Finite Group Databasebeta

← Group #72220505

Character table — Group #72220505

Order 7776.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1222233666666669121212121818181818181818181818181818181818181818242424242736363636484848487272727272727272727272727272727272727272818196969696108108108108243288288288288324324324324432432432432
order133332266666666233333666666666666666666633332666633333333666666666666666622333366662333366666666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-11111111111111111111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111−1+i32−1−i321111111111111111111111−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ4111111111111111111−1+i32−1−i321111111111111111111111−1+i32−1−i32-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32-1−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321−i321+i321+i32
χ5111111111111111111−1−i32−1+i321111111111111111111111−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ6111111111111111111−1−i32−1+i321111111111111111111111−1−i32−1+i32-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32-1−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321+i321−i321−i32
χ71111111111111111−1+i32−1−i321111111111111111111111−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ81111111111111111−1+i32−1−i321111111111111111111111−1+i32−1−i3211-1−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321+i321−i321+i32
χ91111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1−i321−1+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−i3211−1−i3211−1+i32−1+i32−1−i32−1+i32−1−i321−1−i3211−1+i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32
χ101111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1−i32-1−1+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−i32-1-1−1−i3211−1+i321−i321+i321−i321+i32-1−1−i3211−1+i321−i321+i321−i321+i321+i32-1-11−i32
χ111111111111111111−1+i32−1−i32−1−i32−1+i3211111111111111111111−1+i32−1−i32−1−i32−1+i321−1+i32−1−i32−1−i32−1+i321−1+i32−1−i321−1+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+i32111−1+i32−1−i321−1+i32−1−i32−1−i32−1+i3211−1+i32−1−i321−1+i32−1−i32−1−i32−1+i321−1+i32−1−i321
χ121111111111111111−1+i32−1−i32−1−i32−1+i3211111111111111111111−1+i32−1−i32−1−i32−1+i32-1−1+i32−1−i32−1−i32−1+i321−1+i32−1−i321−1+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+i32-1-11−1+i32−1−i3211−i321+i321+i321−i32-11−1+i32−1−i3211−i321+i321+i321−i32-11−i321+i32-1
χ131111111111111111−1−i32−1+i321111111111111111111111−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ141111111111111111−1−i32−1+i321111111111111111111111−1−i32−1+i3211-1−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i32-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321−i321+i321−i32
χ151111111111111111−1−i32−1+i32−1+i32−1−i3211111111111111111111−1−i32−1+i32−1+i32−1−i321−1−i32−1+i32−1+i32−1−i321−1−i32−1+i321−1−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−i32111−1−i32−1+i321−1−i32−1+i32−1+i32−1−i3211−1−i32−1+i321−1−i32−1+i32−1+i32−1−i321−1−i32−1+i321
χ161111111111111111−1−i32−1+i32−1+i32−1−i3211111111111111111111−1−i32−1+i32−1+i32−1−i32-1−1−i32−1+i32−1+i32−1−i321−1−i32−1+i321−1−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−i32-1-11−1−i32−1+i3211+i321−i321−i321+i32-11−1−i32−1+i3211+i321−i321−i321+i32-11+i321−i32-1
χ171111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1+i321−1−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+i3211−1+i3211−1−i32−1−i32−1+i32−1−i32−1+i321−1+i3211−1−i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32
χ181111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1+i32-1−1−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+i32-1-1−1+i3211−1−i321+i321−i321+i321−i32-1−1+i3211−1−i321+i321−i321+i321−i321−i32-1-11+i32
χ1922222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222022222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100222200000-1-1-1-100000000
χ20222222222222222222−1+i3−1−i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122−1+i3−1−i3022−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-11−i321+i3222−1+i3−1−i3-1-1-1-1-1-11−i321−i321−i321+i321+i321+i3200−1+i3−1+i3−1−i3−1−i3000001−i321−i321+i321+i3200000000
χ21222222222222222222−1−i3−1+i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122−1−i3−1+i3022−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321−i3222−1−i3−1+i3-1-1-1-1-1-11+i321+i321+i321−i321−i321−i3200−1−i3−1−i3−1+i3−1+i3000001+i321+i321−i321−i3200000000
