Finite Group Databasebeta

← Group #12158291

Character table — Group #12158291

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size111111112222222222222222222244444444444444444444444444888888888888888888888888888888888888888888810101010161616161616161616202020202020202040404040404040404080
order1222222244445510101010101010101010101010104444448888202020202020202020202020202020204444488202020202020202020202020202020202020202040404040404040404040404040404040444442020202020202020444488884444444884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111
χ5111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1
χ6111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111-1-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-111-1
χ91111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111111111-1-1-111-1-1-1
χ101111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1111
χ111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111
χ121111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-111-1-11111-1-111111-1-1-1
χ131111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-11
χ141111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-111111-1
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-111-11111-1
χ161111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1111111-1-11-1-1-1-11
χ17222222222222−1+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+52−1−522222222222−1+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+52−1−522222222−1+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+52−1−52−1−52−1−52−1−5200002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ18222222222222−1+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+52−1−52222222-2-2-2-2−1+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+52−1−5222-2-22-2-2−1+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+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+520000-21−521−521+521+521−521−521+521+52000000000000000000
χ19222222222222−1+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+52−1−5222-2-2-2-22222−1+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+52−1−52-2-2-2-2222−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-21−521−521+521+521−521−521+521+52000000000000000000
χ20222222222222−1+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+52−1−5222-2-2-2-2-2-2-2-2−1+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+52−1−52-2-2222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200002−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ21222222222222−1+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+52−1−52-2-222222222−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−52-2-222-2-2-21−521−521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+520000-21−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ22222222222222−1+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+52−1−52-2-22222-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−52-2-2-2-2-2221−521−521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200002−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ23222222222222−1+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+52−1−52-2-2-2-2-2-22222−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−5222-2-2-2-2-21−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200002−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ24222222222222−1+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+52−1−52-2-2-2-2-2-2-2-2-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−522222-2221−521−521+521+521−521−521−521−521+521+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+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-21−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ25222222222222−1−52−1+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+522222222222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+522222222−1−52−1−52−1+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+52−1+52−1+5200002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ26222222222222−1−52−1+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+52222222-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+5222-2-22-2-2−1−52−1−52−1+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+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−520000-21+521+521−521−521+521+521−521−52000000000000000000
χ27222222222222−1−52−1+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+5222-2-2-2-22222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52-2-2-2-2222−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-21+521+521−521−521+521+521−521−52000000000000000000
χ28222222222222−1−52−1+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+5222-2-2-2-2-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52-2-2222-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200002−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ29222222222222−1−52−1+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+52-2-222222222−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+52-2-222-2-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−520000-21+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ30222222222222−1−52−1+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+52-2-22222-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+52-2-2-2-2-2221+521+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+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200002−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ31222222222222−1−52−1+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+52-2-2-2-2-2-22222−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+5222-2-2-2-2-21+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200002−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ32222222222222−1−52−1+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+52-2-2-2-2-2-2-2-2-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+522222-2221+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-21+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ3322222222-2-2-2-222222222222222222200000000-2-2-2-2-2-222222222-2-20000-200-2-2-2-200000000000000000000000000000000222200000000022-2-200000000-200000
