Finite Group Databasebeta

← Group #14278150

Character table — Group #14278150

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444448888888888888888888888888888888888888888888882020202040404040404040404040120120120120120120120120
order1222223666666651010101010101015153030303030303030303030303030444121212121212202020202020202020202020606060606060606060606060606060606060606060606060444444121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−i−i−iii
χ8111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iiiii−i−i
χ922222222222222222222222222222222222222-200-2-20000-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000002-2-22000000-2-22200000000
χ1022222222222222222222222222222222222222-200-2-20000-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-222-200000022-2-200000000
χ11222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ12222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ13222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-1-111112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-21111-1-1-1-100000000
χ14222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-1-111112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-222-1-1-1-1111100000000
χ15222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-20011−i3−i3i3i3-2-2-2-20000000011111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-2-2200−i3−i3i3i311-1-100000000
χ16222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-20011−i3−i3i3i3-2-2-2-20000000011111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-222-200i3i3−i3−i3-1-11100000000
χ17222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-20011i3i3−i3−i3-2-2-2-20000000011111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-2-2200i3i3−i3−i311-1-100000000
χ18222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-20011i3i3−i3−i3-2-2-2-20000000011111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-222-200−i3−i3i3i3-1-11100000000
χ192-2-222-2222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000002i−2i00000002i−2i0000001+i−1−i1−i−1+i
χ202-2-222-2222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000002i−2i00000002i−2i000000−1−i1+i−1+i1−i
χ212-2-222-2222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000000000−2i2i0000000−2i2i0000001−i−1+i1+i−1−i
χ222-2-222-2222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000000000−2i2i0000000−2i2i000000−1+i1−i−1−i1+i
χ232-2-22-222-2-2-222-222-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000200-2000000002-2−i2i2−i2i20000
χ242-2-22-222-2-2-222-222-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000200-2000000002-2i2−i2i2−i20000
χ252-2-22-222-2-2-222-222-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000-200200000000-222−2−220000
χ262-2-22-222-2-2-222-222-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000-200200000000-22−222−20000
χ2744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ2844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14-4-444-4-4-4-4-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111110000000000000000000000
χ2944444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-400-4-400001111−5−5−5−5555511111111−5−5−5−55555−5−5−5−555550000000000000000000000
χ3044444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-400-4-4000011115555−5−5−5−5111111115555−5−5−5−55555−5−5−5−50000000000000000000000
χ31444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152444-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1520000000000000000000000
χ32444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1524-4-4-2-22222-1-1-1-1111111111−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1520000000000000000000000
χ33444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-40022−2i3−2i32i32i311115555−5−5−5−5−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ1160000000000000000000000
χ34444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-400222i32i3−2i3−2i31111−5−5−5−55555−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ1160000000000000000000000
χ35444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152444-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1520000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1524-4-4-2-22222-1-1-1-1111111111+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1520000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-40022−2i3−2i32i32i31111−5−5−5−55555−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ920000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-400222i32i3−2i3−2i311115555−5−5−5−5−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ920000000000000000000000
χ394444-4-44-4-44-4-4444-4-4-4-444444-4-4-4-4-4-4-4-44444440000000000000000000000000000000000000000000000000000000000000000000
χ404444-4-44-4-44-4-444-11111-1-1-1-1-111111111-1-1-1-1-1-1000000000−5−555ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−5−555−5−555ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ1160000000000000000000000
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χ424444-4-44-4-44-4-444-11111-1-1-1-1-111111111-1-1-1-1-1-100000000055−5−5ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ11655−5−555−5−5ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ1160000000000000000000000
χ434444-4-44-4-44-4-444-11111-1-1-1-1-111111111-1-1-1-1-1-100000000055−5−5−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ11655−5−555−5−5−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ1160000000000000000000000
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χ9988-8-800-44i3−4i3-44i3−4i344-225−25−2525-2221+i151−i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1161+i151−i15−1−i15−1+i15−1−i15−1+i150000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-888-8888-8-8-8-88-2-2-22222-2-2-2-2-2-2-222222222-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-888-8-4-4-44444-4-2-2-22222-21−i151+i151−i151−i151+i151+i15−1+i15−1+i15−1−i15−1−i15−1+i15−1−i15−1+i15−1−i151−i151+i150000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-888-8-4-4-44444-4-2-2-22222-21+i151−i151+i151+i151−i151−i15−1−i15−1−i15−1+i15−1+i15−1−i15−1+i15−1−i15−1+i151+i151−i150000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-888-8-8-888-88-222-2-222-2-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-88-4444-4-44-4-222-2-222-21−i151+i15−1+i15−1+i15−1−i15−1−i151−i151−i151+i151+i15−1+i15−1−i15−1+i15−1−i151−i151+i150000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-88-4444-4-44-4-222-2-222-21+i151−i15−1−i15−1−i15−1+i15−1+i151+i151+i151−i151−i15−1−i15−1+i15−1−i15−1+i151+i151−i150000000000000000000000000000000000000000000000000000000000000000000

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