from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, base_ring=CyclotomicField(1932))
M = H._module
chi = DirichletCharacter(H, M([897,1183]))
chi.galois_orbit()
[g,chi] = znchar(Mod(14,8033))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1932\) | 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: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
First 31 of 528 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8033}(14,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{322}\right)\) | \(e\left(\frac{845}{1932}\right)\) | \(e\left(\frac{153}{161}\right)\) | \(e\left(\frac{1597}{1932}\right)\) | \(e\left(\frac{1763}{1932}\right)\) | \(e\left(\frac{41}{966}\right)\) | \(e\left(\frac{137}{322}\right)\) | \(e\left(\frac{845}{966}\right)\) | \(e\left(\frac{583}{1932}\right)\) | \(e\left(\frac{863}{966}\right)\) |
| \(\chi_{8033}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{305}{322}\right)\) | \(e\left(\frac{407}{1932}\right)\) | \(e\left(\frac{144}{161}\right)\) | \(e\left(\frac{1039}{1932}\right)\) | \(e\left(\frac{305}{1932}\right)\) | \(e\left(\frac{389}{966}\right)\) | \(e\left(\frac{271}{322}\right)\) | \(e\left(\frac{407}{966}\right)\) | \(e\left(\frac{937}{1932}\right)\) | \(e\left(\frac{83}{966}\right)\) |
| \(\chi_{8033}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{311}{322}\right)\) | \(e\left(\frac{1021}{1932}\right)\) | \(e\left(\frac{150}{161}\right)\) | \(e\left(\frac{1733}{1932}\right)\) | \(e\left(\frac{955}{1932}\right)\) | \(e\left(\frac{157}{966}\right)\) | \(e\left(\frac{289}{322}\right)\) | \(e\left(\frac{55}{966}\right)\) | \(e\left(\frac{1667}{1932}\right)\) | \(e\left(\frac{925}{966}\right)\) |
| \(\chi_{8033}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{322}\right)\) | \(e\left(\frac{107}{1932}\right)\) | \(e\left(\frac{43}{161}\right)\) | \(e\left(\frac{895}{1932}\right)\) | \(e\left(\frac{365}{1932}\right)\) | \(e\left(\frac{323}{966}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{107}{966}\right)\) | \(e\left(\frac{1153}{1932}\right)\) | \(e\left(\frac{131}{966}\right)\) |
| \(\chi_{8033}(72,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{195}{322}\right)\) | \(e\left(\frac{1601}{1932}\right)\) | \(e\left(\frac{34}{161}\right)\) | \(e\left(\frac{337}{1932}\right)\) | \(e\left(\frac{839}{1932}\right)\) | \(e\left(\frac{671}{966}\right)\) | \(e\left(\frac{263}{322}\right)\) | \(e\left(\frac{635}{966}\right)\) | \(e\left(\frac{1507}{1932}\right)\) | \(e\left(\frac{317}{966}\right)\) |
| \(\chi_{8033}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{247}{322}\right)\) | \(e\left(\frac{697}{1932}\right)\) | \(e\left(\frac{86}{161}\right)\) | \(e\left(\frac{341}{1932}\right)\) | \(e\left(\frac{247}{1932}\right)\) | \(e\left(\frac{163}{966}\right)\) | \(e\left(\frac{97}{322}\right)\) | \(e\left(\frac{697}{966}\right)\) | \(e\left(\frac{1823}{1932}\right)\) | \(e\left(\frac{745}{966}\right)\) |
| \(\chi_{8033}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{279}{322}\right)\) | \(e\left(\frac{1181}{1932}\right)\) | \(e\left(\frac{118}{161}\right)\) | \(e\left(\frac{1681}{1932}\right)\) | \(e\left(\frac{923}{1932}\right)\) | \(e\left(\frac{965}{966}\right)\) | \(e\left(\frac{193}{322}\right)\) | \(e\left(\frac{215}{966}\right)\) | \(e\left(\frac{1423}{1932}\right)\) | \(e\left(\frac{191}{966}\right)\) |
| \(\chi_{8033}(105,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{249}{322}\right)\) | \(e\left(\frac{1331}{1932}\right)\) | \(e\left(\frac{88}{161}\right)\) | \(e\left(\frac{787}{1932}\right)\) | \(e\left(\frac{893}{1932}\right)\) | \(e\left(\frac{515}{966}\right)\) | \(e\left(\frac{103}{322}\right)\) | \(e\left(\frac{365}{966}\right)\) | \(e\left(\frac{349}{1932}\right)\) | \(e\left(\frac{167}{966}\right)\) |
| \(\chi_{8033}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{322}\right)\) | \(e\left(\frac{1003}{1932}\right)\) | \(e\left(\frac{57}{161}\right)\) | \(e\left(\frac{1763}{1932}\right)\) | \(e\left(\frac{1345}{1932}\right)\) | \(e\left(\frac{211}{966}\right)\) | \(e\left(\frac{171}{322}\right)\) | \(e\left(\frac{37}{966}\right)\) | \(e\left(\frac{173}{1932}\right)\) | \(e\left(\frac{271}{966}\right)\) |
