Finite Group Databasebeta

← Group #72322766

Character table — Group #72322766

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size112222222222222222222224444444444444444444448888888888888888888888888888888888888888888888886464646464646464
order122224444881616161632323232323232328881616161616163232323232323232323232324488161616163232323232323232646464646464646464646464646464646464646464646464646464646464646444444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111
χ911-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−ii−i1-11-1i−i
χ1011-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii-11-11−ii
χ1111-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiii−i-11-11i−i
χ1211-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−ii1-11-1−ii
χ1311-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiii−i1-1-11−ii
χ1411-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii-111-1i−i
χ1511-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−ii−i-111-1−ii
χ1611-1-11-111-111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−ii1-1-11i−i
χ17222222222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ18222222222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ1922222222222-2-2-2-200000000222-2-2-2-2-2-20000000000002222-2-2-2-2000000002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−200000000
χ2022222222222-2-2-2-200000000222-2-2-2-2-2-20000000000002222-2-2-2-200000000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2222200000000
χ2122222222222-2-2-2-200000000222-2-2-2-2-2-2000000000000-2-2-2-22222000000002222−2−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−2222200000000
χ2222222222222-2-2-2-200000000222-2-2-2-2-2-2000000000000-2-2-2-2222200000000−2−2−2−22222−2−2−2−222222222−2−2−2−22222−2−2−2−200000000
χ23222222222-2-200002222−2−2−2−2-2-2-200000022−2−22222−2−2−2−222-2-2000022−2−222−2−2ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ1000000000
χ24222222222-2-200002222−2−2−2−2-2-2-200000022−2−22222−2−2−2−222-2-2000022−2−222−2−2−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ1000000000
χ25222222222-2-200002222−2−2−2−2-2-2-200000022−2−22222−2−2−2−2-2-2220000−2−222−2−222ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ1000000000
χ26222222222-2-200002222−2−2−2−2-2-2-200000022−2−22222−2−2−2−2-2-2220000−2−222−2−222−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ1000000000
χ27222222222-2-20000−2−2−2−22222-2-2-2000000−2−222−2−2−2−2222222-2-20000−2−222−2−222ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ1400000000
χ28222222222-2-20000−2−2−2−22222-2-2-2000000−2−222−2−2−2−2222222-2-20000−2−222−2−222−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ1400000000
χ29222222222-2-20000−2−2−2−22222-2-2-2000000−2−222−2−2−2−22222-2-222000022−2−222−2−2ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ1400000000
χ30222222222-2-20000−2−2−2−22222-2-2-2000000−2−222−2−2−2−22222-2-222000022−2−222−2−2−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ1400000000
χ31222-2-222-2-2222222222222222-2-222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000002-22-22-22-22-22-22-22-200000000
χ32222-2-222-2-2222222222222222-2-222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000-22-22-22-22-22-22-22-2200000000
χ33222-2-222-2-2222222-2-2-2-2-2-2-2-22-2-222-2-2-2-22222-2-222-2-22200000000000000002-22-22-22-22-22-22-22-2000000000000000000000000
χ34222-2-222-2-2222222-2-2-2-2-2-2-2-22-2-222-2-2-2-22222-2-222-2-2220000000000000000-22-22-22-22-22-22-22-22000000000000000000000000
χ35222-2-222-2-222-2-2-2-2000000002-2-2-2-22222000000000000000000002-22-22-22-22−22−2−22−222−22−2−22−222−22−2−22−222−22−2−22−2200000000
χ36222-2-222-2-222-2-2-2-2000000002-2-2-2-22222000000000000000000002-22-22-22-2−22−222−22−2−22−222−22−2−22−222−22−2−22−222−22−200000000
χ37222-2-222-2-222-2-2-2-2000000002-2-2-2-2222200000000000000000000-22-22-22-222−22−2−22−222−22−2−22−22−22−222−22−2−22−222−22−200000000
χ38222-2-222-2-222-2-2-2-2000000002-2-2-2-2222200000000000000000000-22-22-22-22−22−222−22−2−22−222−22−22−22−2−22−222−22−2−22−2200000000
χ39222-2-222-2-2-2-200002222−2−2−2−2-222000000−2−22222−2−2−2−22200002-22-22−2−222−2−22ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ1000000000
χ40222-2-222-2-2-2-200002222−2−2−2−2-222000000−2−22222−2−2−2−22200002-22-22−2−222−2−22−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ1000000000
χ41222-2-222-2-2-2-200002222−2−2−2−2-222000000−2−22222−2−2−2−2220000-22-22−222−2−222−2ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ1000000000
χ42222-2-222-2-2-2-200002222−2−2−2−2-222000000−2−22222−2−2−2−2220000-22-22−222−2−222−2−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ1000000000
χ43222-2-222-2-2-2-20000−2−2−2−22222-22200000022−2−2−2−22222−2−200002-22-2−222−2−222−2ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ1400000000
χ44222-2-222-2-2-2-20000−2−2−2−22222-22200000022−2−2−2−22222−2−200002-22-2−222−2−222−2−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ1400000000
χ45222-2-222-2-2-2-20000−2−2−2−22222-22200000022−2−2−2−22222−2−20000-22-222−2−222−2−22ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ1400000000
χ46222-2-222-2-2-2-20000−2−2−2−22222-22200000022−2−2−2−22222−2−20000-22-222−2−222−2−22−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ1400000000
χ4722-22-2-22-2222222222222222-22-2-2-222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000
χ4822-22-2-22-2222222222222222-22-2-2-222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000
χ4922-22-2-22-22222222-2-2-2-2-2-2-2-2-22-2-2-222-2-2222222-2-222-2-200000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5022-22-2-22-22222222-2-2-2-2-2-2-2-2-22-2-2-222-2-2222222-2-222-2-20000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5122-22-2-22-2222-2-2-2-200000000-22-222-2-222000000000000000000002-22-2-22-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ5222-22-2-22-2222-2-2-2-200000000-22-222-2-222000000000000000000002-22-2-22-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ5322-22-2-22-2222-2-2-2-200000000-22-222-2-22200000000000000000000-22-222-22-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ5422-22-2-22-2222-2-2-2-200000000-22-222-2-22200000000000000000000-22-222-22-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ5522-22-2-22-22-2-200002222−2−2−2−22-22000000−2−222−2−22222−2−200002-2-222−2−22−222−2ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ1400000000
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Here ζ is a primitive root of unity of order 32 (ζ32 = 1); i = ζ8.