Finite Group Databasebeta

← Group #13086852

Character table — Group #13086852

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11222222222222244444444444444444444444444444444444444202020202020202020363636363690901122222222222224444444444444444444444444444444444444420202020202020202036363636369090
order1233334556666101012121212151515151515151520203030303030303030606060606060606060606060606060604121212121212121242020202088226666410106666101012121212303030303030303020203030303030303030606060606060606060606060606060604121212121212121242020202088
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ52222222−1−52−1+522222−1−52−1+522222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000002−1−52−1−52−1+52−1+52002222222−1−52−1+522222−1−52−1+522222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000002−1−52−1−52−1+52−1+5200
χ62222222−1−52−1+522222−1−52−1+522222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52000000000-21+521+521−521−52002222222−1−52−1+522222−1−52−1+522222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52000000000-21+521+521−521−5200
χ72222222−1+52−1−522222−1+52−1−522222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000002−1+52−1+52−1−52−1−52002222222−1+52−1−522222−1+52−1−522222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000002−1+52−1+52−1−52−1−5200
χ82222222−1+52−1−522222−1+52−1−522222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52000000000-21−521−521+521+52002222222−1+52−1−522222−1+52−1−522222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52000000000-21−521−521+521+5200
χ9222222-222222222-2-2-2-222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222-222222222-2-2-2-222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000
χ10222222-2−1−52−1+522222−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000000000−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11600222222-2−1−52−1+522222−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000000000−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11600
χ11222222-2−1−52−1+522222−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000000000ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11600222222-2−1−52−1+522222−1−52−1+52-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000000000ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11600
χ12222222-2−1+52−1−522222−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+520000000000ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9200222222-2−1+52−1−522222−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+520000000000ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9200
χ13222222-2−1+52−1−522222−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+520000000000−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9200222222-2−1+52−1−522222−1+52−1−52-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+520000000000−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9200
χ14222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000
χ15222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-21111110000000222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-21111110000000
χ16222-1-1-1-2222-1-1-122-21112-1-1-12-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-2111111000−i3−i3−i3i3i3i30000000222-1-1-1-2222-1-1-122-21112-1-1-12-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-2111111000−i3−i3−i3i3i3i30000000
χ17222-1-1-1-2222-1-1-122-21112-1-1-12-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-2111111000i3i3i3−i3−i3−i30000000222-1-1-1-2222-1-1-122-21112-1-1-12-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-2111111000i3i3i3−i3−i3−i30000000
χ1822-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-12-1-12-1-1000000022-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-12-1-12-1-10000000
χ1922-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-211-211-211000000022-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-211-211-2110000000
χ2022-12-1-1-222-12-1-1221-211-12-1-1-12-1-1-2-2-12-1-1-12-1-111-2-2111111-2-211110−i3i30−i3i30−i3i3000000022-12-1-1-222-12-1-1221-211-12-1-1-12-1-1-2-2-12-1-1-12-1-111-2-2111111-2-211110−i3i30−i3i30−i3i30000000
χ2122-12-1-1-222-12-1-1221-211-12-1-1-12-1-1-2-2-12-1-1-12-1-111-2-2111111-2-211110i3−i30i3−i30i3−i3000000022-12-1-1-222-12-1-1221-211-12-1-1-12-1-1-2-2-12-1-1-12-1-111-2-2111111-2-211110i3−i30i3−i30i3−i30000000
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χ2322-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-122-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2111-2111-2000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-122-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2111-2111-20000000
χ2422-1-12-1-222-1-12-12211-21-1-12-1-1-12-1-2-2-1-12-1-1-12-11111-2-2111111-2-2110−i3i3i30−i3−i3i30000000022-1-12-1-222-1-12-12211-21-1-12-1-1-12-1-2-2-1-12-1-1-12-11111-2-2111111-2-2110−i3i3i30−i3−i3i300000000
