Finite Group Databasebeta

← Group #13085406

Character table — Group #13085406

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112224444488881010101012121212122020202020202060606011222444448888101010101212121212202020202020206060601122244444888810101010121212121220202020202020606060
order122365610101015303030226642020202044612121212244366361563030301530303066661260606060121261212121261212366361563030301530303066661260606060121261212121261212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-11-1-1-1-11-1-111111111111111111111111-1-11-1-1-1-11-1-111111111111111111111111-1-11-1-1-1-11-1-1
χ3111111111111111111-1-1-1-1-11111111-1-1-1111111111111111111-1-1-1-1-11111111-1-1-1111111111111111111-1-1-1-1-11111111-1-1-1
χ4111111111111111111-1-1-1-1-1-1-11-1-1-1-1-111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-111
χ511111111111111-1-1-1-111111i−i-1ii−i−i-1i−i11111111111111-1-1-1-111111i−i-1ii−i−i-1i−i11111111111111-1-1-1-111111i−i-1ii−i−i-1i−i
χ611111111111111-1-1-1-111111−ii-1−i−iii-1−ii11111111111111-1-1-1-111111−ii-1−i−iii-1−ii11111111111111-1-1-1-111111−ii-1−i−iii-1−ii
χ711111111111111-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1−ii11111111111111-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1−ii11111111111111-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1−ii
χ811111111111111-1-1-1-1-1-1-1-1-1−ii-1−i−iii1i−i11111111111111-1-1-1-1-1-1-1-1-1−ii-1−i−iii1i−i11111111111111-1-1-1-1-1-1-1-1-1−ii-1−i−iii1i−i
χ9222-1-12-1222-1-1-1-122-1-10000022-1-1-1-1-1000222-1-12-1222-1-1-1-122-1-10000022-1-1-1-1-1000222-1-12-1222-1-1-1-122-1-10000022-1-1-1-1-1000
χ10222-1-12-1222-1-1-1-122-1-100000-2-2-11111000222-1-12-1222-1-1-1-122-1-100000-2-2-11111000222-1-12-1222-1-1-1-122-1-100000-2-2-11111000
χ11222-1-12-1222-1-1-1-1-2-211000002i−2i1−i−iii000222-1-12-1222-1-1-1-1-2-211000002i−2i1−i−iii000222-1-12-1222-1-1-1-1-2-211000002i−2i1−i−iii000
χ12222-1-12-1222-1-1-1-1-2-21100000−2i2i1ii−i−i000222-1-12-1222-1-1-1-1-2-21100000−2i2i1ii−i−i000222-1-12-1222-1-1-1-1-2-21100000−2i2i1ii−i−i000
χ1322-2222-2-2-2222-2-22-2220000000-2000000022-2222-2-2-2222-2-22-2220000000-2000000022-2222-2-2-2222-2-22-2220000000-20000000
χ1422-2222-2-2-2222-2-2-22-2-200000002000000022-2222-2-2-2222-2-2-22-2-200000002000000022-2222-2-2-2222-2-2-22-2-2000000020000000
χ1522-2-1-121-2-22-1-1112-2-1-100000001−i3i3−i3i300022-2-1-121-2-22-1-1112-2-1-100000001−i3i3−i3i300022-2-1-121-2-22-1-1112-2-1-100000001−i3i3−i3i3000
χ1622-2-1-121-2-22-1-1112-2-1-100000001i3−i3i3−i300022-2-1-121-2-22-1-1112-2-1-100000001i3−i3i3−i300022-2-1-121-2-22-1-1112-2-1-100000001i3−i3i3−i3000
χ1722-2-1-121-2-22-1-111-22110000000-13−3−3300022-2-1-121-2-22-1-111-22110000000-13−3−3300022-2-1-121-2-22-1-111-22110000000-13−3−33000
χ1822-2-1-121-2-22-1-111-22110000000-1−333−300022-2-1-121-2-22-1-111-22110000000-1−333−300022-2-1-121-2-22-1-111-22110000000-1−333−3000
χ1944444-14-1-1-1-1-1-1-100004-1-1-1-1000000000044444-14-1-1-1-1-1-1-100004-1-1-1-1000000000044444-14-1-1-1-1-1-1-100004-1-1-1-10000000000
χ2044444-14-1-1-1-1-1-1-10000-41111000000000044444-14-1-1-1-1-1-1-10000-41111000000000044444-14-1-1-1-1-1-1-10000-411110000000000
χ2144-444-1-411-1-1-11100000−5−555000000000044-444-1-411-1-1-11100000−5−555000000000044-444-1-411-1-1-11100000−5−5550000000000
χ2244-444-1-411-1-1-1110000055−5−5000000000044-444-1-411-1-1-1110000055−5−5000000000044-444-1-411-1-1-1110000055−5−50000000000
χ234-404-44000-44-40000000000000000000004-404-44000-44-40000000000000000000004-404-44000-44-4000000000000000000000
