Finite Group Databasebeta

← Group #13164572

Character table — Group #13164572

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222334446666666666666991212121212121212121212121212121212121218181824242424242424242424272736363636484848484848545454727272727272
order12223462266122246691818181818181844336666121818181818181818363636362446666991212181844121212121818181836362446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111−1−i32−1+i3211−1−i32−1+i321111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111−1+i32−1−i3211−1+i32−1−i321111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111111111111111111111-1-11111111111111111111-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111-1-1−1−i32−1+i3211−1−i32−1+i321111111111111-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i32
χ61111111111111111111111111-1-1−1+i32−1−i3211−1+i32−1−i321111111111111-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i32
χ7111-11-11111-1-11-1-1111111111111111-111-11111-1-1-1-1-1-1-1-1-11-11-11-111-1-1111111111-11-1-1-1-11-1-1-11-11-1
χ8111-11-11111-1-11-1-1111111111111−1−i32−1+i321-1−1−i32−1+i32-11111-1-1-1-1-1-1-1-1-11-1−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i32-11-11+i321−i32−1−i321+i32−1+i321−i32
χ9111-11-11111-1-11-1-1111111111111−1+i32−1−i321-1−1+i32−1−i32-11111-1-1-1-1-1-1-1-1-11-1−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i32-11-11−i321+i32−1+i321−i32−1−i321+i32
χ10111-11-11111-1-11-1-11111111111-1-1111-111-11111-1-1-1-1-1-1-1-11-111-11-111-1-111-1-1-1-1-1-11-11-1-1-11-1111-11-11
χ11111-11-11111-1-11-1-11111111111-1-1−1−i32−1+i321-1−1−i32−1+i32-11111-1-1-1-1-1-1-1-11-11−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ12111-11-11111-1-11-1-11111111111-1-1−1+i32−1−i321-1−1+i32−1−i32-11111-1-1-1-1-1-1-1-11-11−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1311-111-1111-11-1-11-111111111111111-1111-1-1-1-1-11111-1-1-1-1-1-11-11-1111-1-111111111-11-11-1-1-1-11-1-1-11-11
χ1411-111-1111-11-1-11-1111111111111−1−i32−1+i32-11−1−i32−1+i32-1-1-1-1-11111-1-1-1-1-1-111+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i32-1-111+i321−i321+i32−1−i321−i32−1+i32
χ1511-111-1111-11-1-11-1111111111111−1+i32−1−i32-11−1+i32−1−i32-1-1-1-1-11111-1-1-1-1-1-111−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i32-1-111−i321+i321−i32−1+i321+i32−1−i32
χ1611-111-1111-11-1-11-11111111111-1-111-1111-1-1-1-1-11111-1-1-1-111-1-11-1111-1-111-1-1-1-1-1-1-11-11-1-111-1111-11-1
χ1711-111-1111-11-1-11-11111111111-1-1−1−i32−1+i32-11−1−i32−1+i32-1-1-1-1-11111-1-1-1-111-11+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i3211-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ1811-111-1111-11-1-11-11111111111-1-1−1+i32−1−i32-11−1+i32−1−i32-1-1-1-1-11111-1-1-1-111-11−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i3211-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ1911-1-111111-1-11-1-1111111111111111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-1-1-1
χ2011-1-111111-1-11-1-11111111111111−1−i32−1+i32-1-1−1−i32−1+i321-1-1-1-1-1-1-1-111111-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32
χ2111-1-111111-1-11-1-11111111111111−1+i32−1−i32-1-1−1+i32−1−i321-1-1-1-1-1-1-1-111111-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i32
χ2211-1-111111-1-11-1-111111111111-1-111-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ2311-1-111111-1-11-1-111111111111-1-1−1−i32−1+i32-1-1−1−i32−1+i321-1-1-1-1-1-1-1-11111-1111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ2411-1-111111-1-11-1-111111111111-1-1−1+i32−1−i32-1-1−1+i32−1−i321-1-1-1-1-1-1-1-11111-1111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222222-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-1-1-10002222-1-122-1-1000000-1-1-1-1-1-1000000000
χ2622222222222222222-1-1-1-1-1-1-1-100−1−i3−1+i322−1−i3−1+i32-1-1-1-1-1-1-1-1-1-1-1-1000−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i31+i321−i320000001+i321+i321−i321−i321+i321−i32000000000
χ2722222222222222222-1-1-1-1-1-1-1-100−1+i3−1−i322−1+i3−1−i32-1-1-1-1-1-1-1-1-1-1-1-1000−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i31−i321+i320000001−i321−i321+i321+i321−i321+i32000000000
