from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(966))
M = H._module
chi = DirichletCharacter(H, M([483,828,700]))
chi.galois_orbit()
[g,chi] = znchar(Mod(49,40310))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(20155\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(966\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 20155.fq | 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 966 polynomial (not computed) |
First 31 of 264 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{40310}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{479}{966}\right)\) | \(e\left(\frac{17}{966}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{242}{483}\right)\) | \(e\left(\frac{295}{966}\right)\) | \(e\left(\frac{5}{138}\right)\) | \(e\left(\frac{443}{483}\right)\) | \(e\left(\frac{248}{483}\right)\) | \(e\left(\frac{67}{322}\right)\) | \(e\left(\frac{157}{322}\right)\) |
| \(\chi_{40310}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{925}{966}\right)\) | \(e\left(\frac{295}{966}\right)\) | \(e\left(\frac{442}{483}\right)\) | \(e\left(\frac{307}{483}\right)\) | \(e\left(\frac{5}{966}\right)\) | \(e\left(\frac{103}{138}\right)\) | \(e\left(\frac{73}{483}\right)\) | \(e\left(\frac{127}{483}\right)\) | \(e\left(\frac{83}{322}\right)\) | \(e\left(\frac{281}{322}\right)\) |
| \(\chi_{40310}(719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{966}\right)\) | \(e\left(\frac{13}{966}\right)\) | \(e\left(\frac{139}{483}\right)\) | \(e\left(\frac{43}{483}\right)\) | \(e\left(\frac{737}{966}\right)\) | \(e\left(\frac{85}{138}\right)\) | \(e\left(\frac{424}{483}\right)\) | \(e\left(\frac{76}{483}\right)\) | \(e\left(\frac{127}{322}\right)\) | \(e\left(\frac{139}{322}\right)\) |
| \(\chi_{40310}(749,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{743}{966}\right)\) | \(e\left(\frac{827}{966}\right)\) | \(e\left(\frac{260}{483}\right)\) | \(e\left(\frac{209}{483}\right)\) | \(e\left(\frac{145}{966}\right)\) | \(e\left(\frac{89}{138}\right)\) | \(e\left(\frac{185}{483}\right)\) | \(e\left(\frac{302}{483}\right)\) | \(e\left(\frac{153}{322}\right)\) | \(e\left(\frac{99}{322}\right)\) |
| \(\chi_{40310}(819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{845}{966}\right)\) | \(e\left(\frac{635}{966}\right)\) | \(e\left(\frac{362}{483}\right)\) | \(e\left(\frac{317}{483}\right)\) | \(e\left(\frac{109}{966}\right)\) | \(e\left(\frac{65}{138}\right)\) | \(e\left(\frac{239}{483}\right)\) | \(e\left(\frac{257}{483}\right)\) | \(e\left(\frac{135}{322}\right)\) | \(e\left(\frac{201}{322}\right)\) |
| \(\chi_{40310}(1039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{953}{966}\right)\) | \(e\left(\frac{659}{966}\right)\) | \(e\left(\frac{470}{483}\right)\) | \(e\left(\frac{62}{483}\right)\) | \(e\left(\frac{355}{966}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{353}{483}\right)\) | \(e\left(\frac{323}{483}\right)\) | \(e\left(\frac{97}{322}\right)\) | \(e\left(\frac{309}{322}\right)\) |
| \(\chi_{40310}(1109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{313}{966}\right)\) | \(e\left(\frac{481}{966}\right)\) | \(e\left(\frac{313}{483}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{221}{966}\right)\) | \(e\left(\frac{109}{138}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{397}{483}\right)\) | \(e\left(\frac{191}{322}\right)\) | \(e\left(\frac{313}{322}\right)\) |
