from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1129, base_ring=CyclotomicField(1128))
M = H._module
chi = DirichletCharacter(H, M([1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,1129))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(1129\) | |
| Conductor: | \(1129\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1128})$ |
| Fixed field: | Number field defined by a degree 1128 polynomial (not computed) |
First 31 of 368 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1129}(11,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{149}{564}\right)\) | \(e\left(\frac{557}{564}\right)\) | \(e\left(\frac{149}{282}\right)\) | \(e\left(\frac{193}{282}\right)\) | \(e\left(\frac{71}{282}\right)\) | \(e\left(\frac{265}{564}\right)\) | \(e\left(\frac{149}{188}\right)\) | \(e\left(\frac{275}{282}\right)\) | \(e\left(\frac{535}{564}\right)\) | \(e\left(\frac{1}{1128}\right)\) |
| \(\chi_{1129}(13,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{455}{564}\right)\) | \(e\left(\frac{395}{564}\right)\) | \(e\left(\frac{173}{282}\right)\) | \(e\left(\frac{67}{282}\right)\) | \(e\left(\frac{143}{282}\right)\) | \(e\left(\frac{355}{564}\right)\) | \(e\left(\frac{79}{188}\right)\) | \(e\left(\frac{113}{282}\right)\) | \(e\left(\frac{25}{564}\right)\) | \(e\left(\frac{991}{1128}\right)\) |
| \(\chi_{1129}(17,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{409}{564}\right)\) | \(e\left(\frac{541}{564}\right)\) | \(e\left(\frac{127}{282}\right)\) | \(e\left(\frac{191}{282}\right)\) | \(e\left(\frac{193}{282}\right)\) | \(e\left(\frac{65}{564}\right)\) | \(e\left(\frac{33}{188}\right)\) | \(e\left(\frac{259}{282}\right)\) | \(e\left(\frac{227}{564}\right)\) | \(e\left(\frac{809}{1128}\right)\) |
| \(\chi_{1129}(22,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{559}{564}\right)\) | \(e\left(\frac{163}{564}\right)\) | \(e\left(\frac{277}{282}\right)\) | \(e\left(\frac{179}{282}\right)\) | \(e\left(\frac{79}{282}\right)\) | \(e\left(\frac{275}{564}\right)\) | \(e\left(\frac{183}{188}\right)\) | \(e\left(\frac{163}{282}\right)\) | \(e\left(\frac{353}{564}\right)\) | \(e\left(\frac{299}{1128}\right)\) |
| \(\chi_{1129}(26,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{301}{564}\right)\) | \(e\left(\frac{1}{564}\right)\) | \(e\left(\frac{19}{282}\right)\) | \(e\left(\frac{53}{282}\right)\) | \(e\left(\frac{151}{282}\right)\) | \(e\left(\frac{365}{564}\right)\) | \(e\left(\frac{113}{188}\right)\) | \(e\left(\frac{1}{282}\right)\) | \(e\left(\frac{407}{564}\right)\) | \(e\left(\frac{161}{1128}\right)\) |
| \(\chi_{1129}(29,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{349}{564}\right)\) | \(e\left(\frac{241}{564}\right)\) | \(e\left(\frac{67}{282}\right)\) | \(e\left(\frac{83}{282}\right)\) | \(e\left(\frac{13}{282}\right)\) | \(e\left(\frac{545}{564}\right)\) | \(e\left(\frac{161}{188}\right)\) | \(e\left(\frac{241}{282}\right)\) | \(e\left(\frac{515}{564}\right)\) | \(e\left(\frac{449}{1128}\right)\) |
| \(\chi_{1129}(33,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{319}{564}\right)\) | \(e\left(\frac{91}{564}\right)\) | \(e\left(\frac{37}{282}\right)\) | \(e\left(\frac{29}{282}\right)\) | \(e\left(\frac{205}{282}\right)\) | \(e\left(\frac{503}{564}\right)\) | \(e\left(\frac{131}{188}\right)\) | \(e\left(\frac{91}{282}\right)\) | \(e\left(\frac{377}{564}\right)\) | \(e\left(\frac{1115}{1128}\right)\) |
