Finite Group Databasebeta

← Group #72342917

Character table — Group #72342917

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size1122222444444444444488888888888888888888881616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232323232326464128128128
order12244882224444481616161622244444444888881616161616164488888161616161616161616161616323232323232323222222444444444432323232323232323232323224888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111-1-11-1-11-1-1-1-11111111111111-1-11-1-111-1-1-1-111-1-1-1-1111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1
χ6111111111111111111111-1-11-1-11-1-1-1-11111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-111
χ7111111111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-11-1-11-1-1-1-111111111111-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111111-1-1
χ91111111111-1-111111111-11-1-11-1-111-1-1-1-1111111111111-1-11-1-1-111-1-1-1-111-1-111111111-111-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-111-11-1
χ101111111111-1-111111111-11-1-11-1-111-1-1-1-1111111111111-1-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-11111-1-1-1-11111-1-11-11
χ111111111111-1-111111111-11-1-11-1-111-1-1-1-1111111111-1-11-1-11-1-1-111-1-1-1-111-1-1111111111-1-1111-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-11
χ121111111111-1-111111111-11-1-11-1-111-1-1-1-1111111111-1-11-1-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-111-1-1111111-1-1-1-1111111-11-1
χ131111111111-1-111111111-1-11-1-11-1-1-111-1-111111111111-11-1-11-1-1-1-111-1-1-1-11111111111-1-1-111-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11
χ141111111111-1-111111111-1-11-1-11-1-1-111-1-111111111111-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11111111111-1-1-1-1-1-111-1
χ151111111111-1-111111111-1-11-1-11-1-1-111-1-1111111111-1-1-11-1-11-1-1-1-111-1-1-1-11111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1
χ161111111111-1-111111111-1-11-1-11-1-1-111-1-1111111111-1-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-11111-1-111111111-1-1-1-111-1-11
χ172222222222222222-2-2-2-22222222222222222-2-2-2-2-2-20022222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ182222222222222222-2-2-2-22-2-22-2-22-2-2-2-222222-2-2-2-2-2-200-2-22-2-2-2-22222-2-222220000000000000000000000000000000000000000
χ192222222222-2-22222-2-2-2-2-22-2-22-2-222-2-2-2-2222-2-2-2-2-2-2002-2-22-222-2-22222-2-2220000000000000000000000000000000000000000
χ202222222222-2-22222-2-2-2-2-2-22-2-22-2-2-222-2-2222-2-2-2-2-2-200-22-2-222222-2-22222-2-20000000000000000000000000000000000000000
χ2122222222-2-2002-2-222222002002000-2-2002-2-222-2-2-2-2220-20020000220000-2-200000000000-2-202-2-200002200000000000000000
χ2222222222-2-2002-2-222222002002000-2-2002-2-222-2-2-2-2-2-20-20020000220000-2-200000000000220-2220000-2-200000000000000000
χ2322222222-2-2002-2-22222200-200-200022002-2-222-2-2-2-2220200-20000-2-2000022000000000002202-2-20000-2-200000000000000000
χ2422222222-2-2002-2-22222200-200-200022002-2-222-2-2-2-2-2-20200-20000-2-200002200000000000-2-20-22200002200000000000000000
χ2522222222-2-2002-2-22-2-2-2-2002002000-2-2002-2-2-2-22222000-20020000-2-20000220000000022-200-20002-22-20000000000000000000
χ2622222222-2-2002-2-22-2-2-2-2002002000-2-2002-2-2-2-22222000-20020000-2-200002200000000-2-22002000-22-220000000000000000000
χ2722222222-2-2002-2-22-2-2-2-200-200-200022002-2-2-2-22222000200-20000220000-2-2000000002-2200-20002-2-220000000000000000000
χ2822222222-2-2002-2-22-2-2-2-200-200-200022002-2-2-2-22222000200-20000220000-2-200000000-22-2002000-222-20000000000000000000
χ292222222-22-200-22-2222220200200-2-20000-22-2-2-222-2-222-2002000220000-2-200000000000-2-2000-22-200220000000000000000000
χ302222222-22-200-22-2222220200200-2-20000-22-2-2-222-2-2-2-2-2002000220000-2-200000000000220002-2200-2-20000000000000000000
χ312222222-22-200-22-2222220-200-200220000-22-2-2-222-2-222200-2000-2-20000220000000000022000-22-200-2-20000000000000000000
χ322222222-22-200-22-2222220-200-200220000-22-2-2-222-2-2-2-2200-2000-2-200002200000000000-2-20002-2200220000000000000000000
χ332222222-22-200-22-22-2-2-2-20200200-2-20000-22-222-2-22200-2002000-2-200002200000000002002-2-2000-22002-200000000000000000
