Finite Group Databasebeta

← Group #13147220

Character table — Group #13147220

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111333444666666121212161616161616161616161616222666888121212121212242424323232323232323232323232333999121212181818181818363636484848484848484848484848
order1332662662266664121299999918181818181833366666666666612121299999918181818181826626626622666641212181818181818181818181818
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ3111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111-1-1-1111111-1-1-1111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1111111-1-1-1-1-1-1
χ5111111-1-1-1111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32111111-1-1-1111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32111111-1-1-1111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ6111111-1-1-1111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32111111-1-1-1111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32111111-1-1-1111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ71−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8
χ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5
χ91−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2
χ101−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ81−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ81−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ8
χ111−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ51−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ51−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ5
χ121−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ21−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ21−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ2
χ131−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7
χ141−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4
χ151−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ
χ161−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ71−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ71−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ7
χ171−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ41−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ41−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ4
χ181−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ1−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ1−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ
χ19333333333-1-1-1-1-1-1-1-1-1000000000000333333333-1-1-1-1-1-1-1-1-1000000000000333333333-1-1-1-1-1-1-1-1-1000000000000
χ20333333-3-3-3-1-1-1-1-1-1111000000000000333333-3-3-3-1-1-1-1-1-1111000000000000333333-3-3-3-1-1-1-1-1-1111000000000000
χ213−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-11−i321+i320000000000003−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-11−i321+i320000000000003−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-11−i321+i32000000000000
χ223−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-1-11−i321−i321+i321+i321−1+i32−1−i320000000000003−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-1-11−i321−i321+i321+i321−1+i32−1−i320000000000003−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-1-11−i321−i321+i321+i321−1+i32−1−i32000000000000
χ233−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-11+i321−i320000000000003−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-11+i321−i320000000000003−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-11+i321−i32000000000000
χ243−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-1-11+i321+i321−i321−i321−1−i32−1+i320000000000003−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-1-11+i321+i321−i321−i321−1−i32−1+i320000000000003−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-1-11+i321+i321−i321−i321−1−i32−1+i32000000000000
χ25666-2-2-20002-22-22-2000000000000000666-2-2-20002-22-22-2000000000000000666-2-2-20002-22-22-2000000000000000
χ26666-2-2-2000-22-22-22000000000000000666-2-2-2000-22-22-22000000000000000666-2-2-2000-22-22-22000000000000000
χ276−3+3i3−3−3i3-21−i31+i30002-2−1+i31−i3−1−i31+i30000000000000006−3+3i3−3−3i3-21−i31+i30002-2−1+i31−i3−1−i31+i30000000000000006−3+3i3−3−3i3-21−i31+i30002-2−1+i31−i3−1−i31+i3000000000000000
χ286−3+3i3−3−3i3-21−i31+i3000-221−i3−1+i31+i3−1−i30000000000000006−3+3i3−3−3i3-21−i31+i3000-221−i3−1+i31+i3−1−i30000000000000006−3+3i3−3−3i3-21−i31+i3000-221−i3−1+i31+i3−1−i3000000000000000
χ296−3−3i3−3+3i3-21+i31−i30002-2−1−i31+i3−1+i31−i30000000000000006−3−3i3−3+3i3-21+i31−i30002-2−1−i31+i3−1+i31−i30000000000000006−3−3i3−3+3i3-21+i31−i30002-2−1−i31+i3−1+i31−i3000000000000000
χ306−3−3i3−3+3i3-21+i31−i3000-221+i3−1−i31−i3−1+i30000000000000006−3−3i3−3+3i3-21+i31−i3000-221+i3−1−i31−i3−1+i30000000000000006−3−3i3−3+3i3-21+i31−i3000-221+i3−1−i31−i3−1+i3000000000000000
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ33111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
χ34111111-1-1-1111111-1-1-1111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111
