Finite Group Databasebeta

← Group #14277183

Character table — Group #14277183

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222444444444444444555588888888888888888888101010101010101012121212202020202020202424242424242424404040404040404040404040606060606060606060606060
order1222344446664510101012121212121220202020222215202020203030306060606060606060606060604444666688884121212121212404040404040404044441212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111iiii−i−i−i−i
χ911111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i111-1-1-1-1iiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i111-1-1-1-1iiii−i−i−i−i-11-11-1-111-1-111ii−i−i−i−iii−i−iii
χ1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii111-1-1-1-1−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii−i−iii
χ1211111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii111-1-1-1-1−i−i−i−iiiii-11-11-1-111-1-111−i−iiiii−i−iii−i−i
χ1311111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-1-1-11111iiii−i−i−i−ii−i−iiii−i−i−i−iii−i−iii-1-11111-1-1
χ1411111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i-1-1-11111iiii−i−i−i−i−iii−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1511111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-1-1-11111−i−i−i−iiiiii−i−iiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1611111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii-1-1-11111−i−i−i−iiiii−iii−i−i−iiiii−i−iii−i−i-1-11111-1-1
χ172222222-2-2222-22222-2-222-2-2-2-2-2-222222-2-222222-2-2-2-22222-2-2-2-22-2-2222220000-2-2-222-2-200000000000000000000000000000000
χ182222222-2-2222-22222-2-222-2-2-2-2-2-2-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-222-2-2-2-2-20000222-2-22200000000000000000000000000000000
χ1922222-2-222222-22222-2-2-2-222222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-222-222220000-2-2-2-2-22200000000000000000000000000000000
χ2022222-2-222222-22222-2-2-2-2222222-2-2-2-22-2-2-2-2222-2-2-2-2-2-2-2-222222-2-22-2-2-2-2000022222-2-200000000000000000000000000000000
χ212222-12222-1-1-122222-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100002-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ222222-12222-1-1-122222-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100002-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ232222-12222-1-1-122222-1-1-1-1-1-12222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-2111111000000002i2i−2i−2i−i−i−i−iiiii000000000000
χ242222-12222-1-1-122222-1-1-1-1-1-12222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-211111100000000−2i−2i2i2iiiii−i−i−i−i000000000000
χ252222-122-2-2-1-1-1-2222211-1-111-2-2-2-22222-1-2-222-1-1-11111-1-1-1-111112-2-22-1-1-1-10000-211-1-111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ262222-122-2-2-1-1-1-2222211-1-111-2-2-2-22222-1-2-222-1-1-11111-1-1-1-111112-2-22-1-1-1-10000-211-1-111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ272222-122-2-2-1-1-1-2222211-1-111-2-2-2-2-2-2-2-2-1-2-222-1-1-11111-1-1-1-11111-222-2111100002-1-111-1-10000000000003−33−3−33−33000000000000
χ282222-122-2-2-1-1-1-2222211-1-111-2-2-2-2-2-2-2-2-1-2-222-1-1-11111-1-1-1-11111-222-2111100002-1-111-1-1000000000000−33−333−33−3000000000000
