sage: H = DirichletGroup(1069)
pari: g = idealstar(,1069,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1068 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{1068}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{1069}(6,\cdot)$ |
First 32 of 1068 characters
Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.
| Character | Orbit | Order | Primitive | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1069}(1,\cdot)\) | 1069.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{1069}(2,\cdot)\) | 1069.j | 356 | yes | \(-1\) | \(1\) | \(e\left(\frac{295}{356}\right)\) | \(e\left(\frac{175}{178}\right)\) | \(e\left(\frac{117}{178}\right)\) | \(e\left(\frac{73}{89}\right)\) | \(e\left(\frac{289}{356}\right)\) | \(e\left(\frac{335}{356}\right)\) | \(e\left(\frac{173}{356}\right)\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{231}{356}\right)\) | \(e\left(\frac{91}{356}\right)\) |
| \(\chi_{1069}(3,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{175}{178}\right)\) | \(e\left(\frac{55}{267}\right)\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{112}{267}\right)\) | \(e\left(\frac{101}{534}\right)\) | \(e\left(\frac{385}{534}\right)\) | \(e\left(\frac{169}{178}\right)\) | \(e\left(\frac{110}{267}\right)\) | \(e\left(\frac{215}{534}\right)\) | \(e\left(\frac{527}{534}\right)\) |
| \(\chi_{1069}(4,\cdot)\) | 1069.h | 178 | yes | \(1\) | \(1\) | \(e\left(\frac{117}{178}\right)\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{28}{89}\right)\) | \(e\left(\frac{57}{89}\right)\) | \(e\left(\frac{111}{178}\right)\) | \(e\left(\frac{157}{178}\right)\) | \(e\left(\frac{173}{178}\right)\) | \(e\left(\frac{83}{89}\right)\) | \(e\left(\frac{53}{178}\right)\) | \(e\left(\frac{91}{178}\right)\) |
| \(\chi_{1069}(5,\cdot)\) | 1069.i | 267 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{89}\right)\) | \(e\left(\frac{112}{267}\right)\) | \(e\left(\frac{57}{89}\right)\) | \(e\left(\frac{97}{267}\right)\) | \(e\left(\frac{64}{267}\right)\) | \(e\left(\frac{125}{267}\right)\) | \(e\left(\frac{41}{89}\right)\) | \(e\left(\frac{224}{267}\right)\) | \(e\left(\frac{49}{267}\right)\) | \(e\left(\frac{22}{267}\right)\) |
| \(\chi_{1069}(6,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{289}{356}\right)\) | \(e\left(\frac{101}{534}\right)\) | \(e\left(\frac{111}{178}\right)\) | \(e\left(\frac{64}{267}\right)\) | \(e\left(\frac{1}{1068}\right)\) | \(e\left(\frac{707}{1068}\right)\) | \(e\left(\frac{155}{356}\right)\) | \(e\left(\frac{101}{267}\right)\) | \(e\left(\frac{55}{1068}\right)\) | \(e\left(\frac{259}{1068}\right)\) |
| \(\chi_{1069}(7,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{335}{356}\right)\) | \(e\left(\frac{385}{534}\right)\) | \(e\left(\frac{157}{178}\right)\) | \(e\left(\frac{125}{267}\right)\) | \(e\left(\frac{707}{1068}\right)\) | \(e\left(\frac{25}{1068}\right)\) | \(e\left(\frac{293}{356}\right)\) | \(e\left(\frac{118}{267}\right)\) | \(e\left(\frac{437}{1068}\right)\) | \(e\left(\frac{485}{1068}\right)\) |
| \(\chi_{1069}(8,\cdot)\) | 1069.j | 356 | yes | \(-1\) | \(1\) | \(e\left(\frac{173}{356}\right)\) | \(e\left(\frac{169}{178}\right)\) | \(e\left(\frac{173}{178}\right)\) | \(e\left(\frac{41}{89}\right)\) | \(e\left(\frac{155}{356}\right)\) | \(e\left(\frac{293}{356}\right)\) | \(e\left(\frac{163}{356}\right)\) | \(e\left(\frac{80}{89}\right)\) | \(e\left(\frac{337}{356}\right)\) | \(e\left(\frac{273}{356}\right)\) |
