Finite Group Databasebeta

← Group #13173025

Character table — Group #13173025

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222226666888888888888888888888888121212123636363636363636111122222222226666888888888888888888888888121212123636363636363636111122222222226666888888888888888888888888121212123636363636363636
order12442346661212121222443336666666661212121212121212121212126612124444888836121263126661212121266121233366666666612121212121212121212121266121212121212242424243612126312666121212126612123336666666661212121212121212121212126612121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-11111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-11111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-1
χ41111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-1-111-1-1111111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-1-111-1-1111111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-1-111-1-111
χ511-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−ii−ii−i11-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−ii−ii−i11-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−ii−ii−i
χ611-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−ii−ii11-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−ii−ii11-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−ii−ii
χ711-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1i−i−iii−i−ii11-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1i−i−iii−i−ii11-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1i−i−iii−i−ii
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χ1722-2-222-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-2220000000022-2-222-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-2220000000022-2-222-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-22200000000
χ1822-2-22-1-2-1-1-11111-2-2222-1-122-1-1-1-12-1-1-2-21111-2-2111111-1-10000000022-2-22-1-2-1-1-11111-2-2222-1-122-1-1-1-12-1-1-2-21111-2-2111111-1-10000000022-2-22-1-2-1-1-11111-2-2222-1-122-1-1-1-12-1-1-2-21111-2-2111111-1-100000000
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χ2122-2-2-222-2-22-2-2222-22-2-1-1-1111111-1-1-1111111-1-1-1-1-1-1-222-20000000022-2-2-222-2-22-2-2222-22-2-1-1-1111111-1-1-1111111-1-1-1-1-1-1-222-20000000022-2-2-222-2-22-2-2222-22-2-1-1-1111111-1-1-1111111-1-1-1-1-1-1-222-200000000
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χ2322-2-2-2-1211-111-1-12-22-2-12-111-2-211-12-111-2-211-1-122-1-11-1-110000000022-2-2-2-1211-111-1-12-22-2-12-111-2-211-12-111-2-211-1-122-1-11-1-110000000022-2-2-2-1211-111-1-12-22-2-12-111-2-211-12-111-2-211-1-122-1-11-1-1100000000
χ2422-2-2-2-1211-111-1-12-22-2-1-121111-2-2-1-121111-2-2-1-1-1-1221-1-110000000022-2-2-2-1211-111-1-12-22-2-1-121111-2-2-1-121111-2-2-1-1-1-1221-1-110000000022-2-2-2-1211-111-1-12-22-2-1-121111-2-2-1-121111-2-2-1-1-1-1221-1-1100000000
χ2533333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-133333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-133333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-1
χ2633333333333333-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1111133333333333333-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1111133333333333333-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-11111