χ244-404-4-10−551-11−5500000ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ5900000000004-404-4-10−551-11−5500000ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ5900000000004-404-4-10−551-11−5500000ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ590000000000
χ254-404-4-10−551-11−5500000−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ5900000000004-404-4-10−551-11−5500000−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ5900000000004-404-4-10−551-11−5500000−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ590000000000
χ264-404-4-105−51-115−500000ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ5900000000004-404-4-105−51-115−500000ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ5900000000004-404-4-105−51-115−500000ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ590000000000
χ274-404-4-105−51-115−500000−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ5900000000004-404-4-105−51-115−500000−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ5900000000004-404-4-105−51-115−500000−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ590000000000
χ284-40-224000-4-220000−2i32i30000000000000004-40-224000-4-220000−2i32i30000000000000004-40-224000-4-220000−2i32i3000000000000000
χ294-40-224000-4-2200002i3−2i30000000000000004-40-224000-4-2200002i3−2i30000000000000004-40-224000-4-2200002i3−2i3000000000000000
χ30888-4-4-2-4-2-2-211110000000000000000000888-4-4-2-4-2-2-211110000000000000000000888-4-4-2-4-2-2-211110000000000000000000
χ3188-8-4-4-2422-211-1-1000000000000000000088-8-4-4-2422-211-1-1000000000000000000088-8-4-4-2422-211-1-10000000000000000000
χ328-80-44-20−252521-15−500000000000000000008-80-44-20−252521-15−500000000000000000008-80-44-20−252521-15−50000000000000000000
χ338-80-44-2025−2521-1−5500000000000000000008-80-44-2025−2521-1−5500000000000000000008-80-44-2025−2521-1−550000000000000000000
χ34111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ3511111111111111111111111-1-11-1-1-1-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32
χ36111111111111111111-1-1-1-1-11111111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ37111111111111111111-1-1-1-1-1-1-11-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ3811111111111111-1-1-1-111111i−i-1ii−i−i-1i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ3911111111111111-1-1-1-111111−ii-1−i−iii-1−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ4011111111111111-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ4111111111111111-1-1-1-1-1-1-1-1-1−ii-1−i−iii1i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−1+i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−1−i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ42222-1-12-1222-1-1-1-122-1-10000022-1-1-1-1-1000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i3200000−1+i3−1+i31−i321−i321−i321−i321−i32000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i3200000−1−i3−1−i31+i321+i321+i321+i321+i32000
χ43222-1-12-1222-1-1-1-122-1-100000-2-2-11111000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i32000001−i31−i31−i32−1+i32−1+i32−1+i32−1+i32000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i32000001+i31+i31+i32−1−i32−1−i32−1−i32−1−i32000
χ44222-1-12-1222-1-1-1-1-2-211000002i−2i1−i−iii000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i3200000−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−1+i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i3200000−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−1−i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43000
