Finite Group Databasebeta

← Group #13178274

Character table — Group #13178274

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122222222222222222244444444444444444444444444444444444444888888888888888888888888888888181818181818181818181818181818181818363636363636363636363636363636363636363636363636363636
order122222333444466666666633333666666666666666666666121212121212121212121212666666666612121212121212121212121212121212121212124444441212121212121212121212122444444446612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-11111-1-111-1-1
χ5111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ6111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-111111111-1-1-1-111
χ7111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-1-1111-11111-1-1-1-1111111-1-1-1-1
χ8111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11-11-1111111111-1-1-1-1-1-111-1-1
χ91111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1
χ101111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1111-1-111-1-111-1-1111111-1-1
χ111111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1111-1-1-1111-1-111-1-1-1-111-1-11111
χ121111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11-11-11-111-1-1-1-11111-1-111-1-111
χ131111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1
χ141111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-11111-1-111-1-111-1-11111-1-1
χ151111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-11-111-11-1-111-1-11111-1-1-1-11111
χ161111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111-111-1-1-11111-1-1-1-11111-1-111
χ1722222222-12222-1-1222222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122000000000000-1-1-1-1200200200-1-1-1-1000000000000-1-1
χ1822222222-12222-1-1222222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20000000000001111-200-200-200111100000000000011
χ1922222222-1-2-2-2-2-1-1222222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-111-2-2-2-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-21111111122000000000000-1-1-1-1-200200-2001111000000000000-1-1
χ2022222222-1-2-2-2-2-1-1222222-12-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-111-2-2-2-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-20000000000001111200-200200-1-1-1-100000000000011
χ212222222-1222222222-1-12-12-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000220000-1-1-1-1000000200200200000000-1-1-1-100-1-100
χ222222222-1222222222-1-12-12-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-12222-1-122-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200001111000000-200-200-2000000001111001100
χ232222222-12-2-2-2-22222-1-12-12-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211-2-211-2-2-1-122-1-1-1-1-1-111-2-211111111-2-21111110000220000-1-1-1-1000000-200-200200000000111100-1-100
χ242222222-12-2-2-2-22222-1-12-12-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211-2-211-2-2-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-200001111000000200200-200000000-1-1-1-1001100
χ25222222-122222222-1-122-122-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002200-1-1-1-1000000000200200200000-1-1-1-10000-1-10000
χ26222222-122222222-1-122-122-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2001111000000000-200-200-20000011110000110000
χ27222222-122-2-2-2-222-1-122-122-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-211-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-21111002200-1-1-1-1000000000-200-20020000011110000-1-10000
χ28222222-122-2-2-2-222-1-122-122-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-211-2-2-2-2-1-1-1-122-1-1-1-11111-2-211111111-2-2111100-2-2001111000000000200200-200000-1-1-1-10000110000
χ292222-2-222-122-2-2-1-1222222-12-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-211-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122000000000000-1-1-1-1-200-20020011-1-100000000000011
