Finite Group Databasebeta

← Group #13054944

Character table — Group #13054944

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11112222223333333344444444444466666666666677777777121212121212121212121212121212121212121212121212141414141414141414141414282828282828282828282828282828282828282828282828
order12442224447714142828282822448888888814141414141428282828282833661212121214141414282828285656565656565656565656565656565666666612121212121266661212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ41111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+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−i321−i321−i32
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−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+i321+i321+i32
χ7111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ9111111111111111111-1-1-1-11111-1-1-1-1111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ11111111111111111111-1-1-1-1-1-1-1-11111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1−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+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ12111111111111111111-1-1-1-1-1-1-1-11111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1+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−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ1311111-1-11-1-1111111111-11-1ii−i−iii−i−i11-1-1-1-111-1-1-1-11111111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11-1-111-1-1-1-11-11-11-11-1ii−i−iii−i−iii−i−iii−i−i
χ1411111-1-11-1-1111111111-11-1ii−i−iii−i−i11-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ1511111-1-11-1-1111111111-11-1ii−i−iii−i−i11-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ1611111-1-11-1-1111111111-11-1−i−iii−i−iii11-1-1-1-111-1-1-1-11111111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11-1-111-1-1-1-11-11-11-11-1−i−iii−i−iii−i−iii−i−iii
χ1711111-1-11-1-1111111111-11-1−i−iii−i−iii11-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ1811111-1-11-1-1111111111-11-1−i−iii−i−iii11-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ1911111-1-11-1-111111111-11-11ii−i−i−i−iii11-1-1-1-111-1-1-1-111111111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-111-1-1-1-1-11-11-11-11ii−i−i−i−iiiii−i−i−i−iii
χ2011111-1-11-1-111111111-11-11ii−i−i−i−iii11-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ2111111-1-11-1-111111111-11-11ii−i−i−i−iii11-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ2211111-1-11-1-111111111-11-11−i−iiiii−i−i11-1-1-1-111-1-1-1-111111111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-111-1-1-1-1-11-11-11-11−i−iiiii−i−i−i−iiiii−i−i
χ2311111-1-11-1-111111111-11-11−i−iiiii−i−i11-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ2411111-1-11-1-111111111-11-11−i−iiiii−i−i11-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ2511-1-1111-1-1-11111-1-1-1-11-1-11i−ii−ii−ii−i111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i111111-1-1-1-1-1-11-11-1-11-11i−ii−ii−ii−ii−ii−ii−ii−i
χ2611-1-1111-1-1-11111-1-1-1-11-1-11i−ii−ii−ii−i111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1-1-111ii−i−iii−i−iii−i−iii−i−i−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ2711-1-1111-1-1-11111-1-1-1-11-1-11i−ii−ii−ii−i111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1-1-111ii−i−iii−i−iii−i−iii−i−i−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ2811-1-1111-1-1-11111-1-1-1-11-1-11−ii−ii−ii−ii111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii111111-1-1-1-1-1-11-11-1-11-11−ii−ii−ii−ii−ii−ii−ii−ii
χ2911-1-1111-1-1-11111-1-1-1-11-1-11−ii−ii−ii−ii111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1-1-111−i−iii−i−iii−i−iii−i−iii−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ3011-1-1111-1-1-11111-1-1-1-11-1-11−ii−ii−ii−ii111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1-1-111−i−iii−i−iii−i−iii−i−iii−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ3111-1-1111-1-1-11111-1-1-1-1-111-1i−ii−i−ii−ii111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii111111-1-1-1-1-1-1-11-111-11-1i−ii−i−ii−iii−ii−i−ii−ii
χ3211-1-1111-1-1-11111-1-1-1-1-111-1i−ii−i−ii−ii111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ3311-1-1111-1-1-11111-1-1-1-1-111-1i−ii−i−ii−ii111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ3411-1-1111-1-1-11111-1-1-1-1-111-1−ii−iii−ii−i111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i111111-1-1-1-1-1-1-11-111-11-1−ii−iii−ii−i−ii−iii−ii−i
χ3511-1-1111-1-1-11111-1-1-1-1-111-1−ii−iii−ii−i111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ3611-1-1111-1-1-11111-1-1-1-1-111-1−ii−iii−ii−i111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ3711-1-11-1-1-1111111-1-1-1-111-1-11-1-111-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-11-1-1-1-111111111-1-1-1-11-1-111-1-111-1-111-1-11
χ3811-1-11-1-1-1111111-1-1-1-111-1-11-1-111-1-1111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-1-1-111-1-1-1-11111-1-1-1-111−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ3911-1-11-1-1-1111111-1-1-1-111-1-11-1-111-1-1111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-1-1-111-1-1-1-11111-1-1-1-111−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ4011-1-11-1-1-1111111-1-1-1-111-1-1-111-1-111-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11-1-1-1-111111111-1-1-1-1-111-1-111-1-111-1-111-1
χ4111-1-11-1-1-1111111-1-1-1-111-1-1-111-1-111-111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321111-1-1-1-1-1-11111-1-1-1-11111-1-1−1−i321+i321+i32−1+i321−i321−i321+i321−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−i321+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32
χ4211-1-11-1-1-1111111-1-1-1-111-1-1-111-1-111-111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321111-1-1-1-1-1-11111-1-1-1-11111-1-1−1+i321−i321−i32−1−i321+i321+i321−i321+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+i321−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32
χ4311-1-11-1-1-1111111-1-1-1-1-1-1111-1-11-111-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11-1-11-1-1-1-11111-1-1-1-111111-1-11-111-11-1-11-111-1
χ4411-1-11-1-1-1111111-1-1-1-1-1-1111-1-11-111-111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-1111111-1-1-1-111-1-11111-1-1−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32
χ4511-1-11-1-1-1111111-1-1-1-1-1-1111-1-11-111-111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-1111111-1-1-1-111-1-11111-1-1−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32
χ4611-1-11-1-1-1111111-1-1-1-1-1-111-111-11-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-111-11-1-11-111-11-1-11
χ4711-1-11-1-1-1111111-1-1-1-1-1-111-111-11-1-1111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-11111-1-11111-1-111-1-1-1-111−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32
χ4811-1-11-1-1-1111111-1-1-1-1-1-111-111-11-1-1111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-11111-1-11111-1-111-1-1-1-111−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.