Finite Group Databasebeta

← Group #11787685

Character table — Group #11787685

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order1222223344446666661212121234444666666612121212121212121212661212121212121212121212121212121212124444121212121212121244888812121212242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ91-11-11-1111-11-11-1-1-1-11-1-1111i−ii−i11-11-1-1-11-111-111-1-1-11-1iiii−i−i−i−i1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i1-11-1i−i11-1-111-1-1ii−i−i1-11-1ii−i−i
χ101-11-11-1111-11-11-1-1-1-11-1-1111i−ii−i11-11-1-1-11-111-111-1-1-11-1iiii−i−i−i−i1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i-111-1−ii-1-11111-1-1−i−iii-11-11−i−iii
χ111-11-11-1111-11-11-1-1-1-11-1-1111i−ii−i11-11-1-1-11-111-111-1-1-11-1iiii−i−i−i−i1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii1-1-11i−i11-1-1-1-111ii−i−i-11-11−i−iii
χ121-11-11-1111-11-11-1-1-1-11-1-1111i−ii−i11-11-1-1-11-111-111-1-1-11-1iiii−i−i−i−i1-1iiii−i−i−i−i−i−iii−i−i−i−iiiii-11-11−ii-1-111-1-111−i−iii1-11-1ii−i−i
χ131-11-11-1111-11-11-1-1-1-11-1-1111−ii−ii11-11-1-1-11-111-111-1-1-11-1−i−i−i−iiiii1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-1-11−ii11-1-1-1-111−i−iii-11-11ii−i−i
χ141-11-11-1111-11-11-1-1-1-11-1-1111−ii−ii11-11-1-1-11-111-111-1-1-11-1−i−i−i−iiiii1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-11i−i-1-111-1-111ii−i−i1-11-1−i−iii
χ151-11-11-1111-11-11-1-1-1-11-1-1111−ii−ii11-11-1-1-11-111-111-1-1-11-1−i−i−i−iiiii1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii1-11-1−ii11-1-111-1-1−i−iii1-11-1−i−iii
χ161-11-11-1111-11-11-1-1-1-11-1-1111−ii−ii11-11-1-1-11-111-111-1-1-11-1−i−i−i−iiiii1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii-111-1i−i-1-11111-1-1ii−i−i-11-11ii−i−i
χ1722222222-2-2-2-2222222-2-2-2-2200002222222-2-2-2-2-2-2-2-2-2-22200000000-2-20000000000000000000000000000000000000000002-22-2
χ1822222222-2-2-2-2222222-2-2-2-2200002222222-2-2-2-2-2-2-2-2-2-22200000000-2-2000000000000000000000000000000000000000000-22-22
χ192222222-12222222-1-1-12222-122222-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000220022-1-1-1-10000-1-1-1-100000000
χ202222222-12222222-1-1-12222-122222-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-200-2-211110000111100000000
χ212222222-12222222-1-1-12222-1-2-2-2-22-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-211-2-211-1-1111111110000000000002200-2-2-1-1-1-10000111100000000
χ222222222-12222222-1-1-12222-1-2-2-2-22-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-211-2-211-1-111111111000000000000-2-2002211110000-1-1-1-100000000
χ23222222-122222-1-1-1222-1-1-1-1-12222-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022000000-1-1-1-1000000000000
χ24222222-122222-1-1-1222-1-1-1-1-12222-122-1-1-1-1-1-1222-1-1-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100-2-20000001111000000000000
χ25222222-122222-1-1-1222-1-1-1-1-1-2-2-2-2-122-1-1-1-1-1-1222-1-1-1-12-1-111-2-211-2-2-1-1111111112222-1-1-1-1-1-1-1-100-2-20000001111000000000000
χ26222222-122222-1-1-1222-1-1-1-1-1-2-2-2-2-122-1-1-1-1-1-1222-1-1-1-12-1-111-2-211-2-2-1-111111111-2-2-2-2111111110022000000-1-1-1-1000000000000
χ272222-2-2222-2-22222222-2-2-2-2222-2-2-2-2-2222-2222-2-2-2-2-2-22-2-22-22-22-22-22222-2-222-2-200000000000000000000000000000000000000
χ282222-2-2222-2-22222222-2-2-2-22-2-222-2-2-2222-2222-2-2-2-2-2-22-2-2-22-22-22-2222-2-222-2-22200000000000000000000000000000000000000
