Finite Group Databasebeta

← Group #13146940

Character table — Group #13146940

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222222222333333333333333333336666666666666666666666666666666666242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order122222366666662222336666666666666622666666666666666666666666666666663336666666666666666666664444444412121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ5111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ6111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ71111-1-11111-1-1-1-111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ81111-1-11111-1-1-1-111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ91111-1-11111-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11111-1-1-1-1−1−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−i321−i321−i321−i321−i321−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3211-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ101111-1-11111-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11111-1-1-1-1−1−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−i321−i321−i321−i321−i321−1−i32−1+i32111-1-1-1-1−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-111-1-1111+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ111111-1-11111-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11111-1-1-1-1−1+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+i321+i321+i321+i321+i321−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ121111-1-11111-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11111-1-1-1-1−1+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+i321+i321+i321+i321+i321−1+i32−1−i32111-1-1-1-1−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-111-1-1111−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ1311-1-11-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11-1-111-1-11-1-111-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ1411-1-11-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11-1-111-1-11-1-111-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ1511-1-11-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-111-1-111-1-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−1−i32−1+i321-1-111-1-1−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32i−ii−ii−ii−iζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ1611-1-11-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-111-1-111-1-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−1−i32−1+i321-1-111-1-1−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ii−ii−ii−ii−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ1711-1-11-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-111-1-111-1-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−1+i32−1−i321-1-111-1-1−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32i−ii−ii−ii−iζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ1811-1-11-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-111-1-111-1-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−1+i32−1−i321-1-111-1-1−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ii−ii−ii−ii−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ1911-1-1-1111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ2011-1-1-1111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ2111-1-1-1111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1111-1-1-1-111−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321-1-1-1-111−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32i−i−iii−i−iiζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ2211-1-1-1111-1-1-1-11111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1111-1-1-1-111−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321-1-1-1-111−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−iii−i−iii−i−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ2311-1-1-1111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1111-1-1-1-111−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321-1-1-1-111−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32i−i−iii−i−iiζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ2411-1-1-1111-1-1-1-11111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1111-1-1-1-111−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321-1-1-1-111−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−iii−i−iii−i−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ2522222222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ26222222222222222222−1−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+i32222222222−1−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+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i32000000000000000000000000
χ27222222222222222222−1+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−i32222222222−1+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−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i32000000000000000000000000