χ292222-1-2-222-1-1-1-222221111-1-122222222-1-2-2-2-2-1-1-111111111-1-1-1-1-222-2-1-1-1-10000-21111-1-1000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ302222-1-2-222-1-1-1-222221111-1-122222222-1-2-2-2-2-1-1-111111111-1-1-1-1-222-2-1-1-1-10000-21111-1-1000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ312222-1-2-222-1-1-1-222221111-1-12222-2-2-2-2-1-2-2-2-2-1-1-111111111-1-1-1-12-2-22111100002-1-1-1-1110000000000003−3−33−333−3000000000000
χ322222-1-2-222-1-1-1-222221111-1-12222-2-2-2-2-1-2-2-2-2-1-1-111111111-1-1-1-12-2-22111100002-1-1-1-111000000000000−333−33−3−33000000000000
χ332222-1-2-2-2-2-1-1-122222-1-11111-2-2-2-22222-122-2-2-1-1-1-1-1-1-111111111-2-2-2-2-1-1-1-100002-1-11111000000002-22-2-1-111-1-111000000000000
χ342222-1-2-2-2-2-1-1-122222-1-11111-2-2-2-22222-122-2-2-1-1-1-1-1-1-111111111-2-2-2-2-1-1-1-100002-1-1111100000000-22-2211-1-111-1-1000000000000
χ352222-1-2-2-2-2-1-1-122222-1-11111-2-2-2-2-2-2-2-2-122-2-2-1-1-1-1-1-1-111111111222211110000-211-1-1-1-1000000002i−2i−2i2i−i−iiiii−i−i000000000000
χ362222-1-2-2-2-2-1-1-122222-1-11111-2-2-2-2-2-2-2-2-122-2-2-1-1-1-1-1-1-111111111222211110000-211-1-1-1-100000000−2i2i2i−2iii−i−i−i−iii000000000000
χ3722-2-22002-22-2-2022-2-200002-222-2-222-2-2200002-2-20000000022-2-202-2022-2-20000000002-20000000000000000000000002−22−22−22−2
χ3822-2-22002-22-2-2022-2-200002-222-2-222-2-2200002-2-20000000022-2-202-2022-2-20000000002-2000000000000000000000000−22−22−22−22
χ3922-2-22002-22-2-2022-2-200002-222-2-2-2-222200002-2-20000000022-2-20-220-2-222000000000-22000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4022-2-22002-22-2-2022-2-200002-222-2-2-2-222200002-2-20000000022-2-20-220-2-222000000000-22000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4122-2-2200-222-2-2022-2-20000-22-2-22222-2-2200002-2-200000000-2-2220-22022-2-2000000000-22000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4222-2-2200-222-2-2022-2-20000-22-2-22222-2-2200002-2-200000000-2-2220-22022-2-2000000000-22000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4322-2-2200-222-2-2022-2-20000-22-2-222-2-222200002-2-200000000-2-22202-20-2-2220000000002-20000000000000000000000002−2−22−222−2
χ4422-2-2200-222-2-2022-2-20000-22-2-222-2-222200002-2-200000000-2-22202-20-2-2220000000002-2000000000000000000000000−222−22−2−22
χ452-22-222-200-22-202-22-2002-20000002-22-22002-2-22-2000022-2-20000200-22-22-22−22−20002-20022−2−222−2−20000000000002−22−200000000
χ462-22-222-200-22-202-22-2002-20000002-22-22002-2-22-2000022-2-20000200-22-22-2−22−220002-200−2−222−2−222000000000000−22−2200000000
χ472-22-222-200-22-202-22-2002-2000000-22-222002-2-22-2000022-2-20000-2002-22-222−22−2000-220022−2−222−2−2000000000000−22−2200000000
χ482-22-222-200-22-202-22-2002-2000000-22-222002-2-22-2000022-2-20000-2002-22-22−22−22000-2200−2−222−2−2220000000000002−22−200000000
χ492-22-22-2200-22-202-22-200-220000002-22-2200-22-22-20000-2-2220000-20022-22-2−i2i2i2−i2000-2200−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i200000000
χ502-22-22-2200-22-202-22-200-220000002-22-2200-22-22-20000-2-2220000-20022-22-2i2−i2−i2i2000-2200i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i200000000
χ512-22-22-2200-22-202-22-200-22000000-22-22200-22-22-20000-2-2220000200-2-22-22−i2i2i2−i20002-200−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i200000000
χ522-22-22-2200-22-202-22-200-22000000-22-22200-22-22-20000-2-2220000200-2-22-22i2−i2−i2i20002-200i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i200000000