χ342222222-22-200-22-22-2-2-2-20200200-2-20000-22-222-2-22200-2002000-2-20000220000000000-200-2220002-200-2200000000000000000
χ352222222-22-200-22-22-2-2-2-20-200-200220000-22-222-2-22200200-2000220000-2-20000000000200-22-2000-2200-2200000000000000000
χ362222222-22-200-22-22-2-2-2-20-200-200220000-22-222-2-22200200-2000220000-2-20000000000-2002-220002-2002-200000000000000000
χ372222222-2-2222-2-2222222-200-2002000022-2-22-2-2-2-2222200-200-2-2000022000000000000200002-2-22-2-2000000000000000000000
χ382222222-2-2222-2-2222222-200-2002000022-2-22-2-2-2-222-2-200-200-2-2000022000000000000-20000-222-222000000000000000000000
χ392222222-2-2222-2-222-2-2-2-2-200-2002000022-2-222222-2-20000-200220000-2-200000000000002-22-2000000-22-2200000000000000000
χ402222222-2-2222-2-222-2-2-2-2-200-2002000022-2-222222-2-20000-200220000-2-20000000000000-22-220000002-22-200000000000000000
χ412222222-2-22-2-2-2-2222222200200-20000-2-2-2-22-2-2-2-2222200200220000-2-2000000000000-20000-2-2-2222000000000000000000000
χ422222222-2-22-2-2-2-2222222200200-20000-2-2-2-22-2-2-2-222-2-200200220000-2-200000000000020000222-2-2-2000000000000000000000
χ432222222-2-22-2-2-2-222-2-2-2-2200200-20000-2-2-2-222222-2-20000200-2-200002200000000000002-2-22000000-222-200000000000000000
χ442222222-2-22-2-2-2-222-2-2-2-2200200-20000-2-2-2-222222-2-20000200-2-20000220000000000000-222-20000002-2-2200000000000000000
χ4522222-2-222222222-2000022222222222-2-2-2-2-200000000-2-2-2-2-20000000000002222−2−2−2−200000000000000022−2−222−2−222−2−200000
χ4622222-2-222222222-2000022222222222-2-2-2-2-200000000-2-2-2-2-2000000000000−2−2−2−22222000000000000000−2−222−2−222−2−22200000
χ4722222-2-222222222-200002-2-22-2-22-2-2-2-2-2-2-2-2-20000000022-2220000000000002222−2−2−2−200000000000000022−2−2−2−222−2−22200000
χ4822222-2-222222222-200002-2-22-2-22-2-2-2-2-2-2-2-2-20000000022-222000000000000−2−2−2−22222000000000000000−2−22222−2−222−2−200000
χ4922222-2-2222-2-2222-20000-22-2-22-2-222-2-222-2-2-200000000-222-220000000000002222−2−2−2−2000000000000000−2−22222−2−2−2−22200000
χ5022222-2-2222-2-2222-20000-22-2-22-2-222-2-222-2-2-200000000-222-22000000000000−2−2−2−2222200000000000000022−2−2−2−22222−2−200000
χ5122222-2-2222-2-2222-20000-2-22-2-22-2-2-22222-2-2-2000000002-222-20000000000002222−2−2−2−2000000000000000−2−222−2−22222−2−200000
χ5222222-2-2222-2-2222-20000-2-22-2-22-2-2-22222-2-2-2000000002-222-2000000000000−2−2−2−2222200000000000000022−2−222−2−2−2−22200000
χ53222-2-200-2-2-22222202−22−2-2222-2-2-22-22-2000002−22−22−200000002−22−22−22−22−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000
χ54222-2-200-2-2-22222202−22−2-2222-2-2-22-22-2000002−22−22−200000002−22−22−22−22−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000
χ55222-2-200-2-2-22222202−22−2-2-2-2222-2-22-22000002−22−22−200000002−2−22−222−2−22−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000
χ56222-2-200-2-2-22222202−22−2-2-2-2222-2-22-22000002−22−22−200000002−2−22−222−2−22−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000
χ57222-2-200-2-2-2222220−22−22-2222-2-2-22-22-200000−22−22−220000000−22−22−22−22−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000
χ58222-2-200-2-2-2222220−22−22-2222-2-2-22-22-200000−22−22−220000000−22−22−22−22−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000
χ59222-2-200-2-2-2222220−22−22-2-2-2222-2-22-2200000−22−22−220000000−222−22−2−222−22−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000
χ60222-2-200-2-2-2222220−22−22-2-2-2222-2-22-2200000−22−22−220000000−222−22−2−222−22−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000
χ61222-2-200-2-2-2-2-222202−22−222-2-2-2222-2-22000002−22−22−20000000−222−2−22−222−2−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000
χ62222-2-200-2-2-2-2-222202−22−222-2-2-2222-2-22000002−22−22−20000000−222−2−22−222−2−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000
χ63222-2-200-2-2-2-2-222202−22−22-22-22-22-222-2000002−22−22−20000000−22−222−2−22−222−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000
χ64222-2-200-2-2-2-2-222202−22−22-22-22-22-222-2000002−22−22−20000000−22−222−2−22−222−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000