χ292222-2-222-222-2222222222220000-2-2-2222-2-2-2-2222222-2-2-200000000-2-20000000000000000000000000000000000000022-2-20000
χ302222-2-222-222-2222222222220000-2-2-2222-2-2-2-2222222-2-2-200000000-2-200000000000000000000000000000000000000-2-2220000
χ312222-2-22-12-2-22222-1-1-1-2-2-2-2-122-2-2-211-1-1-1-222-1111111-1112-2-112-2-11-1-1-1-111-1-111000000000000000000−i3i3−i3i30000−i3i3−i3i300000000
χ322222-2-22-12-2-22222-1-1-1-2-2-2-2-122-2-2-211-1-1-1-222-1111111-1112-2-112-2-11-1-1-1-111-1-111000000000000000000i3−i3i3−i30000i3−i3i3−i300000000
χ332222-2-22-12-2-22222-1-1-1-2-2-2-2-1-2-222-211-1-1-1-222-1111111-111-221-1-221-1-1-111-1-111-1-1000000000000000000−i3i3−i3i30000i3−i3i3−i300000000
χ342222-2-22-12-2-22222-1-1-1-2-2-2-2-1-2-222-211-1-1-1-222-1111111-111-221-1-221-1-1-111-1-111-1-1000000000000000000i3−i3i3−i30000−i3i3−i3i300000000
χ352222-2-2-122-2-22-1-1-12221111-122-2-21-2-2-1-1-11-1-12-2-21111211-112-2-112-2-1-1-1-111-1-111000033−3−333−3−300000000003−33−3000000000000
χ362222-2-2-122-2-22-1-1-12221111-122-2-21-2-2-1-1-11-1-12-2-21111211-112-2-112-2-1-1-1-111-1-1110000−3−333−3−3330000000000−33−33000000000000
χ372222-2-2-122-2-22-1-1-12221111-1-2-2221-2-2-1-1-11-1-12-2-211112111-1-221-1-22-1-111-1-111-1-1000033−3−333−3−30000000000−33−33000000000000
χ382222-2-2-122-2-22-1-1-12221111-1-2-2221-2-2-1-1-11-1-12-2-211112111-1-221-1-22-1-111-1-111-1-10000−3−333−3−33300000000003−33−3000000000000
χ392-22-22-222-22-222-2-2-2-2222-2-22000022-22-2-2-2-22-2-22-2-22222-200000000-220000000000000000000000000000000000000000002i−2i−2i2i
χ402-22-22-222-22-222-2-2-2-2222-2-22000022-22-2-2-2-22-2-22-2-22222-200000000-22000000000000000000000000000000000000000000−2i2i2i−2i
χ412-22-22-22-12-22-22-2-211-1-2-222-12i−2i2i−2i2-11-111-22-2-1-11-1-1111-112i2i−i−i−2i−2iii-11−i−i−i−iiiii0000000000002-2002i−2i-1-1110000−i−iii00000000
χ422-22-22-22-12-22-22-2-211-1-2-222-12i−2i2i−2i2-11-111-22-2-1-11-1-1111-112i2i−i−i−2i−2iii-11−i−i−i−iiiii000000000000-2200−2i2i11-1-10000ii−i−i00000000
χ432-22-22-22-12-22-22-2-211-1-2-222-1−2i2i−2i2i2-11-111-22-2-1-11-1-1111-11−2i−2iii2i2i−i−i-11iiii−i−i−i−i0000000000002-200−2i2i-1-1110000ii−i−i00000000
χ442-22-22-22-12-22-22-2-211-1-2-222-1−2i2i−2i2i2-11-111-22-2-1-11-1-1111-11−2i−2iii2i2i−i−i-11iiii−i−i−i−i000000000000-22002i−2i11-1-10000−i−iii00000000
χ452-22-22-2-122-22-2-111-2-2211-1-1-12i−2i2i−2i-12-2-1111-1122-2-1-111-2-11−i−i2i2iii−2i−2i-11−i−i−i−iiiii2i2i−2i−2i−i−i−i−iiiii002-2000000-1-111000000000000
χ462-22-22-2-122-22-2-111-2-2211-1-1-12i−2i2i−2i-12-2-1111-1122-2-1-111-2-11−i−i2i2iii−2i−2i-11−i−i−i−iiiii−2i−2i2i2iiiii−i−i−i−i00-2200000011-1-1000000000000
χ472-22-22-2-122-22-2-111-2-2211-1-1-1−2i2i−2i2i-12-2-1111-1122-2-1-111-2-11ii−2i−2i−i−i2i2i-11iiii−i−i−i−i2i2i−2i−2i−i−i−i−iiiii00-2200000011-1-1000000000000
χ482-22-22-2-122-22-2-111-2-2211-1-1-1−2i2i−2i2i-12-2-1111-1122-2-1-111-2-11ii−2i−2i−i−i2i2i-11iiii−i−i−i−i−2i−2i2i2iiiii−i−i−i−i002-2000000-1-111000000000000
χ492-22-2-222222-2-22-2-2-2-2222-2-222i−2i−2i2i-2-222-2-222-22-22-2-222-2-222i−2i2i−2i−2i2i−2i2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000
χ502-22-2-222222-2-22-2-2-2-2222-2-22−2i2i2i−2i-2-222-2-222-22-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000
χ512-22-2-2222-2-2222-2-2-2-22-2-22220000-2-222-2-22-22-22-222-2-22-2200000000-22000000000000000000000000000000000000002-2-220000
χ522-22-2-2222-2-2222-2-2-2-22-2-22220000-2-222-2-22-22-22-222-2-22-2200000000-2200000000000000000000000000000000000000-222-20000