χ282222-2-22222-2-2-2-222222222222222222222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-1-1-1-11111-1-1-11111-1-1-11111000000000000000000000000
χ292222-2-22222-2-2-2-22222−1−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+i3-2-22222-2-2-2-2−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i31+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i31−i3-11+i321−i32-1-1-111111+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000000000000000
χ302222-2-22222-2-2-2-22222−1+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−i3-2-22222-2-2-2-2−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i31−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i31+i3-11−i321+i32-1-1-111111−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000000000000000
χ3122-2-22-222-2-222-2-222-2-222222222-2-2-2-2-2-2-2-22-222-2-222-2-222-2-22222-2-2-2-222-2-22222-2-2-2-2-1-1-1-111-1-111-111-1-111-111-1-111000000000000000000000000
χ3222-2-22-222-2-222-2-222-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i32-222-2-222-2-2−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3-11+i321−i32-111-1-1111+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32000000000000000000000000
χ3322-2-22-222-2-222-2-222-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i32-222-2-222-2-2−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3-11−i321+i32-111-1-1111−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32000000000000000000000000
χ3422-2-2-2222-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-22222-1-1-1-11111-1-1-11111-1-1-11111-1-1000000000000000000000000
χ3522-2-2-2222-2-2-2-22222-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i3-2222-2-2-2-222−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-11111-1-11+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32000000000000000000000000
χ3622-2-2-2222-2-2-2-22222-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i3-2222-2-2-2-222−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-11111-1-11−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32000000000000000000000000
χ372-22-2002-22-200002-22-2222-2-22-2-222-2-222-2-2002-22-200002-22-2000000002-22-200000000222-22-20000-22-20000-22-20000000000000000000000000000
χ382-22-2002-22-200002-22-2222-2-22-2-222-2-222-2-2002-22-200002-22-2000000002-22-200000000-1-1-11-11−i3i3−i3i31-11−i3i3−i3i31-11−i3i3−i3i3000000000000000000000000
χ392-22-2002-22-200002-22-2222-2-22-2-222-2-222-2-2002-22-200002-22-2000000002-22-200000000-1-1-11-11i3−i3i3−i31-11i3−i3i3−i31-11i3−i3i3−i3000000000000000000000000
χ402-22-2002-22-200002-22-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3002-22-20000−1−i31+i3−1−i31+i300000000−1+i31−i3−1+i31−i3000000002−1−i3−1+i3-22-200001+i3−1−i31+i300001−i3−1+i31−i30000000000000000000000000000
χ412-22-2002-22-200002-22-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3002-22-20000−1−i31+i3−1−i31+i300000000−1+i31−i3−1+i31−i300000000-11+i321−i321-11−i3i3−i3i3−1−i321+i32−1−i32−3+i323−i32−3+i323−i32−1+i321−i32−1+i323+i32−3−i323+i32−3−i32000000000000000000000000
χ422-22-2002-22-200002-22-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3002-22-20000−1−i31+i3−1−i31+i300000000−1+i31−i3−1+i31−i300000000-11+i321−i321-11i3−i3i3−i3−1−i321+i32−1−i323−i32−3+i323−i32−3+i32−1+i321−i32−1+i32−3−i323+i32−3−i323+i32000000000000000000000000
χ432-22-2002-22-200002-22-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3002-22-20000−1+i31−i3−1+i31−i300000000−1−i31+i3−1−i31+i3000000002−1+i3−1−i3-22-200001−i3−1+i31−i300001+i3−1−i31+i30000000000000000000000000000
χ442-22-2002-22-200002-22-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3002-22-20000−1+i31−i3−1+i31−i300000000−1−i31+i3−1−i31+i300000000-11−i321+i321-11−i3i3−i3i3−1+i321−i32−1+i323+i32−3−i323+i32−3−i32−1−i321+i32−1−i32−3+i323−i32−3+i323−i32000000000000000000000000
χ452-22-2002-22-200002-22-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i3002-22-20000−1+i31−i3−1+i31−i300000000−1−i31+i3−1−i31+i300000000-11−i321+i321-11i3−i3i3−i3−1+i321−i32−1+i32−3−i323+i32−3−i323+i32−1−i321+i32−1−i323−i32−3+i323−i32−3+i32000000000000000000000000
χ462-2-22002-2-2200002-2-22222-2-22-2-2-2-222-2-222002-2-2200002-2-22000000002-2-2200000000222-2-220000-2-220000-2-220000000000000000000000000000
χ472-2-22002-2-2200002-2-22222-2-22-2-2-2-222-2-222002-2-2200002-2-22000000002-2-2200000000-1-1-111-1−i3i3i3−i311-1−i3i3i3−i311-1−i3i3i3−i3000000000000000000000000
χ482-2-22002-2-2200002-2-22222-2-22-2-2-2-222-2-222002-2-2200002-2-22000000002-2-2200000000-1-1-111-1i3−i3−i3i311-1i3−i3−i3i311-1i3−i3−i3i3000000000000000000000000
χ492-2-22002-2-2200002-2-22−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3002-2-220000−1−i31+i31+i3−1−i300000000−1+i31−i31−i3−1+i3000000002−1−i3−1+i3-2-2200001+i31+i3−1−i300001−i31−i3−1+i30000000000000000000000000000