| \(\chi_{1069}(9,\cdot)\) | 1069.i | 267 | yes | \(1\) | \(1\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{110}{267}\right)\) | \(e\left(\frac{83}{89}\right)\) | \(e\left(\frac{224}{267}\right)\) | \(e\left(\frac{101}{267}\right)\) | \(e\left(\frac{118}{267}\right)\) | \(e\left(\frac{80}{89}\right)\) | \(e\left(\frac{220}{267}\right)\) | \(e\left(\frac{215}{267}\right)\) | \(e\left(\frac{260}{267}\right)\) |
| \(\chi_{1069}(10,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{231}{356}\right)\) | \(e\left(\frac{215}{534}\right)\) | \(e\left(\frac{53}{178}\right)\) | \(e\left(\frac{49}{267}\right)\) | \(e\left(\frac{55}{1068}\right)\) | \(e\left(\frac{437}{1068}\right)\) | \(e\left(\frac{337}{356}\right)\) | \(e\left(\frac{215}{267}\right)\) | \(e\left(\frac{889}{1068}\right)\) | \(e\left(\frac{361}{1068}\right)\) |
| \(\chi_{1069}(11,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{91}{356}\right)\) | \(e\left(\frac{527}{534}\right)\) | \(e\left(\frac{91}{178}\right)\) | \(e\left(\frac{22}{267}\right)\) | \(e\left(\frac{259}{1068}\right)\) | \(e\left(\frac{485}{1068}\right)\) | \(e\left(\frac{273}{356}\right)\) | \(e\left(\frac{260}{267}\right)\) | \(e\left(\frac{361}{1068}\right)\) | \(e\left(\frac{865}{1068}\right)\) |
| \(\chi_{1069}(12,\cdot)\) | 1069.i | 267 | yes | \(1\) | \(1\) | \(e\left(\frac{57}{89}\right)\) | \(e\left(\frac{46}{267}\right)\) | \(e\left(\frac{25}{89}\right)\) | \(e\left(\frac{16}{267}\right)\) | \(e\left(\frac{217}{267}\right)\) | \(e\left(\frac{161}{267}\right)\) | \(e\left(\frac{82}{89}\right)\) | \(e\left(\frac{92}{267}\right)\) | \(e\left(\frac{187}{267}\right)\) | \(e\left(\frac{133}{267}\right)\) |
| \(\chi_{1069}(13,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{157}{178}\right)\) | \(e\left(\frac{29}{267}\right)\) | \(e\left(\frac{68}{89}\right)\) | \(e\left(\frac{161}{267}\right)\) | \(e\left(\frac{529}{534}\right)\) | \(e\left(\frac{203}{534}\right)\) | \(e\left(\frac{115}{178}\right)\) | \(e\left(\frac{58}{267}\right)\) | \(e\left(\frac{259}{534}\right)\) | \(e\left(\frac{307}{534}\right)\) |
| \(\chi_{1069}(14,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{137}{178}\right)\) | \(e\left(\frac{188}{267}\right)\) | \(e\left(\frac{48}{89}\right)\) | \(e\left(\frac{77}{267}\right)\) | \(e\left(\frac{253}{534}\right)\) | \(e\left(\frac{515}{534}\right)\) | \(e\left(\frac{55}{178}\right)\) | \(e\left(\frac{109}{267}\right)\) | \(e\left(\frac{31}{534}\right)\) | \(e\left(\frac{379}{534}\right)\) |
| \(\chi_{1069}(15,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{143}{178}\right)\) | \(e\left(\frac{167}{267}\right)\) | \(e\left(\frac{54}{89}\right)\) | \(e\left(\frac{209}{267}\right)\) | \(e\left(\frac{229}{534}\right)\) | \(e\left(\frac{101}{534}\right)\) | \(e\left(\frac{73}{178}\right)\) | \(e\left(\frac{67}{267}\right)\) | \(e\left(\frac{313}{534}\right)\) | \(e\left(\frac{37}{534}\right)\) |
| \(\chi_{1069}(16,\cdot)\) | 1069.g | 89 | yes | \(1\) | \(1\) | \(e\left(\frac{28}{89}\right)\) | \(e\left(\frac{83}{89}\right)\) | \(e\left(\frac{56}{89}\right)\) | \(e\left(\frac{25}{89}\right)\) | \(e\left(\frac{22}{89}\right)\) | \(e\left(\frac{68}{89}\right)\) | \(e\left(\frac{84}{89}\right)\) | \(e\left(\frac{77}{89}\right)\) | \(e\left(\frac{53}{89}\right)\) | \(e\left(\frac{2}{89}\right)\) |