| \(\chi_{40310}(1329,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{407}{966}\right)\) | \(e\left(\frac{323}{966}\right)\) | \(e\left(\frac{407}{483}\right)\) | \(e\left(\frac{251}{483}\right)\) | \(e\left(\frac{775}{966}\right)\) | \(e\left(\frac{95}{138}\right)\) | \(e\left(\frac{206}{483}\right)\) | \(e\left(\frac{365}{483}\right)\) | \(e\left(\frac{307}{322}\right)\) | \(e\left(\frac{85}{322}\right)\) |
| \(\chi_{40310}(1399,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{966}\right)\) | \(e\left(\frac{341}{966}\right)\) | \(e\left(\frac{5}{483}\right)\) | \(e\left(\frac{422}{483}\right)\) | \(e\left(\frac{235}{966}\right)\) | \(e\left(\frac{11}{138}\right)\) | \(e\left(\frac{50}{483}\right)\) | \(e\left(\frac{173}{483}\right)\) | \(e\left(\frac{37}{322}\right)\) | \(e\left(\frac{5}{322}\right)\) |
| \(\chi_{40310}(1649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{947}{966}\right)\) | \(e\left(\frac{443}{966}\right)\) | \(e\left(\frac{464}{483}\right)\) | \(e\left(\frac{425}{483}\right)\) | \(e\left(\frac{73}{966}\right)\) | \(e\left(\frac{41}{138}\right)\) | \(e\left(\frac{293}{483}\right)\) | \(e\left(\frac{212}{483}\right)\) | \(e\left(\frac{117}{322}\right)\) | \(e\left(\frac{303}{322}\right)\) |
| \(\chi_{40310}(1789,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{913}{966}\right)\) | \(e\left(\frac{829}{966}\right)\) | \(e\left(\frac{430}{483}\right)\) | \(e\left(\frac{67}{483}\right)\) | \(e\left(\frac{407}{966}\right)\) | \(e\left(\frac{49}{138}\right)\) | \(e\left(\frac{436}{483}\right)\) | \(e\left(\frac{388}{483}\right)\) | \(e\left(\frac{123}{322}\right)\) | \(e\left(\frac{269}{322}\right)\) |
| \(\chi_{40310}(1959,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{966}\right)\) | \(e\left(\frac{389}{966}\right)\) | \(e\left(\frac{221}{483}\right)\) | \(e\left(\frac{395}{483}\right)\) | \(e\left(\frac{727}{966}\right)\) | \(e\left(\frac{17}{138}\right)\) | \(e\left(\frac{278}{483}\right)\) | \(e\left(\frac{305}{483}\right)\) | \(e\left(\frac{283}{322}\right)\) | \(e\left(\frac{221}{322}\right)\) |
| \(\chi_{40310}(2229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{877}{966}\right)\) | \(e\left(\frac{499}{966}\right)\) | \(e\left(\frac{394}{483}\right)\) | \(e\left(\frac{313}{483}\right)\) | \(e\left(\frac{647}{966}\right)\) | \(e\left(\frac{25}{138}\right)\) | \(e\left(\frac{76}{483}\right)\) | \(e\left(\frac{205}{483}\right)\) | \(e\left(\frac{243}{322}\right)\) | \(e\left(\frac{233}{322}\right)\) |
| \(\chi_{40310}(2249,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{305}{966}\right)\) | \(e\left(\frac{515}{966}\right)\) | \(e\left(\frac{305}{483}\right)\) | \(e\left(\frac{143}{483}\right)\) | \(e\left(\frac{811}{966}\right)\) | \(e\left(\frac{119}{138}\right)\) | \(e\left(\frac{152}{483}\right)\) | \(e\left(\frac{410}{483}\right)\) | \(e\left(\frac{3}{322}\right)\) | \(e\left(\frac{305}{322}\right)\) |
| \(\chi_{40310}(2539,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{949}{966}\right)\) | \(e\left(\frac{193}{966}\right)\) | \(e\left(\frac{466}{483}\right)\) | \(e\left(\frac{304}{483}\right)\) | \(e\left(\frac{167}{966}\right)\) | \(e\left(\frac{73}{138}\right)\) | \(e\left(\frac{313}{483}\right)\) | \(e\left(\frac{88}{483}\right)\) | \(e\left(\frac{3}{322}\right)\) | \(e\left(\frac{305}{322}\right)\) |