χ302222-2-222-122-2-2-1-1222222-12-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-211-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-20000000000001111200200-200-1-111000000000000-1-1
χ312222-2-222-1-2-222-1-1222222-12-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-111-2-2-2-22222-1-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-122000000000000-1-1-1-1200-200-200-1-11100000000000011
χ322222-2-222-1-2-222-1-1222222-12-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-111-2-2-2-22222-1-1-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-20000000000001111-20020020011-1-1000000000000-1-1
χ332222-2-22-1222-2-22222-1-12-12-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-2-211-2-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000220000-1-1-1-1000000-200200-200000000-1-111001100
χ342222-2-22-1222-2-22222-1-12-12-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-2-211-2-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000-2-200001111000000200-20020000000011-1-100-1-100
χ352222-2-22-12-2-2222222-1-12-12-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-21122-1-12211-2-211111111-2-2111111-1-122-1-1-1-1-1-10000220000-1-1-1-1000000200-200-20000000011-1-1001100
χ362222-2-22-12-2-2222222-1-12-12-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-2-21122-1-12211-2-211111111-2-2111111-1-122-1-1-1-1-1-10000-2-200001111000000-200200200000000-1-11100-1-100
χ372222-2-2-12222-2-222-1-122-122-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-122-1-12211-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111002200-1-1-1-1000000000-200200-200000-1-1110000110000
χ382222-2-2-12222-2-222-1-122-122-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-122-1-12211-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100-2-2001111000000000200-20020000011-1-10000-1-10000
χ392222-2-2-122-2-22222-1-122-122-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-1-122221111-2-211111111-2-21111-1-1-1-122-1-1-1-1002200-1-1-1-1000000000200-200-20000011-1-10000110000
χ402222-2-2-122-2-22222-1-122-122-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-1-122221111-2-211111111-2-21111-1-1-1-122-1-1-1-100-2-2001111000000000-200200200000-1-1110000-1-10000
χ412-22-2002220000-2-22-22-2-2-2222222000000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000
χ422-22-2002220000-2-22-22-2-2-2222222000000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000
χ432-22-2002220000-2-22-22-2-2-2222222000000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000
χ442-22-2002220000-2-22-22-2-2-2222222000000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000
χ452-2-222-22222i−2i2i−2i-22-2-2-2-222-2222222-22-22-222222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-222-2-22i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000
χ462-2-222-2222−2i2i−2i2i-22-2-2-2-222-2222222-22-22-222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-222-2-2−2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000000000000000000
χ472-2-222-222-12i−2i2i−2i1-1-2-2-2-22212-1-1-1-12-22-2-112-1-1-1-1-2-211111111−ii2i−2i2i−2i2i−2i2i−2i−ii2-2-11-11-1-1112i−2i−ii−ii−i−iii2i−2i−ii−ii−i−iii000000000000003−33−3000000000−i3i3−i3i30000000000003−3
χ482-2-222-222-12i−2i2i−2i1-1-2-2-2-22212-1-1-1-12-22-2-112-1-1-1-1-2-211111111−ii2i−2i2i−2i2i−2i2i−2i−ii2-2-11-11-1-1112i−2i−ii−ii−i−iii2i−2i−ii−ii−i−iii00000000000000−33−33000000000i3−i3i3−i3000000000000−33
χ492-2-222-222-1−2i2i−2i2i1-1-2-2-2-22212-1-1-1-12-22-2-112-1-1-1-1-2-211111111i−i−2i2i−2i2i−2i2i−2i2ii−i2-2-11-11-1-111−2i2ii−ii−iii−i−i−2i2ii−ii−iii−i−i000000000000003−33−3000000000i3−i3i3−i30000000000003−3
χ502-2-222-222-1−2i2i−2i2i1-1-2-2-2-22212-1-1-1-12-22-2-112-1-1-1-1-2-211111111i−i−2i2i−2i2i−2i2i−2i2ii−i2-2-11-11-1-111−2i2ii−ii−iii−i−i−2i2ii−ii−iii−i−i00000000000000−33−33000000000−i3i3−i3i3000000000000−33
χ512-2-222-22-122i−2i2i−2i-22-2-2112-1-2-12-1-1-12-2-112-2-12-1-1-111-2-21111112i−2i2i−2i−ii2i−2i−ii2i−2i-112-2-11-1-111−ii2i−2i−ii−i−iii−ii2i−2i−ii−i−iii0000000000−i3i3−i3i30000000000000000000003−33−300−i3i300