χ65222-2-200-2-2-2-2-22220−22−2222-2-2-2222-2-2200000−22−22−2200000002−2−222−22−2−222−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000
χ66222-2-200-2-2-2-2-22220−22−2222-2-2-2222-2-2200000−22−22−2200000002−2−222−22−2−222−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000
χ67222-2-200-2-2-2-2-22220−22−222-22-22-22-222-200000−22−22−2200000002−22−2−222−22−2−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000
χ68222-2-200-2-2-2-2-22220−22−222-22-22-22-222-200000−22−22−2200000002−22−2−222−22−2−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000
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χ7044444-4-44-4-4004-4-4-4000000-400-40004400-444000000000-40040000000000000000000000000000000000000000000000000000
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χ75444-4-40044-444-4-44022−2222−22400-400-4000000000−2222−222222−220000000−2222000022−2200000000000000000000000000000000000000000000
χ76444-4-40044-444-4-440−2222−2222400-400-400000000022−2222−22−2222000000022−220000−222200000000000000000000000000000000000000000000
χ77444-4-40044-4-4-4-4-44022−2222−22-4004004000000000−2222−222222−22000000022−220000−222200000000000000000000000000000000000000000000
χ78444-4-40044-4-4-4-4-440−2222−2222-400400400000000022−2222−22−22220000000−2222000022−2200000000000000000000000000000000000000000000
χ79444-4-4004-4400-44-4022−2222−220400-400-440000000−222222−22−222200000000022−220000−2222000000000000000000000000000000000000000000
χ80444-4-4004-4400-44-4022−2222−220-4004004-40000000−222222−22−2222000000000−2222000022−22000000000000000000000000000000000000000000
χ81444-4-4004-4400-44-40−2222−22220400-400-44000000022−22−222222−22000000000−2222000022−22000000000000000000000000000000000000000000
χ82444-4-4004-4400-44-40−2222−22220-4004004-4000000022−22−222222−2200000000022−220000−2222000000000000000000000000000000000000000000
χ83444-4-400-444004-4-4022−2222−2200400-4000-440000022−22−2222−22220000000000022−220000−22220000000000000000000000000000000000000000
χ84444-4-400-444004-4-4022−2222−2200-40040004-40000022−22−2222−222200000000000−2222000022−220000000000000000000000000000000000000000
χ85444-4-400-444004-4-40−2222−222200400-4000-4400000−222222−2222−2200000000000−2222000022−220000000000000000000000000000000000000000
χ86444-4-400-444004-4-40−2222−222200-40040004-400000−222222−2222−220000000000022−220000−22220000000000000000000000000000000000000000
χ8744-4-444400000000-444-4-400000000000000000000004i−4i000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000002-2000
χ8844-4-444400000000-444-4-400000000000000000000004i−4i00000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000-22000
χ8944-4-444400000000-444-4-40000000000000000000000−4i4i000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000-22000
χ9044-4-444400000000-444-4-40000000000000000000000−4i4i00000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000002-2000
χ9188-88-80000000000042−42−4242000000000000000000000000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ9288-88-80000000000042−42−424200000000000000000000000000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ9388-88-800000000000−424242−42000000000000000000000000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ9488-88-800000000000−424242−4200000000000000000000000000000000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ9588-8-888800000000-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-88-8-80000000080000000000000000000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ9788-8-88-8-8000000008000000000000000000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ9816-1600082−820008-8000000000000000000042−4200000000000000000000000000000000000000000000000000000000000000000000
χ9916-1600082−82000-880000000000000000000−424200000000000000000000000000000000000000000000000000000000000000000000
χ10016-16000−82820008-80000000000000000000−424200000000000000000000000000000000000000000000000000000000000000000000
χ10116-16000−8282000-88000000000000000000042−4200000000000000000000000000000000000000000000000000000000000000000000

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