χ28222-22-22222-2-22-2-222-1-1-1-1-1-1-1-100222-222-2-1-1-1-1111111110002-22-2-1-1-2-2-1-1000000-11-1111000000000
χ29222-22-22222-2-22-2-222-1-1-1-1-1-1-1-100−1−i3−1+i32-2−1−i3−1+i3-2-1-1-1-111111111000−1−i31+i3−1+i31−i31+i321−i321+i31−i31+i321−i320000001+i32−1−i321−i32−1+i32−1−i32−1+i32000000000
χ30222-22-22222-2-22-2-222-1-1-1-1-1-1-1-100−1+i3−1−i32-2−1+i3−1−i3-2-1-1-1-111111111000−1+i31−i3−1−i31+i31−i321+i321−i31+i31−i321+i320000001−i32−1+i321+i32−1−i32−1+i32−1−i32000000000
χ3122-222-2222-22-2-22-222-1-1-1-1-1-1-1-10022-2222-21111-1-1-1-11111000-22-22-1-1-2-2-1-10000001-11-111000000000
χ3222-222-2222-22-2-22-222-1-1-1-1-1-1-1-100−1−i3−1+i3-22−1−i3−1+i3-21111-1-1-1-111110001+i3−1−i31−i3−1+i31+i321−i321+i31−i31+i321−i32000000−1−i321+i32−1+i321−i32−1−i32−1+i32000000000
χ3322-222-2222-22-2-22-222-1-1-1-1-1-1-1-100−1+i3−1−i3-22−1+i3−1−i3-21111-1-1-1-111110001−i3−1+i31+i3−1−i31−i321+i321−i31+i31−i321+i32000000−1+i321−i32−1−i321+i32−1+i32−1−i32000000000
χ3422-2-222222-2-22-2-2222-1-1-1-1-1-1-1-10022-2-222211111111-1-1-1-1000-2-2-2-2-1-122-1-10000001111-1-1000000000
χ3522-2-222222-2-22-2-2222-1-1-1-1-1-1-1-100−1−i3−1+i3-2-2−1−i3−1+i3211111111-1-1-1-10001+i31+i31−i31−i31+i321−i32−1−i3−1+i31+i321−i32000000−1−i32−1−i32−1+i32−1+i321+i321−i32000000000
χ3622-2-222222-2-22-2-2222-1-1-1-1-1-1-1-100−1+i3−1−i3-2-2−1+i3−1−i3211111111-1-1-1-10001−i31−i31+i31+i31−i321+i32−1+i3−1−i31−i321+i32000000−1+i32−1+i32−1−i32−1−i321−i321+i32000000000
χ372-20020-22-20000002-22222-2-2-2-22i−2i2200-2-2000000000000000000002200-2-22i−2i2i−2i2i−2i000000000000000
χ382-20020-22-20000002-22222-2-2-2-22i−2i−1−i3−1+i3001+i31−i300000000000000000000−1−i3−1+i3001+i31−i32i−2i−2ζ152ζ15−2ζ32ζ3000000000000000
χ392-20020-22-20000002-22222-2-2-2-22i−2i−1+i3−1−i3001−i31+i300000000000000000000−1+i3−1−i3001−i31+i32i−2i−2ζ32ζ3−2ζ152ζ15000000000000000
χ402-20020-22-20000002-22222-2-2-2-2−2i2i2200-2-2000000000000000000002200-2-2−2i2i−2i2i−2i2i000000000000000
χ412-20020-22-20000002-22222-2-2-2-2−2i2i−1−i3−1+i3001+i31−i300000000000000000000−1−i3−1+i3001+i31−i3−2i2i2ζ15−2ζ152ζ3−2ζ3000000000000000
χ422-20020-22-20000002-22222-2-2-2-2−2i2i−1+i3−1−i3001−i31+i300000000000000000000−1+i3−1−i3001−i31+i3−2i2i2ζ3−2ζ32ζ15−2ζ15000000000000000
χ433333333-1-1333-1-1-1-1-13-1-1-1-1-1-133300-1-100-13-1-1-13-1-1-13-1-1-13330000000000-1-10000000000-1-1-1000000
χ443333333-1-1333-1-1-1-1-13-1-1-1-1-1-13-3-300-1-100-13-1-1-13-1-1-13-1-1-1-3-3-30000000000110000000000111000000
χ45333-33-33-1-13-3-3-111-1-13-1-1-1-1-1-133300-110013-1-1-1-3111-3111-33-30000000000-1-100000000001-11000000
χ46333-33-33-1-13-3-3-111-1-13-1-1-1-1-1-13-3-300-110013-1-1-1-3111-31113-330000000000110000000000-11-1000000
χ4733-333-33-1-1-33-31-11-1-13-1-1-1-1-1-1333001-1001-31113-1-1-1-3111-3-330000000000-1-1000000000011-1000000
χ4833-333-33-1-1-33-31-11-1-13-1-1-1-1-1-13-3-3001-1001-31113-1-1-1-311133-30000000000110000000000-1-11000000
χ4933-3-3333-1-1-3-3311-1-1-13-1-1-1-1-1-1333001100-1-3111-31113-1-1-13-3-30000000000-1-10000000000-111000000
χ5033-3-3333-1-1-3-3311-1-1-13-1-1-1-1-1-13-3-3001100-1-3111-31113-1-1-1-33300000000001100000000001-1-1000000
χ514-40040-44-40000004-4-2-2-2-22222004400-4-400000000000000000000-2-20022000000000000000000000
χ524-40040-44-40000004-4-2-2-2-2222200−2−2i3−2+2i3002+2i32−2i3000000000000000000001+i31−i300−1−i3−1+i3000000000000000000000
χ534-40040-44-40000004-4-2-2-2-2222200−2+2i3−2−2i3002−2i32+2i3000000000000000000001−i31+i300−1+i3−1−i3000000000000000000000
χ546666666-2-2666-2-2-2-2-2-3111111-30000-2-200-2-3111-3111-31110000000000000000000000000000000000
χ556666-36-366-3-3-3666-3-3000000000000-3-300-30000000000000000000000000000000000000000000000
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χ576666-36-3-2-2-3-3-3-2-2-2110−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ3400000110010−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ340−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ340−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ340000000000000000000000000000000000