χ35111111-1-1-1111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32111111-1-1-1111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32-1-1-1-1-1-1111-1-1-1-1-1-11111−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ36111111-1-1-1111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32111111-1-1-1111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32-1-1-1-1-1-1111-1-1-1-1-1-11111+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ371−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ81−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ8
χ381−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ51−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ5
χ391−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ21−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ2
χ401−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ81−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζζ4ζ7ζ2ζ5ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ8-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8ζζ4ζ7ζ2ζ5ζ8
χ411−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ51−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ4ζ7ζζ8ζ2ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ5-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5ζ4ζ7ζζ8ζ2ζ5
χ421−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ21−1+i32−1−i321−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32ζ7ζζ4ζ5ζ8ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ2-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2ζ7ζζ4ζ5ζ8ζ2
χ431−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ7
χ441−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ41−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ4
χ451−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ1−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ
χ461−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ71−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ2ζ8ζ5ζ4ζζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ7-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7ζ2ζ8ζ5ζ4ζζ7
χ471−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ41−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ5ζ2ζ8ζζ7ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ4-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4ζ5ζ2ζ8ζζ7ζ4
χ481−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ1−1−i32−1+i321−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32ζ8ζ5ζ2ζ7ζ4ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζζ8ζ5ζ2ζ7ζ4ζ
χ49333333333-1-1-1-1-1-1-1-1-1000000000000333333333-1-1-1-1-1-1-1-1-1000000000000-3-3-3-3-3-3-3-3-3111111111000000000000
χ50333333-3-3-3-1-1-1-1-1-1111000000000000333333-3-3-3-1-1-1-1-1-1111000000000000-3-3-3-3-3-3333111111-1-1-1000000000000
χ513−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-11−i321+i320000000000003−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-11−i321+i32000000000000-33−3i323+3i32-33−3i323+3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32000000000000
χ523−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-1-11−i321−i321+i321+i321−1+i32−1−i320000000000003−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-1-11−i321−i321+i321+i321−1+i32−1−i32000000000000-33−3i323+3i32-33−3i323+3i323−3+3i32−3−3i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000000000
χ533−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-11+i321−i320000000000003−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-11+i321−i32000000000000-33+3i323−3i32-33+3i323−3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32000000000000
χ543−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-1-11+i321+i321−i321−i321−1−i32−1+i320000000000003−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-1-11+i321+i321−i321−i321−1−i32−1+i32000000000000-33+3i323−3i32-33+3i323−3i323−3−3i32−3+3i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000000000
χ55666-2-2-20002-22-22-2000000000000000666-2-2-20002-22-22-2000000000000000-6-6-6222000-22-22-22000000000000000
χ56666-2-2-2000-22-22-22000000000000000666-2-2-2000-22-22-22000000000000000-6-6-62220002-22-22-2000000000000000
χ576−3+3i3−3−3i3-21−i31+i30002-2−1+i31−i3−1−i31+i30000000000000006−3+3i3−3−3i3-21−i31+i30002-2−1+i31−i3−1−i31+i3000000000000000-63−3i33+3i32−1+i3−1−i3000-221−i3−1+i31+i3−1−i3000000000000000
χ586−3+3i3−3−3i3-21−i31+i3000-221−i3−1+i31+i3−1−i30000000000000006−3+3i3−3−3i3-21−i31+i3000-221−i3−1+i31+i3−1−i3000000000000000-63−3i33+3i32−1+i3−1−i30002-2−1+i31−i3−1−i31+i3000000000000000
χ596−3−3i3−3+3i3-21+i31−i30002-2−1−i31+i3−1+i31−i30000000000000006−3−3i3−3+3i3-21+i31−i30002-2−1−i31+i3−1+i31−i3000000000000000-63+3i33−3i32−1−i3−1+i3000-221+i3−1−i31−i3−1+i3000000000000000
χ606−3−3i3−3+3i3-21+i31−i3000-221+i3−1−i31−i3−1+i30000000000000006−3−3i3−3+3i3-21+i31−i3000-221+i3−1−i31−i3−1+i3000000000000000-63+3i33−3i32−1−i3−1+i30002-2−1−i31+i3−1+i31−i3000000000000000
χ61222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ62222222222222222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32000000000000000000000000000000
χ63222222222222222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32000000000000000000000000000000
