Finite Group Databasebeta

← Group #122484

Character table — Group #122484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122244444444888888888888888888888888888888882444888888881616161616161616161616161616161616161616161616161616161616161616224488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-11-111-1-1iiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-11-11-1-111−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-11-111-1-1−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-11-11-1-111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−iii
χ171111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-111-1-1ii−i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ21-1-11i−ii−iζ2−ζ2ζ6−ζ6ζ6−ζ6ζ2−ζ2
χ181111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-111-1-1ii−i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-111-1−ii−ii−ζ2ζ2−ζ6ζ6−ζ6ζ6−ζ2ζ2
χ191111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-111-1-1ii−i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ21-1-11i−ii−i−ζ2ζ2−ζ6ζ6−ζ6ζ6−ζ2ζ2
χ201111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-111-1-1ii−i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-111-1−ii−iiζ2−ζ2ζ6−ζ6ζ6−ζ6ζ2−ζ2
χ211111-1-1-1-111-1-1ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii-1-11111-1-1ii−i−iζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ611-1-1i−i−iiζ6−ζ6−ζ2ζ2ζ2−ζ2−ζ6ζ6
χ221111-1-1-1-111-1-1ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii-1-11111-1-1ii−i−iζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-1-111−iii−i−ζ6ζ6ζ2−ζ2−ζ2ζ2ζ6−ζ6
χ231111-1-1-1-111-1-1ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii-1-11111-1-1ii−i−i−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ611-1-1i−i−ii−ζ6ζ6ζ2−ζ2−ζ2ζ2ζ6−ζ6
χ241111-1-1-1-111-1-1ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii-1-11111-1-1ii−i−i−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-1-111−iii−iζ6−ζ6−ζ2ζ2ζ2−ζ2−ζ6ζ6
χ251111-1-1-1-111-1-1−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i-1-11111-1-1−i−iiiζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ211-1-1−iii−iζ2−ζ2−ζ6ζ6ζ6−ζ6−ζ2ζ2
χ261111-1-1-1-111-1-1−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i-1-11111-1-1−i−iiiζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-1-111i−i−ii−ζ2ζ2ζ6−ζ6−ζ6ζ6ζ2−ζ2
χ271111-1-1-1-111-1-1−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i-1-11111-1-1−i−iii−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ211-1-1−iii−i−ζ2ζ2ζ6−ζ6−ζ6ζ6ζ2−ζ2
χ281111-1-1-1-111-1-1−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i-1-11111-1-1−i−iii−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-1-111i−i−iiζ2−ζ2−ζ6ζ6ζ6−ζ6−ζ2ζ2
χ291111-1-1-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-111-1-1−i−iiiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ61-1-11−ii−iiζ6−ζ6ζ2−ζ2ζ2−ζ2ζ6−ζ6
χ301111-1-1-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-111-1-1−i−iiiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-111-1i−ii−i−ζ6ζ6−ζ2ζ2−ζ2ζ2−ζ6ζ6
χ311111-1-1-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-111-1-1−i−iii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ61-1-11−ii−ii−ζ6ζ6−ζ2ζ2−ζ2ζ2−ζ6ζ6
χ321111-1-1-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-111-1-1−i−iii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-111-1i−ii−iζ6−ζ6ζ2−ζ2ζ2−ζ2ζ6−ζ6
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-2-222-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822222222-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-2-222-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022222-2-220000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022222-2-2200000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ4122222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-22-2-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4222222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-22-2-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-222-20000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-222-200000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ452222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ462222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i-2-222-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ472222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i-2-222-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ482222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i2i2i22-2-2-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ492222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i-22-22000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ502222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i2i2i-22-2200000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ512222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000002i2i−2i−2i2-22-2000000001+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
χ522222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000002i2i−2i−2i2-22-200000000−1−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
χ532222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000−2i−2i2i2i2-22-2000000001−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
χ542222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000−2i−2i2i2i2-22-200000000−1+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
χ552222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i-22-22000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ562222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000002i2i−2i−2i-22-2200000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ5722-2-22i−2i2i−2i2-22i−2i000000002ζ2−2ζ22ζ6−2ζ6000000002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ62ζ2−2ζ22ζ6−2ζ600002-22i−2i0000000000002ζ3−2ζ32ζ3−2ζ32ζ7−2ζ72ζ7−2ζ7000000002ζ−2ζ2ζ−2ζ2ζ5−2ζ52ζ5−2ζ50000000000000000
χ5822-2-22i−2i2i−2i2-22i−2i000000002ζ2−2ζ22ζ6−2ζ6000000002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ62ζ2−2ζ22ζ6−2ζ600002-22i−2i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ72ζ7−2ζ72ζ700000000−2ζ2ζ−2ζ2ζ−2ζ52ζ5−2ζ52ζ50000000000000000
χ5922-2-22i−2i2i−2i2-22i−2i000000002ζ2−2ζ22ζ6−2ζ600000000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ62ζ2−2ζ22ζ6−2ζ60000-22−2i2i00002ζ5−2ζ52ζ5−2ζ52ζ−2ζ2ζ−2ζ000000002ζ7−2ζ72ζ7−2ζ72ζ3−2ζ32ζ3−2ζ3000000000000000000000000
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χ1044-4-44-4-44400000000-444-40000−222222−2222−22−222222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000000000

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