Finite Group Databasebeta

← Group #13145576

Character table — Group #13145576

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174
size1111222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818242424242424242424242424242424242424216216
order124423333346666666888812121212121212121212121224242424242424243333666666666666666612121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424241616161616161616484848484848484848484848484848482466666666121212121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-111111111-1-1-1-1-1-1-1-1i−i
χ611-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-11-1-1-1-1-1-1-1-111111111−ii
χ711-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1-111111111-1-1-1-1-1-1-1-1−ii
χ811-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-11-1-1-1-1-1-1-1-111111111i−i
χ9222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ102222222-1-1-122222-1-1-122222222-1-1-1-1-1-122222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-1-1-1-1-122-1-1-1-1-1-100
χ112222222-1-1-122222-1-1-122222222-1-1-1-1-1-122222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-2111111-2-211111100
χ122222222-1-1-122222-1-1-1-2-2-2-22222-1-1-1-1-1-122-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000000−i3−i3−i3i3i3i300−i3−i3−i3i3i3i300
χ132222222-1-1-122222-1-1-1-2-2-2-22222-1-1-1-1-1-122-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000000i3i3i3−i3−i3−i300i3i3i3−i3−i3−i300
χ14222222-12-1-12222-12-1-1222222-1-122-1-1-1-12222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-12-1-12-1-1-1-12-1-12-1-100
χ15222222-12-1-12222-12-1-1222222-1-122-1-1-1-12222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-211-211-21111-211-21100
χ16222222-12-1-12222-12-1-1-2-2-2-222-1-122-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111100000000000000000000000000−i3i30−i3i30−i3i3−i3i30−i3i30−i3i300
χ17222222-12-1-12222-12-1-1-2-2-2-222-1-122-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111100000000000000000000000000i3−i30i3−i30i3−i3i3−i30i3−i30i3−i300
χ18222222-1-12-12222-1-12-1222222-1-1-1-122-1-12222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-100000000000000000000000022-1-1-12-1-1-12-1-1-12-1-1-1200
χ19222222-1-12-12222-1-12-1222222-1-1-1-122-1-12222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1000000000000000000000000-2-2111-2111-2111-2111-200
χ20222222-1-12-12222-1-12-1-2-2-2-222-1-1-1-122-1-122-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1111111111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111100000000000000000000000000−i3i3i30−i3−i3i30−i3i3i30−i3−i3i3000
χ21222222-1-12-12222-1-12-1-2-2-2-222-1-1-1-122-1-122-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1111111111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111100000000000000000000000000i3−i3−i30i3i3−i30i3−i3−i30i3i3−i3000
χ22222222-1-1-122222-1-1-12222222-1-1-1-1-1-1222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000000000000000000022-1-1-1-12-12-1-1-1-1-12-12-100
χ23222222-1-1-122222-1-1-12222222-1-1-1-1-1-1222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222000000000000000000000000-2-21111-21-211111-21-2100
χ24222222-1-1-122222-1-1-12-2-2-2-222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122111111111111111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-200000000000000000000000000−i3i3−i3i30i30−i3−i3i3−i3i30i30−i300
χ25222222-1-1-122222-1-1-12-2-2-2-222-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122111111111111111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-200000000000000000000000000i3−i3i3−i30−i30i3i3−i3i3−i30−i30i300
χ2622222-122222-1-1-122222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2722222-122222-1-1-122222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2822222-122222-1-1-12222-2-2-2-2-1-122222222-1-111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2-21111-2-21111-2-21111-2-21111-2-21111-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−300000000000000000000
χ2922222-122222-1-1-12222-2-2-2-2-1-122222222-1-111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2-21111-2-21111-2-21111-2-21111-2-21111-2-21111-2-2111100000000−3−3−3−33333−3−3−3−3333300000000000000000000
χ302222-222222-2-2-22222200002222222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000022−2−222−2−222−2−222−2−222−2−222−2−200000000000000000000