| \(\chi_{1129}(38,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{161}{564}\right)\) | \(e\left(\frac{53}{564}\right)\) | \(e\left(\frac{161}{282}\right)\) | \(e\left(\frac{271}{282}\right)\) | \(e\left(\frac{107}{282}\right)\) | \(e\left(\frac{169}{564}\right)\) | \(e\left(\frac{161}{188}\right)\) | \(e\left(\frac{53}{282}\right)\) | \(e\left(\frac{139}{564}\right)\) | \(e\left(\frac{73}{1128}\right)\) |
| \(\chi_{1129}(39,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{564}\right)\) | \(e\left(\frac{493}{564}\right)\) | \(e\left(\frac{61}{282}\right)\) | \(e\left(\frac{185}{282}\right)\) | \(e\left(\frac{277}{282}\right)\) | \(e\left(\frac{29}{564}\right)\) | \(e\left(\frac{61}{188}\right)\) | \(e\left(\frac{211}{282}\right)\) | \(e\left(\frac{431}{564}\right)\) | \(e\left(\frac{977}{1128}\right)\) |
| \(\chi_{1129}(41,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{564}\right)\) | \(e\left(\frac{433}{564}\right)\) | \(e\left(\frac{49}{282}\right)\) | \(e\left(\frac{107}{282}\right)\) | \(e\left(\frac{241}{282}\right)\) | \(e\left(\frac{125}{564}\right)\) | \(e\left(\frac{49}{188}\right)\) | \(e\left(\frac{151}{282}\right)\) | \(e\left(\frac{263}{564}\right)\) | \(e\left(\frac{905}{1128}\right)\) |
| \(\chi_{1129}(55,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{121}{564}\right)\) | \(e\left(\frac{229}{564}\right)\) | \(e\left(\frac{121}{282}\right)\) | \(e\left(\frac{11}{282}\right)\) | \(e\left(\frac{175}{282}\right)\) | \(e\left(\frac{113}{564}\right)\) | \(e\left(\frac{121}{188}\right)\) | \(e\left(\frac{229}{282}\right)\) | \(e\left(\frac{143}{564}\right)\) | \(e\left(\frac{773}{1128}\right)\) |
| \(\chi_{1129}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{485}{564}\right)\) | \(e\left(\frac{545}{564}\right)\) | \(e\left(\frac{203}{282}\right)\) | \(e\left(\frac{121}{282}\right)\) | \(e\left(\frac{233}{282}\right)\) | \(e\left(\frac{397}{564}\right)\) | \(e\left(\frac{109}{188}\right)\) | \(e\left(\frac{263}{282}\right)\) | \(e\left(\frac{163}{564}\right)\) | \(e\left(\frac{889}{1128}\right)\) |
| \(\chi_{1129}(62,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{269}{564}\right)\) | \(e\left(\frac{29}{564}\right)\) | \(e\left(\frac{269}{282}\right)\) | \(e\left(\frac{127}{282}\right)\) | \(e\left(\frac{149}{282}\right)\) | \(e\left(\frac{433}{564}\right)\) | \(e\left(\frac{81}{188}\right)\) | \(e\left(\frac{29}{282}\right)\) | \(e\left(\frac{523}{564}\right)\) | \(e\left(\frac{157}{1128}\right)\) |
| \(\chi_{1129}(65,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{427}{564}\right)\) | \(e\left(\frac{67}{564}\right)\) | \(e\left(\frac{145}{282}\right)\) | \(e\left(\frac{167}{282}\right)\) | \(e\left(\frac{247}{282}\right)\) | \(e\left(\frac{203}{564}\right)\) | \(e\left(\frac{51}{188}\right)\) | \(e\left(\frac{67}{282}\right)\) | \(e\left(\frac{197}{564}\right)\) | \(e\left(\frac{635}{1128}\right)\) |
| \(\chi_{1129}(68,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{101}{564}\right)\) | \(e\left(\frac{317}{564}\right)\) | \(e\left(\frac{101}{282}\right)\) | \(e\left(\frac{163}{282}\right)\) | \(e\left(\frac{209}{282}\right)\) | \(e\left(\frac{85}{564}\right)\) | \(e\left(\frac{101}{188}\right)\) | \(e\left(\frac{35}{282}\right)\) | \(e\left(\frac{427}{564}\right)\) | \(e\left(\frac{277}{1128}\right)\) |
