Finite Group Databasebeta

← Group #13165843

Character table — Group #13165843

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111144444444999999999999333312121212121212122727272727272727272727274444161616161616161636363636363636363636363644441616161616161616363636363636363636363636
order124433661212121288881616161616161616224466661212121288881616161616161616361212336612121212242424244848484848484848361212336612121212242424244848484848484848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiii−i−i−i−i
χ4111111111111-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−iiiii
χ511-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ611-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ711-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ811-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ91-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ29
χ101-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ29
χ111-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ41
χ121-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ41
χ131-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ47
χ141-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ47
χ151-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ43
χ161-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ43
χ1744441-21-21-21-200000000000044441-21-21-21-200000000000044441-21-21-21-200000000000044441-21-21-21-2000000000000
χ184444-21-21-21-210000000000004444-21-21-21-210000000000004444-21-21-21-210000000000004444-21-21-21-21000000000000
χ1944-4-41-21-2-12-1200000000000044-4-41-21-2-12-1200000000000044-4-41-21-2-12-1200000000000044-4-41-21-2-12-12000000000000
χ2044-4-4-21-212-12-100000000000044-4-4-21-212-12-100000000000044-4-4-21-212-12-100000000000044-4-4-21-212-12-1000000000000
χ214-44i−4i1-2-12i−2i−i2i0000000000004-44i−4i1-2-12i−2i−i2i0000000000004-44i−4i1-2-12i−2i−i2i0000000000004-44i−4i1-2-12i−2i−i2i000000000000
χ224-44i−4i-212-1−2ii2i−i0000000000004-44i−4i-212-1−2ii2i−i0000000000004-44i−4i-212-1−2ii2i−i0000000000004-44i−4i-212-1−2ii2i−i000000000000
χ234-4−4i4i1-2-12−i2ii−2i0000000000004-4−4i4i1-2-12−i2ii−2i0000000000004-4−4i4i1-2-12−i2ii−2i0000000000004-4−4i4i1-2-12−i2ii−2i000000000000
χ244-4−4i4i-212-12i−i−2ii0000000000004-4−4i4i-212-12i−i−2ii0000000000004-4−4i4i-212-12i−i−2ii0000000000004-4−4i4i-212-12i−i−2ii000000000000
χ25111111111111111111111111111111111111111111111111−1+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
χ261111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1+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+i321−i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ27111111111111-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiii−i−i−i−i−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−i32ζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ28−1−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+i32ζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ44
χ28111111111111-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−iiiii−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−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ28−1−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−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ44
χ2911-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46−ζ46ζ46ζ46−ζ10−ζ10ζ10ζ10−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14−ζ14ζ14ζ14−ζ26−ζ26ζ26ζ26
χ3011-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1-11111-1-1-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32ζ28ζ28−ζ28−ζ28ζ46ζ46−ζ46−ζ46ζ10ζ10−ζ10−ζ10−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32ζ44ζ44−ζ44−ζ44ζ14ζ14−ζ14−ζ14ζ26ζ26−ζ26−ζ26
χ3111-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1-11111-1-1-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−ζ28−ζ28ζ28ζ28−ζ10−ζ10ζ10ζ10−ζ46−ζ46ζ46ζ46−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−ζ44−ζ44ζ44ζ44−ζ26−ζ26ζ26ζ26−ζ14−ζ14ζ14ζ14
χ3211-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1-11111-1-1-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−ζ28−ζ28ζ28ζ28ζ10ζ10−ζ10−ζ10ζ46ζ46−ζ46−ζ46−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−ζ44−ζ44ζ44ζ44ζ26ζ26−ζ26−ζ26ζ14ζ14−ζ14−ζ14
χ331-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ29−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46ζ46−ζ10ζ10−ζ43ζ43ζ31−ζ31ζ25−ζ25−ζ13ζ13−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14ζ14−ζ26ζ26−ζ11ζ11ζ47−ζ47ζ41−ζ41−ζ29ζ29
χ341-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ29−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46ζ46−ζ10ζ10ζ43−ζ43−ζ31ζ31−ζ25ζ25ζ13−ζ13−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14ζ14−ζ26ζ26ζ11−ζ11−ζ47ζ47−ζ41ζ41ζ29−ζ29
χ351-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ41−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28ζ46−ζ46ζ10−ζ10ζ31−ζ31ζ43−ζ43ζ13−ζ13ζ25−ζ25−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44ζ14−ζ14ζ26−ζ26ζ47−ζ47ζ11−ζ11ζ29−ζ29ζ41−ζ41
χ361-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ41−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28ζ46−ζ46ζ10−ζ10−ζ31ζ31−ζ43ζ43−ζ13ζ13−ζ25ζ25−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44ζ14−ζ14ζ26−ζ26−ζ47ζ47−ζ11ζ11−ζ29ζ29−ζ41ζ41
