i−2i−2i2i2i−2i−2i2-2-2-2-2222-2-2222i−2i−2i2i−2i2i2i−2i−2i2i−2i2i000000000000000000002-22-200000000000000002i−2i2i−2i00000000000000000000
χ482222-2-2-2-22i2i−2i−2i2i2i−2i−2i2-2-2-2-2222-2-2222i−2i−2i2i−2i2i2i−2i−2i2i−2i2i00000000000000000000-22-220000000000000000−2i2i−2i2i00000000000000000000
χ492222-2-2-2-22i2i−2i−2i2i2i−2i−2i-22-22-2-2-2222-22−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i00000000000000000022000000-2-2000000000000000000002i−2i2i−2i000000000000
χ502222-2-2-2-22i2i−2i−2i2i2i−2i−2i-22-22-2-2-2222-22−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i000000000000000000-2-20000002200000000000000000000−2i2i−2i2i000000000000
χ512222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-22-22-22-2222-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000022000000-2-20000000000000000002i−2i2i−2i0000000000000000
χ522222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-22-22-22-2222-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000-2-200000022000000000000000000−2i2i−2i2i0000000000000000
χ532222-2-2-2-2−2i−2i2i2i−2i−2i2i2i222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ542222-2-2-2-2−2i−2i2i2i−2i−2i2i2i222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-2-2-2-222222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ552222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2-2-2-2-2222-2-222−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i000000000000000000002-22-20000000000000000−2i2i−2i2i00000000000000000000
χ562222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2-2-2-2-2222-2-222−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i00000000000000000000-22-2200000000000000002i−2i2i−2i00000000000000000000
χ572222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-22-22-2-2-2222-222i−2i−2i2i2i−2i2i−2i−2i2i2i−2i00000000000000000022000000-2-200000000000000000000−2i2i−2i2i000000000000
χ582222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-22-22-2-2-2222-222i−2i−2i2i2i−2i2i−2i−2i2i2i−2i000000000000000000-2-200000022000000000000000000002i−2i2i−2i000000000000
χ592222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-22-22-22-2222-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000022000000-2-2000000000000000000−2i2i−2i2i0000000000000000
χ602222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-22-22-22-2222-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000-2-2000000220000000000000000002i−2i2i−2i0000000000000000
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χ622-2-2222-2-22i2i2i2i−2i−2i−2i−2i222-2-2-2-2-2-22222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000−2i2i2i−2i00000000000000000000-222-2
χ632-2-2222-2-22i2i2i2i−2i−2i−2i−2i-22-2-222-222-22-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000000000000000000000002-2-22000000000000000000002i−2i−2i2i00000000
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χ682-2-2222-2-2−2i−2i−2i−2i2i2i2i2i222-2-2-2-2-2-2222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000−2i2i2i−2i000000000000000000002-2-22
χ692-2-2222-2-2−2i−2i−2i−2i2i2i2i2i-22-2-222-222-22-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000002-2-2200000000000000000000−2i2i2i−2i00000000
χ702-2-2222-2-2−2i−2i−2i−2i2i2i2i2i-22-2-222-222-22-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i0000000000000000000000000000-222-2000000000000000000002i−2i−2i2i00000000
χ712-2-2222-2-2−2i−2i−2i−2i2i2i2i2i-2-222-222-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002-2-2200000000000000000000−2i2i2i−2i0000
