Finite Group Databasebeta

← Group #13178239

Character table — Group #13178239

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222244444444444444444444444444444888888888888888888888888888888888888181818181818181818181818363636363636363636363636363636363636727272727272
order12223336666666662333334466666666666666666121212126666666666661212121212121212121212121212121212121212121212122222224444442244446666661212121212126612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-111-111-1-1-1-1-1-111-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-11-1-1-11-1-1-1-1-1-111-1-1111-1-1-1-11
χ51111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1-11-1111111-1-1-1-1111-1-1-11-1
χ61111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-1-111111111-1-1-1-1-11-11
χ71111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-1-1-1-111-111
χ81111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-111-1-1
χ101111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-111-111-1-111-1-1-1-111-1-11-11-111
χ111111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1111-1-111-1-1-1-1-1-111-11-11
χ121111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-11-1-1-1-1-111111111-11-1-11-1
χ131111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111111-1-1-1-111111-1-1-1-11111-11-1-1-11
χ141111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-111-1-1-111-1-111-1-1-1-111-111-1
χ151111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-111-1-1-111-1-1111111-1-11-11-1-1-1
χ161111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111
χ17222222-122-1-122-12222-1-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000000020200000-1-1-1-10000000-1-1000
χ18222222-122-1-122-12222-1-1-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-20-2000001111000000011000
χ19222222-122-1-122-12222-1-1-1-1-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-211-2-2-211111111-2-211111111222200000000-20-200000-1-1-1-1000000011000
χ20222222-122-1-122-12222-1-1-1-1-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-211-2-2-211111111-2-211111111-2-2-2-2000000002020000011110000000-1-1000
χ21222222-122-1-122-122-22-1-1-1-12-2112-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2111111112-11-222-1-1-1-1-1-1-1-1-2-21111111122-2-200000000-20200000-1-11100000001-1000
χ22222222-122-1-122-122-22-1-1-1-12-2112-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2111111112-11-222-1-1-1-1-1-1-1-1-2-211111111-2-2220000000020-20000011-1-10000000-11000
χ23222222-122-1-122-122-22-1-1-1-1-22112-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2-2-211111111-21-12-2-21111111122-1-1-1-1-1-1-1-122-2-20000000020-200000-1-1110000000-11000
χ24222222-122-1-122-122-22-1-1-1-1-22112-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2-2-211111111-21-12-2-21111111122-1-1-1-1-1-1-1-1-2-22200000000-2020000011-1-100000001-1000
χ2522222-122-1222-122-12-12-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000022002200000220-1-1000000-1-100000-1-10
χ2622222-122-1222-122-12-12-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200-2-200000-2-20110000001100000110
χ2722222-122-1222-122-12-12-1-1-1-2-222-12-1-1-1-1-122-1-1-1-1-1-1-2-2112-1-1-122-1-1-1-1-1-11-2-2-211-2-211111111-2-211111100002200-2-200000-220-1-100000011000001-10
χ2822222-122-1222-122-12-12-1-1-1-2-222-12-1-1-1-1-122-1-1-1-1-1-1-2-2112-1-1-122-1-1-1-1-1-11-2-2-211-2-211111111-2-21111110000-2-20022000002-2011000000-1-100000-110
χ2922222-122-1222-122-1-2-12-1-1-12-2-2-2-12-1-1-1-1-122-1-1-1-1-1-12211-2111-2-2111111-12-2-2-1-122-1-1-1-1-1-111-2-211111100002200-2-2000002-20-1-10000001100000-110
χ3022222-122-1222-122-1-2-12-1-1-12-2-2-2-12-1-1-1-1-122-1-1-1-1-1-12211-2111-2-2111111-12-2-2-1-122-1-1-1-1-1-111-2-21111110000-2-2002200000-22011000000-1-1000001-10
χ3122222-122-1222-122-1-2-12-1-1-1-22-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-1-1-2111-2-21111111-22211-2-2111111-1-122-1-1-1-1-1-1000022002200000-2-20-1-1000000-1-100000110
χ3222222-122-1222-122-1-2-12-1-1-1-22-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-2-1-1-2111-2-21111111-22211-2-2111111-1-122-1-1-1-1-1-10000-2-200-2-200000220110000001100000-1-10
χ332222-122-1222-122-122-1-12-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000220022020002000000-1-100-1-1-10000-1