| \(\chi_{1129}(73,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{564}\right)\) | \(e\left(\frac{377}{564}\right)\) | \(e\left(\frac{113}{282}\right)\) | \(e\left(\frac{241}{282}\right)\) | \(e\left(\frac{245}{282}\right)\) | \(e\left(\frac{553}{564}\right)\) | \(e\left(\frac{113}{188}\right)\) | \(e\left(\frac{95}{282}\right)\) | \(e\left(\frac{31}{564}\right)\) | \(e\left(\frac{913}{1128}\right)\) |
| \(\chi_{1129}(74,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{173}{564}\right)\) | \(e\left(\frac{113}{564}\right)\) | \(e\left(\frac{173}{282}\right)\) | \(e\left(\frac{67}{282}\right)\) | \(e\left(\frac{143}{282}\right)\) | \(e\left(\frac{73}{564}\right)\) | \(e\left(\frac{173}{188}\right)\) | \(e\left(\frac{113}{282}\right)\) | \(e\left(\frac{307}{564}\right)\) | \(e\left(\frac{709}{1128}\right)\) |
| \(\chi_{1129}(76,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{564}\right)\) | \(e\left(\frac{223}{564}\right)\) | \(e\left(\frac{7}{282}\right)\) | \(e\left(\frac{257}{282}\right)\) | \(e\left(\frac{115}{282}\right)\) | \(e\left(\frac{179}{564}\right)\) | \(e\left(\frac{7}{188}\right)\) | \(e\left(\frac{223}{282}\right)\) | \(e\left(\frac{521}{564}\right)\) | \(e\left(\frac{371}{1128}\right)\) |
| \(\chi_{1129}(83,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{463}{564}\right)\) | \(e\left(\frac{247}{564}\right)\) | \(e\left(\frac{181}{282}\right)\) | \(e\left(\frac{119}{282}\right)\) | \(e\left(\frac{73}{282}\right)\) | \(e\left(\frac{479}{564}\right)\) | \(e\left(\frac{87}{188}\right)\) | \(e\left(\frac{247}{282}\right)\) | \(e\left(\frac{137}{564}\right)\) | \(e\left(\frac{287}{1128}\right)\) |
| \(\chi_{1129}(88,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{251}{564}\right)\) | \(e\left(\frac{503}{564}\right)\) | \(e\left(\frac{251}{282}\right)\) | \(e\left(\frac{151}{282}\right)\) | \(e\left(\frac{95}{282}\right)\) | \(e\left(\frac{295}{564}\right)\) | \(e\left(\frac{63}{188}\right)\) | \(e\left(\frac{221}{282}\right)\) | \(e\left(\frac{553}{564}\right)\) | \(e\left(\frac{895}{1128}\right)\) |
| \(\chi_{1129}(93,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{564}\right)\) | \(e\left(\frac{521}{564}\right)\) | \(e\left(\frac{29}{282}\right)\) | \(e\left(\frac{259}{282}\right)\) | \(e\left(\frac{275}{282}\right)\) | \(e\left(\frac{97}{564}\right)\) | \(e\left(\frac{29}{188}\right)\) | \(e\left(\frac{239}{282}\right)\) | \(e\left(\frac{547}{564}\right)\) | \(e\left(\frac{973}{1128}\right)\) |
| \(\chi_{1129}(95,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{287}{564}\right)\) | \(e\left(\frac{119}{564}\right)\) | \(e\left(\frac{5}{282}\right)\) | \(e\left(\frac{103}{282}\right)\) | \(e\left(\frac{203}{282}\right)\) | \(e\left(\frac{7}{564}\right)\) | \(e\left(\frac{99}{188}\right)\) | \(e\left(\frac{119}{282}\right)\) | \(e\left(\frac{493}{564}\right)\) | \(e\left(\frac{547}{1128}\right)\) |
| \(\chi_{1129}(101,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{564}\right)\) | \(e\left(\frac{373}{564}\right)\) | \(e\left(\frac{37}{282}\right)\) | \(e\left(\frac{29}{282}\right)\) | \(e\left(\frac{205}{282}\right)\) | \(e\left(\frac{221}{564}\right)\) | \(e\left(\frac{37}{188}\right)\) | \(e\left(\frac{91}{282}\right)\) | \(e\left(\frac{95}{564}\right)\) | \(e\left(\frac{833}{1128}\right)\) |