χ532-22-2-222-122-2-22-2-211-122-2-2-12i−2i−2i2i-21-1-11122-2-11-111-1-111-12i−2i−ii−2i2ii−i-11−i−iiiii−i−i000000000000000000−i3i3i3−i300003−3−3300000000
χ542-22-2-222-122-2-22-2-211-122-2-2-12i−2i−2i2i-21-1-11122-2-11-111-1-111-12i−2i−ii−2i2ii−i-11−i−iiiii−i−i000000000000000000i3−i3−i3i30000−333−300000000
χ552-22-2-222-122-2-22-2-211-122-2-2-1−2i2i2i−2i-21-1-11122-2-11-111-1-111-1−2i2ii−i2i−2i−ii-11ii−i−i−i−iii000000000000000000−i3i3i3−i30000−333−300000000
χ562-22-2-222-122-2-22-2-211-122-2-2-1−2i2i2i−2i-21-1-11122-2-11-111-1-111-1−2i2ii−i2i−2i−ii-11ii−i−i−i−iii000000000000000000i3−i3−i3i300003−3−3300000000
χ572-22-2-22-1222-2-2-111-2-22-1-111-12i−2i−2i2i1-22-111-1-112-2211-1-1-21-1−ii2i−2ii−i−2i2i-11−i−iiiii−i−i0000−i3−i3i3i3i3i3−i3−i30000000000−333−3000000000000
χ582-22-2-22-1222-2-2-111-2-22-1-111-12i−2i−2i2i1-22-111-1-112-2211-1-1-21-1−ii2i−2ii−i−2i2i-11−i−iiiii−i−i0000i3i3−i3−i3−i3−i3i3i300000000003−3−33000000000000
χ592-22-2-22-1222-2-2-111-2-22-1-111-1−2i2i2i−2i1-22-111-1-112-2211-1-1-21-1i−i−2i2i−ii2i−2i-11ii−i−i−i−iii0000−i3−i3i3i3i3i3−i3−i300000000003−3−33000000000000
χ602-22-2-22-1222-2-2-111-2-22-1-111-1−2i2i2i−2i1-22-111-1-112-2211-1-1-21-1i−i−2i2i−ii2i−2i-11ii−i−i−i−iii0000i3i3−i3−i3−i3−i3i3i30000000000−333−3000000000000
χ614444444-2-4-4-4-4444-2-2-2-4-4-4-4-200004-2-2-2-2-24-4-422222222-2-200000000220000000000000000000000000000000000000000000000
χ62444444-24-4-4-4-4-2-2-24442222-20000-244-2-2-2-222-4-4-42222-4-2-200000000220000000000000000000000000000000000000000000000
χ63444444-2-24444-2-2-2-2-2-2-2-2-2-214444-2-2-2111-2-2-2-2-2-21111-211-2-2-2-2-2-2-2-2111111111100000000000000000000000000000000000000
χ64444444-2-24444-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2111-2-2-2-2-2-21111-2112222222211-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ65444444-2-2-4-4-4-4-2-2-2-2-2-2222210000-2-2-2111-222222-1-1-1-121100000000-1-13-33-33-33-300000000000000000000000000000000000000
χ66444444-2-2-4-4-4-4-2-2-2-2-2-2222210000-2-2-2111-222222-1-1-1-121100000000-1-1-33-33-33-3300000000000000000000000000000000000000
χ674444-4-44-2-444-4444-2-2-24444-20000-422-2-2-2-4-4-42-2-2-2-2-2-222200000000220000000000000000000000000000000000000000000000
χ684444-4-4-24-444-4-2-2-2444-2-2-2-2-200002-4-4-2-2-2222-444-2-2-2-2-42200000000220000000000000000000000000000000000000000000000
χ694444-4-4-2-24-4-44-2-2-2-2-2-22222144-4-42221112-2-2-222-1-1-1-1-2-1-1-22-22-22-221111-1-111-1-100000000000000000000000000000000000000
χ704444-4-4-2-24-4-44-2-2-2-2-2-222221-4-4442221112-2-2-222-1-1-1-1-2-1-12-22-22-22-211-1-111-1-11100000000000000000000000000000000000000
χ714444-4-4-2-2-444-4-2-2-2-2-2-2-2-2-2-2100002221112222-2-211112-1-100000000-1-13-3-333-3-3300000000000000000000000000000000000000
χ724444-4-4-2-2-444-4-2-2-2-2-2-2-2-2-2-2100002221112222-2-211112-1-100000000-1-1-333-3-333-300000000000000000000000000000000000000
χ7344-4-400440000-44-44-4-4000040000000-44-400000000000000000000000000000002-22-22-22-22-22-200000000000000000000000000
χ7444-4-400440000-44-44-4-4000040000000-44-40000000000000000000000000000000-22-22-22-22-22-2200000000000000000000000000
χ7544-4-400-2400002-224-4-423−2323−23-200000002-2200000023−2323−230000000000000000000002-22-2−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000000000
χ7644-4-400-2400002-224-4-423−2323−23-200000002-2200000023−2323−23000000000000000000000-22-221−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000000000
