from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(967, base_ring=CyclotomicField(966))
M = H._module
chi = DirichletCharacter(H, M([374]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,967))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(967\) | |
| Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(483\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
First 31 of 264 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{967}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{386}{483}\right)\) | \(e\left(\frac{122}{161}\right)\) | \(e\left(\frac{289}{483}\right)\) | \(e\left(\frac{187}{483}\right)\) | \(e\left(\frac{269}{483}\right)\) | \(e\left(\frac{454}{483}\right)\) | \(e\left(\frac{64}{161}\right)\) | \(e\left(\frac{83}{161}\right)\) | \(e\left(\frac{30}{161}\right)\) | \(e\left(\frac{129}{161}\right)\) |
| \(\chi_{967}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{483}\right)\) | \(e\left(\frac{83}{161}\right)\) | \(e\left(\frac{95}{483}\right)\) | \(e\left(\frac{374}{483}\right)\) | \(e\left(\frac{55}{483}\right)\) | \(e\left(\frac{425}{483}\right)\) | \(e\left(\frac{128}{161}\right)\) | \(e\left(\frac{5}{161}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{97}{161}\right)\) |
| \(\chi_{967}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{483}\right)\) | \(e\left(\frac{5}{161}\right)\) | \(e\left(\frac{190}{483}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{367}{483}\right)\) | \(e\left(\frac{95}{161}\right)\) | \(e\left(\frac{10}{161}\right)\) | \(e\left(\frac{120}{161}\right)\) | \(e\left(\frac{33}{161}\right)\) |
| \(\chi_{967}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{152}{483}\right)\) | \(e\left(\frac{8}{161}\right)\) | \(e\left(\frac{304}{483}\right)\) | \(e\left(\frac{424}{483}\right)\) | \(e\left(\frac{176}{483}\right)\) | \(e\left(\frac{394}{483}\right)\) | \(e\left(\frac{152}{161}\right)\) | \(e\left(\frac{16}{161}\right)\) | \(e\left(\frac{31}{161}\right)\) | \(e\left(\frac{85}{161}\right)\) |
| \(\chi_{967}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{337}{483}\right)\) | \(e\left(\frac{94}{161}\right)\) | \(e\left(\frac{191}{483}\right)\) | \(e\left(\frac{152}{483}\right)\) | \(e\left(\frac{136}{483}\right)\) | \(e\left(\frac{41}{483}\right)\) | \(e\left(\frac{15}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{2}{161}\right)\) | \(e\left(\frac{73}{161}\right)\) |
| \(\chi_{967}(22,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{290}{483}\right)\) | \(e\left(\frac{100}{161}\right)\) | \(e\left(\frac{97}{483}\right)\) | \(e\left(\frac{148}{483}\right)\) | \(e\left(\frac{107}{483}\right)\) | \(e\left(\frac{256}{483}\right)\) | \(e\left(\frac{129}{161}\right)\) | \(e\left(\frac{39}{161}\right)\) | \(e\left(\frac{146}{161}\right)\) | \(e\left(\frac{16}{161}\right)\) |
| \(\chi_{967}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{374}{483}\right)\) | \(e\left(\frac{79}{161}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{1}{483}\right)\) | \(e\left(\frac{128}{483}\right)\) | \(e\left(\frac{67}{483}\right)\) | \(e\left(\frac{52}{161}\right)\) | \(e\left(\frac{158}{161}\right)\) | \(e\left(\frac{125}{161}\right)\) | \(e\left(\frac{135}{161}\right)\) |
| \(\chi_{967}(31,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{376}{483}\right)\) | \(e\left(\frac{113}{161}\right)\) | \(e\left(\frac{269}{483}\right)\) | \(e\left(\frac{32}{483}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{212}{483}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{65}{161}\right)\) | \(e\left(\frac{136}{161}\right)\) | \(e\left(\frac{134}{161}\right)\) |
| \(\chi_{967}(32,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{481}{483}\right)\) | \(e\left(\frac{127}{161}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{452}{483}\right)\) | \(e\left(\frac{379}{483}\right)\) | \(e\left(\frac{338}{483}\right)\) | \(e\left(\frac{159}{161}\right)\) | \(e\left(\frac{93}{161}\right)\) | \(e\left(\frac{150}{161}\right)\) | \(e\left(\frac{1}{161}\right)\) |
| \(\chi_{967}(34,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{293}{483}\right)\) | \(e\left(\frac{151}{161}\right)\) | \(e\left(\frac{103}{483}\right)\) | \(e\left(\frac{436}{483}\right)\) | \(e\left(\frac{263}{483}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{132}{161}\right)\) | \(e\left(\frac{141}{161}\right)\) | \(e\left(\frac{82}{161}\right)\) | \(e\left(\frac{95}{161}\right)\) |
