Finite Group Databasebeta

← Group #13157028

Character table — Group #13157028

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112233661212121212121212161616163232323236364848484811223366121212121212121216161616323232323636484848481122336612121212121212121616161632323232363648484848
order12362266224412121212336633664466663636666666121212121212336633661212666636366666661212121212123366336612126666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ31111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ411111111-1-111111111111111-1-1-1-1-1-111111111-1-111111111111111-1-1-1-1-1-111111111-1-111111111111111-1-1-1-1-1-1
χ511111111-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211111111-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211111111-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32
χ611111111-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211111111-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211111111-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32
χ722-1-122-1-10022-1-1-1-12222-1-1-1-100000022-1-122-1-10022-1-1-1-12222-1-1-1-100000022-1-122-1-10022-1-1-1-12222-1-1-1-1000000
χ822-1-122-1-10022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i3200000022-1-122-1-10022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i3200000022-1-122-1-10022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i32000000
χ922-1-122-1-10022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i3200000022-1-122-1-10022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i3200000022-1-122-1-10022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i32000000
χ102-22-22-22-22-2000000-1-111-1-111001-11-12-22-22-22-22-2000000-1-111-1-111001-11-12-22-22-22-22-2000000-1-111-1-111001-11-1
χ112-22-22-22-22-20000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i322-22-22-22-22-20000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i322-22-22-22-22-20000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32
χ122-22-22-22-22-20000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i322-22-22-22-22-20000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i322-22-22-22-22-20000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32
χ132-22-22-22-2-22000000-1-111-1-11100-11-112-22-22-22-2-22000000-1-111-1-11100-11-112-22-22-22-2-22000000-1-111-1-11100-11-11
χ142-22-22-22-2-220000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i322-22-22-22-2-220000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i322-22-22-22-2-220000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32
χ152-22-22-22-2-220000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i322-22-22-22-2-220000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i322-22-22-22-2-220000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32
χ163333333333-1-1-1-1-1-100000000-1-100003333333333-1-1-1-1-1-100000000-1-100003333333333-1-1-1-1-1-100000000-1-10000
χ1733333333-3-3-1-1-1-1-1-10000000011000033333333-3-3-1-1-1-1-1-10000000011000033333333-3-3-1-1-1-1-1-100000000110000
χ184-4-224-4-2200000000-2-22211-1-10000004-4-224-4-2200000000-2-22211-1-10000004-4-224-4-2200000000-2-22211-1-1000000
χ194-4-224-4-22000000001+i31−i3−1−i3−1+i3−1−i32−1+i321+i321−i320000004-4-224-4-22000000001+i31−i3−1−i3−1+i3−1−i32−1+i321+i321−i320000004-4-224-4-22000000001+i31−i3−1−i3−1+i3−1−i32−1+i321+i321−i32000000
χ204-4-224-4-22000000001−i31+i3−1+i3−1−i3−1+i32−1−i321−i321+i320000004-4-224-4-22000000001−i31+i3−1+i3−1−i3−1+i32−1−i321−i321+i320000004-4-224-4-22000000001−i31+i3−1+i3−1−i3−1+i32−1−i321−i321+i32000000
χ216666-2-2-2-2002i−2i2i2i−2i−2i000000000000006666-2-2-2-2002i−2i2i2i−2i−2i000000000000006666-2-2-2-2002i−2i2i2i−2i−2i00000000000000
χ226666-2-2-2-200−2i2i−2i−2i2i2i000000000000006666-2-2-2-200−2i2i−2i−2i2i2i000000000000006666-2-2-2-200−2i2i−2i−2i2i2i00000000000000
χ2366-3-366-3-300-2-211110000000000000066-3-366-3-300-2-211110000000000000066-3-366-3-300-2-2111100000000000000
χ2466-3-3-2-211002i−2i−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ110000000000000066-3-3-2-211002i−2i−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ110000000000000066-3-3-2-211002i−2i−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ1100000000000000
χ2566-3-3-2-211002i−2iζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ100000000000000066-3-3-2-211002i−2iζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ100000000000000066-3-3-2-211002i−2iζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ1000000000000000
χ2666-3-3-2-21100−2i2i−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ110000000000000066-3-3-2-21100−2i2i−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ110000000000000066-3-3-2-21100−2i2i−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ1100000000000000
χ2766-3-3-2-21100−2i2iζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ100000000000000066-3-3-2-21100−2i2iζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ100000000000000066-3-3-2-21100−2i2iζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ1000000000000000
χ286-66-6-22-2200000000000000002-200006-66-6-22-2200000000000000002-200006-66-6-22-2200000000000000002-20000
χ296-66-6-22-220000000000000000-2200006-66-6-22-220000000000000000-2200006-66-6-22-220000000000000000-220000
χ3012-12-66-442-2000000000000000000000012-12-66-442-2000000000000000000000012-12-66-442-20000000000000000000000
χ31111111111111111111111111111111−1+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+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−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
χ321111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i321−1−i321−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1+i321−1+i321−1−i32−1−i32−1+i32−1+i3211
