Finite Group Databasebeta

← Group #14282201

Character table — Group #14282201

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222224444444444444555588888888888888888888101010101010101010101010121212122020202020202020202020202020202020202020202020202020202020242424242424242460606060120120120120
order122234444666121212122566101010121220202020444410101520203030303030303060606060606060604444121212121212121222444888888881212121224242424242424242424242424242424101010102020202044448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1ii−i−i
χ611111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−iii
χ711111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111−i−iii
χ811111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111ii−i−i
χ91111111-1-11111111-11-1-1111-1-1-1-1-1-11111-1-111111-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111-1-11111111-11-1-1111-1-1-1-1-1-11111-1-111111-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-11-11
χ111111111-1-11111111-11-1-1111-1-1-1-1-1-11111-1-111111-1-1-1-111111-1-1-1-1-1-11111111111-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11-11
χ121111111-1-11111111-11-1-1111-1-1-1-1-1-11111-1-111111-1-1-1-111111-1-1-1-1-1-11111111111-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111-1-11111111-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111i−i−ii
χ141111111-1-11111111-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−iii−i
χ151111111-1-11111111-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−iii−i
χ161111111-1-11111111-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1i−i−ii
χ1722222-2-222222-2-2-2-2-22-2-22222222222222-2-22-2-222-2-2-2-22-2-2-2-2222222-2-22222-2-2-2-20000-20000000022-2-200000000000000000000000000000000
χ1822222-2-222222-2-2-2-2-22-2-2222222222-2-2-2-2-2-22-2-222-2-2-2-22-2-2-2-22222-2-222-2-2-2-222220000200000000-2-22200000000000000000000000000000000
χ1922222-2-2-2-2222-2-2-2-22222222-2-2-2-2-2-22222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000200000000-2-22200000000000000000000000000000000
χ2022222-2-2-2-2222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-222220000-20000000022-2-200000000000000000000000000000000
χ212222-12222-1-1-1-1-1-1-122-1-1222-1-12222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ222222-12222-1-1-1-1-1-1-122-1-1222-1-12222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ232222-12222-1-1-1-1-1-1-122-1-1222-1-12222-2-2-2-222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000-22i2i2i2i−2i−2i−2i−2i1111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ242222-12222-1-1-1-1-1-1-122-1-1222-1-12222-2-2-2-222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000-2−2i−2i−2i−2i2i2i2i2i1111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ252222-122-2-2-1-1-1-1-1-1-1-221122211-2-2-2-22222-2-2-122-1-11111-1-1-1-1-11111-2-222-1-1-1-1-1-1-1-10000-222-2-222-2-21111-1-1-1-11111-1-1-1-111110000000000000000
χ262222-122-2-2-1-1-1-1-1-1-1-221122211-2-2-2-22222-2-2-122-1-11111-1-1-1-1-11111-2-222-1-1-1-1-1-1-1-10000-2-2-222-2-22211111111-1-1-1-11111-1-1-1-10000000000000000
χ272222-122-2-2-1-1-1-1-1-1-1-221122211-2-2-2-2-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-211111111000022i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ282222-122-2-2-1-1-1-1-1-1-1-221122211-2-2-2-2-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-21111111100002−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ292222-1-2-222-1-1-11111-2211222-1-122222222-2-2-1-2-2-1-11111-11111-1-1-1-122-2-2-1-1-1-111110000-200000000-1-11133−3−333−3−333−3−333−3−30000000000000000
χ302222-1-2-222-1-1-11111-2211222-1-122222222-2-2-1-2-2-1-11111-11111-1-1-1-122-2-2-1-1-1-111110000-200000000-1-111−3−333−3−333−3−333−3−3330000000000000000