| \(\chi_{967}(35,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{158}{483}\right)\) | \(e\left(\frac{110}{161}\right)\) | \(e\left(\frac{316}{483}\right)\) | \(e\left(\frac{34}{483}\right)\) | \(e\left(\frac{5}{483}\right)\) | \(e\left(\frac{346}{483}\right)\) | \(e\left(\frac{158}{161}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{64}{161}\right)\) | \(e\left(\frac{82}{161}\right)\) |
| \(\chi_{967}(36,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{483}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{128}{483}\right)\) | \(e\left(\frac{445}{483}\right)\) | \(e\left(\frac{365}{483}\right)\) | \(e\left(\frac{55}{161}\right)\) | \(e\left(\frac{99}{161}\right)\) | \(e\left(\frac{61}{161}\right)\) | \(e\left(\frac{53}{161}\right)\) |
| \(\chi_{967}(44,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{483}\right)\) | \(e\left(\frac{61}{161}\right)\) | \(e\left(\frac{386}{483}\right)\) | \(e\left(\frac{335}{483}\right)\) | \(e\left(\frac{376}{483}\right)\) | \(e\left(\frac{227}{483}\right)\) | \(e\left(\frac{32}{161}\right)\) | \(e\left(\frac{122}{161}\right)\) | \(e\left(\frac{15}{161}\right)\) | \(e\left(\frac{145}{161}\right)\) |
| \(\chi_{967}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{425}{483}\right)\) | \(e\left(\frac{141}{161}\right)\) | \(e\left(\frac{367}{483}\right)\) | \(e\left(\frac{67}{483}\right)\) | \(e\left(\frac{365}{483}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{103}{161}\right)\) | \(e\left(\frac{121}{161}\right)\) | \(e\left(\frac{3}{161}\right)\) | \(e\left(\frac{29}{161}\right)\) |
| \(\chi_{967}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{483}\right)\) | \(e\left(\frac{40}{161}\right)\) | \(e\left(\frac{71}{483}\right)\) | \(e\left(\frac{188}{483}\right)\) | \(e\left(\frac{397}{483}\right)\) | \(e\left(\frac{38}{483}\right)\) | \(e\left(\frac{116}{161}\right)\) | \(e\left(\frac{80}{161}\right)\) | \(e\left(\frac{155}{161}\right)\) | \(e\left(\frac{103}{161}\right)\) |
| \(\chi_{967}(57,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{93}{161}\right)\) | \(e\left(\frac{475}{483}\right)\) | \(e\left(\frac{421}{483}\right)\) | \(e\left(\frac{275}{483}\right)\) | \(e\left(\frac{193}{483}\right)\) | \(e\left(\frac{157}{161}\right)\) | \(e\left(\frac{25}{161}\right)\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{2}{161}\right)\) |
| \(\chi_{967}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{148}{483}\right)\) | \(e\left(\frac{101}{161}\right)\) | \(e\left(\frac{296}{483}\right)\) | \(e\left(\frac{362}{483}\right)\) | \(e\left(\frac{451}{483}\right)\) | \(e\left(\frac{104}{483}\right)\) | \(e\left(\frac{148}{161}\right)\) | \(e\left(\frac{41}{161}\right)\) | \(e\left(\frac{9}{161}\right)\) | \(e\left(\frac{87}{161}\right)\) |
| \(\chi_{967}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{359}{483}\right)\) | \(e\left(\frac{146}{161}\right)\) | \(e\left(\frac{235}{483}\right)\) | \(e\left(\frac{10}{483}\right)\) | \(e\left(\frac{314}{483}\right)\) | \(e\left(\frac{187}{483}\right)\) | \(e\left(\frac{37}{161}\right)\) | \(e\left(\frac{131}{161}\right)\) | \(e\left(\frac{123}{161}\right)\) | \(e\left(\frac{62}{161}\right)\) |
| \(\chi_{967}(65,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{122}{483}\right)\) | \(e\left(\frac{142}{161}\right)\) | \(e\left(\frac{244}{483}\right)\) | \(e\left(\frac{442}{483}\right)\) | \(e\left(\frac{65}{483}\right)\) | \(e\left(\frac{151}{483}\right)\) | \(e\left(\frac{122}{161}\right)\) | \(e\left(\frac{123}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{100}{161}\right)\) |
| \(\chi_{967}(70,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{483}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{122}{483}\right)\) | \(e\left(\frac{221}{483}\right)\) | \(e\left(\frac{274}{483}\right)\) | \(e\left(\frac{317}{483}\right)\) | \(e\left(\frac{61}{161}\right)\) | \(e\left(\frac{142}{161}\right)\) | \(e\left(\frac{94}{161}\right)\) | \(e\left(\frac{50}{161}\right)\) |