χ331111111111111111−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1−i321−1−i321−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i321−1+i321−1+i32−1−i32−1−i3211−1+i32−1+i32
χ3411111111-1-111111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i321+i321+i321+i321+i321+i32
χ3511111111-1-1111111−1−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+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i321−1−i321−1−i321−i321−i32-1-11+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1+i321−1+i3211+i321+i321−i321−i32-1-1
χ3611111111-1-1111111−1+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+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1−i321−1−i3211−i321−i321+i321+i32-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i321−1+i321−1+i321+i321+i32-1-11−i321−i32
χ3722-1-122-1-10022-1-1-1-12222-1-1-1-1000000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i32000000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i32000000
χ3822-1-122-1-10022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i32000000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i321−i321−i322−1−i32−1−i3-11+i32-11+i32000000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i321+i321+i32−1+i32−1+i321−i32-11−i32-1000000
χ3922-1-122-1-10022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i32000000−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i321−i321−i32−1−i32−1−i321+i32-11+i32-1000000−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i321+i321+i322−1+i32−1+i3-11−i32-11−i32000000
χ402-22-22-22-22-2000000-1-111-1-111001-11-1−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i30000001−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i3200−1+i321−i32−1+i321−i32−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i30000001+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i3200−1−i321+i32−1−i321+i32
χ412-22-22-22-22-20000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000-11+i321−1−i32-11+i321−1−i32001-1−1−i321+i32−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i30000001−i32-1−1+i3211−i32-1−1+i32100−1+i321−i321-1
χ422-22-22-22-22-20000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i30000001+i32-1−1−i3211+i32-1−1−i32100−1−i321+i321-1−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000-11−i321−1+i32-11−i321−1+i32001-1−1+i321−i32
χ432-22-22-22-2-22000000-1-111-1-11100-11-11−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i30000001−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32001−i32−1+i321−i32−1+i32−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i30000001+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32001+i32−1−i321+i32−1−i32
χ442-22-22-22-2-220000001+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i3000000-11+i321−1−i32-11+i321−1−i3200-111+i32−1−i32−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i30000001−i32-1−1+i3211−i32-1−1+i321001−i32−1+i32-11
χ452-22-22-22-2-220000001−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i30000001+i32-1−1−i3211+i32-1−1−i321001+i32−1−i32-11−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i3000000-11−i321−1+i32-11−i321−1+i3200-111−i32−1+i32
χ463333333333-1-1-1-1-1-100000000-1-10000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i32000000001−i321−i320000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i32000000001+i321+i320000
χ4733333333-3-3-1-1-1-1-1-100000000110000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i321−i321−i321−i321−i3200000000−1+i32−1+i320000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i321+i321+i321+i321+i3200000000−1−i32−1−i320000
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χ8466-3-3-2-211002i−2i−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ1100000000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i32002ζ11−2ζ11−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ1000000000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i32002ζ7−2ζ72ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ1100000000000000
χ8566-3-3-2-211002i−2iζ2−ζ10+2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2−2ζ7+ζ1000000000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i32002ζ11−2ζ11ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ1100000000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i32002ζ7−2ζ7−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ1100000000000000
χ8666-3-3-2-21100−2i2i−ζ2−2ζ7+ζ10ζ2−ζ10−2ζ11−ζ2+2ζ7+ζ10ζ2−ζ10+2ζ1100000000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i3200−2ζ112ζ11−ζ2+2ζ7−2ζ10+2ζ11ζ2−2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ11ζ2+2ζ7+2ζ1000000000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i3200−2ζ72ζ72ζ2+ζ10−2ζ11−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10+2ζ11−2ζ2−2ζ7−ζ10−2ζ1100000000000000
χ8766-3-3-2-21100−2i2iζ2−ζ10−2ζ11−ζ2−2ζ7+ζ10ζ2−ζ10+2ζ11−ζ2+2ζ7+ζ1000000000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−1−i32−1−i3200−2ζ112ζ11ζ2−2ζ7+2ζ10−ζ2+2ζ7−2ζ10+2ζ11ζ2+2ζ7+2ζ10−ζ2−2ζ7−2ζ10−2ζ1100000000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−1+i32−1+i3200−2ζ72ζ7−2ζ2+2ζ7−ζ10+2ζ112ζ2+ζ10−2ζ11−2ζ2−2ζ7−ζ10−2ζ112ζ2+ζ10+2ζ1100000000000000
χ886-66-6-22-2200000000000000002-20000−3−3i33+3i3−3−3i33+3i31+i3−1−i31+i3−1−i30000000000000000−1−i31+i30000−3+3i33−3i3−3+3i33−3i31−i3−1+i31−i3−1+i30000000000000000−1+i31−i30000
χ896-66-6-22-220000000000000000-220000−3−3i33+3i3−3−3i33+3i31+i3−1−i31+i3−1−i300000000000000001+i3−1−i30000−3+3i33−3i3−3+3i33−3i31−i3−1+i31−i3−1+i300000000000000001−i3−1+i30000
χ9012-12-66-442-20000000000000000000000−6−6i36+6i33+3i3−3−3i32+2i3−2−2i3−1−i31+i30000000000000000000000−6+6i36−6i33−3i3−3+3i32−2i3−2+2i3−1+i31−i30000000000000000000000

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