Finite Group Databasebeta

← Group #511959

Character table — Group #511959

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444444444444444444444444444444444443232323232323232
order122222224444888888881616161616161616161616161616161622222244444488888888888816161616161616161616161616161616161616161616161624444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-1-11-11
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-111-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-11-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-111-11-1-11
χ17222222222222-2-2-2-2-2-2-2-20000000000000000222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-20000000022222222−2−2−2−2−2−2−2−22222-2-2-2-2-2-2220000000000002222−2−2−2−22222−2−2−2−22222−2−2−2−200000000
χ2222222222-2-2-2-20000000022222222−2−2−2−2−2−2−2−222-2-222-2-222-2-20000000000002222−2−2−2−2−2−2−2−22222−2−2−2−2222200000000
χ2322222222-2-2-2-20000000022222222−2−2−2−2−2−2−2−2-2-2222222-2-2-2-2000000000000−2−2−2−222222222−2−2−2−2−2−2−2−2222200000000
χ2422222222-2-2-2-20000000022222222−2−2−2−2−2−2−2−2-2-2-2-2-2-2222222000000000000−2−2−2−22222−2−2−2−222222222−2−2−2−200000000
χ2522222222-2-2-2-200000000−2−2−2−2−2−2−2−2222222222222-2-2-2-2-2-222000000000000−2−2−2−22222−2−2−2−22222−2−2−2−2222200000000
χ2622222222-2-2-2-200000000−2−2−2−2−2−2−2−22222222222-2-222-2-222-2-2000000000000−2−2−2−222222222−2−2−2−22222−2−2−2−200000000
χ2722222222-2-2-2-200000000−2−2−2−2−2−2−2−222222222-2-2222222-2-2-2-20000000000002222−2−2−2−2−2−2−2−222222222−2−2−2−200000000
χ2822222222-2-2-2-200000000−2−2−2−2−2−2−2−222222222-2-2-2-2-2-22222220000000000002222−2−2−2−22222−2−2−2−2−2−2−2−2222200000000
χ2922-2-2-222-222-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-200002-22i2i−2i−2i2i2i−2i−2i000022−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
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χ3322-2-2-222-222-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002-200002-22i2i−2i−2i2i2i−2i−2i0000−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ3422-2-2-222-222-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002-200002-2−2i−2i2i2i−2i−2i2i2i000022−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ3522-2-2-222-222-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-220000-222i2i−2i−2i−2i−2i2i2i0000−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ3622-2-2-222-222-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-220000-22−2i−2i2i2i2i2i−2i−2i000022−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ3722-2-2-222-2-2-2222222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00002-20000-220000000022-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ3822-2-2-222-2-2-2222222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000-2200002-200000000-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ3922-2-2-222-2-2-2222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00002-20000-220000000022-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
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χ4122-2-2-222-2-2-222-2-2-2-22222000000000000000000002-20000-2200000000-2-22222-2-2-2-222-2-22222-2-20000000000000000
χ4222-2-2-222-2-2-222-2-2-2-22222000000000000000000002-20000-2200000000-2-222-2-22222-2-222-2-2-2-2220000000000000000
χ4322-2-2-222-2-2-222-2-2-2-2222200000000000000000000-2200002-20000000022-2-222-2-2-2-22222-2-2-2-2220000000000000000
χ4422-2-2-222-2-2-222-2-2-2-2222200000000000000000000-2200002-20000000022-2-2-2-22222-2-2-2-22222-2-20000000000000000
χ452-22-2-22-222-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-200002-2002i−2i2i−2i00002i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ462-22-2-22-222-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-200002-200−2i2i−2i2i0000−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ472-22-2-22-222-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-220000-22002i−2i2i−2i0000−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ482-22-2-22-222-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-220000-2200−2i2i−2i2i00002i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ492-22-2-22-222-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-200002-2002i−2i2i−2i00002i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ502-22-2-22-222-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-200002-200−2i2i−2i2i0000−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ512-22-2-22-222-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-220000-22002i−2i2i−2i0000−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ522-22-2-22-222-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-220000-2200−2i2i−2i2i00002i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ532-22-2-22-22-22-2222-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i002-20000-220000002-22-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ542-22-2-22-22-22-2222-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00-2200002-2000000-22-22000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ552-22-2-22-22-22-2222-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i002-20000-220000002-22-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ562-22-2-22-22-22-2222-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00-2200002-2000000-22-220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ572-22-2-22-22-22-22-2-222-2-2220000000000000000002-20000-22000000-22-2200002-22-2-22-22000000002-22-2-22-2200000000
χ582-22-2-22-22-22-22-2-222-2-2220000000000000000002-20000-22000000-22-220000-22-222-22-200000000-22-222-22-200000000
χ592-22-2-22-22-22-22-2-222-2-222000000000000000000-2200002-20000002-22-200002-22-2-22-2200000000-22-222-22-200000000
χ602-22-2-22-22-22-22-2-222-2-222000000000000000000-2200002-20000002-22-20000-22-222-22-2000000002-22-2-22-2200000000
χ612-2-2222-2-22-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-2222-200002-200002-2-22000000002-2-222-2-22000000000000000000000000
χ622-2-2222-2-22-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-222-220000-220000-222-200000000-222-2-222-2000000000000000000000000
χ632-2-2222-2-22-2-2222-2-2-2-222-2-22222-2-2-2-22222-2-22-200002-200002-2-2200000000-222-2-222-2000000000000000000000000
χ642-2-2222-2-22-2-2222-2-2-2-222-2-22222-2-2-2-22222-2-2-220000-220000-222-2000000002-2-222-2-22000000000000000000000000
χ652-2-2222-2-22-2-22-2-22222-2-200000000000000002-200002-20000-222-200000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000
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χ672-2-2222-2-22-2-22-2-22222-2-20000000000000000-220000-2200002-2-2200000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000
χ682-2-2222-2-22-2-22-2-22222-2-20000000000000000-220000-2200002-2-220000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000
χ692-2-2222-2-2-222-20000000022−2−2−2−222−2−22222−2−22-20000-22000000002i−2i−2i2i−2i2i2i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ702-2-2222-2-2-222-20000000022−2−2−2−222−2−22222−2−22-20000-2200000000−2i2i2i−2i2i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ712-2-2222-2-2-222-20000000022−2−2−2−222−2−22222−2−2-2200002-2000000002i−2i−2i2i2i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ722-2-2222-2-2-222-20000000022−2−2−2−222−2−22222−2−2-2200002-200000000−2i2i2i−2i−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ732-2-2222-2-2-222-200000000−2−22222−2−222−2−2−2−2222-20000-22000000002i−2i−2i2i−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ742-2-2222-2-2-222-200000000−2−22222−2−222−2−2−2−2222-20000-2200000000−2i2i2i−2i2i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ752-2-2222-2-2-222-200000000−2−22222−2−222−2−2−2−222-2200002-2000000002i−2i−2i2i2i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
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χ774444-4-4-4-4000022−2222−2222−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000000000000000
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χ794444-4-4-4-40000−2222−2222−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-40000−2222−2222−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000000000000000
χ8144-4-44-4-44000022−2222−22−2222−22222ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000000000000000000000
χ8244-4-44-4-44000022−2222−22−2222−2222−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000000000000000000000
χ8344-4-44-4-440000−2222−222222−2222−222ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-440000−2222−222222−2222−22−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000000000000000000000
χ854-44-44-44-4000022−22−222222−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000000000000000000000
χ864-44-44-44-4000022−22−222222−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000000000000000000000
χ874-44-44-44-40000−222222−22−222222−222ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000000000000000000000
χ884-44-44-44-40000−222222−22−222222−22−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000000000000000000000
χ894-4-44-4-444000022−22−2222−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000000000000000
χ904-4-44-4-444000022−22−2222−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4440000−222222−2222−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4440000−222222−2222−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000000000000000

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