χ222222222222222222−1+i3−1−i322-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3220−1+i3−1−i322−1+i3−1−i3−1+i3−1−i31−i321+i32-1-1−1+i3−1−i3221−i321−i321−i321+i321+i321+i32-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i3000001−i321+i321−i321+i3200000000
χ232222222222222222−1+i3−1−i3−1+i3−1−i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i30−1+i3−1−i3−1+i3−1−i3−1−i322−1+i31−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i3200−1−i322−1+i3000001+i32-1-11−i3200000000
χ242222222222222222−1+i3−1−i3−1−i3−1+i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1−i3−1+i30−1+i3−1−i3−1−i3−1+i32−1+i3−1−i321−i321+i321+i321−i32−1+i3−1−i3−1−i3−1+i31−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i32002−1+i3−1−i3200000-11−i321+i32-100000000
χ252222222222222222−1−i3−1+i322-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3220−1−i3−1+i322−1−i3−1+i3−1−i3−1+i31+i321−i32-1-1−1−i3−1+i3221+i321+i321+i321−i321−i321−i32-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i3000001+i321−i321+i321−i3200000000
χ262222222222222222−1−i3−1+i3−1+i3−1−i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1+i3−1−i30−1−i3−1+i3−1+i3−1−i32−1−i3−1+i321+i321−i321−i321+i32−1−i3−1+i3−1+i3−1−i31+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i32002−1−i3−1+i3200000-11+i321−i32-100000000
χ272222222222222222−1−i3−1+i3−1−i3−1+i3-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i30−1−i3−1+i3−1−i3−1+i3−1+i322−1−i31+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i3200−1+i322−1−i3000001−i32-1-11+i3200000000
χ28333333-13333-1-1-1-1-100333-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-10033300-1-10000003300-1-1000000-1-1-1-1-1-13-100000033-1000000-1-10000
χ29333333-13333-1-1-1-1-100333-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-10033-300-1-10000003300-1-1000000-1-1-1-1-1-1-31000000-3-31000000110000
χ30333333-13333-1-1-1-1-100−3+3i32−3−3i323-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-100−3+3i32−3−3i323001−i321+i32000000−3+3i32−3−3i32001−i321+i320000001−i321−i321−i321+i321+i321+i323-1000000−3+3i32−3−3i32-10000001−i321+i320000
χ31333333-13333-1-1-1-1-100−3+3i32−3−3i323-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-100−3+3i32−3−3i32-3001−i321+i32000000−3+3i32−3−3i32001−i321+i320000001−i321−i321−i321+i321+i321+i32-310000003−3i323+3i321000000−1+i32−1−i320000
χ32333333-13333-1-1-1-1-100−3−3i32−3+3i323-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-100−3−3i32−3+3i323001+i321−i32000000−3−3i32−3+3i32001+i321−i320000001+i321+i321+i321−i321−i321−i323-1000000−3−3i32−3+3i32-10000001+i321−i320000
χ33333333-13333-1-1-1-1-100−3−3i32−3+3i323-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-100−3−3i32−3+3i32-3001+i321−i32000000−3−3i32−3+3i32001+i321−i320000001+i321+i321+i321−i321−i321−i32-310000003+3i323−3i321000000−1−i32−1+i320000
χ3433333-13-1-1-1-13333-133003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-133003-1-10000003300-1-100-1-1-1-1-1-1000000-1300003300-10000-1-1000000
χ3533333-13-1-1-1-13333-133003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-13300-3-1-10000003300-1-100-1-1-1-1-1-10000001-30000-3-3001000011000000
χ3633333-13-1-1-1-13333-1−3+3i32−3−3i32003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1−3+3i32−3−3i320031−i321+i32000000−3+3i32−3−3i32001−i321+i32001−i321−i321−i321+i321+i321+i32000000-130000−3+3i32−3−3i3200-100001−i321+i32000000
χ3733333-13-1-1-1-13333-1−3+3i32−3−3i32003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1−3+3i32−3−3i3200-31−i321+i32000000−3+3i32−3−3i32001−i321+i32001−i321−i321−i321+i321+i321+i320000001-300003−3i323+3i320010000−1+i32−1−i32000000
χ3833333-13-1-1-1-13333-1−3−3i32−3+3i32003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1−3−3i32−3+3i320031+i321−i32000000−3−3i32−3+3i32001+i321−i32001+i321+i321+i321−i321−i321−i32000000-130000−3−3i32−3+3i3200-100001+i321−i32000000
χ3933333-13-1-1-1-13333-1−3−3i32−3+3i32003-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1−3−3i32−3+3i3200-31+i321−i32000000−3−3i32−3+3i32001+i321−i32001+i321+i321+i321−i321−i321−i320000001-300003+3i323−3i320010000−1−i32−1+i32000000
χ40666666-26666-2-2-2-2-20066-3-2-2-2-2-3-3-31111111111110066000-2-2000000-3-300-2-200000011111100000000000000000000000
χ41666666-26666-2-2-2-2-200−3+3i3−3−3i3-3-2-2-2-2-3-3-311111111111100−3+3i3−3−3i30001−i31+i30000003−3i323+3i32001−i31+i3000000−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000
χ42666666-26666-2-2-2-2-200−3−3i3−3+3i3-3-2-2-2-2-3-3-311111111111100−3−3i3−3+3i30001+i31−i30000003+3i323−3i32001+i31−i3000000−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000