χ534444444444444-1-1-1-1444444-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044440000000-1-1-1-1-1-1-1-1000000000000000000000000
χ544444444444444-1-1-1-1444444-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4-4-4000000011111111000000000000000000000000
χ554444444-4-4444-4-1-1-1-1-4-444-4-411110000-111-1-1-1-1-11111-1-1-1-111110000000000000000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000
χ564444444-4-4444-4-1-1-1-1-4-444-4-411110000-111-1-1-1-1-11111-1-1-1-111110000000000000000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000
χ5744444-4-444444-4-1-1-1-1-4-4-4-444-1-1-1-10000-11111-1-1-111111111-1-1-1-10000000000000000000−55−555−55−5000000000000000000000000
χ5844444-4-444444-4-1-1-1-1-4-4-4-444-1-1-1-10000-11111-1-1-111111111-1-1-1-100000000000000000005−55−5−55−55000000000000000000000000
χ5944444-4-4-4-44444-1-1-1-144-4-4-4-411110000-1-1-111-1-1-1-1-1-1-111111111000000004i4i−4i−4i0000000−i−i−i−iiiii000000000000000000000000
χ6044444-4-4-4-44444-1-1-1-144-4-4-4-411110000-1-1-111-1-1-1-1-1-1-11111111100000000−4i−4i4i4i0000000iiii−i−i−i−i000000000000000000000000
χ6144-4-4-2004-4-222044-4-40000-2244-4-444-4-4-20000-22200000000-2-22204-40-2-222000000000-2200000000000000000000000000000000
χ6244-4-4-2004-4-222044-4-40000-2244-4-4-4-444-20000-22200000000-2-2220-44022-2-20000000002-200000000000000000000000000000000
χ6344-4-4-200-44-222044-4-400002-2-4-44444-4-4-20000-2220000000022-2-20-440-2-2220000000002-200000000000000000000000000000000
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χ654-44-444-400-44-40-11-11004-400−i5i5−i5i50000-1−i5i5-111-11−i5−i5i5i5-1-111−i5i5−i5i50000000022−2222−220000000−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119000000000000000000000000
χ664-44-444-400-44-40-11-11004-400−i5i5−i5i50000-1−i5i5-111-11−i5−i5i5i5-1-111−i5i5−i5i500000000−2222−22220000000ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119ζ7+ζ23−ζ29+ζ47−ζ61−ζ101+ζ103−ζ109−ζ13+ζ31−ζ37−ζ53+ζ71−ζ77+ζ79+ζ119−ζ7−ζ23+ζ29−ζ47+ζ61+ζ101−ζ103+ζ109ζ13−ζ31+ζ37+ζ53−ζ71+ζ77−ζ79−ζ119000000000000000000000000
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χ704-44-44-4400-44-40-11-1100-4400−i5i5−i5i50000-1i5−i51-11-11i5i5−i5−i511-1-1−i5i5−i5i5000000002i2−2i2−2i22i20000000−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119000000000000000000000000
χ714-44-44-4400-44-40-11-1100-4400i5−i5i5−i50000-1−i5i51-11-11−i5−i5i5i511-1-1i5−i5i5−i500000000−2i22i22i2−2i20000000ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109000000000000000000000000
χ724-44-44-4400-44-40-11-1100-4400i5−i5i5−i50000-1−i5i51-11-11−i5−i5i5i511-1-1i5−i5i5−i5000000002i2−2i2−2i22i20000000−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109ζ13+ζ31+ζ37+ζ53+ζ71+ζ77+ζ79+ζ119ζ7+ζ23+ζ29+ζ47+ζ61+ζ101+ζ103+ζ109−ζ13−ζ31−ζ37−ζ53−ζ71−ζ77−ζ79−ζ119−ζ7−ζ23−ζ29−ζ47−ζ61−ζ101−ζ103−ζ109000000000000000000000000
χ734-44-4-24-4002-2204-44-400-220000004-44-4-2004-42-220000-2-2220000400-4-22-220000000-220000000000000000000000000000000000
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χ774-4-4440000-4-4404-4-4400000000004-4-4440000-4-4400000000000000004-4-440000000000000000000000000000000000000000000
χ784-4-4440000-4-4404-4-440000000000-444-440000-4-440000000000000000-444-40000000000000000000000000000000000000000000