χ342222-122-1222-122-122-1-12-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000-2-200-2-20-2000-2000000110011100001
χ352222-122-1222-122-122-1-12-1-1-2-222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-12-1-1-1-122-1-1-1-1-2-2-211111-2-211111111-2-211110000002200-2-20-20002000000-1-1001110000-1
χ362222-122-1222-122-122-1-12-1-1-2-222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-12-1-1-1-122-1-1-1-1-2-2-211111-2-211111111-2-21111000000-2-2002202000-20000001100-1-1-100001
χ372222-122-1222-122-12-2-1-12-1-12-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-1-2-21-21111-2-2111122-21-1-1-1-122-1-1-1-11111-2-211110000002200220-2000-2000000-1-100-1-1100001
χ382222-122-1222-122-12-2-1-12-1-12-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-1-2-21-21111-2-2111122-21-1-1-1-122-1-1-1-11111-2-21111000000-2-200-2-2020002000000110011-10000-1
χ392222-122-1222-122-12-2-1-12-1-1-22-2-2-1-12-1-1-1-1-1-122-1-1-1-111221-21111-2-21111-2-22-11111-2-21111-1-1-1-122-1-1-1-10000002200-2-202000-2000000-1-10011-100001
χ402222-122-1222-122-12-2-1-12-1-1-22-2-2-1-12-1-1-1-1-1-122-1-1-1-111221-21111-2-21111-2-22-11111-2-21111-1-1-1-122-1-1-1-1000000-2-200220-200020000001100-1-110000-1
χ4122-2-2222222-2-2-2-2-2-20222220000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000002-2002i−2i2i−2i0000000000002-22i−2i2i−2i00000000
χ4222-2-2222222-2-2-2-2-2-20222220000-2-2-2-2-22-22-22-222-2-20000000000000000000000000000000000000000002-200−2i2i−2i2i0000000000002-2−2i2i−2i2i00000000
χ4322-2-2222222-2-2-2-2-2-20222220000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000-22002i−2i−2i2i000000000000-222i−2i−2i2i00000000
χ4422-2-2222222-2-2-2-2-2-20222220000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000-2200−2i2i2i−2i000000000000-22−2i2i2i−2i00000000
χ452-2-22222-2-2-22-2-2-2220222220000-2-2-2-2-2-22-22-22-2-22200000000000000000000000000000000000000002-2002-200002-20000002-22-20000002-2000000
χ462-2-22222-2-2-22-2-2-2220222220000-2-2-2-2-2-22-22-22-2-22200000000000000000000000000000000000000002-200-220000-22000000-222-2000000-22000000
χ472-2-22222-2-2-22-2-2-2220222220000-2-2-2-2-2-22-22-22-2-2220000000000000000000000000000000000000000-22002-20000-220000002-2-22000000-22000000
χ482-2-22222-2-2-22-2-2-2220222220000-2-2-2-2-2-22-22-22-2-2220000000000000000000000000000000000000000-2200-2200002-2000000-22-220000002-2000000
χ4944444-2-24-2-2-24-2-24-24-2-211144-2-2-2-2111-2-2-2-211111144-2-24-2-2-2-2-2111111-2-2-24-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5044444-2-24-2-2-24-2-24-24-2-2111-4-4-2-2-2-2111-2-2-2-2111111-4-4224-2-2-2-2-2111111222-42222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-2-24-2-2-24-2-24-2-4-2-21114-422-2-2111-2-2-2-21111114422-422222-1-1-1-1-1-1-2-22-4-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5244444-2-24-2-2-24-2-24-2-4-2-2111-4422-2-2111-2-2-2-2111111-4-4-2-2-422222-1-1-1-1-1-122-242222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ534444-24-2-24-2-2-24-2-244-21-21144-2-2-21-211-2-211-2-21111-2-244-24-2-211-2-211114-2-2-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ544444-24-2-24-2-2-24-2-244-21-211-4-4-2-2-21-211-2-211-2-2111122-4-4-24-2-211-2-21111-422222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ554444-24-2-24-2-2-24-2-24-4-21-2114-422-21-211-2-211-2-21111-2-2-4-42-422-1-122-1-1-1-14-222-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ564444-24-2-24-2-2-24-2-24-4-21-211-4422-21-211-2-211-2-2111122442-422-1-122-1-1-1-1-42-2-222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ574444-2-24-2-244-2-24-2-241-2-21144441-2-21111-2-2-2-21111-2-2-2-2-2-211-2-2-2-21111-244-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ584444-2-24-2-244-2-24-2-241-2-211-4-4441-2-21111-2-2-2-211112222-2-211-2-2-2-211112-4-42-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-2-244-2-24-2-2-41-2-2114-4-4-41-2-21111-2-2-2-21111-2-22222-1-12222-1-1-1-1-24-4211-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-2-244-2-24-2-2-41-2-211-44-4-41-2-21111-2-2-2-2111122-2-222-1-12222-1-1-1-12-44-2-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ614444-2-2-2-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i3244-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ624444-2-2-2-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i32-4-4-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