χ312222-222222-2-2-22222200002222222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2−222−2−222−2−222−2−222−2−222−2−22200000000000000000000
χ322222-2-12222-211-122220000-1-1222222221133−3−333−3−3-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110033−3−30033−3−30033−3−30033−3−30033−3−30033−3−30033−3−30033−3−322−2−222−2−2ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ4600000000000000000000
χ332222-2-12222-211-122220000-1-1222222221133−3−333−3−3-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110033−3−30033−3−30033−3−30033−3−30033−3−30033−3−30033−3−30033−3−3−2−222−2−222−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ4600000000000000000000
χ342222-2-12222-211-122220000-1-12222222211−3−333−3−333-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100−3−33300−3−33300−3−33300−3−33300−3−33300−3−33300−3−33300−3−33322−2−222−2−2ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ1400000000000000000000
χ352222-2-12222-211-122220000-1-12222222211−3−333−3−333-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100−3−33300−3−33300−3−33300−3−33300−3−33300−3−33300−3−33300−3−333−2−222−2−222−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ1400000000000000000000
χ3622-2-2222222-222222220000-2-2-2-2-2-2-2-2-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ3722-2-2222222-222222220000-2-2-2-2-2-2-2-2-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ3822-2-22-12222-2-1-1-12222000011-2-2-2-2-2-2-2-21133−3−3−3−333-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2111111110033−3−30033−3−30033−3−30033−3−300−3−33300−3−33300−3−33300−3−333−i2−i2i2i2i2i2−i2−i2ζ26+ζ46ζ26+ζ46−ζ26−ζ46−ζ26−ζ46ζ10+ζ14ζ10+ζ14−ζ10−ζ14−ζ10−ζ14−ζ26−ζ46−ζ26−ζ46ζ26+ζ46ζ26+ζ46−ζ10−ζ14−ζ10−ζ14ζ10+ζ14ζ10+ζ1400000000000000000000
χ3922-2-22-12222-2-1-1-12222000011-2-2-2-2-2-2-2-21133−3−3−3−333-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2111111110033−3−30033−3−30033−3−30033−3−300−3−33300−3−33300−3−33300−3−333i2i2−i2−i2−i2−i2i2i2−ζ26−ζ46−ζ26−ζ46ζ26+ζ46ζ26+ζ46−ζ10−ζ14−ζ10−ζ14ζ10+ζ14ζ10+ζ14ζ26+ζ46ζ26+ζ46−ζ26−ζ46−ζ26−ζ46ζ10+ζ14ζ10+ζ14−ζ10−ζ14−ζ10−ζ1400000000000000000000
χ4022-2-22-12222-2-1-1-12222000011-2-2-2-2-2-2-2-211−3−33333−3−3-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-21111111100−3−33300−3−33300−3−33300−3−3330033−3−30033−3−30033−3−30033−3−3−i2−i2i2i2i2i2−i2−i2ζ10+ζ14ζ10+ζ14−ζ10−ζ14−ζ10−ζ14ζ26+ζ46ζ26+ζ46−ζ26−ζ46−ζ26−ζ46−ζ10−ζ14−ζ10−ζ14ζ10+ζ14ζ10+ζ14−ζ26−ζ46−ζ26−ζ46ζ26+ζ46ζ26+ζ4600000000000000000000
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χ1724-4−4i4i0-2-2-2-240−2i32i32222-4−2222−2i22i22i−2i2i−2i2i−2i2i−2i−4i4i−2323−2ζ26+2ζ462ζ26−2ζ46−2ζ10+2ζ142ζ10−2ζ142ζ10+2ζ14−2ζ10−2ζ142ζ26+2ζ46−2ζ26−2ζ46111-20000i3−i3i3−i3i3−i3−2i32i3-1-1-12−ii−ii−ii2i−2i00003−33−33−3−23232−2ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ142−2ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ142−2ζ26−ζ46−ζ26+ζ46ζ10−ζ14−ζ10+ζ14−2222−2ζ26+2ζ462ζ26−2ζ46−2ζ10+2ζ142ζ10−2ζ14i2−i2−ζ10−ζ14ζ10+ζ14−ζ26−ζ46ζ26+ζ46i2−i2−ζ10−ζ14ζ10+ζ14−ζ26−ζ46ζ26+ζ46i2−i2−ζ10−ζ14ζ10+ζ14−ζ26−ζ46ζ26+ζ46−2i22i22ζ10+2ζ14−2ζ10−2ζ142ζ26+2ζ46−2ζ26−2ζ4600000000000000000000000000000000000000000000
χ1734-4−4i4i0-2-2-2-2402i3−2i32222-422−222i2−2i22i−2i2i−2i2i−2i2i−2i−4i4i23−232ζ10−2ζ14−2ζ10+2ζ142ζ26−2ζ46−2ζ26+2ζ46−2ζ26−2ζ462ζ26+2ζ46−2ζ10−2ζ142ζ10+2ζ14111-20000−i3i3−i3i3−i3i32i3−2i3-1-1-12−ii−ii−ii2i−2i0000−33−33−3323−23−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ46−22−ζ10+ζ14ζ10−ζ14−ζ26+ζ46ζ26−ζ4622−222ζ10−2ζ14−2ζ10+2ζ142ζ26−2ζ46−2ζ26+2ζ46−i2i2ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14−i2i2ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ14−i2i2ζ26+ζ46−ζ26−ζ46ζ10+ζ14−ζ10−ζ142i2−2i2−2ζ26−2ζ462ζ26+2ζ46−2ζ10−2ζ142ζ10+2ζ1400000000000000000000000000000000000000000000
χ1744-4−4i4i0-2-2-2-2402i3−2i32222-4−2222−2i22i22i−2i2i−2i2i−2i2i−2i−4i4i23−23−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ462ζ26+2ζ46−2ζ26−2ζ462ζ10+2ζ14−2ζ10−2ζ14111-20000−i3i3−i3i3−i3i32i3−2i3-1-1-12−ii−ii−ii2i−2i0000−33−33−3323−232−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ462−2ζ10−ζ14−ζ10+ζ14ζ26−ζ46−ζ26+ζ46−2222−2ζ10+2ζ142ζ10−2ζ14−2ζ26+2ζ462ζ26−2ζ46i2−i2−ζ26−ζ46ζ26+ζ46−ζ10−ζ14ζ10+ζ14i2−i2−ζ26−ζ46ζ26+ζ46−ζ10−ζ14ζ10+ζ14i2−i2−ζ26−ζ46ζ26+ζ46−ζ10−ζ14ζ10+ζ14−2i22i22ζ26+2ζ46−2ζ26−2ζ462ζ10+2ζ14−2ζ10−2ζ1400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.