χ45222-1-12-1222-1-1-1-1-2-21100000−2i2i1ii−i−i000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i32000002ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59−1+i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i32000002ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43−1−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43000
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χ7111111111111111-1-1-1-111111i−i-1ii−i−i-1i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ7211111111111111-1-1-1-111111−ii-1−i−iii-1−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ7311111111111111-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1−ii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ431+i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−1−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ591−i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−1+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ7411111111111111-1-1-1-1-1-1-1-1-1−ii-1−i−iii1i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ431+i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−1−i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ591−i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−1+i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ75222-1-12-1222-1-1-1-122-1-10000022-1-1-1-1-1000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i3200000−1−i3−1−i31+i321+i321+i321+i321+i32000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i3200000−1+i3−1+i31−i321−i321−i321−i321−i32000
χ76222-1-12-1222-1-1-1-122-1-100000-2-2-11111000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i32000001+i31+i31+i32−1−i32−1−i32−1−i32−1−i32000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i32000001−i31−i31−i32−1+i32−1+i32−1+i32−1+i32000
χ77222-1-12-1222-1-1-1-1-2-211000002i−2i1−i−iii000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i3200000−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−1−i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i3200000−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−1+i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59000
χ78222-1-12-1222-1-1-1-1-2-21100000−2i2i1ii−i−i000−1−i3−1−i3−1−i31+i321+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i32000002ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43−1−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43000−1+i3−1+i3−1+i31−i321−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i32000002ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59−1+i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59000
χ7922-2222-2-2-2222-2-22-2220000000-20000000−1−i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i3−1−i300000001+i30000000−1+i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i3−1+i300000001−i30000000
χ8022-2222-2-2-2222-2-2-22-2-2000000020000000−1−i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i31+i31+i30000000−1−i30000000−1+i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i31−i31−i30000000−1+i30000000
χ8122-2-1-121-2-22-1-1112-2-1-100000001−i3i3−i3i3000−1−i3−1−i31+i31+i321+i32−1−i3−1−i321+i31+i3−1−i31+i321+i32−1−i32−1−i32−1−i31+i31+i321+i320000000−1−i32−3+i323−i32−3+i323−i32000−1+i3−1+i31−i31−i321−i32−1+i3−1+i321−i31−i3−1+i31−i321−i32−1+i32−1+i32−1+i31−i31−i321−i320000000−1+i323+i32−3−i323+i32−3−i32000