i322222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i322222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ634444-2-2-2-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i3244-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ644444-2-2-2-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i32-4-4-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i322222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i322222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ654444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i324-422111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-22222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ664444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-4422111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i3222-2-222-1-1-1-1-1-11+3i321+3i321−3i321−3i3222-2-2-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ674444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i324-422111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ684444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i32-4422111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i3222-2-222-1-1-1-1-1-11−3i321−3i321+3i321+3i3222-2-2-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ6944-4-444-244-22-4-42-4-404-2-2-2-20000-422224-4-22-22-2-2220000000000000000000000000000000000000000004-4000000000000000000-22000000000000
χ7044-4-444-244-22-4-42-4-404-2-2-2-20000-422224-4-22-22-2-222000000000000000000000000000000000000000000-440000000000000000002-2000000000000
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χ964-44-4-2-2-22222-2-2-2220111−1−3i32−1+3i32002i3−2i3111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i3223−23−232300-33−i3i3−i3i33+i32−3−i32−3+i323−i320000−33−333i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ113−3−3i3i3−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000000000000000000000000
χ974-44-4-2-2-22222-2-2-2220111−1−3i32−1+3i32002i3−2i3111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32−232323−2300-33−i3i3−i3i33+i32−3−i32−3+i323−i3200003−33−3−3i3i−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ11−333i−3i−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000000000000000000000000
χ984-44-4-2-2-22222-2-2-2220111−1+3i32−1−3i3200−2i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i3223−23−232300-33i3−i3i3−i33−i32−3+i32−3−i323+i320000−33−33−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ113−33i−3i3−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000000000000000000000
χ994-44-4-2-2-22222-2-2-2220111−1+3i32−1−3i3200−2i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−232323−2300-33i3−i3i3−i33−i32−3+i32−3−i323+i3200003−33−33i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−33−3i3i−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000000000000000000000
χ1004-44-4-2-2-22222-2-2-2220111−1+3i32−1−3i32002i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i3223−2323−23003-3−i3i3−i3i3−3+i323−i323+i32−3−i320000−33−33−3i3i−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11−33−3i3i−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000000000000000000000
χ1014-44-4-2-2-22222-2-2-2220111−1+3i32−1−3i32002i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32−2323−2323003-3−i3i3−i3i3−3+i323−i323+i32−3−i3200003−33−33i−3i2ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ113−33i−3i3−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000000000000000000000
χ1024-4-4444-2-4-42-2-4-424404-2-2-2-20000-42222-442-22-222-2-200000000000000000000000000000000000000004-4000000000000000000-2200000000000000
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χ11188-8-8-4-4-4-4-4-44444440222−1−3i3−1+3i30000-2-2-21+3i31−3i32-22-22-2−1−3i3−1+3i31+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ11288-8-8-4-4-4-4-4-44444440222−1+3i3−1−3i30000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-888-4-4-844-4-8448-40-4-4222000044-2-2-24-44-4-22-2-2220000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1158-8-88-4-4844-8844-8-4-402-4-4220000-244-2-2-224-44-4-2-2220000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-4444-4-40222−1−3i3−1+3i30000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-4444-4-40222−1+3i3−1−3i30000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.