Finite Group Databasebeta

← Group #72276972

Character table — Group #72276972

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109
size1122222224444666677778888121212121212141414141414141414141414141424242424242424242424242428282828282828282828282828282828282828282828282828282828282828285656565656565656565656565656565656565656
order122224444222271414143366448814142828282866666612121212121212121414141428282828565656562222444466666666666666661212121212121212448812121212121212122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ511111111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ611111111111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111-1-1-1-1-1-1-1-1−1−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−i321−i321−i32-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ711111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ811111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−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−i321−i321−i3211111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ911111111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ1011111111111111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111-1-1-1-1-1-1-1-1−1+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+i321+i321+i32-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ1211111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+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+i321+i321+i3211111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ13111111111-1-1-1-11111111111-1-111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ14111111111-1-1-1-11111111111-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ15111111111-1-1-1-111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ16111111111-1-1-1-111111111-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ17111111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i3211-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-111-1-111-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ18111111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i3211-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-1-1-111-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ19111111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1111111-1-111-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ20111111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111-1-111-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ21111111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i3211-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-111-1-111-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ22111111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i3211-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-1-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ23111111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1111111-1-111-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ24111111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ25111-1-111-1-111-1-111-1-11111i−ii−i1-111-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1111-1-1-111-1-111-1-11-1111-1111-1-1-11-1-1-1i−ii−ii−ii−ii−ii−ii−ii−ii−ii−i
χ26111-1-111-1-111-1-111-1-11111i−ii−i1-111-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i-11-1-1-111111-1-111-1-1-11-1-1-11-1-1-1111-1111−ii−iii−ii−i−ii−iii−ii−i−ii−ii
χ27111-1-111-1-111-1-111-1-11111−ii−ii1-111-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1111-1-1-111-1-111-1-11-1111-1111-1-1-11-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii−ii−ii
χ28111-1-111-1-111-1-111-1-11111−ii−ii1-111-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii-11-1-1-111111-1-111-1-1-11-1-1-11-1-1-1111-1111i−ii−i−ii−iii−ii−i−ii−iii−ii−i
χ29111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32i−ii−i1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1ii−i−iii−i−i1-1111-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1+i321−i321−i321−i32i−ii−iζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ30111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32i−ii−i1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1ii−i−iii−i−i-11-1-1-1111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321+i321+i321−i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i32−ii−iiζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ31111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−ii−ii1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1−i−iii−i−iii1-1111-1-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1+i321−i321−i321−i32−ii−ii−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ32111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−ii−ii1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1−i−iii−i−iii-11-1-1-1111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321+i321+i321−i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i32i−ii−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ33111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32i−ii−i1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1ii−i−iii−i−i1-1111-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1−i321+i321+i321+i32i−ii−iζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ34111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32i−ii−i1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1ii−i−iii−i−i-11-1-1-1111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321−i321−i321+i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i32−ii−iiζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ35111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−ii−ii1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1−i−iii−i−iii1-1111-1-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1−i321+i321+i321+i32−ii−ii−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ36111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−ii−ii1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1−i−iii−i−iii-11-1-1-1111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321−i321−i321+i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i32i−ii−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ37111-1-111-1-1-1-11111-1-11111i−i−ii1-111-1-111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii1-1-1-11-111-1-111-1-1111-1-1-11-1-1-11-1111-111i−i−iii−ii−ii−ii−i−ii−ii−ii−ii
χ38111-1-111-1-1-1-11111-1-11111i−i−ii1-111-1-111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1111-11-1-1-1-111-1-111-1111-1111-11-1-1-11-1-1−iii−ii−ii−i−ii−ii−ii−iii−ii−i
χ39111-1-111-1-1-1-11111-1-11111−iii−i1-111-1-111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i1-1-1-11-111-1-111-1-1111-1-1-11-1-1-11-1111-111−iii−i−ii−ii−ii−iii−ii−ii−ii−i
χ40111-1-111-1-1-1-11111-1-11111−iii−i1-111-1-111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1111-11-1-1-1-111-1-111-1111-1111-11-1-1-11-1-1i−i−ii−ii−iii−ii−ii−ii−i−ii−ii
χ41111-1-111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32i−i−ii1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111ii−i−i−i−iii1-1-1-11-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1+i321−i321−i321−i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i32i−i−iiζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ42111-1-111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32i−i−ii1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111ii−i−i−i−iii-1111-11-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i321+i321+i321−i32−1+i321−i321−i32−iii−iζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ43111-1-111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−iii−i1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111−i−iiiii−i−i1-1-1-11-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i32−1+i321−i321−i321−i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i32−iii−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ44111-1-111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1+i32−iii−i1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111−i−iiiii−i−i-1111-11-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i321+i321+i321−i32−1+i321−i321−i32i−i−ii−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ45111-1-111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32i−i−ii1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111ii−i−i−i−iii1-1-1-11-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1−i321+i321+i321+i32−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i32i−i−iiζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ46111-1-111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32i−i−ii1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111ii−i−i−i−iii-1111-11-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i321−i321−i321+i32−1−i321+i321+i32−iii−iζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ47111-1-111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−iii−i1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111−i−iiiii−i−i1-1-1-11-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i32−1−i321+i321+i321+i32−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i32−iii−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ48111-1-111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1−i32−iii−i1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111−i−iiiii−i−i-1111-11-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i321−i321−i321+i32−1−i321+i321+i32i−i−ii−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.