χ8222-2-1-121-2-22-1-1112-2-1-100000001i3−i3i3−i3000−1−i3−1−i31+i31+i321+i32−1−i3−1−i321+i31+i3−1−i31+i321+i32−1−i32−1−i32−1−i31+i31+i321+i320000000−1−i323−i32−3+i323−i32−3+i32000−1+i3−1+i31−i31−i321−i32−1+i3−1+i321−i31−i3−1+i31−i321−i32−1+i32−1+i32−1+i31−i31−i321−i320000000−1+i32−3−i323+i32−3−i323+i32000
χ8322-2-1-121-2-22-1-111-22110000000-13−3−33000−1−i3−1−i31+i31+i321+i32−1−i3−1−i321+i31+i3−1−i31+i321+i32−1−i32−1−i321+i3−1−i3−1−i32−1−i3200000001+i32−ζ7−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−2ζ59ζ7+2ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+2ζ59ζ7+2ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+2ζ59−ζ7−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−2ζ59000−1+i3−1+i31−i31−i321−i32−1+i3−1+i321−i31−i3−1+i31−i321−i32−1+i32−1+i321−i3−1+i3−1+i32−1+i3200000001−i322ζ7+ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+ζ59−2ζ7−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−ζ59−2ζ7−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−ζ592ζ7+ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+ζ59000
χ8422-2-1-121-2-22-1-111-22110000000-1−333−3000−1−i3−1−i31+i31+i321+i32−1−i3−1−i321+i31+i3−1−i31+i321+i32−1−i32−1−i321+i3−1−i3−1−i32−1−i3200000001+i32ζ7+2ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+2ζ59−ζ7−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−2ζ59−ζ7−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−2ζ59ζ7+2ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+2ζ59000−1+i3−1+i31−i31−i321−i32−1+i3−1+i321−i31−i3−1+i31−i321−i32−1+i32−1+i321−i3−1+i3−1+i32−1+i3200000001−i32−2ζ7−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−ζ592ζ7+ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+ζ592ζ7+ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+ζ59−2ζ7−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−ζ59000
χ8544444-14-1-1-1-1-1-1-100004-1-1-1-10000000000−2−2i3−2−2i3−2−2i3−2−2i3−2−2i31+i32−2−2i31+i321+i321+i321+i321+i321+i321+i320000−2−2i31+i321+i321+i321+i320000000000−2+2i3−2+2i3−2+2i3−2+2i3−2+2i31−i32−2+2i31−i321−i321−i321−i321−i321−i321−i320000−2+2i31−i321−i321−i321−i320000000000
χ8644444-14-1-1-1-1-1-1-10000-411110000000000−2−2i3−2−2i3−2−2i3−2−2i3−2−2i31+i32−2−2i31+i321+i321+i321+i321+i321+i321+i3200002+2i3−1−i32−1−i32−1−i32−1−i320000000000−2+2i3−2+2i3−2+2i3−2+2i3−2+2i31−i32−2+2i31−i321−i321−i321−i321−i321−i321−i3200002−2i3−1+i32−1+i32−1+i32−1+i320000000000
χ8744-444-1-411-1-1-11100000−5−5550000000000−2−2i3−2−2i32+2i3−2−2i3−2−2i31+i322+2i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i3200000ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ580000000000−2+2i3−2+2i32−2i3−2+2i3−2+2i31−i322−2i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i3200000ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ380000000000
χ8844-444-1-411-1-1-1110000055−5−50000000000−2−2i3−2−2i32+2i3−2−2i3−2−2i31+i322+2i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i3200000−ζ22+ζ34+ζ46−ζ58−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ58ζ22−ζ34−ζ46+ζ580000000000−2+2i3−2+2i32−2i3−2+2i3−2+2i31−i322−2i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i3200000−ζ2+ζ14+ζ26−ζ38−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ38ζ2−ζ14−ζ26+ζ380000000000
χ894-404-44000-44-4000000000000000000000−2−2i32+2i30−2−2i32+2i3−2−2i30002+2i3−2−2i32+2i3000000000000000000000−2+2i32−2i30−2+2i32−2i3−2+2i30002−2i3−2+2i32−2i3000000000000000000000
