Finite Group Databasebeta

← Group #12012717

Character table — Group #12012717

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222224444444444444444444488888888881616161616161616161616161616161616161632323232324040404040408080808080
order12244551010448888101020202020404040404040404024202020204040404081010161620204040404080808080808080804202020202488882481616
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ4111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111111111111111-1-111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1111111-1-11-1-1
χ611111111111111111111111111111-1-111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111
χ711111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111
χ811111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1-1-1
χ922222222222-2-2-2-2222222-2-2-2-2-2-2-2-2002222-2-2-2-20000000000000000000000000000002-2000
χ1022222222222-2-2-2-2222222-2-2-2-2-2-2-2-2002222-2-2-2-2000000000000000000000000000000-22000
χ11222222222-2-22-2-222222222222-2-2-2-200-2-2-2-2-2-22200000000000000000000000022000000-200
χ12222222222-2-22-2-222222222222-2-2-2-200-2-2-2-2-2-222000000000000000000000000-2-2000000200
χ13222222222-2-2-222-2222222-2-2-2-2222222-2-2-2-222-2-2-2220022-2-2-2-2000000000000000000000000
χ14222222222-2-2-222-2222222-2-2-2-22222-2-2-2-2-2-222-2-22-2-200-2-22222000000000000000000000000
χ1522222−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−5200000000000
χ1622222−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−522−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-21−521−521+521+5200000000000
χ1722222−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-21−521+52221−521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521−521+521+5200000000000
χ1822222−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-21−521+52-2-21−521+521−521−521+521+521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−5200000000000
χ1922222−1+52−1−52−1+52−1−52-2-2-222-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1−521−521+52-2−1+52−1−5200−1+52−1−521−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600000000000
χ2022222−1+52−1−52−1+52−1−52-2-2-222-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52221−521−521+521+52−1+52−1−521−521+52-2−1+52−1−5200−1+52−1−521−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600000000000
χ2122222−1+52−1−52−1+52−1−52-2-2-222-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-2-21−521−521+521+52−1+52−1−521−521+5221−521+52001−521+52−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600000000000
χ2222222−1+52−1−52−1+52−1−52-2-2-222-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-2-21−521−521+521+52−1+52−1−521−521+5221−521+52001−521+52−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600000000000
χ2322222−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+522−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522−1−52−1−52−1+52−1+5200000000000
χ2422222−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+522−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-21+521+521−521−5200000000000
χ2522222−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-21+521−52221+521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−5200000000000
χ2622222−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-21+521−52-2-21+521−521+521+521−521−521+521+521+521+521−521−521−521−522−1−52−1−52−1+52−1+5200000000000
χ2722222−1−52−1+52−1−52−1+52-2-2-222-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1+521+521−52-2−1−52−1+5200−1−52−1+521+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800000000000
χ2822222−1−52−1+52−1−52−1+52-2-2-222-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52221+521+521−521−52−1−52−1+521+521−52-2−1−52−1+5200−1−52−1+521+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800000000000
χ2922222−1−52−1+52−1−52−1+52-2-2-222-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-2-21+521+521−521−52−1−52−1+521+521−5221+521−52001+521−52−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800000000000
χ3022222−1−52−1+52−1−52−1+52-2-2-222-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-2-21+521+521−521−52−1−52−1+521+521−5221+521−52001+521−52−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800000000000
χ3122-22-2222200-2002-2-2-2-222-2-2-2-2000000000000220002−20000002−22−22−22−2000002-222−2−200000
χ3222-22-2222200-2002-2-2-2-222-2-2-2-2000000000000220002−20000002−22−22−22−200000-22−2−22200000
χ3322-22-2222200-2002-2-2-2-222-2-2-2-200000000000022000−22000000−22−22−22−22000002-2−2−22200000
χ3422-22-2222200-2002-2-2-2-222-2-2-2-200000000000022000−22000000−22−22−22−2200000-2222−2−200000
χ3522-2-222222000-220-2-222-2-2000022222-20000-2-20002200-2-200000000000000000002−22−20002−2
χ3622-2-222222000-220-2-222-2-2000022222-20000-2-20002200-2-20000000000000000000−22−22000−22
χ3722-2-222222000-220-2-222-2-200002222-220000-2-2000-2-2002200000000000000000002−22−2000−22
χ3822-2-222222000-220-2-222-2-200002222-220000-2-2000-2-200220000000000000000000−22−220002−2