χ64222222-2-2-2222222-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111000000000000000000000000000000
χ65222222-2-2-2222222-2-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i3-1-1-1-1-1-1111-1-1-1-1-1-11111−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000000000000000000
χ66222222-2-2-2222222-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i3-1-1-1-1-1-1111-1-1-1-1-1-11111+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000000000000000000000
χ672−1+i3−1−i32−1+i3−1−i32−1+i3−1−i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i32ζ2ζ42ζ72ζ22ζ52ζ82ζ2ζ42ζ72ζ22ζ52ζ8-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8−ζ−ζ4−ζ7−ζ2−ζ5−ζ8000000000000000000000000000000
χ682−1+i3−1−i32−1+i3−1−i32−1+i3−1−i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i32ζ42ζ72ζ2ζ82ζ22ζ52ζ42ζ72ζ2ζ82ζ22ζ5-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5−ζ4−ζ7−ζ−ζ8−ζ2−ζ5000000000000000000000000000000
χ692−1+i3−1−i32−1+i3−1−i32−1+i3−1−i322−1+i3−1+i3−1−i3−1−i32−1+i3−1−i32ζ72ζ2ζ42ζ52ζ82ζ22ζ72ζ2ζ42ζ52ζ82ζ2-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2−ζ7−ζ−ζ4−ζ5−ζ8−ζ2000000000000000000000000000000
χ702−1+i3−1−i32−1+i3−1−i3-21−i31+i322−1+i3−1+i3−1−i3−1−i3-21−i31+i32ζ2ζ42ζ72ζ22ζ52ζ8−2ζ−2ζ4−2ζ7−2ζ2−2ζ5−2ζ8-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8ζζ4ζ7ζ2ζ5ζ8000000000000000000000000000000
χ712−1+i3−1−i32−1+i3−1−i3-21−i31+i322−1+i3−1+i3−1−i3−1−i3-21−i31+i32ζ42ζ72ζ2ζ82ζ22ζ5−2ζ4−2ζ7−2ζ−2ζ8−2ζ2−2ζ5-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5ζ4ζ7ζζ8ζ2ζ5000000000000000000000000000000
χ722−1+i3−1−i32−1+i3−1−i3-21−i31+i322−1+i3−1+i3−1−i3−1−i3-21−i31+i32ζ72ζ2ζ42ζ52ζ82ζ2−2ζ7−2ζ−2ζ4−2ζ5−2ζ8−2ζ2-11−i321+i32-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2ζ7ζζ4ζ5ζ8ζ2000000000000000000000000000000
χ732−1−i3−1+i32−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i32ζ22ζ82ζ52ζ42ζ2ζ72ζ22ζ82ζ52ζ42ζ2ζ7-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7−ζ2−ζ8−ζ5−ζ4−ζ−ζ7000000000000000000000000000000
χ742−1−i3−1+i32−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i32ζ52ζ22ζ82ζ2ζ72ζ42ζ52ζ22ζ82ζ2ζ72ζ4-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4−ζ5−ζ2−ζ8−ζ−ζ7−ζ4000000000000000000000000000000
χ752−1−i3−1+i32−1−i3−1+i32−1−i3−1+i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i32ζ82ζ52ζ22ζ72ζ42ζ2ζ82ζ52ζ22ζ72ζ42ζ-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ−ζ8−ζ5−ζ2−ζ7−ζ4−ζ000000000000000000000000000000
χ762−1−i3−1+i32−1−i3−1+i3-21+i31−i322−1−i3−1−i3−1+i3−1+i3-21+i31−i32ζ22ζ82ζ52ζ42ζ2ζ7−2ζ2−2ζ8−2ζ5−2ζ4−2ζ−2ζ7-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7ζ2ζ8ζ5ζ4ζζ7000000000000000000000000000000
χ772−1−i3−1+i32−1−i3−1+i3-21+i31−i322−1−i3−1−i3−1+i3−1+i3-21+i31−i32ζ52ζ22ζ82ζ2ζ72ζ4−2ζ5−2ζ2−2ζ8−2ζ−2ζ7−2ζ4-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4ζ5ζ2ζ8ζζ7ζ4000000000000000000000000000000
χ782−1−i3−1+i32−1−i3−1+i3-21+i31−i322−1−i3−1−i3−1+i3−1+i3-21+i31−i32ζ82ζ52ζ22ζ72ζ42ζ−2ζ8−2ζ5−2ζ2−2ζ7−2ζ4−2ζ-11+i321−i32-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζζ8ζ5ζ2ζ7ζ4ζ000000000000000000000000000000
χ79666666666-2-2-2-2-2-2-2-2-2000000000000-3-3-3-3-3-3-3-3-3111111111000000000000000000000000000000000000000000
χ80666666-6-6-6-2-2-2-2-2-2222000000000000-3-3-3-3-3-3333111111-1-1-1000000000000000000000000000000000000000000
χ816−3+3i3−3−3i36−3+3i3−3−3i36−3+3i3−3−3i3-2-21−i31−i31+i31+i3-21−i31+i3000000000000-33−3i323+3i32-33−3i323+3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32000000000000000000000000000000000000000000
χ826−3+3i3−3−3i36−3+3i3−3−3i3-63−3i33+3i3-2-21−i31−i31+i31+i32−1+i3−1−i3000000000000-33−3i323+3i32-33−3i323+3i323−3+3i32−3−3i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32000000000000000000000000000000000000000000
χ836−3−3i3−3+3i36−3−3i3−3+3i36−3−3i3−3+3i3-2-21+i31+i31−i31−i3-21+i31−i3000000000000-33+3i323−3i32-33+3i323−3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32000000000000000000000000000000000000000000
χ846−3−3i3−3+3i36−3−3i3−3+3i3-63+3i33−3i3-2-21+i31+i31−i31−i32−1−i3−1+i3000000000000-33+3i323−3i32-33+3i323−3i323−3−3i32−3+3i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32000000000000000000000000000000000000000000
χ85121212-4-4-40004-44-44-4000000000000000-6-6-6222000-22-22-22000000000000000000000000000000000000000000000
χ86121212-4-4-4000-44-44-44000000000000000-6-6-62220002-22-22-2000000000000000000000000000000000000000000000
χ8712−6+6i3−6−6i3-42−2i32+2i30004-4−2+2i32−2i3−2−2i32+2i3000000000000000-63−3i33+3i32−1+i3−1−i3000-221−i3−1+i31+i3−1−i3000000000000000000000000000000000000000000000
χ8812−6+6i3−6−6i3-42−2i32+2i3000-442−2i3−2+2i32+2i3−2−2i3000000000000000-63−3i33+3i32−1+i3−1−i30002-2−1+i31−i3−1−i31+i3000000000000000000000000000000000000000000000
χ8912−6−6i3−6+6i3-42+2i32−2i30004-4−2−2i32+2i3−2+2i32−2i3000000000000000-63+3i33−3i32−1−i3−1+i3000-221+i3−1−i31−i3−1+i3000000000000000000000000000000000000000000000
χ9012−6−6i3−6+6i3-42+2i32−2i3000-442+2i3−2−2i32−2i3−2+2i3000000000000000-63+3i33−3i32−1−i3−1+i30002-2−1−i31+i3−1+i31−i3000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.