| \(\chi_{40310}(2809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{275}{966}\right)\) | \(e\left(\frac{401}{966}\right)\) | \(e\left(\frac{275}{483}\right)\) | \(e\left(\frac{26}{483}\right)\) | \(e\left(\frac{367}{966}\right)\) | \(e\left(\frac{53}{138}\right)\) | \(e\left(\frac{335}{483}\right)\) | \(e\left(\frac{338}{483}\right)\) | \(e\left(\frac{103}{322}\right)\) | \(e\left(\frac{275}{322}\right)\) |
| \(\chi_{40310}(2829,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{893}{966}\right)\) | \(e\left(\frac{431}{966}\right)\) | \(e\left(\frac{410}{483}\right)\) | \(e\left(\frac{311}{483}\right)\) | \(e\left(\frac{433}{966}\right)\) | \(e\left(\frac{5}{138}\right)\) | \(e\left(\frac{236}{483}\right)\) | \(e\left(\frac{179}{483}\right)\) | \(e\left(\frac{297}{322}\right)\) | \(e\left(\frac{249}{322}\right)\) |
| \(\chi_{40310}(2849,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{817}{966}\right)\) | \(e\left(\frac{271}{966}\right)\) | \(e\left(\frac{334}{483}\right)\) | \(e\left(\frac{79}{483}\right)\) | \(e\left(\frac{725}{966}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{442}{483}\right)\) | \(e\left(\frac{61}{483}\right)\) | \(e\left(\frac{121}{322}\right)\) | \(e\left(\frac{173}{322}\right)\) |
| \(\chi_{40310}(2949,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{787}{966}\right)\) | \(e\left(\frac{157}{966}\right)\) | \(e\left(\frac{304}{483}\right)\) | \(e\left(\frac{445}{483}\right)\) | \(e\left(\frac{281}{966}\right)\) | \(e\left(\frac{103}{138}\right)\) | \(e\left(\frac{142}{483}\right)\) | \(e\left(\frac{472}{483}\right)\) | \(e\left(\frac{221}{322}\right)\) | \(e\left(\frac{143}{322}\right)\) |
| \(\chi_{40310}(3039,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{671}{966}\right)\) | \(e\left(\frac{167}{966}\right)\) | \(e\left(\frac{188}{483}\right)\) | \(e\left(\frac{218}{483}\right)\) | \(e\left(\frac{625}{966}\right)\) | \(e\left(\frac{41}{138}\right)\) | \(e\left(\frac{431}{483}\right)\) | \(e\left(\frac{419}{483}\right)\) | \(e\left(\frac{71}{322}\right)\) | \(e\left(\frac{27}{322}\right)\) |
| \(\chi_{40310}(3069,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{491}{966}\right)\) | \(e\left(\frac{449}{966}\right)\) | \(e\left(\frac{8}{483}\right)\) | \(e\left(\frac{482}{483}\right)\) | \(e\left(\frac{859}{966}\right)\) | \(e\left(\frac{59}{138}\right)\) | \(e\left(\frac{80}{483}\right)\) | \(e\left(\frac{470}{483}\right)\) | \(e\left(\frac{27}{322}\right)\) | \(e\left(\frac{169}{322}\right)\) |
| \(\chi_{40310}(3099,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{835}{966}\right)\) | \(e\left(\frac{919}{966}\right)\) | \(e\left(\frac{352}{483}\right)\) | \(e\left(\frac{439}{483}\right)\) | \(e\left(\frac{605}{966}\right)\) | \(e\left(\frac{43}{138}\right)\) | \(e\left(\frac{139}{483}\right)\) | \(e\left(\frac{394}{483}\right)\) | \(e\left(\frac{61}{322}\right)\) | \(e\left(\frac{191}{322}\right)\) |
| \(\chi_{40310}(3139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{355}{966}\right)\) | \(e\left(\frac{61}{966}\right)\) | \(e\left(\frac{355}{483}\right)\) | \(e\left(\frac{16}{483}\right)\) | \(e\left(\frac{263}{966}\right)\) | \(e\left(\frac{91}{138}\right)\) | \(e\left(\frac{169}{483}\right)\) | \(e\left(\frac{208}{483}\right)\) | \(e\left(\frac{51}{322}\right)\) | \(e\left(\frac{33}{322}\right)\) |