χ2522-1-12-1-222-1-12-12211-21-1-12-1-1-12-1-2-2-1-12-1-1-12-11111-2-2111111-2-2110i3−i3−i30i3i3−i30000000022-1-12-1-222-1-12-12211-21-1-12-1-1-12-1-2-2-1-12-1-1-12-11111-2-2111111-2-2110i3−i3−i30i3i3−i300000000
χ2622-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-1-12-12-1000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-1-12-12-10000000
χ2722-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-21111-21-21000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-21111-21-210000000
χ2822-1-1-12-222-1-1-1222111-2-1-1-12-1-1-12-2-2-1-1-12-1-1-12111111-2-2111111-2-20−i3i3−i3i30i30−i3000000022-1-1-12-222-1-1-1222111-2-1-1-12-1-1-12-2-2-1-1-12-1-1-12111111-2-2111111-2-20−i3i3−i3i30i30−i30000000
χ2922-1-1-12-222-1-1-1222111-2-1-1-12-1-1-12-2-2-1-1-12-1-1-12111111-2-2111111-2-20i3−i3i3−i30−i30i3000000022-1-1-12-222-1-1-1222111-2-1-1-12-1-1-12-2-2-1-1-12-1-1-12111111-2-2111111-2-20i3−i3i3−i30−i30i30000000
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χ312-22222022-2-2-2-2-2-200002222222200-2-2-2-2-2-2-2-2000000000000000000000000000000−222-22222022-2-2-2-2-2-200002222222200-2-2-2-2-2-2-2-2000000000000000000000000000000−22
χ32444-2-2-24−1−5−1+54-2-2-2−1−5−1+54-2-2-2−1−51+521+521+52−1+51−521−521−52−1−5−1+5−1−51+521+521+52−1+51−521−521−52−1−5−1−51+521+521+521+521+521+52−1+5−1+51−521−521−521−521−521−520000000000000000444-2-2-24−1−5−1+54-2-2-2−1−5−1+54-2-2-2−1−51+521+521+52−1+51−521−521−52−1−5−1+5−1−51+521+521+52−1+51−521−521−52−1−5−1−51+521+521+521+521+521+52−1+5−1+51−521−521−521−521−521−520000000000000000
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χ34444-2-2-2-4−1−5−1+54-2-2-2−1−5−1+5-4222−1−51+521+521+52−1+51−521−521−521+51−5−1−51+521+521+52−1+51−521−521−521+51+5−1−52−1−52−1−52−1−52−1−52−1−521−51−5−1+52−1+52−1+52−1+52−1+52−1+520000000000000000444-2-2-2-4−1−5−1+54-2-2-2−1−5−1+5-4222−1−51+521+521+52−1+51−521−521−521+51−5−1−51+521+521+52−1+51−521−521−521+51+5−1−52−1−52−1−52−1−52−1−52−1−521−51−5−1+52−1+52−1+52−1+52−1+52−1+520000000000000000
χ35444-2-2-2-4−1+5−1−54-2-2-2−1+5−1−5-4222−1+51−521−521−52−1−51+521+521+521−51+5−1+51−521−521−52−1−51+521+521+521−51−5−1+52−1+52−1+52−1+52−1+52−1+521+51+5−1−52−1−52−1−52−1−52−1−52−1−520000000000000000444-2-2-2-4−1+5−1−54-2-2-2−1+5−1−5-4222−1+51−521−521−52−1−51+521+521+521−51+5−1+51−521−521−52−1−51+521+521+521−51−5−1+52−1+52−1+52−1+52−1+52−1+521+51+5−1−52−1−52−1−52−1−52−1−52−1−520000000000000000
χ3644-24-2-24−1−5−1+5-24-2-2−1−5−1+5-24-2-21+52−1−51+521+521−52−1+51−521−52−1−5−1+51+52−1−51+521+521−52−1+51−521−521+521+52−1−5−1−51+521+521+521+521−521−52−1+5−1+51−521−521−521−52000000000000000044-24-2-24−1−5−1+5-24-2-2−1−5−1+5-24-2-21+52−1−51+521+521−52−1+51−521−52−1−5−1+51+52−1−51+521+521−52−1+51−521−521+521+52−1−5−1−51+521+521+521+521−521−52−1+5−1+51−521−521−521−520000000000000000
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χ1354-4-2-2-240−1−5−1+5222-41+51−500001+521+521+52−1−51−521−521−52−1+500−1−52−1−52−1−521+5−1+52−1+52−1+521−5ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ11800−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94000000000000000000-44222-401+51−5-2-2-24−1−5−1+50000−1−52−1−52−1−521+5−1+52−1+52−1+521−5001+521+521+52−1−51−521−521−52−1+5−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ11800ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94000000000000000000
χ1364-4-2-2-240−1−5−1+5222-41+51−500001+521+521+52−1−51−521−521−52−1+500−1−52−1−52−1−521+5−1+52−1+52−1+521−5−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ11800ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94000000000000000000-44222-401+51−5-2-2-24−1−5−1+50000−1−52−1−52−1−521+5−1+52−1+52−1+521−5001+521+521+52−1−51−521−521−52−1+5ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ11800−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94000000000000000000
χ1374-4-2-2-240−1+5−1−5222-41−51+500001−521−521−52−1+51+521+521+52−1−500−1+52−1+52−1+521−5−1−52−1−52−1−521+5−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ9400−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118000000000000000000-44222-401−51+5-2-2-24−1+5−1−50000−1+52−1+52−1+521−5−1−52−1−52−1−521+5001−521−521−52−1+51+521+521+52−1−5ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ9400ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118000000000000000000
χ1384-4-2-2-240−1+5−1−5222-41−51+500001−521−521−52−1+51+521+521+52−1−500−1+52−1+52−1+521−5−1−52−1−52−1−521+5ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ9400ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118000000000000000000-44222-401−51+5-2-2-24−1+5−1−50000−1+52−1+52−1+521−5−1−52−1−52−1−521+5001−521−521−52−1+51+521+521+52−1−5−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ94ζ14+ζ46−ζ86−ζ94ζ14+ζ46−ζ86−ζ94−ζ14−ζ46+ζ86+ζ9400−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118ζ22+ζ38−ζ62−ζ118ζ22+ζ38−ζ62−ζ118−ζ22−ζ38+ζ62+ζ118000000000000000000

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