Finite Group Databasebeta

← Group #13160231

Character table — Group #13160231

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222224446666888242244444888121212121616164822444448881212121216161648224444488812121212161616482244444888121212121616164899181818181836363654545454727272216
order12346881224241616161641212436312624241224244848484812121212363126242412242448484848121212123631262424122424484848481212121236312624241224244848484812121212226468812242416161616412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1
χ31111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-1
χ41111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-11
χ522222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-200000000
χ6222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000
χ7222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000
χ822-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-10
χ922-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-2110
χ1022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i30
χ1122-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i30
χ122-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000
χ132-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000
χ142-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000
χ152-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000
χ1644-2-4-2002000000000044-2-4-2002000000000044-2-4-2002000000000044-2-4-2002000000000044-2-4-2002000000000044-2-4-20020000000000
χ174-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−2200000000
χ184-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−200000000
χ19111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2011111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ211111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-11111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ221111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111-1
χ2322222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-20000000022222-2-22-2-200000000-2-2-2-2-222-22200000000
χ24222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000222-2200-20022−2−20000-2-2-22-200200−2−2220000
χ25222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000222-2200-200−2−2220000-2-2-22-20020022−2−20000
χ2622-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-1022-12-122-1-1-100002-1-10-2-21-21-2-21110000-2110
χ2722-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-211022-12-122-1-1-10000-2110-2-21-21-2-211100002-1-10
χ2822-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i3022-12-1-2-2-11100000−i3i30-2-21-21221-1-100000i3−i30
χ2922-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i3022-12-1-2-2-11100000i3−i30-2-21-21221-1-100000−i3i30
χ302-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300002-220-22−202−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000
χ312-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300002-220-22−202−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000
χ322-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700002-220-2−220−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000
χ332-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700002-220-2−220−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000
χ3444-2-4-2002000000000044-2-4-2002000000000044-2-4-2002000000000044-2-4-2002000000000044-2-4-20020000000000-4-424200-20000000000
χ354-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−22000000004-4-20222−220−2200000000-4420-2−222202−200000000
χ364-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−2000000004-4-202−222202−200000000-4420-222−220−2200000000
χ37222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3822222222222222-2-2-2-222222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ392222222222-2-2-2-2222-22222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-11000000000000000000
χ402222222222-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-1000000000000000000
χ4144444-4-44-4-40000000044444-4-44-4-400000000-2-2-2-2-222-22200000000-2-2-2-2-222-22200000000-2-2-2-2-222-22200000000000000000000000000
χ42444-4400-4002222−22−220000444-4400-4002222−22−220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000000000000000000000
χ43444-4400-400−22−2222220000444-4400-400−22−2222220000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000000000000000000000
χ4444-24-244-2-2-200004-2-2044-24-244-2-2-200004-2-20-2-21-21-2-21110000-2110-2-21-21-2-21110000-2110-2-21-21-2-21110000-2110000000000000000000
χ4544-24-244-2-2-20000-422044-24-244-2-2-20000-4220-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-10000000000000000000
χ4644-24-2-4-4-22200000−2i32i3044-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i30000000000000000000
χ4744-24-2-4-4-222000002i3−2i3044-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i30000000000000000000
χ484-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300004-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000000000
χ494-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300004-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000000000
χ504-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700004-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000000000000
χ514-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700004-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000000000
χ5288-4-8-4004000000000088-4-8-40040000000000-4-424200-20000000000-4-424200-20000000000-4-424200-20000000000000000000000000000
χ538-8-40442−420−2222000000008-8-40442−420−222200000000-4420-2−222202−200000000-4420-2−222202−200000000-4420-2−222202−200000000000000000000000000
χ548-8-404−4242022−22000000008-8-404−4242022−2200000000-4420-222−220−2200000000-4420-222−220−2200000000-4420-222−220−2200000000000000000000000000
χ55222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ5622222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ572222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-112222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-11000000000000000000
χ582222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-12222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-1000000000000000000
χ5944444-4-44-4-400000000-2-2-2-2-222-2220000000044444-4-44-4-400000000-2-2-2-2-222-22200000000-2-2-2-2-222-22200000000000000000000000000
χ60444-4400-4002222−22−220000-2-2-22-200200−2−2220000444-4400-4002222−22−220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000000000000000000000
χ61444-4400-400−22−2222220000-2-2-22-20020022−2−20000444-4400-400−22−2222220000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000000000000000000000
