from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(790142, base_ring=CyclotomicField(1056))
M = H._module
chi = DirichletCharacter(H, M([768,780,935]))
chi.galois_orbit()
[g,chi] = znchar(Mod(1383,790142))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(790142\) | |
| Conductor: | \(395071\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1056\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 395071.dbe | 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: | $\Q(\zeta_{1056})$ |
| Fixed field: | Number field defined by a degree 1056 polynomial (not computed) |
First 31 of 320 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{790142}(1383,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{335}{1056}\right)\) | \(e\left(\frac{193}{264}\right)\) | \(-1\) | \(e\left(\frac{219}{352}\right)\) | \(e\left(\frac{5}{352}\right)\) | \(e\left(\frac{71}{1056}\right)\) | \(e\left(\frac{1025}{1056}\right)\) | \(e\left(\frac{155}{1056}\right)\) | \(e\left(\frac{127}{264}\right)\) |
| \(\chi_{790142}(1637,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{169}{1056}\right)\) | \(e\left(\frac{95}{264}\right)\) | \(-1\) | \(e\left(\frac{349}{352}\right)\) | \(e\left(\frac{323}{352}\right)\) | \(e\left(\frac{433}{1056}\right)\) | \(e\left(\frac{391}{1056}\right)\) | \(e\left(\frac{157}{1056}\right)\) | \(e\left(\frac{161}{264}\right)\) |
| \(\chi_{790142}(4925,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{313}{1056}\right)\) | \(e\left(\frac{215}{264}\right)\) | \(-1\) | \(e\left(\frac{109}{352}\right)\) | \(e\left(\frac{115}{352}\right)\) | \(e\left(\frac{577}{1056}\right)\) | \(e\left(\frac{343}{1056}\right)\) | \(e\left(\frac{397}{1056}\right)\) | \(e\left(\frac{17}{264}\right)\) |
| \(\chi_{790142}(11755,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{79}{1056}\right)\) | \(e\left(\frac{185}{264}\right)\) | \(-1\) | \(e\left(\frac{59}{352}\right)\) | \(e\left(\frac{101}{352}\right)\) | \(e\left(\frac{871}{1056}\right)\) | \(e\left(\frac{289}{1056}\right)\) | \(e\left(\frac{667}{1056}\right)\) | \(e\left(\frac{119}{264}\right)\) |
| \(\chi_{790142}(13323,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{865}{1056}\right)\) | \(e\left(\frac{191}{264}\right)\) | \(-1\) | \(e\left(\frac{245}{352}\right)\) | \(e\left(\frac{139}{352}\right)\) | \(e\left(\frac{73}{1056}\right)\) | \(e\left(\frac{1039}{1056}\right)\) | \(e\left(\frac{85}{1056}\right)\) | \(e\left(\frac{257}{264}\right)\) |
| \(\chi_{790142}(13927,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{427}{1056}\right)\) | \(e\left(\frac{101}{264}\right)\) | \(-1\) | \(e\left(\frac{7}{352}\right)\) | \(e\left(\frac{185}{352}\right)\) | \(e\left(\frac{163}{1056}\right)\) | \(e\left(\frac{613}{1056}\right)\) | \(e\left(\frac{103}{1056}\right)\) | \(e\left(\frac{35}{264}\right)\) |
| \(\chi_{790142}(15193,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{685}{1056}\right)\) | \(e\left(\frac{107}{264}\right)\) | \(-1\) | \(e\left(\frac{17}{352}\right)\) | \(e\left(\frac{47}{352}\right)\) | \(e\left(\frac{949}{1056}\right)\) | \(e\left(\frac{835}{1056}\right)\) | \(e\left(\frac{49}{1056}\right)\) | \(e\left(\frac{173}{264}\right)\) |
| \(\chi_{790142}(17231,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{829}{1056}\right)\) | \(e\left(\frac{227}{264}\right)\) | \(-1\) | \(e\left(\frac{129}{352}\right)\) | \(e\left(\frac{191}{352}\right)\) | \(e\left(\frac{37}{1056}\right)\) | \(e\left(\frac{787}{1056}\right)\) | \(e\left(\frac{289}{1056}\right)\) | \(e\left(\frac{29}{264}\right)\) |
| \(\chi_{790142}(18839,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{1025}{1056}\right)\) | \(e\left(\frac{31}{264}\right)\) | \(-1\) | \(e\left(\frac{213}{352}\right)\) | \(e\left(\frac{299}{352}\right)\) | \(e\left(\frac{233}{1056}\right)\) | \(e\left(\frac{47}{1056}\right)\) | \(e\left(\frac{821}{1056}\right)\) | \(e\left(\frac{97}{264}\right)\) |