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χ561111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−1+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+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+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−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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ571111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ581111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-1-111-1-111−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ5911-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−ii−ii−i−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ6011-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−ii−ii−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ6111-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1i−i−iii−i−ii−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11
χ6211-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1−iii−i−iii−i−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11
χ63222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i300000000
χ6422222-12-1-1-1-1-1-1-122222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200000000
χ6522222-12-1-1-1-1-1-1-12222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000000
χ6622222-12-1-1-1-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i3200000000
χ672222-22-2-2-2222-2-2-222-2-1-1-1111111-1-1-1-1-1-1-1-1-11111112-22-200000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i3−1+i31−i300000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i3−1−i31+i300000000
χ682222-2-1-211-1-1-111-222-22-1-1-2-211112-1-122-1-1-1-1-2-21111-11-1100000000−1+i3−1+i3−1+i3−1+i31−i31−i321−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i3−1+i3−1+i31−i3−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i3200000000−1−i3−1−i3−1−i3−1−i31+i31+i321+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i3−1−i3−1−i31+i3−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i3200000000
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χ1111111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ1121111-11-1-1-1111-1-1-111-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-1-1-111-1-111−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ11311-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111i−ii−ii−ii−i−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ11411-1-111-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−ii−ii−ii−ii−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ11511-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1i−i−iii−i−ii−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7
χ11611-1-1-111-1-11-1-1111-11-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-1−iii−i−iii−i−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7
χ117222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i300000000
χ11822222-12-1-1-1-1-1-1-122222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200000000
χ11922222-12-1-1-1-1-1-1-12222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-1-1-1-100000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000000
χ12022222-12-1-1-1-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-1-1-1-100000000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i3200000000
χ1212222-22-2-2-2222-2-2-222-2-1-1-1111111-1-1-1-1-1-1-1-1-11111112-22-200000000−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i3−1−i31+i300000000−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i3−1+i31−i300000000
χ1222222-2-1-211-1-1-111-222-22-1-1-2-211112-1-122-1-1-1-1-2-21111-11-1100000000−1−i3−1−i3−1−i3−1−i31+i31+i321+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i3−1−i3−1−i31+i3−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i31−i321−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i3−1+i3−1+i31−i3−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i3200000000