χ794-4-44-2000022-204-4-44−2i32i3000000004-4-44-2000022-2−2i32i3−2i32i3000000000000-222-200000−2i32i3000000000000000000000000000000000000
χ804-4-44-2000022-204-4-44−2i32i300000000-444-4-2000022-2−2i32i3−2i32i30000000000002-2-22000002i3−2i3000000000000000000000000000000000000
χ814-4-44-2000022-204-4-442i3−2i3000000004-4-44-2000022-22i3−2i32i3−2i3000000000000-222-2000002i3−2i3000000000000000000000000000000000000
χ824-4-44-2000022-204-4-442i3−2i300000000-444-4-2000022-22i3−2i32i3−2i30000000000002-2-2200000−2i32i3000000000000000000000000000000000000
χ838888-48888-4-4-48-2-2-2-2-4-4-4-4-4-4-2-2-2-200001-2-2-2-2111111111111111000000000000000000000000000000000000000000000000000
χ848888-488-8-8-4-4-4-8-2-2-2-244-4-44422220000122-2-2111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000000000000000000
χ858888-4-8-888-4-4-4-8-2-2-2-24444-4-4-2-2-2-2000012222111-1-1-1-1-1-1-1-11111000000000000000000000000000000000000000000000000000
χ868888-4-8-8-8-8-4-4-48-2-2-2-2-4-44444222200001-2-2221111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000
χ8788-8-88008-88-8-80-2-22200008-8-2-2220000-20000-22200000000-2-222000000000000000000000000000000000000000000000000000
χ8888-8-8800-888-8-80-2-2220000-8822-2-20000-20000-2220000000022-2-2000000000000000000000000000000000000000000000000000
χ8988-8-8-4008-8-4440-2-2220000-44-2-2220000100001-1-1−151515−15−1515−151511-1-1000000000000000000000000000000000000000000000000000
χ9088-8-8-4008-8-4440-2-2220000-44-2-2220000100001-1-115−15−151515−1515−1511-1-1000000000000000000000000000000000000000000000000000
χ9188-8-8-400-88-4440-2-22200004-422-2-20000100001-1-1−151515−1515−1515−15-1-111000000000000000000000000000000000000000000000000000
χ9288-8-8-400-88-4440-2-22200004-422-2-20000100001-1-115−15−1515−1515−1515-1-111000000000000000000000000000000000000000000000000000
χ938-88-8-48-8004-440-22-2200-4400−2i52i5−2i52i500001−2i52i5-22-11-1i5i5−i5−i511-1-1i5−i5i5−i5000000000000000000000000000000000000000000000000000
χ948-88-8-48-8004-440-22-2200-44002i5−2i52i5−2i5000012i5−2i5-22-11-1−i5−i5i5i511-1-1−i5i5−i5i5000000000000000000000000000000000000000000000000000
χ958-88-8-4-88004-440-22-22004-400−2i52i5−2i52i5000012i5−2i52-2-11-1−i5−i5i5i5-1-111i5−i5i5−i5000000000000000000000000000000000000000000000000000
χ968-88-8-4-88004-440-22-22004-4002i5−2i52i5−2i500001−2i52i52-2-11-1i5i5−i5−i5-1-111−i5i5−i5i5000000000000000000000000000000000000000000000000000
χ978-8-8880000-8-880-222-2000000−2i52i52i5−2i50000-2000022-200000000−2i52i52i5−2i5000000000000000000000000000000000000000000000000000
χ988-8-8880000-8-880-222-20000002i5−2i5−2i52i50000-2000022-2000000002i5−2i5−2i52i5000000000000000000000000000000000000000000000000000
χ998-8-88-4000044-40-222-2−4i34i30000−2i52i52i5−2i5000010000-1-11i3−i3i3−i315−15−1515i5−i5−i5i5000000000000000000000000000000000000000000000000000
χ1008-8-88-4000044-40-222-2−4i34i300002i5−2i5−2i52i5000010000-1-11i3−i3i3−i3−151515−15−i5i5i5−i5000000000000000000000000000000000000000000000000000
χ1018-8-88-4000044-40-222-24i3−4i30000−2i52i52i5−2i5000010000-1-11−i3i3−i3i3−151515−15i5−i5−i5i5000000000000000000000000000000000000000000000000000
χ1028-8-88-4000044-40-222-24i3−4i300002i5−2i5−2i52i5000010000-1-11−i3i3−i3i315−15−1515−i5i5i5−i5000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.