| \(\chi_{790142}(20597,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{493}{1056}\right)\) | \(e\left(\frac{35}{264}\right)\) | \(-1\) | \(e\left(\frac{337}{352}\right)\) | \(e\left(\frac{207}{352}\right)\) | \(e\left(\frac{757}{1056}\right)\) | \(e\left(\frac{547}{1056}\right)\) | \(e\left(\frac{433}{1056}\right)\) | \(e\left(\frac{101}{264}\right)\) |
| \(\chi_{790142}(24143,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{415}{1056}\right)\) | \(e\left(\frac{113}{264}\right)\) | \(-1\) | \(e\left(\frac{203}{352}\right)\) | \(e\left(\frac{85}{352}\right)\) | \(e\left(\frac{151}{1056}\right)\) | \(e\left(\frac{529}{1056}\right)\) | \(e\left(\frac{523}{1056}\right)\) | \(e\left(\frac{47}{264}\right)\) |
| \(\chi_{790142}(26845,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{895}{1056}\right)\) | \(e\left(\frac{161}{264}\right)\) | \(-1\) | \(e\left(\frac{107}{352}\right)\) | \(e\left(\frac{213}{352}\right)\) | \(e\left(\frac{631}{1056}\right)\) | \(e\left(\frac{721}{1056}\right)\) | \(e\left(\frac{619}{1056}\right)\) | \(e\left(\frac{95}{264}\right)\) |
| \(\chi_{790142}(30295,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{433}{1056}\right)\) | \(e\left(\frac{95}{264}\right)\) | \(-1\) | \(e\left(\frac{261}{352}\right)\) | \(e\left(\frac{59}{352}\right)\) | \(e\left(\frac{697}{1056}\right)\) | \(e\left(\frac{127}{1056}\right)\) | \(e\left(\frac{421}{1056}\right)\) | \(e\left(\frac{161}{264}\right)\) |
| \(\chi_{790142}(30303,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{163}{1056}\right)\) | \(e\left(\frac{101}{264}\right)\) | \(-1\) | \(e\left(\frac{95}{352}\right)\) | \(e\left(\frac{97}{352}\right)\) | \(e\left(\frac{955}{1056}\right)\) | \(e\left(\frac{877}{1056}\right)\) | \(e\left(\frac{895}{1056}\right)\) | \(e\left(\frac{35}{264}\right)\) |
| \(\chi_{790142}(41477,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{655}{1056}\right)\) | \(e\left(\frac{137}{264}\right)\) | \(-1\) | \(e\left(\frac{155}{352}\right)\) | \(e\left(\frac{325}{352}\right)\) | \(e\left(\frac{391}{1056}\right)\) | \(e\left(\frac{97}{1056}\right)\) | \(e\left(\frac{571}{1056}\right)\) | \(e\left(\frac{71}{264}\right)\) |
| \(\chi_{790142}(41981,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{601}{1056}\right)\) | \(e\left(\frac{191}{264}\right)\) | \(-1\) | \(e\left(\frac{333}{352}\right)\) | \(e\left(\frac{51}{352}\right)\) | \(e\left(\frac{865}{1056}\right)\) | \(e\left(\frac{247}{1056}\right)\) | \(e\left(\frac{877}{1056}\right)\) | \(e\left(\frac{257}{264}\right)\) |
| \(\chi_{790142}(47067,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{131}{1056}\right)\) | \(e\left(\frac{133}{264}\right)\) | \(-1\) | \(e\left(\frac{31}{352}\right)\) | \(e\left(\frac{65}{352}\right)\) | \(e\left(\frac{923}{1056}\right)\) | \(e\left(\frac{653}{1056}\right)\) | \(e\left(\frac{959}{1056}\right)\) | \(e\left(\frac{67}{264}\right)\) |
| \(\chi_{790142}(48175,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{641}{1056}\right)\) | \(e\left(\frac{151}{264}\right)\) | \(-1\) | \(e\left(\frac{149}{352}\right)\) | \(e\left(\frac{267}{352}\right)\) | \(e\left(\frac{905}{1056}\right)\) | \(e\left(\frac{527}{1056}\right)\) | \(e\left(\frac{533}{1056}\right)\) | \(e\left(\frac{217}{264}\right)\) |
| \(\chi_{790142}(49859,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{133}{1056}\right)\) | \(e\left(\frac{131}{264}\right)\) | \(-1\) | \(e\left(\frac{233}{352}\right)\) | \(e\left(\frac{23}{352}\right)\) | \(e\left(\frac{397}{1056}\right)\) | \(e\left(\frac{139}{1056}\right)\) | \(e\left(\frac{361}{1056}\right)\) | \(e\left(\frac{197}{264}\right)\) |
| \(\chi_{790142}(50765,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{961}{1056}\right)\) | \(e\left(\frac{95}{264}\right)\) | \(-1\) | \(e\left(\frac{85}{352}\right)\) | \(e\left(\frac{235}{352}\right)\) | \(e\left(\frac{169}{1056}\right)\) | \(e\left(\frac{655}{1056}\right)\) | \(e\left(\frac{949}{1056}\right)\) | \(e\left(\frac{161}{264}\right)\) |