χ312222-1-2-222-1-1-11111-2211222-1-12222-2-2-2-2-2-2-1-2-2-1-11111-11111-1-1-1-1-2-2221111-1-1-1-1000020000000011-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ322222-1-2-222-1-1-11111-2211222-1-12222-2-2-2-2-2-2-1-2-2-1-11111-11111-1-1-1-1-2-2221111-1-1-1-1000020000000011-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ332222-1-2-2-2-2-1-1-1111122-1-122211-2-2-2-2222222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-2-1-1-1-11111000020000000011-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ342222-1-2-2-2-2-1-1-1111122-1-122211-2-2-2-2222222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-2-1-1-1-11111000020000000011-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ352222-1-2-2-2-2-1-1-1111122-1-122211-2-2-2-2-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122221111-1-1-1-10000-200000000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ362222-1-2-2-2-2-1-1-1111122-1-122211-2-2-2-2-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122221111-1-1-1-10000-200000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3722-2-222-2002-2-222-2-20200-2-220000002i2i−2i−2i0022-2-2-20000222-2-20000002i−2i2i2i−2i−2i2i2i−2i−2i002-200000000000000000000000000000000022-2-2002i−2i0000
χ3822-2-222-2002-2-222-2-20200-2-220000002i2i−2i−2i0022-2-2-20000222-2-20000002i−2i2i2i−2i−2i2i2i−2i−2i00-22000000000000000000000000000000000-2-22200−2i2i0000
χ3922-2-222-2002-2-222-2-20200-2-22000000−2i−2i2i2i0022-2-2-20000222-2-2000000−2i2i−2i−2i2i2i−2i−2i2i2i002-200000000000000000000000000000000022-2-200−2i2i0000
χ4022-2-222-2002-2-222-2-20200-2-22000000−2i−2i2i2i0022-2-2-20000222-2-2000000−2i2i−2i−2i2i2i−2i−2i2i2i00-22000000000000000000000000000000000-2-222002i−2i0000
χ4122-2-22-22002-2-2-2-2220200-2-220000002i2i−2i−2i002-22-2-200002-2-222000000−2i2i2i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000000000022-2-200002i−2i000000
χ4222-2-22-22002-2-2-2-2220200-2-220000002i2i−2i−2i002-22-2-200002-2-222000000−2i2i2i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000-2-2220000−2i2i000000
χ4322-2-22-22002-2-2-2-2220200-2-22000000−2i−2i2i2i002-22-2-200002-2-2220000002i−2i−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000000000022-2-20000−2i2i000000
χ4422-2-22-22002-2-2-2-2220200-2-22000000−2i−2i2i2i002-22-2-200002-2-2220000002i−2i−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000-2-22200002i−2i000000
χ452-22-22002i−2i-22-2000002002-2-22i−2i2i2i−2i−2i2-22-2002002-20000-200002i2i−2i−2i2i−2i002-22-20000000002−2−i2i22−2−i2i22i−2i002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ462-22-22002i−2i-22-2000002002-2-22i−2i2i2i−2i−2i2-22-2002002-20000-200002i2i−2i−2i2i−2i002-22-2000000000−22i2−i2−22i2−i22i−2i00−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ472-22-22002i−2i-22-2000002002-2-22i−2i2i2i−2i−2i-22-22002002-20000-200002i2i−2i−2i−2i2i00-22-22000000000−i2i2−22i2−i22−2−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ482-22-22002i−2i-22-2000002002-2-22i−2i2i2i−2i−2i-22-22002002-20000-200002i2i−2i−2i−2i2i00-22-22000000000i2−i22−2−i2i2−22−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ492-22-2200−2i2i-22-2000002002-2-2−2i2i−2i−2i2i2i2-22-2002002-20000-20000−2i−2i2i2i−2i2i002-22-20000000002−2i2−i22−2i2−i2−2i2i002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ502-22-2200−2i2i-22-2000002002-2-2−2i2i−2i−2i2i2i2-22-2002002-20000-20000−2i−2i2i2i−2i2i002-22-2000000000−22−i2i2−22−i2i2−2i2i00−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ512-22-2200−2i2i-22-2000002002-2-2−2i2i−2i−2i2i2i-22-22002002-20000-20000−2i−2i2i2i2i−2i00-22-22000000000−i2i22−2i2−i2−222i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ522-22-2200−2i2i-22-2000002002-2-2−2i2i−2i−2i2i2i-22-22002002-20000-20000−2i−2i2i2i2i−2i00-22-22000000000i2−i2−22−i2i22−22i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ532-22-2-1002i−2i1-113−33−302−i3i32-2-2−ii2i2i−2i−2i2-22-200-100-11−i3−i3i3i313−33−3−i−iii2i−2i00-11-113−33−3000002−2−i2i22−2−i2i2−ii−i3i3−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ1030000000000000000
χ542-22-2-1002i−2i1-113−33−302−i3i32-2-2−ii2i2i−2i−2i2-22-200-100-11−i3−i3i3i313−33−3−i−iii2i−2i00-11-113−33−300000−22i2−i2−22i2−i2−ii−i3i3ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ1030000000000000000