χ522-2-222-22-122i−2i2i−2i-22-2-2112-1-2-12-1-1-12-2-112-2-12-1-1-111-2-21111112i−2i2i−2i−ii2i−2i−ii2i−2i-112-2-11-1-111−ii2i−2i−ii−i−iii−ii2i−2i−ii−i−iii0000000000i3−i3i3−i3000000000000000000000−33−3300i3−i300
χ532-2-222-22-12−2i2i−2i2i-22-2-2112-1-2-12-1-1-12-2-112-2-12-1-1-111-2-2111111−2i2i−2i2ii−i−2i2ii−i−2i2i-112-2-11-1-111i−i−2i2ii−iii−i−ii−i−2i2ii−iii−i−i0000000000−i3i3−i3i3000000000000000000000−33−3300−i3i300
χ542-2-222-22-12−2i2i−2i2i-22-2-2112-1-2-12-1-1-12-2-112-2-12-1-1-111-2-2111111−2i2i−2i2ii−i−2i2ii−i−2i2i-112-2-11-1-111i−i−2i2ii−iii−i−ii−i−2i2ii−iii−i−i0000000000i3−i3i3−i30000000000000000000003−33−300i3−i300
χ552-2-222-2-1222i−2i2i−2i-2211-2-2-12-2-1-12-1-1-112-22-2-1-12-1-11111-2-211112i−2i−ii2i−2i−ii2i−2i2i−2i-11-112-2-1-111−ii−ii2i−2i−i−iii−ii−ii2i−2i−i−iii000000−i3i3−i3i30000000000000000000003−33−30000−i3i30000
χ562-2-222-2-1222i−2i2i−2i-2211-2-2-12-2-1-12-1-1-112-22-2-1-12-1-11111-2-211112i−2i−ii2i−2i−ii2i−2i2i−2i-11-112-2-1-111−ii−ii2i−2i−i−iii−ii−ii2i−2i−i−iii000000i3−i3i3−i3000000000000000000000−33−330000i3−i30000
χ572-2-222-2-122−2i2i−2i2i-2211-2-2-12-2-1-12-1-1-112-22-2-1-12-1-11111-2-21111−2i2ii−i−2i2ii−i−2i2i−2i2i-11-112-2-1-111i−ii−i−2i2iii−i−ii−ii−i−2i2iii−i−i000000−i3i3−i3i3000000000000000000000−33−330000−i3i30000
χ582-2-222-2-122−2i2i−2i2i-2211-2-2-12-2-1-12-1-1-112-22-2-1-12-1-11111-2-21111−2i2ii−i−2i2ii−i−2i2i−2i2i-11-112-2-1-111i−ii−i−2i2iii−i−ii−ii−i−2i2iii−i−i000000i3−i3i3−i30000000000000000000003−33−30000i3−i30000
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χ1224-4-44-44-2-2-24i−4i−4i4i2-22222-2-22111−1−3i32−1+3i322-22-22-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i-11-11-111+3i321−3i32−1−3i32−1+3i32i−ii−ii−i−ζ7+2ζ112ζ7−ζ11ζ7−2ζ11−2ζ7+ζ11−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11000000000000000000000000000000000000000000000
χ1234-4-44-44-2-2-24i−4i−4i4i2-22222-2-22111−1+3i32−1−3i322-22-22-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i-11-11-111−3i321+3i32−1+3i32−1−3i32i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11000000000000000000000000000000000000000000000
χ1244-4-44-44-2-2-2−4i4i4i−4i2-22222-2-22111−1−3i32−1+3i322-22-22-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i322i−2i2i−2i2i−2i−2i2i−2i2i−2i2i-11-11-111+3i321−3i32−1−3i32−1+3i32−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11i−ii−ii−i−ζ7+2ζ112ζ7−ζ11ζ7−2ζ11−2ζ7+ζ11000000000000000000000000000000000000000000000
χ1254-4-44-44-2-2-2−4i4i4i−4i2-22222-2-22111−1+3i32−1−3i322-22-22-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i−2i2i−2i2i−2i2i-11-11-111−3i321+3i32−1+3i32−1−3i32−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11000000000000000000000000000000000000000000000
χ12688-8-8008-4-40000-44-884-4-844-4-422200000044-2-2-24-44-4-22-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12788-8-800-48-40000-444-4-884-84-42-4220000004-24-2-24-4-224-4-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12888-8-800-4-4800008-84-44-444-82-4-422000000-244-2-2-224-44-4-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12988-8-800-4-4-40000-444-44-4444222−1−3i3−1+3i3000000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13088-8-800-4-4-40000-444-44-4444222−1+3i3−1−3i3000000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1318-88-8008-4-40000448-8-44-84-4-4-422200000044-2-2-2-44-442-222-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-88-800-48-4000044-448-84-8-4-42-4220000004-24-2-2-442-2-4422-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1338-88-800-4-480000-8-8-44-444482-4-422000000-244-2-22-2-44-4422-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-88-800-4-4-4000044-44-4444-4222−1−3i3−1+3i3000000-2-2-21+3i31−3i32-22-22-2−1−3i3−1+3i31+3i31−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-88-800-4-4-4000044-44-4444-4222−1+3i3−1−3i3000000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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