χ6244-24-244-2-2-200004-2-20-2-21-21-2-21110000-211044-24-244-2-2-200004-2-20-2-21-21-2-21110000-2110-2-21-21-2-21110000-2110000000000000000000
χ6344-24-244-2-2-20000-4220-2-21-21-2-211100002-1-1044-24-244-2-2-20000-4220-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-10000000000000000000
χ6444-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i3044-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i30000000000000000000
χ6544-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i3044-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i30000000000000000000
χ664-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300004-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000000000
χ674-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300004-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000000000
χ684-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700004-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000000000000
χ694-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700004-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000000000
χ7088-4-8-40040000000000-4-424200-2000000000088-4-8-40040000000000-4-424200-20000000000-4-424200-20000000000000000000000000000
χ718-8-40442−420−222200000000-4420-2−222202−2000000008-8-40442−420−222200000000-4420-2−222202−200000000-4420-2−222202−200000000000000000000000000
χ728-8-404−4242022−2200000000-4420-222−220−22000000008-8-404−4242022−2200000000-4420-222−220−2200000000-4420-222−220−2200000000000000000000000000
χ73222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ7422222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ752222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-112222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-11000000000000000000
χ762222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-12222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-1000000000000000000
χ7744444-4-44-4-400000000-2-2-2-2-222-22200000000-2-2-2-2-222-2220000000044444-4-44-4-400000000-2-2-2-2-222-22200000000000000000000000000
χ78444-4400-4002222−22−220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000444-4400-4002222−22−220000-2-2-22-200200−2−2220000000000000000000000
χ79444-4400-400−22−2222220000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000444-4400-400−22−2222220000-2-2-22-20020022−2−20000000000000000000000
χ8044-24-244-2-2-200004-2-20-2-21-21-2-21110000-2110-2-21-21-2-21110000-211044-24-244-2-2-200004-2-20-2-21-21-2-21110000-2110000000000000000000
χ8144-24-244-2-2-20000-4220-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-1044-24-244-2-2-20000-4220-2-21-21-2-211100002-1-10000000000000000000
χ8244-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i3044-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i30000000000000000000
χ8344-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i3044-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i30000000000000000000
χ844-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300004-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000000000000
χ854-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300004-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000000000000
χ864-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700004-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000000000000
χ874-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700004-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000000000000
χ8888-4-8-40040000000000-4-424200-20000000000-4-424200-2000000000088-4-8-40040000000000-4-424200-20000000000000000000000000000
χ898-8-40442−420−222200000000-4420-2−222202−200000000-4420-2−222202−2000000008-8-40442−420−222200000000-4420-2−222202−200000000000000000000000000
χ908-8-404−4242022−2200000000-4420-222−220−2200000000-4420-222−220−22000000008-8-404−4242022−2200000000-4420-222−220−2200000000000000000000000000
χ91222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222000000000000000000
χ9222222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122222222222222-2-2-2-2000000000000000000
χ932222222222-2-2-2-2222-2-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-112222222222-2-2-2-2222-2000000000000000000
χ942222222222-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111-12222222222-2-2-2-2-2-2-22000000000000000000
χ9544444-4-44-4-400000000-2-2-2-2-222-22200000000-2-2-2-2-222-22200000000-2-2-2-2-222-2220000000044444-4-44-4-400000000000000000000000000
χ96444-4400-4002222−22−220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000-2-2-22-200200−2−2220000444-4400-4002222−22−220000000000000000000000
χ97444-4400-400−22−2222220000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000-2-2-22-20020022−2−20000444-4400-400−22−2222220000000000000000000000
χ9844-24-244-2-2-200004-2-20-2-21-21-2-21110000-2110-2-21-21-2-21110000-2110-2-21-21-2-21110000-211044-24-244-2-2-200004-2-20000000000000000000
χ9944-24-244-2-2-20000-4220-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-10-2-21-21-2-211100002-1-1044-24-244-2-2-20000-4220000000000000000000
χ10044-24-2-4-4-22200000−2i32i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i30-2-21-21221-1-100000i3−i3044-24-2-4-4-22200000−2i32i30000000000000000000
χ10144-24-2-4-4-222000002i3−2i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i30-2-21-21221-1-100000−i3i3044-24-2-4-4-222000002i3−2i30000000000000000000
χ1024-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000-22-202−220−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300004-440-422−22022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000000000000000000
χ1034-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000-22-202−220−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300004-440-422−22022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000000000000000000
χ1044-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000-22-2022−202−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ4700004-440-4−22220−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000000000000000000000
χ1054-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000-22-2022−202−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ4700004-440-4−22220−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000000000000000000000
χ10688-4-8-40040000000000-4-424200-20000000000-4-424200-20000000000-4-424200-2000000000088-4-8-40040000000000000000000000000000
χ1078-8-40442−420−222200000000-4420-2−222202−200000000-4420-2−222202−200000000-4420-2−222202−2000000008-8-40442−420−222200000000000000000000000000
χ1088-8-404−4242022−2200000000-4420-222−220−2200000000-4420-222−220−2200000000-4420-222−220−22000000008-8-404−4242022−2200000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.