Finite Group Databasebeta

← Group #147651

Character table — Group #147651

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888888888161616161616161616161616161616162244888816161616161616162244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1iiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ1011-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1iiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ1111-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−i−i−iiiii1-11-1-1-111−i−iiiii−i−i
χ1211-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−i−i−iiiii-11-1111-1-1ii−i−i−i−iii
χ1311-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ1411-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ1511-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111iiii−i−i−i−i1-11-1-1-111ii−i−i−i−iii
χ1611-1-1-111-111-1-1111-1-1-11-11111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111iiii−i−i−i−i-11-1111-1-1−i−iiiii−i−i
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ1922222222-2-2-2-222-22-2-2-220000000000002222−2−2−2−22222−2−2−2−222-2-2000022−2−222−2−20000000000000000
χ2022222222-2-2-2-222-22-2-2-220000000000002222−2−2−2−22222−2−2−2−2-2-2220000−2−222−2−2220000000000000000
χ2122222222-2-2-2-222-22-2-2-22000000000000−2−2−2−22222−2−2−2−2222222-2-20000−2−222−2−2220000000000000000
χ2222222222-2-2-2-222-22-2-2-22000000000000−2−2−2−22222−2−2−2−22222-2-222000022−2−222−2−20000000000000000
χ2322222222-2-2-2-2-2-22-2222-222222222-2-2-2-20000000000000000000000000000000022-2-2000000000000
χ2422222222-2-2-2-2-2-22-2222-222222222-2-2-2-200000000000000000000000000000000-2-222000000000000
χ2522222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002-22-200000000
χ2622222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000-22-2200000000
χ2722-2-2-222-222-2-2222-2-2-22-2-2-2-2-22222-2-22200000000000000002-22-2-2-222000000000000000000000000
χ2822-2-2-222-222-2-2222-2-2-22-2-2-2-2-22222-2-2220000000000000000-22-2222-2-2000000000000000000000000
χ2922-2-2-222-2-2-22222-2-222-2-2000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-220000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3022-2-2-222-2-2-22222-2-222-2-2000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-222-20000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3122-2-2-222-2-2-22222-2-222-2-2000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-220000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3222-2-2-222-2-2-22222-2-222-2-2000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-222-20000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3322-2-2-222-2-2-222-2-222-2-2222222-2-2-2-2-2-222000000000000000000000000000000002-2-22000000000000
χ3422-2-2-222-2-2-222-2-222-2-2222222-2-2-2-2-2-22200000000000000000000000000000000-222-2000000000000
χ3522-2-2-222-2-2-222-2-222-2-222-2-2-2-2222222-2-20000000000000000000000000000000000002-2-2200000000
χ3622-2-2-222-2-2-222-2-222-2-222-2-2-2-2222222-2-2000000000000000000000000000000000000-222-200000000
χ372-222-22-2-22-22-22-22-22-2-2200000000000022−2−222−2−222−2−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ382-222-22-2-22-22-22-22-22-2-2200000000000022−2−222−2−222−2−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-222-22-2-22-22-22-22-22-2-22000000000000−2−222−2−222−2−222−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-222-22-2-22-22-22-22-22-2-22000000000000−2−222−2−222−2−222−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ412-222-22-2-22-22-2-22-22-222-222-2-222-2-22-2-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ422-222-22-2-22-22-2-22-22-222-222-2-222-2-22-2-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ432-222-22-2-22-22-2-22-22-222-2-2-222-2-222-222-2000000000000000000000000000000000000000000002i−2i2i−2i
χ442-222-22-2-22-22-2-22-22-222-2-2-222-2-222-222-200000000000000000000000000000000000000000000−2i2i−2i2i
χ452-222-22-2-2-22-222-2-2-2-222222-2-222-2-2-222-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ462-222-22-2-2-22-222-2-2-2-222222-2-222-2-2-222-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ472-222-22-2-2-22-222-2-2-2-2222-2-222-2-2222-2-2222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ482-222-22-2-2-22-222-2-2-2-2222-2-222-2-2222-2-22-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ492-2-2-222-222-2-222-222-22-2-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i−22−222−22−20000000000000000
χ502-2-2-222-222-2-222-222-22-2-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i2−22−2−22−220000000000000000
χ512-2-2-222-222-2-222-222-22-2-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i2−22−2−22−220000000000000000
χ522-2-2-222-222-2-222-222-22-2-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i−22−222−22−20000000000000000
χ532-2-2-222-222-2-22-22-2-22-22222-2-2-2-2222-22-200000000000000000000000000000000000000002-2-220000
χ542-2-2-222-222-2-22-22-2-22-22222-2-2-2-2222-22-20000000000000000000000000000000000000000-222-20000
χ552-2-2-222-222-2-22-22-2-22-222-2-22222-2-2-22-22000000000000000000000000000000000000000000002-2-22
χ562-2-2-222-222-2-22-22-2-22-222-2-22222-2-2-22-2200000000000000000000000000000000000000000000-222-2
χ572-2-2-222-22-222-22-2-222-22-222-2-2-2-222-22-220000000000000000000000002-2-22-222-20000000000000000
χ582-2-2-222-22-222-22-2-222-22-222-2-2-2-222-22-22000000000000000000000000-222-22-2-220000000000000000
χ592-2-2-222-22-222-22-2-222-22-2-2-22222-2-22-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ602-2-2-222-22-222-22-2-222-22-2-2-22222-2-22-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-400000000000022−2222−2222−2222−220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000000000
χ63444-44-4-4-400000000000022−2222−2222−2222−220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000000000
χ64444-44-4-4-4000000000000−2222−2222−2222−22220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000000000
χ65444-44-4-4-4000000000000−2222−2222−2222−22220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000000000
χ6644-44-4-4-4400000000000022−2222−22−2222−22220000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000000000000000
χ6744-44-4-4-4400000000000022−2222−22−2222−22220000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000000000000000
χ6844-44-4-4-44000000000000−2222−222222−2222−220000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000000000000000
χ6944-44-4-4-44000000000000−2222−222222−2222−220000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000000000000000
χ7044-4-4-444-444-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000
χ714-444-44-4-4-44-44-44444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ724-44-4-4-44400000000000022−22−222222−22−22220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000000000
χ734-44-4-4-44400000000000022−22−222222−22−22220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000000000
χ744-44-4-4-444000000000000−222222−22−222222−220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000000000
χ754-44-4-4-444000000000000−222222−22−222222−220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000000000
χ764-4-444-44-400000000000022−22−2222−222222−220000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000000000000000
χ774-4-444-44-400000000000022−22−2222−222222−220000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000000000000000
χ784-4-444-44-4000000000000−222222−2222−22−22220000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000000000000000
χ794-4-444-44-4000000000000−222222−2222−22−22220000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000000000000000
χ804-4-4-444-44-444-4-444-4-44-44000000000000000000000000000000000000000000000000000000000000

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