χ3944444−1+5−1−5−1+5−1−544-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+500−1+5−1+5−1−5−1−51−51+51−51+500000000000000000000000000000000000
χ4044444−1+5−1−5−1+5−1−5-4-44-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51−51+51+5001−51−51+51+51−51+5−1+5−1−500000000000000000000000000000000000
χ4144444−1−5−1+5−1−5−1+544-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−500−1−5−1−5−1+5−1+51+51−51+51−500000000000000000000000000000000000
χ4244444−1−5−1+5−1−5−1+5-4-44-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51+51−51−5001+51+51−51−51+51−5−1−5−1+500000000000000000000000000000000000
χ43444-4-4444400000044-4-4-4-4000000000000000000000000000000000000000000002-2-2200000
χ44444-4-4444400000044-4-4-4-400000000000000000000000000000000000000000000-222-200000
χ4544-44-4444400400-4-4-4-4-4444444000000000000-4-400000000000000000000000000000000000
χ4644-44-4−1+5−1−5−1+5−1−500400-41−51+51−51+5−1+5−1−5−1+5−1+5−1−5−1−50000000000001−51+500000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ390000000000000000
χ4744-44-4−1+5−1−5−1+5−1−500400-41−51+51−51+5−1+5−1−5−1+5−1+5−1−5−1−50000000000001−51+500000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ390000000000000000
χ4844-44-4−1+5−1−5−1+5−1−500-40041−51+51−51+5−1+5−1−51−51−51+51+5000000000000−1+5−1−500022−22000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000
χ4944-44-4−1+5−1−5−1+5−1−500-40041−51+51−51+5−1+5−1−51−51−51+51+5000000000000−1+5−1−5000−2222000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000
χ5044-44-4−1−5−1+5−1−5−1+500400-41+51−51+51−5−1−5−1+5−1−5−1−5−1+5−1+50000000000001+51−500000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ370000000000000000
χ5144-44-4−1−5−1+5−1−5−1+500400-41+51−51+51−5−1−5−1+5−1−5−1−5−1+5−1+50000000000001+51−500000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ370000000000000000
χ5244-44-4−1−5−1+5−1−5−1+500-40041+51−51+51−5−1−5−1+51+51+51−51−5000000000000−1−5−1+500022−22000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000
χ5344-44-4−1−5−1+5−1−5−1+500-40041+51−51+51−5−1−5−1+51+51+51−51−5000000000000−1−5−1+5000−2222000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000
χ5444-4-4444440004-40-4-444-4-40000-4-4-4-4000000440000000000000000000000000000000000000
χ5544-4-44−1+5−1−5−1+5−1−50004-401−51+5−1+5−1−51−51+500001−51−51+51+5000000−1+5−1−5000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000
χ5644-4-44−1+5−1−5−1+5−1−50004-401−51+5−1+5−1−51−51+500001−51−51+51+5000000−1+5−1−50000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000
χ5744-4-44−1+5−1−5−1+5−1−5000-4401−51+5−1+5−1−51−51+50000−1+5−1+5−1−5−1−54-400001−51+5000−1+5−1−5001−51+50000000000000000000000000000
χ5844-4-44−1+5−1−5−1+5−1−5000-4401−51+5−1+5−1−51−51+50000−1+5−1+5−1−5−1−5-4400001−51+50001−51+500−1+5−1−50000000000000000000000000000
χ5944-4-44−1−5−1+5−1−5−1+50004-401+51−5−1−5−1+51+51−500001+51+51−51−5000000−1−5−1+50000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000
χ6044-4-44−1−5−1+5−1−5−1+50004-401+51−5−1−5−1+51+51−500001+51+51−51−5000000−1−5−1+5000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000
χ6144-4-44−1−5−1+5−1−5−1+5000-4401+51−5−1−5−1+51+51−50000−1−5−1−5−1+5−1+54-400001+51−5000−1−5−1+5001+51−50000000000000000000000000000
χ6244-4-44−1−5−1+5−1−5−1+5000-4401+51−5−1−5−1+51+51−50000−1−5−1−5−1+5−1+5-4400001+51−50001+51−500−1−5−1+50000000000000000000000000000
χ63888-8-8−2+25−2−25−2+25−2−25000000−2+25−2−252−252+252−252+2500000000000000000000000000000000000000000000000000000
χ64888-8-8−2−25−2+25−2−25−2+25000000−2−25−2+252+252−252+252−2500000000000000000000000000000000000000000000000000000
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χ678-8000−2+25−2−252−252+254-40000000000−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ3900−1+51−5−1−51+5000000000000000000000000000000000000000
χ688-8000−2+25−2−252−252+254-400000000002ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ3900−1+51−5−1−51+5000000000000000000000000000000000000000
χ698-8000−2+25−2−252−252+25-440000000000−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39001−5−1+51+5−1−5000000000000000000000000000000000000000
χ708-8000−2+25−2−252−252+25-4400000000002ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ39001−5−1+51+5−1−5000000000000000000000000000000000000000
χ718-8000−2−25−2+252+252−254-40000000000−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ3700−1−51+5−1+51−5000000000000000000000000000000000000000
χ728-8000−2−25−2+252+252−254-400000000002ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ3700−1−51+5−1+51−5000000000000000000000000000000000000000
χ738-8000−2−25−2+252+252−25-440000000000−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ372ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37001+5−1−51−5−1+5000000000000000000000000000000000000000
χ748-8000−2−25−2+252+252−25-4400000000002ζ21−2ζ29−2ζ31+2ζ39−2ζ21+2ζ29+2ζ31−2ζ39−2ζ7−2ζ13+2ζ23+2ζ372ζ7+2ζ13−2ζ23−2ζ37−2ζ21+2ζ29+2ζ31−2ζ392ζ21−2ζ29−2ζ31+2ζ392ζ7+2ζ13−2ζ23−2ζ37−2ζ7−2ζ13+2ζ23+2ζ37001+5−1−51−5−1+5000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1).