Finite Group Databasebeta

← Group #14313211

Character table — Group #14313211

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222244444444444444444888888888888888888888888881010161616161616161616161616202020202020204040404040404040120120120120120120120120
order1223666224566101010151530303030303024666101010101010121212303030303030303030303030221020202030306060606060602246666446121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111-1-11-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111111-1-11-1-11-1-11111-1-1-1-1
χ6111111111111111111111111-1-11-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111111-1-11-1-11-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-111ii−i−i−i−iii
χ8111111111111111111111111-1-11-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-111−i−iiiii−i−i
χ911111111-1-1111111111111111-1-111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-111i−ii−ii−ii−i
χ1011111111-1-1111111111111111-1-111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-111−ii−ii−ii−ii
χ1111111111-1-1111111111111111-1-111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-11-1-111-1-11
χ1211111111-1-1111111111111111-1-111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-111-1-111-1
χ1311111111-1-111111111111111-11-1-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-11111-11-111-1-1-1i−ii−i−ii−ii
χ1411111111-1-111111111111111-11-1-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-11111-11-111-1-1-1−ii−iii−ii−i
χ1511111111-1-111111111111111-11-1-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-11-11-1-11111-1-11-111-1
χ1611111111-1-111111111111111-11-1-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-11-11-1-1111-111-11-1-11
χ172222222-22-22-2-22222222222200200-2-2000000-2-2-2-2-200000000222-20022-2-20000-22-222-2-200200-20000000000
χ182222222-22-22-2-22222222222200200-2-2000000-2-2-2-2-200000000-2-22-20022-2-200002-22-2-22200-20020000000000
χ192222222-2-222-2-22222222222200-200-2-20000002-2-2-2-20000000022-2200-2-2220000-2-2222-2-200-20020000000000
χ202222222-2-222-2-22222222222200-200-2-20000002-2-2-2-200000000-2-2-2200-2-222000022-2-2-22200200-20000000000
χ21222-1-1-1-12222-1-1222-1-1-1-1-1-1-1-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-100000000
χ22222-1-1-1-12222-1-1222-1-1-1-1-1-1-1-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-2-2-21111-2-211111100000000
χ23222-1-1-1-12222-1-1222-1-1-1-1-1-1-1-1-2-2-11122-2-2-2-211-1-1-1-1-1111111112222-2-2-1-1-1-11111222-1-1-1-1-2-2-111-11100000000
χ24222-1-1-1-12222-1-1222-1-1-1-1-1-1-1-1-2-2-11122-2-2-2-211-1-1-1-1-111111111-2-222-2-2-1-1-1-11111-2-2-21111221-1-11-1-100000000
χ25222-1-1-1-12-2-22-1-1222-1-1-1-1-1-1-1-12-21-1-1222222111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2111111112-2-2-1-1-1-12-21111-1-100000000
χ26222-1-1-1-12-2-22-1-1222-1-1-1-1-1-1-1-12-21-1-1222222111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-2221111-22-1-1-1-11100000000
χ27222-1-1-1-12-2-22-1-1222-1-1-1-1-1-1-1-1-2211122-2-2-2-2-1-11-1-1-1-11111111122-2-2221111-1-1-1-12-2-2-1-1-1-1-221-1-111100000000
χ28222-1-1-1-12-2-22-1-1222-1-1-1-1-1-1-1-1-2211122-2-2-2-2-1-11-1-1-1-111111111-2-2-2-2221111-1-1-1-1-22211112-2-111-1-1-100000000
χ29222-1-1-1-1-22-2211222-1-1-1-1-1-1-1-100-1−i3i3-2-20000−i3i311111−i3−i3−i3−i3i3i3i3i3222-200-1-111−i3−i3i3i3-22-2-1-11100-1−i3i31−i3i300000000
χ30222-1-1-1-1-22-2211222-1-1-1-1-1-1-1-100-1−i3i3-2-20000−i3i311111−i3−i3−i3−i3i3i3i3i3-2-22-200-1-111−i3−i3i3i32-2211-1-1001i3−i3-1i3−i300000000
χ31222-1-1-1-1-22-2211222-1-1-1-1-1-1-1-100-1i3−i3-2-20000i3−i311111i3i3i3i3−i3−i3−i3−i3222-200-1-111i3i3−i3−i3-22-2-1-11100-1i3−i31i3−i300000000
χ32222-1-1-1-1-22-2211222-1-1-1-1-1-1-1-100-1i3−i3-2-20000i3−i311111i3i3i3i3−i3−i3−i3−i3-2-22-200-1-111i3i3−i3−i32-2211-1-1001−i3i3-1−i3i300000000
