Finite Group Databasebeta

← Group #72322395

Character table — Group #72322395

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11112222222222222222224444444444444444444444444444448888888888888888888888888888888888888888888832323232323232323232323232323232
order12224444444444888888882488888888888816161616161616161616161616161616888816161616161616163232323232323232323232323232323232323232323232323232323232323232244488881616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-1ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ611-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-1ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ611-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−ii−ii−i1111-1-1-1-1−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii1111-1-1-1-1ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ211-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii1111-1-1-1-1ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ211-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii−ii−ii1111-1-1-1-1−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ171111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-11-1
χ181111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11-11
χ191111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-11-1-11-11-11-11
χ201111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-11-111-11-11-11-1
χ211111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ221111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ231111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ241111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−i11ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−ii11-1-1-1-111ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ61-1-11i−i−iiζ2−ζ2−ζ2ζ2ζ6−ζ6−ζ6ζ6
χ261111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−i11ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−ii11-1-1-1-111ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-111-1−iii−i−ζ2ζ2ζ2−ζ2−ζ6ζ6ζ6−ζ6
χ271111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−i11ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−ii11-1-1-1-111−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ61-1-11i−i−ii−ζ2ζ2ζ2−ζ2−ζ6ζ6ζ6−ζ6
χ281111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−i11ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−ii−ii11-1-1-1-111−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-111-1−iii−iζ2−ζ2−ζ2ζ2ζ6−ζ6−ζ6ζ6
χ291111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii11−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−ii−i11-1-1-1-111ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ21-1-11−iii−iζ6−ζ6−ζ6ζ6ζ2−ζ2−ζ2ζ2
χ301111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii11−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−ii−i11-1-1-1-111ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-111-1i−i−ii−ζ6ζ6ζ6−ζ6−ζ2ζ2ζ2−ζ2
χ311111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii11−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−ii−i11-1-1-1-111−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ21-1-11−iii−i−ζ6ζ6ζ6−ζ6−ζ2ζ2ζ2−ζ2
χ321111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii11−i−iiiiiii−i−i−i−i−i−i−i−iiiiii−ii−i11-1-1-1-111−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-111-1i−i−iiζ6−ζ6−ζ6ζ6ζ2−ζ2−ζ2ζ2
χ33222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222222222-2-2-2-222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3522222222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-20000000000000000-2-22200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3622222222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-20000000000000000-2-22200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3722222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-20000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ3822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000022-2-200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ392222222222-2-2-2-222222222-2-2-2-22i2i−2i−2i-2-2−2i−2i2i2i0000000000000000−2i2i2i−2i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ402222222222-2-2-2-222222222-2-2-2-22i2i−2i−2i-2-2−2i−2i2i2i0000000000000000−2i2i2i−2i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ412222222222-2-2-2-222222222-2-2-2-2−2i−2i2i2i-2-22i2i−2i−2i00000000000000002i−2i−2i2i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000
χ422222222222-2-2-2-222222222-2-2-2-2−2i−2i2i2i-2-22i2i−2i−2i00000000000000002i−2i−2i2i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000
χ432222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222i2i−2i−2i222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i-2-2-2-22222000000000000000000000000000000000000000000000000
χ442222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222−2i−2i2i2i22−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i2i−2i2i-2-2-2-22222000000000000000000000000000000000000000000000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000022-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000022-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ472222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000-2-2220000000022−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−20000000000000000
χ482222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000-2-22200000000−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−2220000000000000000
χ492222-2-2-2-2222222-2-2-2-22222-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ502222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-222-2-222000000000000000000000000000000000000000000000000
χ512222-2-2-2-222-2-2-2-22222-2-2-2-222-2-22i2i−2i−2i222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ522222-2-2-2-222-2-2-2-22222-2-2-2-222-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2i−2i2i−2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ532222-2-2-2-222-2-2-2-2-2-2-2-2222222222i2i−2i−2i-2-2−2i−2i2i2i00000000000000002i−2i−2i2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ542222-2-2-2-222-2-2-2-2-2-2-2-2222222222i2i−2i−2i-2-2−2i−2i2i2i00000000000000002i−2i−2i2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
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χ10444-4-40000-44−4i4i4i−4i−4i−4i4i4i0000004-40000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000000000000000000
χ1058-88-8008i−8i00000042−4242−424i2−4i24i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8008i−8i000000−4242−4242−4i24i2−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-800−8i8i00000042−4242−42−4i24i2−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-800−8i8i000000−4242−42424i2−4i24i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-888i−8i000000004i2−4i2−4i24i242−42−4242000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888i−8i00000000−4i24i24i2−4i2−424242−42000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88−8i8i000000004i2−4i2−4i24i2−424242−42000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88−8i8i00000000−4i24i24i2−4i242−42−4242000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.