| \(\chi_{1069}(17,\cdot)\) | 1069.i | 267 | yes | \(1\) | \(1\) | \(e\left(\frac{82}{89}\right)\) | \(e\left(\frac{227}{267}\right)\) | \(e\left(\frac{75}{89}\right)\) | \(e\left(\frac{137}{267}\right)\) | \(e\left(\frac{206}{267}\right)\) | \(e\left(\frac{127}{267}\right)\) | \(e\left(\frac{68}{89}\right)\) | \(e\left(\frac{187}{267}\right)\) | \(e\left(\frac{116}{267}\right)\) | \(e\left(\frac{221}{267}\right)\) |
| \(\chi_{1069}(18,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{283}{356}\right)\) | \(e\left(\frac{211}{534}\right)\) | \(e\left(\frac{105}{178}\right)\) | \(e\left(\frac{176}{267}\right)\) | \(e\left(\frac{203}{1068}\right)\) | \(e\left(\frac{409}{1068}\right)\) | \(e\left(\frac{137}{356}\right)\) | \(e\left(\frac{211}{267}\right)\) | \(e\left(\frac{485}{1068}\right)\) | \(e\left(\frac{245}{1068}\right)\) |
| \(\chi_{1069}(19,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{159}{178}\right)\) | \(e\left(\frac{200}{267}\right)\) | \(e\left(\frac{70}{89}\right)\) | \(e\left(\frac{116}{267}\right)\) | \(e\left(\frac{343}{534}\right)\) | \(e\left(\frac{65}{534}\right)\) | \(e\left(\frac{121}{178}\right)\) | \(e\left(\frac{133}{267}\right)\) | \(e\left(\frac{175}{534}\right)\) | \(e\left(\frac{193}{534}\right)\) |
| \(\chi_{1069}(20,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{85}{178}\right)\) | \(e\left(\frac{103}{267}\right)\) | \(e\left(\frac{85}{89}\right)\) | \(e\left(\frac{1}{267}\right)\) | \(e\left(\frac{461}{534}\right)\) | \(e\left(\frac{187}{534}\right)\) | \(e\left(\frac{77}{178}\right)\) | \(e\left(\frac{206}{267}\right)\) | \(e\left(\frac{257}{534}\right)\) | \(e\left(\frac{317}{534}\right)\) |
| \(\chi_{1069}(21,\cdot)\) | 1069.j | 356 | yes | \(-1\) | \(1\) | \(e\left(\frac{329}{356}\right)\) | \(e\left(\frac{165}{178}\right)\) | \(e\left(\frac{151}{178}\right)\) | \(e\left(\frac{79}{89}\right)\) | \(e\left(\frac{303}{356}\right)\) | \(e\left(\frac{265}{356}\right)\) | \(e\left(\frac{275}{356}\right)\) | \(e\left(\frac{76}{89}\right)\) | \(e\left(\frac{289}{356}\right)\) | \(e\left(\frac{157}{356}\right)\) |
| \(\chi_{1069}(22,\cdot)\) | 1069.k | 534 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{178}\right)\) | \(e\left(\frac{259}{267}\right)\) | \(e\left(\frac{15}{89}\right)\) | \(e\left(\frac{241}{267}\right)\) | \(e\left(\frac{29}{534}\right)\) | \(e\left(\frac{211}{534}\right)\) | \(e\left(\frac{45}{178}\right)\) | \(e\left(\frac{251}{267}\right)\) | \(e\left(\frac{527}{534}\right)\) | \(e\left(\frac{35}{534}\right)\) |
| \(\chi_{1069}(23,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{165}{356}\right)\) | \(e\left(\frac{1}{534}\right)\) | \(e\left(\frac{165}{178}\right)\) | \(e\left(\frac{35}{267}\right)\) | \(e\left(\frac{497}{1068}\right)\) | \(e\left(\frac{7}{1068}\right)\) | \(e\left(\frac{139}{356}\right)\) | \(e\left(\frac{1}{267}\right)\) | \(e\left(\frac{635}{1068}\right)\) | \(e\left(\frac{563}{1068}\right)\) |
| \(\chi_{1069}(24,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{167}{356}\right)\) | \(e\left(\frac{83}{534}\right)\) | \(e\left(\frac{167}{178}\right)\) | \(e\left(\frac{235}{267}\right)\) | \(e\left(\frac{667}{1068}\right)\) | \(e\left(\frac{581}{1068}\right)\) | \(e\left(\frac{145}{356}\right)\) | \(e\left(\frac{83}{267}\right)\) | \(e\left(\frac{373}{1068}\right)\) | \(e\left(\frac{805}{1068}\right)\) |