χ586666-36-3-2-2-3-3-3-2-2-21102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000001100102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ2202ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ2202ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220000000000000000000000000000000000
χ59666-66-66-2-26-6-6-222-2-2-3111111-30000-22002-31113-1-1-13-1-1-10000000000000000000000000000000000
χ60666-6-3-6-366-3336-6-6-3-3000000000000-330030000000000000000000000000000000000000000000000
χ61666-6-3-6-3-2-2-333-2221102ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ34000001-100-102ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ340−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340000000000000000000000000000000000
χ62666-6-3-6-3-2-2-333-222110−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34000001-100-10−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ3402ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ3402ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340000000000000000000000000000000000
χ63666-6-3-6-3-2-2-333-2221102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ22000001-100-102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220000000000000000000000000000000000
χ6466-666-66-2-2-66-62-22-2-2-3111111-300002-20023-1-1-1-31113-1-1-10000000000000000000000000000000000
χ6566-66-3-6-3663-33-66-6-3-30000000000003-30030000000000000000000000000000000000000000000000
χ6666-66-3-6-3-2-23-332-221102ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ3400000-1100-10−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ3402ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ340−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340000000000000000000000000000000000
χ6766-66-3-6-3-2-23-332-22110−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ3400000-1100-102ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ3402ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340000000000000000000000000000000000
χ6866-66-3-6-3-2-23-332-221102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ2200000-1100-10−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ2202ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220000000000000000000000000000000000
χ6966-6-6666-2-2-6-6622-2-2-2-3111111-300002200-23-1-1-13-1-1-1-31110000000000000000000000000000000000
χ7066-6-6-36-36633-3-6-66-3-30000000000003300-30000000000000000000000000000000000000000000000
χ7166-6-6-36-3-2-233-322-21102ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ3400000-1-10010−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ340−2ζ22+2ζ26−2ζ342ζ14+2ζ22−2ζ14−2ζ26+2ζ3402ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ340000000000000000000000000000000000
χ7266-6-6-36-3-2-233-322-2110−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ3400000-1-100102ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ3402ζ14+2ζ22−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ340−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ340000000000000000000000000000000000
χ7366-6-6-36-3-2-233-322-21102ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ222ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ2200000-1-10010−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ220−2ζ14−2ζ26+2ζ34−2ζ22+2ζ26−2ζ342ζ14+2ζ2202ζ14+2ζ26−2ζ342ζ22−2ζ26+2ζ34−2ζ14−2ζ220000000000000000000000000000000000
χ746-60060-6-22000000-226-2-2-2222-66i−6i00000000000000000000000000000000−2i2i0000000000000000000
χ756-60060-6-22000000-226-2-2-2222-6−6i6i000000000000000000000000000000002i−2i0000000000000000000
χ7612-1200120-12-44000000-44-6222-2-2-260000000000000000000000000000000000000000000000000000000
χ7712-1200-60612-12000000-66000000000000000000000000000000000000000000000000000000000000000
χ7812-1200-606-440000002-204ζ22−4ζ26+4ζ34−4ζ14−4ζ224ζ14+4ζ26−4ζ34−4ζ22+4ζ26−4ζ344ζ14+4ζ22−4ζ14−4ζ26+4ζ3400000000000000000000000000000000000000000000000000000000
χ7912-1200-606-440000002-20−4ζ14−4ζ224ζ14+4ζ26−4ζ344ζ22−4ζ26+4ζ344ζ14+4ζ22−4ζ14−4ζ26+4ζ34−4ζ22+4ζ26−4ζ3400000000000000000000000000000000000000000000000000000000
χ8012-1200-606-440000002-204ζ14+4ζ26−4ζ344ζ22−4ζ26+4ζ34−4ζ14−4ζ22−4ζ14−4ζ26+4ζ34−4ζ22+4ζ26−4ζ344ζ14+4ζ2200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.