χ3422222222-2-2-2-222222222222222222200000000-2-2-2-2-2-222222222-2-20000-200-2-2-2-200000000000000000000000000000000-2-2-2-2000000000-2-22200000000200000
χ3522222222-2-2-2-22222222222222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002002222000000000000000000000000000000002222000000000-2-2-2-200000000200000
χ3622222222-2-2-2-22222222222222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000200222200000000000000000000000000000000-2-2-2-2000000000222200000000-200000
χ3722-222-2-2-222-2-222222-2-22-2-22-22-2-2-20022-2-2000022-222-200000000-2-20000000000022-2-222-2-200000000000000000000000022-2-2000000000002-200002-200000000
χ3822-222-2-2-222-2-222222-2-22-2-22-22-2-2-20022-2-2000022-222-200000000-2-20000000000022-2-222-2-2000000000000000000000000-2-22200000000000-220000-2200000000
χ3922-222-2-2-222-2-222222-2-22-2-22-22-2-2-200-2-222000022-222-200000000-2-200000000000-2-222-2-22200000000000000000000000022-2-2000000000002-20000-2200000000
χ4022-222-2-2-222-2-222222-2-22-2-22-22-2-2-200-2-222000022-222-200000000-2-200000000000-2-222-2-222000000000000000000000000-2-22200000000000-2200002-200000000
χ4122-222-2-2-2-2-22222222-2-22-2-22-22-2-2-20000000000-2-22-2-2200000000222i−2i000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000022-2-200000000000-220000002i−2i000000
χ4222-222-2-2-2-2-22222222-2-22-2-22-22-2-2-20000000000-2-22-2-2200000000222i−2i000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000-2-222000000000002-2000000−2i2i000000
χ4322-222-2-2-2-2-22222222-2-22-2-22-22-2-2-20000000000-2-22-2-220000000022−2i2i00000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000022-2-200000000000-22000000−2i2i000000
χ4422-222-2-2-2-2-22222222-2-22-2-22-22-2-2-20000000000-2-22-2-220000000022−2i2i00000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000-2-222000000000002-20000002i−2i000000
χ4522-2-2-2-22200002222-22-2-22-2-2-2-2-2222i−2i0000i2i2−i2−i20000002i2i−2i−2i2i2i−2i−2i00000002−200000000000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−22-22-20000000002i−2i00i2i2−i2−i200000002−20
χ4622-2-2-2-22200002222-22-2-22-2-2-2-2-2222i−2i0000i2i2−i2−i20000002i2i−2i−2i2i2i−2i−2i00000002−200000000000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2-22-22000000000−2i2i00−i2−i2i2i20000000−220
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χ1174-4-4-4444-44-44-4−1+5−1−51−51+5−1+51−51−5−1−51+51+51−5−1+51+5−1−5−1+5−1−500−4i4i4i−4i0000−1+51−5−1+5−1−51+5−1−5000000001−51+5000000000002ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ382ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000000000000000000000000000
χ1184-4-4-4444-44-44-4−1−5−1+51+51−5−1−51+51+5−1+51−51−51+5−1−51−5−1+5−1−5−1+5004i−4i−4i4i0000−1−51+5−1−5−1+51−5−1+5000000001+51−500000000000−2ζ6−2ζ142ζ6+2ζ142ζ6+2ζ14−2ζ6−2ζ14−2ζ22−2ζ382ζ22+2ζ382ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000000000000000000000000000
χ1194-4-4-4444-44-44-4−1−5−1+51+51−5−1−51+51+5−1+51−51−51+5−1−51−5−1+5−1−5−1+500−4i4i4i−4i0000−1−51+5−1−5−1+51−5−1+5000000001+51−5000000000002ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ142ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000000000000000000000000000
χ1204-4-4-4444-4-44-4444-4-44-4-44-4-4-44-44440000000000-44-4-44-4000000004400000000000000000000000000000000000000000000000000000000000000000000000000
χ1214-4-4-4444-4-44-44−1+5−1−51−51+5−1+51−51−5−1−51+51+51−5−1+51+5−1−5−1+5−1−500000000001−5−1+51−51+5−1−51+500000000−1+5−1−500000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000000000000000000
χ1224-4-4-4444-4-44-44−1+5−1−51−51+5−1+51−51−5−1−51+51+51−5−1+51+5−1−5−1+5−1−500000000001−5−1+51−51+5−1−51+500000000−1+5−1−50000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000000000000000000
χ1234-4-4-4444-4-44-44−1−5−1+51+51−5−1−51+51+5−1+51−51−51+5−1−51−5−1+5−1−5−1+500000000001+5−1−51+51−5−1+51−500000000−1−5−1+50000000000000000000−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000000000000000000
χ1244-4-4-4444-4-44-44−1−5−1+51+51−5−1−51+51+5−1+51−51−51+5−1−51−5−1+5−1−5−1+500000000001+5−1−51+51−5−1+51−500000000−1−5−1+500000000000000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000000000000000000
χ125888-8-88-8-80000−2+25−2−25−2+25−2−252−252−25−2+252+252+25−2−252−25−2+252+25−2−252−252+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ126888-8-88-8-80000−2−25−2+25−2−25−2+252+252+25−2−252−252−25−2+252+25−2−252−25−2+252+252−250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1278-888-8-88-80000−2+25−2−252−252+252−252−25−2+252+252+25−2−25−2+252−25−2−252+25−2+25−2−250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1288-888-8-88-80000−2−25−2+252+252−252+252+25−2−252−252−25−2+25−2−252+25−2+252−25−2−25−2+250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.