| \(\chi_{790142}(55685,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{761}{1056}\right)\) | \(e\left(\frac{31}{264}\right)\) | \(-1\) | \(e\left(\frac{301}{352}\right)\) | \(e\left(\frac{211}{352}\right)\) | \(e\left(\frac{1025}{1056}\right)\) | \(e\left(\frac{311}{1056}\right)\) | \(e\left(\frac{557}{1056}\right)\) | \(e\left(\frac{97}{264}\right)\) |
| \(\chi_{790142}(59089,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{1003}{1056}\right)\) | \(e\left(\frac{53}{264}\right)\) | \(-1\) | \(e\left(\frac{103}{352}\right)\) | \(e\left(\frac{57}{352}\right)\) | \(e\left(\frac{739}{1056}\right)\) | \(e\left(\frac{421}{1056}\right)\) | \(e\left(\frac{7}{1056}\right)\) | \(e\left(\frac{251}{264}\right)\) |
| \(\chi_{790142}(59349,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{923}{1056}\right)\) | \(e\left(\frac{133}{264}\right)\) | \(-1\) | \(e\left(\frac{119}{352}\right)\) | \(e\left(\frac{329}{352}\right)\) | \(e\left(\frac{659}{1056}\right)\) | \(e\left(\frac{917}{1056}\right)\) | \(e\left(\frac{695}{1056}\right)\) | \(e\left(\frac{67}{264}\right)\) |
| \(\chi_{790142}(62821,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{941}{1056}\right)\) | \(e\left(\frac{115}{264}\right)\) | \(-1\) | \(e\left(\frac{177}{352}\right)\) | \(e\left(\frac{303}{352}\right)\) | \(e\left(\frac{149}{1056}\right)\) | \(e\left(\frac{515}{1056}\right)\) | \(e\left(\frac{593}{1056}\right)\) | \(e\left(\frac{181}{264}\right)\) |
| \(\chi_{790142}(63785,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{491}{1056}\right)\) | \(e\left(\frac{37}{264}\right)\) | \(-1\) | \(e\left(\frac{135}{352}\right)\) | \(e\left(\frac{249}{352}\right)\) | \(e\left(\frac{227}{1056}\right)\) | \(e\left(\frac{5}{1056}\right)\) | \(e\left(\frac{1031}{1056}\right)\) | \(e\left(\frac{235}{264}\right)\) |
| \(\chi_{790142}(65715,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{587}{1056}\right)\) | \(e\left(\frac{205}{264}\right)\) | \(-1\) | \(e\left(\frac{327}{352}\right)\) | \(e\left(\frac{345}{352}\right)\) | \(e\left(\frac{323}{1056}\right)\) | \(e\left(\frac{677}{1056}\right)\) | \(e\left(\frac{839}{1056}\right)\) | \(e\left(\frac{139}{264}\right)\) |
| \(\chi_{790142}(66915,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{149}{1056}\right)\) | \(e\left(\frac{115}{264}\right)\) | \(-1\) | \(e\left(\frac{89}{352}\right)\) | \(e\left(\frac{39}{352}\right)\) | \(e\left(\frac{413}{1056}\right)\) | \(e\left(\frac{251}{1056}\right)\) | \(e\left(\frac{857}{1056}\right)\) | \(e\left(\frac{181}{264}\right)\) |
| \(\chi_{790142}(69177,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{1031}{1056}\right)\) | \(e\left(\frac{25}{264}\right)\) | \(-1\) | \(e\left(\frac{115}{352}\right)\) | \(e\left(\frac{173}{352}\right)\) | \(e\left(\frac{767}{1056}\right)\) | \(e\left(\frac{617}{1056}\right)\) | \(e\left(\frac{83}{1056}\right)\) | \(e\left(\frac{223}{264}\right)\) |
| \(\chi_{790142}(71879,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{455}{1056}\right)\) | \(e\left(\frac{73}{264}\right)\) | \(-1\) | \(e\left(\frac{19}{352}\right)\) | \(e\left(\frac{301}{352}\right)\) | \(e\left(\frac{191}{1056}\right)\) | \(e\left(\frac{809}{1056}\right)\) | \(e\left(\frac{179}{1056}\right)\) | \(e\left(\frac{7}{264}\right)\) |
| \(\chi_{790142}(72853,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{713}{1056}\right)\) | \(e\left(\frac{79}{264}\right)\) | \(-1\) | \(e\left(\frac{29}{352}\right)\) | \(e\left(\frac{163}{352}\right)\) | \(e\left(\frac{977}{1056}\right)\) | \(e\left(\frac{1031}{1056}\right)\) | \(e\left(\frac{125}{1056}\right)\) | \(e\left(\frac{145}{264}\right)\) |
| \(\chi_{790142}(73165,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{607}{1056}\right)\) | \(e\left(\frac{185}{264}\right)\) | \(-1\) | \(e\left(\frac{235}{352}\right)\) | \(e\left(\frac{277}{352}\right)\) | \(e\left(\frac{343}{1056}\right)\) | \(e\left(\frac{817}{1056}\right)\) | \(e\left(\frac{139}{1056}\right)\) | \(e\left(\frac{119}{264}\right)\) |