| \(\chi_{1069}(25,\cdot)\) | 1069.i | 267 | yes | \(1\) | \(1\) | \(e\left(\frac{57}{89}\right)\) | \(e\left(\frac{224}{267}\right)\) | \(e\left(\frac{25}{89}\right)\) | \(e\left(\frac{194}{267}\right)\) | \(e\left(\frac{128}{267}\right)\) | \(e\left(\frac{250}{267}\right)\) | \(e\left(\frac{82}{89}\right)\) | \(e\left(\frac{181}{267}\right)\) | \(e\left(\frac{98}{267}\right)\) | \(e\left(\frac{44}{267}\right)\) |
| \(\chi_{1069}(26,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{253}{356}\right)\) | \(e\left(\frac{49}{534}\right)\) | \(e\left(\frac{75}{178}\right)\) | \(e\left(\frac{113}{267}\right)\) | \(e\left(\frac{857}{1068}\right)\) | \(e\left(\frac{343}{1068}\right)\) | \(e\left(\frac{47}{356}\right)\) | \(e\left(\frac{49}{267}\right)\) | \(e\left(\frac{143}{1068}\right)\) | \(e\left(\frac{887}{1068}\right)\) |
| \(\chi_{1069}(27,\cdot)\) | 1069.h | 178 | yes | \(1\) | \(1\) | \(e\left(\frac{169}{178}\right)\) | \(e\left(\frac{55}{89}\right)\) | \(e\left(\frac{80}{89}\right)\) | \(e\left(\frac{23}{89}\right)\) | \(e\left(\frac{101}{178}\right)\) | \(e\left(\frac{29}{178}\right)\) | \(e\left(\frac{151}{178}\right)\) | \(e\left(\frac{21}{89}\right)\) | \(e\left(\frac{37}{178}\right)\) | \(e\left(\frac{171}{178}\right)\) |
| \(\chi_{1069}(28,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{213}{356}\right)\) | \(e\left(\frac{367}{534}\right)\) | \(e\left(\frac{35}{178}\right)\) | \(e\left(\frac{29}{267}\right)\) | \(e\left(\frac{305}{1068}\right)\) | \(e\left(\frac{967}{1068}\right)\) | \(e\left(\frac{283}{356}\right)\) | \(e\left(\frac{100}{267}\right)\) | \(e\left(\frac{755}{1068}\right)\) | \(e\left(\frac{1031}{1068}\right)\) |
| \(\chi_{1069}(29,\cdot)\) | 1069.g | 89 | yes | \(1\) | \(1\) | \(e\left(\frac{46}{89}\right)\) | \(e\left(\frac{41}{89}\right)\) | \(e\left(\frac{3}{89}\right)\) | \(e\left(\frac{22}{89}\right)\) | \(e\left(\frac{87}{89}\right)\) | \(e\left(\frac{10}{89}\right)\) | \(e\left(\frac{49}{89}\right)\) | \(e\left(\frac{82}{89}\right)\) | \(e\left(\frac{68}{89}\right)\) | \(e\left(\frac{16}{89}\right)\) |
| \(\chi_{1069}(30,\cdot)\) | 1069.l | 1068 | yes | \(-1\) | \(1\) | \(e\left(\frac{225}{356}\right)\) | \(e\left(\frac{325}{534}\right)\) | \(e\left(\frac{47}{178}\right)\) | \(e\left(\frac{161}{267}\right)\) | \(e\left(\frac{257}{1068}\right)\) | \(e\left(\frac{139}{1068}\right)\) | \(e\left(\frac{319}{356}\right)\) | \(e\left(\frac{58}{267}\right)\) | \(e\left(\frac{251}{1068}\right)\) | \(e\left(\frac{347}{1068}\right)\) |
| \(\chi_{1069}(31,\cdot)\) | 1069.j | 356 | yes | \(-1\) | \(1\) | \(e\left(\frac{197}{356}\right)\) | \(e\left(\frac{141}{178}\right)\) | \(e\left(\frac{19}{178}\right)\) | \(e\left(\frac{40}{89}\right)\) | \(e\left(\frac{123}{356}\right)\) | \(e\left(\frac{97}{356}\right)\) | \(e\left(\frac{235}{356}\right)\) | \(e\left(\frac{52}{89}\right)\) | \(e\left(\frac{1}{356}\right)\) | \(e\left(\frac{173}{356}\right)\) |
| \(\chi_{1069}(32,\cdot)\) | 1069.j | 356 | yes | \(-1\) | \(1\) | \(e\left(\frac{51}{356}\right)\) | \(e\left(\frac{163}{178}\right)\) | \(e\left(\frac{51}{178}\right)\) | \(e\left(\frac{9}{89}\right)\) | \(e\left(\frac{21}{356}\right)\) | \(e\left(\frac{251}{356}\right)\) | \(e\left(\frac{153}{356}\right)\) | \(e\left(\frac{74}{89}\right)\) | \(e\left(\frac{87}{356}\right)\) | \(e\left(\frac{99}{356}\right)\) |