χ1232222-2-1-211-1-1-111-222-2-12-111-2-211-12-1-1-122-1-111-2-211-11-1100000000−1−i3−1−i3−1−i3−1−i31+i31+i321+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i3−1−i3−1−i31+i31+i32−1−i31+i32−1−i32−1−i321+i31+i3−1−i32−1−i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i32−1−i32−1−i321+i31+i3−1−i32−1−i321+i32−1−i321+i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i31−i321−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i3−1+i3−1+i31−i31−i32−1+i31−i32−1+i32−1+i321−i31−i3−1+i32−1+i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i32−1+i32−1+i321−i31−i3−1+i32−1+i321−i32−1+i321−i32−1+i3200000000
χ1242222-2-1-211-1-1-111-222-2-1-121111-2-2-1-12-1-1-1-1221111-2-2-11-1100000000−1−i3−1−i3−1−i3−1−i31+i31+i321+i3−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i3−1−i3−1−i31+i31+i321+i32−1−i3−1−i32−1−i32−1−i32−1−i321+i31+i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i3−1−i32−1−i32−1−i32−1−i321+i31+i31+i32−1−i321+i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i31−i321−i3−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i3−1+i3−1+i31−i31−i321−i32−1+i3−1+i32−1+i32−1+i32−1+i321−i31−i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i3−1+i32−1+i32−1+i32−1+i321−i31−i31−i32−1+i321−i32−1+i3200000000
χ12522-2-222-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-22200000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i321+i321+i321+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−i321+i31+i3−1−i3−1−i300000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i321−i321−i321−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+i321−i31−i3−1+i3−1+i300000000
χ12622-2-22-1-2-1-1-11111-2-2222-1-122-1-1-1-12-1-1-2-21111-2-2111111-1-100000000−1−i3−1−i31+i31+i3−1−i31+i321+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i3200000000−1+i3−1+i31−i31−i3−1+i31−i321−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i3200000000
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χ1514-4−4i4i04000-4−4i4i000000111i3−i3i3−i3i3−i3-1-1-1−ii−ii−ii3−33−33−3000000000000−2−2i32+2i3−4ζ114ζ110−2−2i30002+2i3−4ζ114ζ11000000−1−i32−1−i32−1−i323−i32−3+i323−i32−3+i323−i32−3+i321+i321+i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i3−4ζ74ζ70−2+2i30002−2i3−4ζ74ζ7000000−1+i32−1+i32−1+i32−3−i323+i32−3−i323+i32−3−i323+i321−i321−i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ1524-4−4i4i04000-4−4i4i000000-2-2-20000002222i−2i2i−2i2i−2i000000000000000000−2−2i32+2i3−4ζ114ζ110−2−2i30002+2i3−4ζ114ζ110000001+i31+i31+i3000000−1−i3−1−i3−1−i32ζ11−2ζ112ζ11−2ζ112ζ11−2ζ11000000000000000000−2+2i32−2i3−4ζ74ζ70−2+2i30002−2i3−4ζ74ζ70000001−i31−i31−i3000000−1+i3−1+i3−1+i32ζ7−2ζ72ζ7−2ζ72ζ7−2ζ7000000000000000000
χ1534-4−4i4i0-20−2i32i322i−2i−2323000011-2−i3i3i3−i300-1-12−ii−ii2i−2i−333−300000000000000−2−2i32+2i3−4ζ114ζ1101+i30−3+i33−i3−1−i32ζ11−2ζ11−4ζ7−2ζ114ζ7+2ζ110000−1−i32−1−i321+i3−3+i323−i323−i32−3+i32001+i321+i32−1−i3−ζ11ζ11−ζ11ζ112ζ11−2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ1100000000000000−2+2i32−2i3−4ζ74ζ701−i303+i3−3−i3−1+i32ζ7−2ζ72ζ7+4ζ11−2ζ7−4ζ110000−1+i32−1+i321−i33+i32−3−i32−3−i323+i32001−i321−i32−1+i3−ζ7ζ7−ζ7ζ72ζ7−2ζ7ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000
χ1544-4−4i4i0-20−2i32i322i−2i−232300001-21i3−i300−i3i3-12-1−ii2i−2i−ii3−300−33000000000000−2−2i32+2i3−4ζ114ζ1101+i30−3+i33−i3−1−i32ζ11−2ζ11−4ζ7−2ζ114ζ7+2ζ110000−1−i321+i3−1−i323−i32−3+i3200−3+i323−i321+i32−1−i31+i32−ζ11ζ112ζ11−2ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ1100−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i3−4ζ74ζ701−i303+i3−3−i3−1+i32ζ7−2ζ72ζ7+4ζ11−2ζ7−4ζ110000−1+i321−i3−1+i32−3−i323+i32003+i32−3−i321−i32−1+i31−i32−ζ7ζ72ζ7−2ζ7−ζ7ζ7−ζ7−2ζ11ζ7+2ζ1100ζ7+2ζ11−ζ7−2ζ11000000000000