χ4366666-26-2-2-2-26666-26600-3-2-2-2-2111-3-3-311111111166000-2-2000000-3-300-2-20011111100000000000000000000000000000
χ4466666-26-2-2-2-26666-2−3+3i3−3−3i300-3-2-2-2-2111-3-3-3111111111−3+3i3−3−3i30001−i31+i30000003−3i323+3i32001−i31+i300−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000000000
χ4566666-26-2-2-2-26666-2−3−3i3−3+3i300-3-2-2-2-2111-3-3-3111111111−3−3i3−3+3i30001+i31−i30000003+3i323−3i32001+i31−i300−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000000000
χ4666-3-3-3666-3-3-36-3-3-36000006-3-3-3000000000000000000000000066000000000000000000000000-3-3000000000000000000
χ4766-3-3-3666-3-3-36-3-3-36000006-3-3-30000000000000000000000000−3+3i3−3−3i30000000000000000000000003−3i323+3i32000000000000000000
χ4866-3-3-3666-3-3-36-3-3-36000006-3-3-30000000000000000000000000−3−3i3−3+3i30000000000000000000000003+3i323−3i32000000000000000000
χ496-36-3-366-36-3-3-36-3-3600000-36-3-300000000000000000000000060060000000000000000000000-300-300000000000000000
χ506-36-3-366-36-3-3-36-3-3600000-36-3-3000000000000000000000000−3+3i300−3−3i300000000000000000000003−3i32003+3i3200000000000000000
χ516-36-3-366-36-3-3-36-3-3600000-36-3-3000000000000000000000000−3−3i300−3+3i300000000000000000000003+3i32003−3i3200000000000000000
χ526-3-36-366-3-36-3-3-36-3600660-3-36-300000000000000000-3-3000660000000000-3-300000000000000000000000000000000000
χ536-3-36-366-3-36-3-3-36-3600−3+3i3−3−3i30-3-36-3000000000000000003−3i323+3i32000−3+3i3−3−3i300000000003−3i323+3i3200000000000000000000000000000000000
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χ626-3-36-36-2-3-36-311-21-200−3−3i3−3+3i3011-21000-24-2-2-2-2444-2-2-2003+3i323−3i320001+i31−i30000000000−1−i32−1+i320000001+i3−2−2i31+i31−i3−2+2i31−i300000000000000000000000
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χ716-3-3-36-26111-2-3-3-36-2−3+3i3−3−3i3000111-2-24-2000-24-2-24-2-24-23−3i323+3i320001−i31+i30000000000−1+i32−1−i32001−i3−2+2i31−i31+i3−2−2i31+i300000000000000000000000000000
χ726-3-3-36-26111-2-3-3-36-2−3+3i3−3−3i3000111-2-2-24000-2-24-2-24-2-243−3i323+3i320001−i31+i30000000000−1+i32−1−i32001−i31−i3−2+2i31+i31+i3−2−2i300000000000000000000000000000
χ736-3-3-36-26111-2-3-3-36-2−3−3i3−3+3i3000111-24-2-20004-2-24-2-24-2-23+3i323−3i320001+i31−i30000000000−1−i32−1+i3200−2−2i31+i31+i3−2+2i31−i31−i300000000000000000000000000000
χ746-3-3-36-26111-2-3-3-36-2−3−3i3−3+3i3000111-2-24-2000-24-2-24-2-24-23+3i323−3i320001+i31−i30000000000−1−i32−1+i32001+i3−2−2i31+i31−i3−2+2i31−i300000000000000000000000000000
χ756-3-3-36-26111-2-3-3-36-2−3−3i3−3+3i3000111-2-2-24000-2-24-2-24-2-243+3i323−3i320001+i31−i30000000000−1−i32−1+i32001+i31+i3−2−2i31−i31−i3−2+2i300000000000000000000000000000
χ7699999-3-3-3-3-3-3-3-3-3-31000091111-3-3-3-3-3-3111111111000090000000000000000000000000000-3-3000000001000000000000
χ7799999-3-3-3-3-3-3-3-3-3-31000091111-3-3-3-3-3-31111111110000-900000000000000000000000000003300000000-1000000000000
χ781818181818-6-6-6-6-6-6-6-6-6-620000-92222333333-1-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
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χ801818-9-9-9-618-633318-9-9-9-600000-633300000000000000000000000000000000000000000000000000000000000000000000000
χ811818-9-9-9-6-6-6333-63332000002-1-1-10000008-4-4-48-4-4-4800000000000000000000000000000000000000000000000000000000
χ821818-9-9-9-6-6-6333-63332000002-1-1-1000000-48-4-4-488-4-400000000000000000000000000000000000000000000000000000000
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χ8418-918-9-918-6-918-9-93-633-6000003-63300000000000000000000000000000000000000000000000000000000000000000000000
χ8518-918-9-9-6183-633-918-9-9-6000003-63300000000000000000000000000000000000000000000000000000000000000000000000
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χ8718-918-9-9-6-63-6333-633200000-12-1-1000000-48-48-4-4-4-4800000000000000000000000000000000000000000000000000000000
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χ8918-9-918-9-61833-63-9-918-9-60000033-6300000000000000000000000000000000000000000000000000000000000000000000000
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χ9318-9-9-91818-6-9-9-918333-6-600000333-600000000000000000000000000000000000000000000000000000000000000000000000
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χ9518-9-9-918-6-6333-6333-6200000-1-1-12-612-60002-422-422-4200000000000000000000000000000000000000000000000000000000
χ9618-9-9-918-6-6333-6333-6200000-1-1-12-6-61200022-422-422-400000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).