χ502-2-22002-2-2200002-2-22−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3002-2-220000−1−i31+i31+i3−1−i300000000−1+i31−i31−i3−1+i300000000-11+i321−i3211-1−i3i3i3−i3−1−i32−1−i321+i32−3+i323−i323−i32−3+i32−1+i32−1+i321−i323+i32−3−i32−3−i323+i32000000000000000000000000
χ512-2-22002-2-2200002-2-22−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3002-2-220000−1−i31+i31+i3−1−i300000000−1+i31−i31−i3−1+i300000000-11+i321−i3211-1i3−i3−i3i3−1−i32−1−i321+i323−i32−3+i32−3+i323−i32−1+i32−1+i321−i32−3−i323+i323+i32−3−i32000000000000000000000000
χ522-2-22002-2-2200002-2-22−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3002-2-220000−1+i31−i31−i3−1+i300000000−1−i31+i31+i3−1−i3000000002−1+i3−1−i3-2-2200001−i31−i3−1+i300001+i31+i3−1−i30000000000000000000000000000
χ532-2-22002-2-2200002-2-22−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3002-2-220000−1+i31−i31−i3−1+i300000000−1−i31+i31+i3−1−i300000000-11−i321+i3211-1−i3i3i3−i3−1+i32−1+i321−i323+i32−3−i32−3−i323+i32−1−i32−1−i321+i32−3+i323−i323−i32−3+i32000000000000000000000000
χ542-2-22002-2-2200002-2-22−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i3002-2-220000−1+i31−i31−i3−1+i300000000−1−i31+i31+i3−1−i300000000-11−i321+i3211-1i3−i3−i3i3−1+i32−1+i321−i32−3−i323+i323+i32−3−i32−1−i32−1−i321+i323−i32−3+i32−3+i323−i32000000000000000000000000
χ5533333333333333-1-1-1-133-13-1-13-13-13-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-1-1-1-1-13-1-1-13-1-1-10000000000000000000000001111-1-1-1-11-11-11-11-11-11-11-11-1
χ5633333333333333-1-1-1-133-13-1-13-13-13-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-1-1-1-1-13-1-1-13-1-1-1000000000000000000000000-1-1-1-11111-11-11-11-11-11-11-11-11
χ5733333333333333-1-1-1-1−3−3i32−3+3i321+i32−3−3i321+i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321−i321−i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i320000000000000000000000001111-1-1-1-1−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ5833333333333333-1-1-1-1−3−3i32−3+3i321+i32−3−3i321+i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321−i321−i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i32000000000000000000000000-1-1-1-111111+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ5933333333333333-1-1-1-1−3+3i32−3−3i321−i32−3+3i321−i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321+i321+i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i320000000000000000000000001111-1-1-1-1−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ6033333333333333-1-1-1-1−3+3i32−3−3i321−i32−3+3i321−i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321+i321+i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i32000000000000000000000000-1-1-1-111111−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ613333-3-33333-3-3-3-3-1-1-1-133-13-1-13-13-13-13-13-111-1-1-1-11111-1-1-1-1-3111-3111-1-1-1-1-3111-311100000000000000000000000011-1-1-1-1111-11-1-11-111-11-1-11-11
χ623333-3-33333-3-3-3-3-1-1-1-133-13-1-13-13-13-13-13-111-1-1-1-11111-1-1-1-1-3111-3111-1-1-1-1-3111-3111000000000000000000000000-1-11111-1-1-11-111-11-1-11-111-11-1
χ633333-3-33333-3-3-3-3-1-1-1-1−3−3i32−3+3i321+i32−3−3i321+i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i3211-1-1-1-111111+i321+i321+i321+i323+3i32−1−i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i321−i321−i321−i321−i323−3i32−1+i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i3200000000000000000000000011-1-1-1-111−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ643333-3-33333-3-3-3-3-1-1-1-1−3−3i32−3+3i321+i32−3−3i321+i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i3211-1-1-1-111111+i321+i321+i321+i323+3i32−1−i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i321−i321−i321−i321−i323−3i32−1+i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i32000000000000000000000000-1-11111-1-11+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ653333-3-33333-3-3-3-3-1-1-1-1−3+3i32−3−3i321−i32−3+3i321−i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i3211-1-1-1-111111−i321−i321−i321−i323−3i32−1+i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i321+i321+i321+i321+i323+3i32−1−i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i3200000000000000000000000011-1-1-1-111−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ663333-3-33333-3-3-3-3-1-1-1-1−3+3i32−3−3i321−i32−3+3i321−i321+i32−3−3i321+i32−3+3i321−i32−3+3i321−i32−3−3i321+i32−3−3i321+i3211-1-1-1-111111−i321−i321−i321−i323−3i32−1+i32−1+i32−1+i323−3i32−1+i32−1+i32−1+i321+i321+i321+i321+i323+3i32−1−i32−1−i32−1−i323+3i32−1−i32−1−i32−1−i32000000000000000000000000-1-11111-1-11−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
χ6733-3-33-333-3-333-3-3-1-11133-13-1-13-1-31-31-31-31-11-1-111-1-111-1-1113-1-1-1-3111-1-1113-1-1-1-3111000000000000000000000000i−ii−i−ii−iii−i−iii−i−iii−i−iii−i−ii
χ6833-3-33-333-3-333-3-3-1-11133-13-1-13-1-31-31-31-31-11-1-111-1-111-1-1113-1-1-1-3111-1-1113-1-1-1-3111000000000000000000000000−ii−iii−ii−i−iii−i−iii−i−iii−i−iii−i
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.