χ1554-4−4i4i0-20−2i32i322i−2i−23230000-21100−i3i3i3−i32-1-12i−2i−ii−ii00−333−3000000000000−2−2i32+2i3−4ζ114ζ1101+i30−3+i33−i3−1−i32ζ11−2ζ11−4ζ7−2ζ114ζ7+2ζ1100001+i3−1−i32−1−i3200−3+i323−i323−i32−3+i32−1−i31+i321+i322ζ11−2ζ11−ζ11ζ11−ζ11ζ1100−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i3−4ζ74ζ701−i303+i3−3−i3−1+i32ζ7−2ζ72ζ7+4ζ11−2ζ7−4ζ1100001−i3−1+i32−1+i32003+i32−3−i32−3−i323+i32−1+i31−i321−i322ζ7−2ζ7−ζ7ζ7−ζ7ζ700ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ1564-4−4i4i0-202i3−2i322i−2i23−23000011-2i3−i3−i3i300-1-12−ii−ii2i−2i3−3−3300000000000000−2−2i32+2i3−4ζ114ζ1101+i303−i3−3+i3−1−i32ζ11−2ζ114ζ7+2ζ11−4ζ7−2ζ110000−1−i32−1−i321+i33−i32−3+i32−3+i323−i32001+i321+i32−1−i3−ζ11ζ11−ζ11ζ112ζ11−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ1100000000000000−2+2i32−2i3−4ζ74ζ701−i30−3−i33+i3−1+i32ζ7−2ζ7−2ζ7−4ζ112ζ7+4ζ110000−1+i32−1+i321−i3−3−i323+i323+i32−3−i32001−i321−i32−1+i3−ζ7ζ7−ζ7ζ72ζ7−2ζ7−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000
χ1574-4−4i4i0-202i3−2i322i−2i23−2300001-21−i3i300i3−i3-12-1−ii2i−2i−ii−33003−3000000000000−2−2i32+2i3−4ζ114ζ1101+i303−i3−3+i3−1−i32ζ11−2ζ114ζ7+2ζ11−4ζ7−2ζ110000−1−i321+i3−1−i32−3+i323−i32003−i32−3+i321+i32−1−i31+i32−ζ11ζ112ζ11−2ζ11−ζ11ζ11−2ζ7−ζ112ζ7+ζ11002ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i3−4ζ74ζ701−i30−3−i33+i3−1+i32ζ7−2ζ7−2ζ7−4ζ112ζ7+4ζ110000−1+i321−i3−1+i323+i32−3−i3200−3−i323+i321−i32−1+i31−i32−ζ7ζ72ζ7−2ζ7−ζ7ζ7ζ7+2ζ11−ζ7−2ζ1100−ζ7−2ζ11ζ7+2ζ11000000000000
χ1584-4−4i4i0-202i3−2i322i−2i23−230000-21100i3−i3−i3i32-1-12i−2i−ii−ii003−3−33000000000000−2−2i32+2i3−4ζ114ζ1101+i303−i3−3+i3−1−i32ζ11−2ζ114ζ7+2ζ11−4ζ7−2ζ1100001+i3−1−i32−1−i32003−i32−3+i32−3+i323−i32−1−i31+i321+i322ζ11−2ζ11−ζ11ζ11−ζ11ζ11002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i3−4ζ74ζ701−i30−3−i33+i3−1+i32ζ7−2ζ7−2ζ7−4ζ112ζ7+4ζ1100001−i3−1+i32−1+i3200−3−i323+i323+i32−3−i32−1+i31−i321−i322ζ7−2ζ7−ζ7ζ7−ζ7ζ700−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ15966666-36-3-3-3-3-3-3-3-2-2-2-2000000000000000000000000111100000000−3−3i3−3−3i3−3−3i3−3−3i3−3−3i33+3i32−3−3i33+3i323+3i323+3i323+3i323+3i323+3i323+3i321+i31+i31+i31+i3000000000000000000000000−1−i32−1−i32−1−i32−1−i3200000000−3+3i3−3+3i3−3+3i3−3+3i3−3+3i33−3i32−3+3i33−3i323−3i323−3i323−3i323−3i323−3i323−3i321−i31−i31−i31−i3000000000000000000000000−1+i32−1+i32−1+i32−1+i3200000000
χ1606666-6-3-633-3-3-3332-2-220000000000000000000000001-11-100000000−3−3i3−3−3i3−3−3i3−3−3i33+3i33+3i323+3i3−3−3i32−3−3i323+3i323+3i323+3i32−3−3i32−3−3i32−1−i31+i31+i3−1−i3000000000000000000000000−1−i321+i32−1−i321+i3200000000−3+3i3−3+3i3−3+3i3−3+3i33−3i33−3i323−3i3−3+3i32−3+3i323−3i323−3i323−3i32−3+3i32−3+3i32−1+i31−i31−i3−1+i3000000000000000000000000−1+i321−i32−1+i321−i3200000000
χ16166-6-66-3-6-3-3-3333322-2-2000000000000000000000000-1-11100000000−3−3i3−3−3i33+3i33+3i3−3−3i33+3i323+3i33+3i323+3i323+3i32−3−3i32−3−3i32−3−3i32−3−3i32−1−i3−1−i31+i31+i30000000000000000000000001+i321+i32−1−i32−1−i3200000000−3+3i3−3+3i33−3i33−3i3−3+3i33−3i323−3i33−3i323−3i323−3i32−3+3i32−3+3i32−3+3i32−3+3i32−1+i3−1+i31−i31−i30000000000000000000000001−i321−i32−1+i32−1+i3200000000
χ16266-6-6-6-3633-333-3-3-22-22000000000000000000000000-111-100000000−3−3i3−3−3i33+3i33+3i33+3i33+3i32−3−3i3−3−3i32−3−3i323+3i32−3−3i32−3−3i323+3i323+3i321+i3−1−i31+i3−1−i30000000000000000000000001+i32−1−i32−1−i321+i3200000000−3+3i3−3+3i33−3i33−3i33−3i33−3i32−3+3i3−3+3i32−3+3i323−3i32−3+3i32−3+3i323−3i323−3i321−i3−1+i31−i3−1+i30000000000000000000000001−i32−1+i32−1+i321−i3200000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.