χ7744-4-400-2400002-224-4-4−2323−2323-200000002-22000000−2323−23230000000000000000000002-22-2−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000000000
χ7844-4-400-2400002-224-4-4−2323−2323-200000002-22000000−2323−2323000000000000000000000-22-221+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000000000
χ794-44-44-44-2-44-444-4-422-244-4-4-200004-22-222-4-4422-222-2-2-2-22000000002-20000000000000000000000000000000000000000000000
χ804-44-44-4-24-44-44-222-4-44-2-222-20000-24-4-22222-2-4-4422-2-24-22000000002-20000000000000000000000000000000000000000000000
χ814-44-44-4-2-24-44-4-22222-222-2-214i−4i4i−4i-2-221-1-12-22-2-2211-1-121-1−2i−2i−2i−2i2i2i2i2i1-1iiii−i−i−i−i00000000000000000000000000000000000000
χ824-44-44-4-2-24-44-4-22222-222-2-21−4i4i−4i4i-2-221-1-12-22-2-2211-1-121-12i2i2i2i−2i−2i−2i−2i1-1−i−i−i−iiiii00000000000000000000000000000000000000
χ834-44-44-4-2-2-44-44-22222-2-2-22210000-2-221-1-122-222-2-1-111-21-100000000-113i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000000000
χ844-44-44-4-2-2-44-44-22222-2-2-22210000-2-221-1-122-222-2-1-111-21-100000000-11−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000000000
χ854-44-4-444-2-4-4444-4-422-2-4-444-20000-42-2-2224-442-22-2-222-22-2000000002-20000000000000000000000000000000000000000000000
χ864-44-4-44-24-4-444-222-4-4422-2-2-200002-44-222-22-2-44-4-2-22242-2000000002-20000000000000000000000000000000000000000000000
χ874-44-4-44-2-244-4-4-22222-2-2-22214i−4i−4i4i22-21-1-1-2-22-22-2-1-1112-11−2i2i−2i2i2i−2i2i−2i1-1ii−i−i−i−iii00000000000000000000000000000000000000
χ884-44-4-44-2-244-4-4-22222-2-2-2221−4i4i4i−4i22-21-1-1-2-22-22-2-1-1112-112i−2i2i−2i−2i2i−2i2i1-1−i−iiiii−i−i00000000000000000000000000000000000000
χ894-44-4-44-2-2-4-444-22222-222-2-21000022-21-1-1-22-22-2211-1-1-2-1100000000-113i−3i−3i3i−3i3i3i−3i00000000000000000000000000000000000000
χ904-44-4-44-2-2-4-444-22222-222-2-21000022-21-1-1-22-22-2211-1-1-2-1100000000-11−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000000000000
χ914-4-4400440000-4-44-44-4000040000000-4-4400000000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ924-4-4400440000-4-44-44-4000040000000-4-440000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ934-4-4400-24000022-2-44-423−23−2323-2000000022-2000000−232323−230000000000000000000002i−2i−2i2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ944-4-4400-24000022-2-44-423−23−2323-2000000022-2000000−232323−23000000000000000000000−2i2i2i−2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ954-4-4400-24000022-2-44-4−232323−23-2000000022-200000023−23−23230000000000000000000002i−2i−2i2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ964-4-4400-24000022-2-44-4−232323−23-2000000022-200000023−23−2323000000000000000000000−2i2i2i−2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ9788-8-8008-40000-88-8-4440000-400000004-44000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-400004-44-44443−4343−4320000000-22-2000000−2323−232300000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-400004-44-444−4343−434320000000-22-200000023−2323−2300000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-40000-8-884-440000-4000000044-4000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-4000044-44-4443−43−434320000000-2-2200000023−23−232300000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-4000044-44-44−434343−4320000000-2-22000000−232323−2300000000000000000000000000000000000000000000000000000000000

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