χ33222-1-1-1-1-2-22211222-1-1-1-1-1-1-1-1001−i3i3-2-20000i3−i3-11111−i3−i3−i3−i3i3i3i3i322-220011-1-1i3i3−i3−i3-2-22-1-111001i3−i3-1−i3i300000000
χ34222-1-1-1-1-2-22211222-1-1-1-1-1-1-1-1001−i3i3-2-20000i3−i3-11111−i3−i3−i3−i3i3i3i3i3-2-2-220011-1-1i3i3−i3−i322-211-1-100-1−i3i31i3−i300000000
χ35222-1-1-1-1-2-22211222-1-1-1-1-1-1-1-1001i3−i3-2-20000−i3i3-11111i3i3i3i3−i3−i3−i3−i322-220011-1-1−i3−i3i3i3-2-22-1-111001−i3i3-1i3−i300000000
χ36222-1-1-1-1-2-22211222-1-1-1-1-1-1-1-1001i3−i3-2-20000−i3i3-11111i3i3i3i3−i3−i3−i3−i3-2-2-220011-1-1−i3−i3i3i322-211-1-100-1i3−i31−i3i300000000
χ374444444444-144-1-1-1-1-1-1-1-1-1-1-144444-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-144-1-1-1-1-1-1-1-1-1-1-1-4-44-4-4-1-11111-4-44-1-1-1-11111111100-1-111-1-1-1-1111100000000000000000000000
χ3944444444-4-4-144-1-1-1-1-1-1-1-1-1-1-14-4-444-1-1-1-1-1-1-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10011111111111100000000000000000000000
χ4044444444-4-4-144-1-1-1-1-1-1-1-1-1-1-1-44-4-4-4-1-1111144-4-1-1-1-1111111110011-1-11111-1-1-1-100000000000000000000000
χ414444444-44-4-1-4-4-1-1-1-1-1-1-1-1-1-1-10040011−5−55500-41111−5−555−5−55500-11−55-1-111−55−5500000000000000000000000
χ424444444-44-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1004001155−5−500-4111155−5−555−5−500-115−5-1-1115−55−500000000000000000000000
χ434444444-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-100-40011−5−5550041111−5−555−5−555001-15−511-1-15−55−500000000000000000000000
χ444444444-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-100-4001155−5−5004111155−5−555−5−5001-1−5511-1-1−55−5500000000000000000000000
χ45444-2-2-2-2444-1-2-2-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i15244-2-2-2-1-1-1-1-1-1-2-2-21−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i15200-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i15200000000000000000000000
χ46444-2-2-2-2444-1-2-2-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i152-4-4-222-1-1111122-21−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i15200-1-1111−i1521+i1521−i1521+i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ47444-2-2-2-2444-1-2-2-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i15244-2-2-2-1-1-1-1-1-1-2-2-21+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i15200-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i15200000000000000000000000
χ48444-2-2-2-2444-1-2-2-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i152-4-4-222-1-1111122-21+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i15200-1-1111+i1521−i1521+i1521−i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ49444-2-2-2-24-4-4-1-2-2-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i1524-42-2-2-1-1-1-1-1-12221−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i152001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1−i152−1+i15200000000000000000000000
χ50444-2-2-2-24-4-4-1-2-2-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i152-44222-1-11111-2-221−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1520011-1-1−1+i152−1−i152−1+i152−1−i1521−i1521+i1521+i1521−i15200000000000000000000000
χ51444-2-2-2-24-4-4-1-2-2-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i1524-42-2-2-1-1-1-1-1-12221+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i152001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1+i152−1−i15200000000000000000000000
χ52444-2-2-2-24-4-4-1-2-2-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i152-44222-1-11111-2-221+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1520011-1-1−1−i152−1+i152−1−i152−1+i1521+i1521−i1521−i1521+i15200000000000000000000000