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χ8744-4-4-2-4400-22222-2-20400-4-440000004i4i−4i−4i00-2-44220000-222-2-2000000−4i4i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000
χ8844-4-4-2-4400-22222-2-20400-4-44000000−4i−4i4i4i00-2-44220000-222-2-20000004i−4i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000
χ894-4-4440000-4-4400000400-44-40000004i−4i−4i4i00400-440000-40000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ904-4-4440000-4-4400000400-44-4000000−4i4i4i−4i00400-440000-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ914-4-44-2000022-223−23−23230400-44-40000004i−4i−4i4i00-2002-20000223−23−232300000000−2i2i2i−2i2i3−2i3−2i32i30000000000000000000000000000000000000000000000000
χ924-4-44-2000022-223−23−23230400-44-4000000−4i4i4i−4i00-2002-20000223−23−2323000000002i−2i−2i2i−2i32i32i3−2i30000000000000000000000000000000000000000000000000
χ934-4-44-2000022-2−232323−230400-44-40000004i−4i−4i4i00-2002-200002−232323−2300000000−2i2i2i−2i−2i32i32i3−2i30000000000000000000000000000000000000000000000000
χ944-4-44-2000022-2−232323−230400-44-4000000−4i4i4i−4i00-2002-200002−232323−23000000002i−2i−2i2i2i3−2i3−2i32i30000000000000000000000000000000000000000000000000
χ958888-48888-4-4-4-4-4-4-48-2-4-4-2-2-2-4-4-2-2-2-20000-2-21-2-21111111111111110000000000000000000000000000000000000000000000000000000000000
χ968888-488-8-8-4-4-4-4-4-4-4-8-244-2-2-24422220000221-2-211-1-1-1-111111-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ978888-4-8-888-4-4-44444-8-244-2-2-2-4-4-2-2-2-200002212211-1-1-1-11-1-1-1-111110000000000000000000000000000000000000000000000000000000000000
χ988888-4-8-8-8-8-4-4-444448-2-4-4-2-2-24422220000-2-21221111111-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-48-800-444-4-4440-20022-200−2525−25250000−25251-22-1-15−55−5111-1-15−55−50000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-800-444-4-4440-20022-20025−2525−25000025−251-22-1-1−55−55111-1-1−55−550000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-8800-44444-4-40-20022-200−2525−2525000025−2512-2-1-1−55−551-1-1115−55−50000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-8800-44444-4-40-20022-20025−2525−250000−252512-2-1-15−55−51-1-111−55−550000000000000000000000000000000000000000000000000000000000000
χ1038-88-88008i−8i-88-800000-200-2228i−8i−2i−2i2i2i000000-200-22000020000−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000
χ1048-88-8800−8i8i-88-800000-200-222−8i8i2i2i−2i−2i000000-200-220000200002i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4008i−8i4-4443−4343−430-2−4i34i3-222−4i4i−2i−2i2i2i0000001001-1i3i3−i3−i3-1−33−33ii−i−i0000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4008i−8i4-44−4343−43430-24i3−4i3-222−4i4i−2i−2i2i2i0000001001-1−i3−i3i3i3-13−33−3ii−i−i0000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-400−8i8i4-4443−4343−430-24i3−4i3-2224i−4i2i2i−2i−2i0000001001-1−i3−i3i3i3-1−33−33−i−iii0000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-400−8i8i4-44−4343−43430-2−4i34i3-2224i−4i2i2i−2i−2i0000001001-1i3i3−i3−i3-13−33−3−i−iii0000000000000000000000000000000000000000000000000000000000000
χ1098-8-8880000-8-8800000-2002-2200−2i52i52i5−2i5000000-2002-2000020000−2i52i52i5−2i50000000000000000000000000000000000000000000000000000000000000
χ1108-8-8880000-8-8800000-2002-22002i5−2i5−2i52i5000000-2002-20000200002i5−2i5−2i52i50000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4000044-443−43−43430-2002-2200−2i52i52i5−2i5000000100-11i15−i15−i15i15-1−333−3i5−i5−i5i50000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4000044-443−43−43430-2002-22002i5−2i5−2i52i5000000100-11−i15i15i15−i15-1−333−3−i5i5i5−i50000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4000044-4−434343−430-2002-2200−2i52i52i5−2i5000000100-11−i15i15i15−i15-13−3−33i5−i5−i5i50000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4000044-4−434343−430-2002-22002i5−2i5−2i52i5000000100-11i15−i15−i15i15-13−3−33−i5i5i5−i50000000000000000000000000000000000000000000000000000000000000

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