| \(\chi_{967}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{483}\right)\) | \(e\left(\frac{134}{161}\right)\) | \(e\left(\frac{262}{483}\right)\) | \(e\left(\frac{340}{483}\right)\) | \(e\left(\frac{50}{483}\right)\) | \(e\left(\frac{79}{483}\right)\) | \(e\left(\frac{131}{161}\right)\) | \(e\left(\frac{107}{161}\right)\) | \(e\left(\frac{157}{161}\right)\) | \(e\left(\frac{15}{161}\right)\) |
| \(\chi_{967}(84,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{483}\right)\) | \(e\left(\frac{16}{161}\right)\) | \(e\left(\frac{286}{483}\right)\) | \(e\left(\frac{43}{483}\right)\) | \(e\left(\frac{191}{483}\right)\) | \(e\left(\frac{466}{483}\right)\) | \(e\left(\frac{143}{161}\right)\) | \(e\left(\frac{32}{161}\right)\) | \(e\left(\frac{62}{161}\right)\) | \(e\left(\frac{9}{161}\right)\) |
| \(\chi_{967}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{389}{483}\right)\) | \(e\left(\frac{12}{161}\right)\) | \(e\left(\frac{295}{483}\right)\) | \(e\left(\frac{475}{483}\right)\) | \(e\left(\frac{425}{483}\right)\) | \(e\left(\frac{430}{483}\right)\) | \(e\left(\frac{67}{161}\right)\) | \(e\left(\frac{24}{161}\right)\) | \(e\left(\frac{127}{161}\right)\) | \(e\left(\frac{47}{161}\right)\) |
| \(\chi_{967}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{328}{483}\right)\) | \(e\left(\frac{102}{161}\right)\) | \(e\left(\frac{173}{483}\right)\) | \(e\left(\frac{254}{483}\right)\) | \(e\left(\frac{151}{483}\right)\) | \(e\left(\frac{113}{483}\right)\) | \(e\left(\frac{6}{161}\right)\) | \(e\left(\frac{43}{161}\right)\) | \(e\left(\frac{33}{161}\right)\) | \(e\left(\frac{158}{161}\right)\) |
| \(\chi_{967}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{440}{483}\right)\) | \(e\left(\frac{74}{161}\right)\) | \(e\left(\frac{397}{483}\right)\) | \(e\left(\frac{58}{483}\right)\) | \(e\left(\frac{179}{483}\right)\) | \(e\left(\frac{22}{483}\right)\) | \(e\left(\frac{118}{161}\right)\) | \(e\left(\frac{148}{161}\right)\) | \(e\left(\frac{5}{161}\right)\) | \(e\left(\frac{102}{161}\right)\) |
| \(\chi_{967}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{130}{483}\right)\) | \(e\left(\frac{117}{161}\right)\) | \(e\left(\frac{260}{483}\right)\) | \(e\left(\frac{83}{483}\right)\) | \(e\left(\frac{481}{483}\right)\) | \(e\left(\frac{248}{483}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{73}{161}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{96}{161}\right)\) |
| \(\chi_{967}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{483}\right)\) | \(e\left(\frac{136}{161}\right)\) | \(e\left(\frac{338}{483}\right)\) | \(e\left(\frac{446}{483}\right)\) | \(e\left(\frac{94}{483}\right)\) | \(e\left(\frac{419}{483}\right)\) | \(e\left(\frac{8}{161}\right)\) | \(e\left(\frac{111}{161}\right)\) | \(e\left(\frac{44}{161}\right)\) | \(e\left(\frac{157}{161}\right)\) |
| \(\chi_{967}(111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{80}{161}\right)\) | \(e\left(\frac{464}{483}\right)\) | \(e\left(\frac{215}{483}\right)\) | \(e\left(\frac{472}{483}\right)\) | \(e\left(\frac{398}{483}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{160}{161}\right)\) | \(e\left(\frac{149}{161}\right)\) | \(e\left(\frac{45}{161}\right)\) |
| \(\chi_{967}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{382}{483}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{281}{483}\right)\) | \(e\left(\frac{125}{483}\right)\) | \(e\left(\frac{61}{483}\right)\) | \(e\left(\frac{164}{483}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{108}{161}\right)\) | \(e\left(\frac{8}{161}\right)\) | \(e\left(\frac{131}{161}\right)\) |
| \(\chi_{967}(115,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{430}{483}\right)\) | \(e\left(\frac{65}{161}\right)\) | \(e\left(\frac{377}{483}\right)\) | \(e\left(\frac{386}{483}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{263}{483}\right)\) | \(e\left(\frac{108}{161}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{111}{161}\right)\) | \(e\left(\frac{107}{161}\right)\) |
| \(\chi_{967}(120,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{262}{483}\right)\) | \(e\left(\frac{107}{161}\right)\) | \(e\left(\frac{41}{483}\right)\) | \(e\left(\frac{197}{483}\right)\) | \(e\left(\frac{100}{483}\right)\) | \(e\left(\frac{158}{483}\right)\) | \(e\left(\frac{101}{161}\right)\) | \(e\left(\frac{53}{161}\right)\) | \(e\left(\frac{153}{161}\right)\) | \(e\left(\frac{30}{161}\right)\) |