| \(\chi_{1129}(102,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{425}{564}\right)\) | \(e\left(\frac{245}{564}\right)\) | \(e\left(\frac{143}{282}\right)\) | \(e\left(\frac{13}{282}\right)\) | \(e\left(\frac{53}{282}\right)\) | \(e\left(\frac{313}{564}\right)\) | \(e\left(\frac{49}{188}\right)\) | \(e\left(\frac{245}{282}\right)\) | \(e\left(\frac{451}{564}\right)\) | \(e\left(\frac{1093}{1128}\right)\) |
| \(\chi_{1129}(103,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{107}{564}\right)\) | \(e\left(\frac{347}{564}\right)\) | \(e\left(\frac{107}{282}\right)\) | \(e\left(\frac{61}{282}\right)\) | \(e\left(\frac{227}{282}\right)\) | \(e\left(\frac{319}{564}\right)\) | \(e\left(\frac{107}{188}\right)\) | \(e\left(\frac{65}{282}\right)\) | \(e\left(\frac{229}{564}\right)\) | \(e\left(\frac{595}{1128}\right)\) |
| \(\chi_{1129}(104,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{557}{564}\right)\) | \(e\left(\frac{341}{564}\right)\) | \(e\left(\frac{275}{282}\right)\) | \(e\left(\frac{25}{282}\right)\) | \(e\left(\frac{167}{282}\right)\) | \(e\left(\frac{385}{564}\right)\) | \(e\left(\frac{181}{188}\right)\) | \(e\left(\frac{59}{282}\right)\) | \(e\left(\frac{43}{564}\right)\) | \(e\left(\frac{757}{1128}\right)\) |
| \(\chi_{1129}(107,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{533}{564}\right)\) | \(e\left(\frac{221}{564}\right)\) | \(e\left(\frac{251}{282}\right)\) | \(e\left(\frac{151}{282}\right)\) | \(e\left(\frac{95}{282}\right)\) | \(e\left(\frac{13}{564}\right)\) | \(e\left(\frac{157}{188}\right)\) | \(e\left(\frac{221}{282}\right)\) | \(e\left(\frac{271}{564}\right)\) | \(e\left(\frac{49}{1128}\right)\) |
| \(\chi_{1129}(111,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{497}{564}\right)\) | \(e\left(\frac{41}{564}\right)\) | \(e\left(\frac{215}{282}\right)\) | \(e\left(\frac{199}{282}\right)\) | \(e\left(\frac{269}{282}\right)\) | \(e\left(\frac{301}{564}\right)\) | \(e\left(\frac{121}{188}\right)\) | \(e\left(\frac{41}{282}\right)\) | \(e\left(\frac{331}{564}\right)\) | \(e\left(\frac{397}{1128}\right)\) |
| \(\chi_{1129}(114,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{331}{564}\right)\) | \(e\left(\frac{151}{564}\right)\) | \(e\left(\frac{49}{282}\right)\) | \(e\left(\frac{107}{282}\right)\) | \(e\left(\frac{241}{282}\right)\) | \(e\left(\frac{407}{564}\right)\) | \(e\left(\frac{143}{188}\right)\) | \(e\left(\frac{151}{282}\right)\) | \(e\left(\frac{545}{564}\right)\) | \(e\left(\frac{59}{1128}\right)\) |
| \(\chi_{1129}(116,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{564}\right)\) | \(e\left(\frac{17}{564}\right)\) | \(e\left(\frac{41}{282}\right)\) | \(e\left(\frac{55}{282}\right)\) | \(e\left(\frac{29}{282}\right)\) | \(e\left(\frac{1}{564}\right)\) | \(e\left(\frac{41}{188}\right)\) | \(e\left(\frac{17}{282}\right)\) | \(e\left(\frac{151}{564}\right)\) | \(e\left(\frac{1045}{1128}\right)\) |
| \(\chi_{1129}(118,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{197}{564}\right)\) | \(e\left(\frac{233}{564}\right)\) | \(e\left(\frac{197}{282}\right)\) | \(e\left(\frac{223}{282}\right)\) | \(e\left(\frac{215}{282}\right)\) | \(e\left(\frac{445}{564}\right)\) | \(e\left(\frac{9}{188}\right)\) | \(e\left(\frac{233}{282}\right)\) | \(e\left(\frac{79}{564}\right)\) | \(e\left(\frac{853}{1128}\right)\) |