χ53444-2-2-2-2-44-4-122-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i15200-2−2i32i31155−5−5−2i32i32−1+i152−1+i152−1−i152−1−i152ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ5800-115−51−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ54444-2-2-2-2-44-4-122-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i15200-22i3−2i311−5−5552i3−2i32−1+i152−1+i152−1−i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ5800-11−551−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ55444-2-2-2-2-44-4-122-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i15200-2−2i32i311−5−555−2i32i32−1−i152−1−i152−1+i152−1+i152ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ4600-11−551+i1521−i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ56444-2-2-2-2-44-4-122-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i15200-22i3−2i31155−5−52i3−2i32−1−i152−1−i152−1+i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ4600-115−51+i1521−i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ57444-2-2-2-2-4-44-122-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i152002−2i32i31155−5−52i3−2i3-2−1+i152−1+i152−1−i152−1−i152ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58001-1−55−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000
χ58444-2-2-2-2-4-44-122-1-1-11−i1521+i1521−i1521−i1521−i1521+i1521+i1521+i1520022i3−2i311−5−555−2i32i3-2−1+i152−1+i152−1−i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58001-15−5−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000
χ59444-2-2-2-2-4-44-122-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i152002−2i32i311−5−5552i3−2i3-2−1−i152−1−i152−1+i152−1+i152ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46001-15−5−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000
χ60444-2-2-2-2-4-44-122-1-1-11+i1521−i1521+i1521+i1521+i1521−i1521−i1521−i1520022i3−2i31155−5−5−2i32i3-2−1−i152−1−i152−1+i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46001-1−55−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000
χ6144-44-4-440004004-4-4444-4-44-4-4000000000000000000000000004-40000000000000004-4000000000000000000
χ6244-44-4-440004004-4-4444-4-44-4-400000000000000000000000000-44000000000000000-44000000000000000000
χ6344-4-222-20004−2i32i34-4-4-2-2-222-22200000000000000−2i32i3−2i32i3000000004-4000000000000000-22−2i32i30000000000000000
χ6444-4-222-20004−2i32i34-4-4-2-2-222-22200000000000000−2i32i3−2i32i300000000-440000000000000002-22i3−2i30000000000000000
χ6544-4-222-200042i3−2i34-4-4-2-2-222-222000000000000002i3−2i32i3−2i3000000004-4000000000000000-222i3−2i30000000000000000
χ6644-4-222-200042i3−2i34-4-4-2-2-222-222000000000000002i3−2i32i3−2i300000000-440000000000000002-2−2i32i30000000000000000
χ6788-88-8-88000-200-222-2-2-222-22200000−25250000000−252525−25000000000000000000000000000000000000000000000
χ6888-88-8-88000-200-222-2-2-222-2220000025−25000000025−25−2525000000000000000000000000000000000000000000000
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χ7088-8-444-4000-2−4i34i3-2221+i151−i151+i15−1−i15−1−i151−i15−1+i15−1+i1500000−252500000002ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58000000000000000000000000000000000000000000000
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χ848-80-44i3−4i34000-2002−25251−i151+i15−1+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ460000000−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800000002ζ14−2ζ26−2ζ14+2ζ26−2ζ2+2ζ382ζ2−2ζ382ζ34−2ζ46−2ζ34+2ζ46−2ζ22+2ζ582ζ22−2ζ580000000000000000000000000000000000000
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χ868-80-44i3−4i34000-200225−251+i151−i15−1−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ5800000002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ460000000−2ζ2+2ζ382ζ2−2ζ38−2ζ14+2ζ262ζ14−2ζ26−2ζ22+2ζ582ζ22−2ζ58−2ζ34+2ζ462ζ34−2ζ460000000000000000000000000000000000000
χ878-80-44i3−4i34000-200225−251+i151−i15−1−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ580000000−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600000002ζ2−2ζ38−2ζ2+2ζ382ζ14−2ζ26−2ζ14+2ζ262ζ22−2ζ58−2ζ22+2ζ582ζ34−2ζ46−2ζ34+2ζ460000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.