Finite Group Databasebeta

← Group #10949047

Character table — Group #10949047

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222223444466688881212121266881212161616161616161624242424242424244848484848484848484848484848484822442244246666121212122222881616161644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-11111-1-1
χ91111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11-11-11-11111-1-1-1-111-1-11-111-1-11-1
χ101111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-11-111-11111-1-1-1-1-1-111-11-1-111-11
χ111111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111-11-1-11-1-1-1-11111-1-1111-111-1-1-11
χ121111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-11-11-1-1-1-1111111-1-1-11-1-1111-1
χ131111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11-11-1-1111-1-1-1-11111-1-11-1-1-111-11
χ141111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-11-1111-1-1-1-111-1-111-1111-1-11-1
χ151111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-11-11-1-1-11111-1-1-1-1111-1-1-1111-1
χ161111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-11-111-1-1-11111-1-111-1-1-1111-1-1-11
χ1722222222222222-2-2-2-2222222-2-22200000000-2-2-2-2-2-2-2-200000000000000000000222200000000000000-2-2000000
χ1822222222222222-2-2-2-2222222-2-22200000000-2-2-2-2-2-2-2-200000000000000000000-2-2-2-20000000000000022000000
χ192222222-2-2-2-22220000-2-2-2-22200-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−200002-2-2200000000000000002−22−200
χ202222222-2-2-2-22220000-2-2-2-22200-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−20000-222-20000000000000000−22−2200
χ212222222-2-2-2-22220000-2-2-2-22200-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−2222200002-2-220000000000000000−22−2200
χ222222222-2-2-2-22220000-2-2-2-22200-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−222220000-222-200000000000000002−22−200
χ23222222-12222-1-1-12222-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ25222222-12222-1-1-12222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-111-1-111000000000000
χ26222222-12222-1-1-12222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-200002211-1-111-1-1000000000000
χ272222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-22222-2-2000000000000000000002-22-200000000000000-22000000
χ282222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-22222-2-200000000000000000000-22-22000000000000002-2000000
χ292222-2-22-222-222200002222-2-200-2-222−2−2−2−222000000002222−2−2−2−2−2−2−2−22222000022-2-200000000000000002−2−2200
χ302222-2-22-222-222200002222-2-200-2-222−2−2−2−222000000002222−2−2−2−2−2−2−2−222220000-2-2220000000000000000−222−200
χ312222-2-22-222-222200002222-2-200-2-2−2−22222−2−200000000−2−2−2−222222222−2−2−2−2000022-2-20000000000000000−222−200
χ322222-2-22-222-222200002222-2-200-2-2−2−22222−2−200000000−2−2−2−222222222−2−2−2−20000-2-22200000000000000002−2−2200
χ332222-2-2-12-2-22-1-1-12222111111-2-2-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
χ342222-2-2-12-2-22-1-1-12222111111-2-2-1-12222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-221111-1-1-1-1000000000000
χ352222-2-2-12-2-22-1-1-12222111111-2-2-1-1-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ362222-2-2-12-2-22-1-1-12222111111-2-2-1-1-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ372-22-22-22-22-22-2-2222-2-222-2-22-22-2-2200000000-2-222-2-22200000000000000002-22-20000002-2002-200000000000000
χ382-22-22-22-22-22-2-2222-2-222-2-22-22-2-2200000000-2-222-2-2220000000000000000-22-22000000-2200-2200000000000000
χ392-22-22-22-22-22-2-22-2-22222-2-22-2-22-220000000022-2-222-2-200000000000000000000000000000000002-22-200000000
χ402-22-22-22-22-22-2-22-2-22222-2-22-2-22-220000000022-2-222-2-20000000000000000000000000000000000-22-2200000000
χ412-22-22-2-1-22-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32-22-2000000-11−i3i3-11−i3i3000000000000
χ422-22-22-2-1-22-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-22-220000001-1i3−i31-1i3−i3000000000000
χ432-22-22-2-1-22-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32-22-2000000-11i3−i3-11i3−i3000000000000
χ442-22-22-2-1-22-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-22-220000001-1−i3i31-1−i3i3000000000000
χ452-22-2-222-2-222-2-2222-2-2-2-222-22-22-2200000000-2-2-2-2222200000000000000002-2-220000002-200-2200000000000000
χ462-22-2-222-2-222-2-2222-2-2-2-222-22-22-2200000000-2-2-2-222220000000000000000-222-2000000-22002-200000000000000
χ472-22-2-222-2-222-2-22-2-222-2-222-222-2-22000000002222-2-2-2-200000000000000000000000000000000002-2-2200000000
χ482-22-2-222-2-222-2-22-2-222-2-222-222-2-22000000002222-2-2-2-20000000000000000000000000000000000-222-200000000
χ492-22-2-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2-22000000-11−i3i31-1i3−i3000000000000
χ502-22-2-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-222-20000001-1i3−i3-11−i3i3000000000000
χ512-22-2-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-2-22000000-11i3−i31-1−i3i3000000000000
χ522-22-2-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-222-20000001-1−i3i3-11i3−i3000000000000
χ53444444-24444-2-2-2-4-4-4-4-2-2-2-2-2-2-4-4-2-200000000222222220000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-200002222-2-200222222−22−222222−22−2200000000−2−2−2−22222−2−2−2−22222000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-200002222-2-20022−22−222222−22−222222000000002222−2−2−2−22222−2−2−2−2000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-4-4-422222244-2-20000000022-2-2-2-2220000000000000000000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-20000-2-2-2-22200222222−22−22−22−22222200000000−2−2−2−222222222−2−2−2−2000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-20000-2-2-2-2220022−22−2222222222−22−22000000002222−2−2−2−2−2−2−2−22222000000000000000000000000000000
χ5944-4-400400004-4-422−2222−22000000000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ4722−22000022−22000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47000000000000000000000000000000
χ6044-4-400400004-4-422−2222−2200000000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4722−22000022−2200000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47000000000000000000000000000000
χ6144-4-400400004-4-4−2222−222200000000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−22220000−222200000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43000000000000000000000000000000
χ6244-4-400400004-4-4−2222−2222000000000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−22220000−2222000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000000000000000000000000000
χ6344-4-400-20000-22222−2222−2223−2323−2300000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−226−66−6−22−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000000000000000000000
χ6444-4-400-20000-22222−2222−2223−2323−230000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−226−66−6−22ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000000000000000000000
χ6544-4-400-20000-22222−2222−22−2323−232300000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−22−66−66−22ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000000000000000000000
χ6644-4-400-20000-22222−2222−22−2323−23230000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−22−66−66−22−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000000000000000000000
χ6744-4-400-20000-222−2222−222223−2323−230000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432−2−66−662−2ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000000000000000000000
χ6844-4-400-20000-222−2222−222223−2323−2300000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432−2−66−662−2−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000000000000000000000
χ6944-4-400-20000-222−2222−2222−2323−23230000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432−26−66−62−2−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000000000000000000000
χ7044-4-400-20000-222−2222−2222−2323−232300000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432−26−66−62−2ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000000000000000000000
χ714-44-44-444-44-4-4-440000-4-4444-4004-400000000000000000000000000000000000000000000000000000000000000
χ724-44-44-4-24-44-422-2000022-2-2-2200-220000000000000000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000000000
χ734-44-44-4-24-44-422-2000022-2-2-2200-220000000000000000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000000000
χ744-44-44-4-2-44-4422-2-4-444-2-222-22-442-200000000-2-222-2-2220000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.