| \(\chi_{40310}(3529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{605}{966}\right)\) | \(e\left(\frac{689}{966}\right)\) | \(e\left(\frac{122}{483}\right)\) | \(e\left(\frac{347}{483}\right)\) | \(e\left(\frac{421}{966}\right)\) | \(e\left(\frac{89}{138}\right)\) | \(e\left(\frac{254}{483}\right)\) | \(e\left(\frac{164}{483}\right)\) | \(e\left(\frac{291}{322}\right)\) | \(e\left(\frac{283}{322}\right)\) |
| \(\chi_{40310}(3619,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{601}{966}\right)\) | \(e\left(\frac{223}{966}\right)\) | \(e\left(\frac{118}{483}\right)\) | \(e\left(\frac{106}{483}\right)\) | \(e\left(\frac{233}{966}\right)\) | \(e\left(\frac{25}{138}\right)\) | \(e\left(\frac{214}{483}\right)\) | \(e\left(\frac{412}{483}\right)\) | \(e\left(\frac{197}{322}\right)\) | \(e\left(\frac{279}{322}\right)\) |
| \(\chi_{40310}(3649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{323}{966}\right)\) | \(e\left(\frac{197}{966}\right)\) | \(e\left(\frac{323}{483}\right)\) | \(e\left(\frac{20}{483}\right)\) | \(e\left(\frac{691}{966}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{332}{483}\right)\) | \(e\left(\frac{260}{483}\right)\) | \(e\left(\frac{265}{322}\right)\) | \(e\left(\frac{1}{322}\right)\) |
| \(\chi_{40310}(3819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{815}{966}\right)\) | \(e\left(\frac{521}{966}\right)\) | \(e\left(\frac{332}{483}\right)\) | \(e\left(\frac{200}{483}\right)\) | \(e\left(\frac{631}{966}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{422}{483}\right)\) | \(e\left(\frac{185}{483}\right)\) | \(e\left(\frac{235}{322}\right)\) | \(e\left(\frac{171}{322}\right)\) |
| \(\chi_{40310}(3939,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{966}\right)\) | \(e\left(\frac{421}{966}\right)\) | \(e\left(\frac{43}{483}\right)\) | \(e\left(\frac{55}{483}\right)\) | \(e\left(\frac{89}{966}\right)\) | \(e\left(\frac{67}{138}\right)\) | \(e\left(\frac{430}{483}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{125}{322}\right)\) | \(e\left(\frac{43}{322}\right)\) |
| \(\chi_{40310}(4009,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{966}\right)\) | \(e\left(\frac{523}{966}\right)\) | \(e\left(\frac{19}{483}\right)\) | \(e\left(\frac{58}{483}\right)\) | \(e\left(\frac{893}{966}\right)\) | \(e\left(\frac{97}{138}\right)\) | \(e\left(\frac{190}{483}\right)\) | \(e\left(\frac{271}{483}\right)\) | \(e\left(\frac{205}{322}\right)\) | \(e\left(\frac{19}{322}\right)\) |
| \(\chi_{40310}(4109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{966}\right)\) | \(e\left(\frac{185}{966}\right)\) | \(e\left(\frac{269}{483}\right)\) | \(e\left(\frac{389}{483}\right)\) | \(e\left(\frac{85}{966}\right)\) | \(e\left(\frac{95}{138}\right)\) | \(e\left(\frac{275}{483}\right)\) | \(e\left(\frac{227}{483}\right)\) | \(e\left(\frac{123}{322}\right)\) | \(e\left(\frac{269}{322}\right)\) |
| \(\chi_{40310}(4199,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{965}{966}\right)\) | \(e\left(\frac{125}{966}\right)\) | \(e\left(\frac{482}{483}\right)\) | \(e\left(\frac{302}{483}\right)\) | \(e\left(\frac{919}{966}\right)\) | \(e\left(\frac{53}{138}\right)\) | \(e\left(\frac{473}{483}\right)\) | \(e\left(\frac{62}{483}\right)\) | \(e\left(\frac{57}{322}\right)\) | \(e\left(\frac{321}{322}\right)\) |