χ904-404-4-10−551-11−5500000ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ590000000000−2−2i32+2i30−2−2i32+2i31+i320ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ58−1−i321+i32−1−i32ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ5800000−ζ7+ζ19−ζ31+ζ43ζ7−ζ19+ζ31−ζ43−ζ7−ζ19+ζ31+ζ43ζ7+ζ19−ζ31−ζ430000000000−2+2i32−2i30−2+2i32−2i31−i320ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ38−1+i321−i32−1+i32ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ3800000−ζ11+ζ23−ζ47+ζ59ζ11−ζ23+ζ47−ζ59ζ11+ζ23−ζ47−ζ59−ζ11−ζ23+ζ47+ζ590000000000
χ914-404-4-10−551-11−5500000−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ590000000000−2−2i32+2i30−2−2i32+2i31+i320ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ58−1−i321+i32−1−i32ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ5800000ζ7−ζ19+ζ31−ζ43−ζ7+ζ19−ζ31+ζ43ζ7+ζ19−ζ31−ζ43−ζ7−ζ19+ζ31+ζ430000000000−2+2i32−2i30−2+2i32−2i31−i320ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ38−1+i321−i32−1+i32ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ3800000ζ11−ζ23+ζ47−ζ59−ζ11+ζ23−ζ47+ζ59−ζ11−ζ23+ζ47+ζ59ζ11+ζ23−ζ47−ζ590000000000
χ924-404-4-105−51-115−500000ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ590000000000−2−2i32+2i30−2−2i32+2i31+i320−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ58−1−i321+i32−1−i32−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ5800000−ζ7−ζ19+ζ31+ζ43ζ7+ζ19−ζ31−ζ43ζ7−ζ19+ζ31−ζ43−ζ7+ζ19−ζ31+ζ430000000000−2+2i32−2i30−2+2i32−2i31−i320−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ38−1+i321−i32−1+i32−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ3800000ζ11+ζ23−ζ47−ζ59−ζ11−ζ23+ζ47+ζ59ζ11−ζ23+ζ47−ζ59−ζ11+ζ23−ζ47+ζ590000000000
χ934-404-4-105−51-115−500000−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ590000000000−2−2i32+2i30−2−2i32+2i31+i320−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ58−1−i321+i32−1−i32−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ5800000ζ7+ζ19−ζ31−ζ43−ζ7−ζ19+ζ31+ζ43−ζ7+ζ19−ζ31+ζ43ζ7−ζ19+ζ31−ζ430000000000−2+2i32−2i30−2+2i32−2i31−i320−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ38−1+i321−i32−1+i32−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ3800000−ζ11−ζ23+ζ47+ζ59ζ11+ζ23−ζ47−ζ59−ζ11+ζ23−ζ47+ζ59ζ11−ζ23+ζ47−ζ590000000000
χ944-40-224000-4-220000−2i32i3000000000000000−2−2i32+2i301+i3−1−i3−2−2i30002+2i31+i3−1−i30000−3+i33−i3000000000000000−2+2i32−2i301−i3−1+i3−2+2i30002−2i31−i3−1+i300003+i3−3−i3000000000000000
χ954-40-224000-4-2200002i3−2i3000000000000000−2−2i32+2i301+i3−1−i3−2−2i30002+2i31+i3−1−i300003−i3−3+i3000000000000000−2+2i32−2i301−i3−1+i3−2+2i30002−2i31−i3−1+i30000−3−i33+i3000000000000000
χ96888-4-4-2-4-2-2-211110000000000000000000−4−4i3−4−4i3−4−4i32+2i32+2i31+i32+2i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i320000000000000000000−4+4i3−4+4i3−4+4i32−2i32−2i31−i32−2i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i320000000000000000000
χ9788-8-4-4-2422-211-1-10000000000000000000−4−4i3−4−4i34+4i32+2i32+2i31+i3−2−2i3−1−i3−1−i31+i3−1−i32−1−i321+i321+i320000000000000000000−4+4i3−4+4i34−4i32−2i32−2i31−i3−2+2i3−1+i3−1+i31−i3−1+i32−1+i321−i321−i320000000000000000000
χ988-80-44-20−252521-15−50000000000000000000−4−4i34+4i302+2i3−2−2i31+i302ζ22−2ζ34−2ζ46+2ζ58−2ζ22+2ζ34+2ζ46−2ζ58−1−i3−1−i321+i32−ζ22+ζ34+ζ46−ζ58ζ22−ζ34−ζ46+ζ580000000000000000000−4+4i34−4i302−2i3−2+2i31−i302ζ2−2ζ14−2ζ26+2ζ38−2ζ2+2ζ14+2ζ26−2ζ38−1+i3−1+i321−i32−ζ2+ζ14+ζ26−ζ38ζ2−ζ14−ζ26+ζ380000000000000000000
χ998-80-44-2025−2521-1−550000000000000000000−4−4i34+4i302+2i3−2−2i31+i30−2ζ22+2ζ34+2ζ46−2ζ582ζ22−2ζ34−2ζ46+2ζ58−1−i3−1−i321+i32ζ22−ζ34−ζ46+ζ58−ζ22+ζ34+ζ46−ζ580000000000000000000−4+4i34−4i302−2i3−2+2i31−i30−2ζ2+2ζ14+2ζ26−2ζ382ζ2−2ζ14−2ζ26+2ζ38−1+i3−1+i321−i32ζ2−ζ14−ζ26+ζ38−ζ2+ζ14+ζ26−ζ380000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.