χ371-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ47−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28−ζ10ζ10−ζ46ζ46ζ25−ζ25ζ13−ζ13ζ43−ζ43ζ31−ζ31−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44−ζ26ζ26−ζ14ζ14ζ41−ζ41ζ29−ζ29ζ11−ζ11ζ47−ζ47
χ381-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ47−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28−ζ10ζ10−ζ46ζ46−ζ25ζ25−ζ13ζ13−ζ43ζ43−ζ31ζ31−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44−ζ26ζ26−ζ14ζ14−ζ41ζ41−ζ29ζ29−ζ11ζ11−ζ47ζ47
χ391-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ43−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28ζ10−ζ10ζ46−ζ46−ζ13ζ13ζ25−ζ25ζ31−ζ31−ζ43ζ43−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44ζ26−ζ26ζ14−ζ14−ζ29ζ29ζ41−ζ41ζ47−ζ47−ζ11ζ11
χ401-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ43−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28ζ10−ζ10ζ46−ζ46ζ13−ζ13−ζ25ζ25−ζ31ζ31ζ43−ζ43−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44ζ26−ζ26ζ14−ζ14ζ29−ζ29−ζ41ζ41−ζ47ζ47ζ11−ζ11
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χ49111111111111111111111111111111111111111111111111−1−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
χ501111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1−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−i321+i321+i321+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+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ51111111111111-1-1-1-1iiii−i−i−i−i111111111111-1-1-1-1iiii−i−i−i−i−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+i32ζ44ζ44ζ44ζ44−ζ44−ζ44−ζ44−ζ44−1+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−i32ζ28ζ28ζ28ζ28−ζ28−ζ28−ζ28−ζ28
χ52111111111111-1-1-1-1−i−i−i−iiiii111111111111-1-1-1-1−i−i−i−iiiii−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−ζ44−ζ44−ζ44−ζ44ζ44ζ44ζ44ζ44−1+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−ζ28−ζ28−ζ28−ζ28ζ28ζ28ζ28ζ28
χ5311-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-11111-1-1-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14−ζ14ζ14ζ14−ζ26−ζ26ζ26ζ26−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46−ζ46ζ46ζ46−ζ10−ζ10ζ10ζ10
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χ571-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ11+ζ43−ζ11−ζ43−ζ31−ζ47ζ31+ζ47−ζ25−ζ41ζ25+ζ41ζ13+ζ29−ζ13−ζ29−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14ζ14−ζ26ζ26−ζ11ζ11ζ47−ζ47ζ41−ζ41−ζ29ζ29−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46ζ46−ζ10ζ10−ζ43ζ43ζ31−ζ31ζ25−ζ25−ζ13ζ13
χ581-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ291-1i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ11−ζ43ζ11+ζ43ζ31+ζ47−ζ31−ζ47ζ25+ζ41−ζ25−ζ41−ζ13−ζ29ζ13+ζ29−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44−ζ14ζ14−ζ26ζ26ζ11−ζ11−ζ47ζ47−ζ41ζ41ζ29−ζ29−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28−ζ46ζ46−ζ10ζ10ζ43−ζ43−ζ31ζ31−ζ25ζ25ζ13−ζ13
χ591-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ31−ζ47ζ31+ζ47−ζ11−ζ43ζ11+ζ43−ζ13−ζ29ζ13+ζ29−ζ25−ζ41ζ25+ζ41−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44ζ14−ζ14ζ26−ζ26ζ47−ζ47ζ11−ζ11ζ29−ζ29ζ41−ζ41−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28ζ46−ζ46ζ10−ζ10ζ31−ζ31ζ43−ζ43ζ13−ζ13ζ25−ζ25
χ601-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ411-1i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ31+ζ47−ζ31−ζ47ζ11+ζ43−ζ11−ζ43ζ13+ζ29−ζ13−ζ29ζ25+ζ41−ζ25−ζ41−1−i321+i32ζ44−ζ44−1−i32−1−i321+i321+i32ζ44ζ44−ζ44−ζ44ζ14−ζ14ζ26−ζ26−ζ47ζ47−ζ11ζ11−ζ29ζ29−ζ41ζ41−1+i321−i32ζ28−ζ28−1+i32−1+i321−i321−i32ζ28ζ28−ζ28−ζ28ζ46−ζ46ζ10−ζ10−ζ31ζ31−ζ43ζ43−ζ13ζ13−ζ25ζ25
χ611-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ25−ζ41ζ25+ζ41−ζ13−ζ29ζ13+ζ29−ζ11−ζ43ζ11+ζ43−ζ31−ζ47ζ31+ζ47−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44−ζ26ζ26−ζ14ζ14ζ41−ζ41ζ29−ζ29ζ11−ζ11ζ47−ζ47−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28−ζ10ζ10−ζ46ζ46ζ25−ζ25ζ13−ζ13ζ43−ζ43ζ31−ζ31
χ621-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ471-1−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ25+ζ41−ζ25−ζ41ζ13+ζ29−ζ13−ζ29ζ11+ζ43−ζ11−ζ43ζ31+ζ47−ζ31−ζ47−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44−ζ26ζ26−ζ14ζ14−ζ41ζ41−ζ29ζ29−ζ11ζ11−ζ47ζ47−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28−ζ10ζ10−ζ46ζ46−ζ25ζ25−ζ13ζ13−ζ43ζ43−ζ31ζ31
χ631-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ13+ζ29−ζ13−ζ29−ζ25−ζ41ζ25+ζ41−ζ31−ζ47ζ31+ζ47ζ11+ζ43−ζ11−ζ43−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44ζ26−ζ26ζ14−ζ14−ζ29ζ29ζ41−ζ41ζ47−ζ47−ζ11ζ11−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28ζ10−ζ10ζ46−ζ46−ζ13ζ13ζ25−ζ25ζ31−ζ31−ζ43ζ43
χ641-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ431-1−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ13−ζ29ζ13+ζ29ζ25+ζ41−ζ25−ζ41ζ31+ζ47−ζ31−ζ47−ζ11−ζ43ζ11+ζ43−1−i321+i32−ζ44ζ44−1−i32−1−i321+i321+i32−ζ44−ζ44ζ44ζ44ζ26−ζ26ζ14−ζ14ζ29−ζ29−ζ41ζ41−ζ47ζ47ζ11−ζ11−1+i321−i32−ζ28ζ28−1+i32−1+i321−i321−i32−ζ28−ζ28ζ28ζ28ζ10−ζ10ζ46−ζ46ζ13−ζ13−ζ25ζ25−ζ31ζ31ζ43−ζ43
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.