χ722-2-2222-2-2−2i−2i−2i−2i2i2i2i2i-2-222-222-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-222-2000000000000000000002i−2i−2i2i0000
χ732-2-22-2-22222-2-2-2-222222-2-2-2222-2-2-22-2-22-22-222-22-2000000000000000000002i−2i−2i2i0000000000000000−2i2i2i−2i00000000000000000000
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χ772-2-22-2-22222-2-2-2-222-22-2-2222-2-22-22-22-222-22-22-2-2200000000000000002-2000000-220000000000000000002-2-220000000000000000
χ782-2-22-2-22222-2-2-2-222-22-2-2222-2-22-22-22-222-22-22-2-220000000000000000-220000002-2000000000000000000-222-20000000000000000
χ792-2-22-2-22222-2-2-2-222-2-222-22-22-222-2-222-2-222-2-222-20000000000000000002-2000000-22000000000000000000002-2-22000000000000
χ802-2-22-2-22222-2-2-2-222-2-222-22-22-222-2-222-2-222-2-222-2000000000000000000-220000002-200000000000000000000-222-2000000000000
χ812-2-22-2-222-2-22222-2-2222-2-2-2222-2-2-2-222-22-22-2-22-22000000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000000000000000
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χ872-2-22-2-222-2-22222-2-2-2-222-22-22-222-22-2-222-2-222-2-220000000000000000002-2000000-2200000000000000000000-222-2000000000000
χ882-2-22-2-222-2-22222-2-2-2-222-22-22-222-22-2-222-2-222-2-22000000000000000000-220000002-2000000000000000000002-2-22000000000000
χ8944-4-44i−4i4i−4i4ζ−4ζ4ζ3−4ζ34ζ−4ζ4ζ3−4ζ30000000000000000000000002-22-22i−2i2i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000000000000000
χ9044-4-44i−4i4i−4i4ζ−4ζ4ζ3−4ζ34ζ−4ζ4ζ3−4ζ3000000000000000000000000-22-22−2i2i−2i2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000000000000000
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χ9344-4-4−4i4i−4i4i4ζ3−4ζ34ζ−4ζ4ζ3−4ζ34ζ−4ζ0000000000000000000000002-22-2−2i2i−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000000000000000
χ9444-4-4−4i4i−4i4i4ζ3−4ζ34ζ−4ζ4ζ3−4ζ34ζ−4ζ000000000000000000000000-22-222i−2i2i−2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000000000000000
χ9544-4-4−4i4i−4i4i−4ζ34ζ3−4ζ4ζ−4ζ34ζ3−4ζ4ζ0000000000000000000000002-22-2−2i2i−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000000000000000
χ9644-4-4−4i4i−4i4i−4ζ34ζ3−4ζ4ζ−4ζ34ζ3−4ζ4ζ000000000000000000000000-22-222i−2i2i−2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000000000000000
χ974-44-44i−4i−4i4i4ζ3−4ζ3−4ζ4ζ−4ζ34ζ34ζ−4ζ0000000000000000000000002-2-222i−2i−2i2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000000000000000000000000000
χ984-44-44i−4i−4i4i4ζ3−4ζ3−4ζ4ζ−4ζ34ζ34ζ−4ζ000000000000000000000000-222-2−2i2i2i−2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000000000000000000000000000
χ994-44-44i−4i−4i4i−4ζ34ζ34ζ−4ζ4ζ3−4ζ3−4ζ4ζ0000000000000000000000002-2-222i−2i−2i2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000000000000000000000000000
χ1004-44-44i−4i−4i4i−4ζ34ζ34ζ−4ζ4ζ3−4ζ3−4ζ4ζ000000000000000000000000-222-2−2i2i2i−2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000000000000000000000000000
χ1014-44-4−4i4i4i−4i4ζ−4ζ−4ζ34ζ3−4ζ4ζ4ζ3−4ζ30000000000000000000000002-2-22−2i2i2i−2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000000000000000000000000000
χ1024-44-4−4i4i4i−4i4ζ−4ζ−4ζ34ζ3−4ζ4ζ4ζ3−4ζ3000000000000000000000000-222-22i−2i−2i2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000000000000000000000000000
χ1034-44-4−4i4i4i−4i−4ζ4ζ4ζ3−4ζ34ζ−4ζ−4ζ34ζ30000000000000000000000002-2-22−2i2i2i−2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000000000000000000000000000
χ1044-44-4−4i4i4i−4i−4ζ4ζ4ζ3−4ζ34ζ−4ζ−4ζ34ζ3000000000000000000000000-222-22i−2i−2i2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.