| \(\chi_{8033}(119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{243}{322}\right)\) | \(e\left(\frac{73}{1932}\right)\) | \(e\left(\frac{82}{161}\right)\) | \(e\left(\frac{737}{1932}\right)\) | \(e\left(\frac{1531}{1932}\right)\) | \(e\left(\frac{103}{966}\right)\) | \(e\left(\frac{85}{322}\right)\) | \(e\left(\frac{73}{966}\right)\) | \(e\left(\frac{263}{1932}\right)\) | \(e\left(\frac{613}{966}\right)\) |
| \(\chi_{8033}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{322}\right)\) | \(e\left(\frac{1835}{1932}\right)\) | \(e\left(\frac{116}{161}\right)\) | \(e\left(\frac{1879}{1932}\right)\) | \(e\left(\frac{1565}{1932}\right)\) | \(e\left(\frac{935}{966}\right)\) | \(e\left(\frac{187}{322}\right)\) | \(e\left(\frac{869}{966}\right)\) | \(e\left(\frac{1609}{1932}\right)\) | \(e\left(\frac{125}{966}\right)\) |
| \(\chi_{8033}(135,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{322}\right)\) | \(e\left(\frac{893}{1932}\right)\) | \(e\left(\frac{79}{161}\right)\) | \(e\left(\frac{229}{1932}\right)\) | \(e\left(\frac{1367}{1932}\right)\) | \(e\left(\frac{863}{966}\right)\) | \(e\left(\frac{237}{322}\right)\) | \(e\left(\frac{893}{966}\right)\) | \(e\left(\frac{703}{1932}\right)\) | \(e\left(\frac{353}{966}\right)\) |
| \(\chi_{8033}(142,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{322}\right)\) | \(e\left(\frac{479}{1932}\right)\) | \(e\left(\frac{33}{161}\right)\) | \(e\left(\frac{919}{1932}\right)\) | \(e\left(\frac{677}{1932}\right)\) | \(e\left(\frac{173}{966}\right)\) | \(e\left(\frac{99}{322}\right)\) | \(e\left(\frac{479}{966}\right)\) | \(e\left(\frac{1117}{1932}\right)\) | \(e\left(\frac{767}{966}\right)\) |
| \(\chi_{8033}(153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{322}\right)\) | \(e\left(\frac{1567}{1932}\right)\) | \(e\left(\frac{73}{161}\right)\) | \(e\left(\frac{179}{1932}\right)\) | \(e\left(\frac{73}{1932}\right)\) | \(e\left(\frac{451}{966}\right)\) | \(e\left(\frac{219}{322}\right)\) | \(e\left(\frac{601}{966}\right)\) | \(e\left(\frac{617}{1932}\right)\) | \(e\left(\frac{799}{966}\right)\) |
| \(\chi_{8033}(166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{322}\right)\) | \(e\left(\frac{685}{1932}\right)\) | \(e\left(\frac{24}{161}\right)\) | \(e\left(\frac{1649}{1932}\right)\) | \(e\left(\frac{1795}{1932}\right)\) | \(e\left(\frac{199}{966}\right)\) | \(e\left(\frac{233}{322}\right)\) | \(e\left(\frac{685}{966}\right)\) | \(e\left(\frac{827}{1932}\right)\) | \(e\left(\frac{631}{966}\right)\) |
| \(\chi_{8033}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{201}{322}\right)\) | \(e\left(\frac{283}{1932}\right)\) | \(e\left(\frac{40}{161}\right)\) | \(e\left(\frac{1031}{1932}\right)\) | \(e\left(\frac{1489}{1932}\right)\) | \(e\left(\frac{439}{966}\right)\) | \(e\left(\frac{281}{322}\right)\) | \(e\left(\frac{283}{966}\right)\) | \(e\left(\frac{305}{1932}\right)\) | \(e\left(\frac{193}{966}\right)\) |
| \(\chi_{8033}(224,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{1301}{1932}\right)\) | \(e\left(\frac{94}{161}\right)\) | \(e\left(\frac{193}{1932}\right)\) | \(e\left(\frac{899}{1932}\right)\) | \(e\left(\frac{605}{966}\right)\) | \(e\left(\frac{121}{322}\right)\) | \(e\left(\frac{335}{966}\right)\) | \(e\left(\frac{1723}{1932}\right)\) | \(e\left(\frac{365}{966}\right)\) |
| \(\chi_{8033}(234,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{267}{322}\right)\) | \(e\left(\frac{1241}{1932}\right)\) | \(e\left(\frac{106}{161}\right)\) | \(e\left(\frac{937}{1932}\right)\) | \(e\left(\frac{911}{1932}\right)\) | \(e\left(\frac{785}{966}\right)\) | \(e\left(\frac{157}{322}\right)\) | \(e\left(\frac{275}{966}\right)\) | \(e\left(\frac{607}{1932}\right)\) | \(e\left(\frac{761}{966}\right)\) |
| \(\chi_{8033}(246,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{321}{322}\right)\) | \(e\left(\frac{649}{1932}\right)\) | \(e\left(\frac{160}{161}\right)\) | \(e\left(\frac{1709}{1932}\right)\) | \(e\left(\frac{643}{1932}\right)\) | \(e\left(\frac{307}{966}\right)\) | \(e\left(\frac{319}{322}\right)\) | \(e\left(\frac{649}{966}\right)\) | \(e\left(\frac{1703}{1932}\right)\) | \(e\left(\frac{289}{966}\right)\) |
| \(\chi_{8033}(282,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{45}{322}\right)\) | \(e\left(\frac{1385}{1932}\right)\) | \(e\left(\frac{45}{161}\right)\) | \(e\left(\frac{697}{1932}\right)\) | \(e\left(\frac{1655}{1932}\right)\) | \(e\left(\frac{353}{966}\right)\) | \(e\left(\frac{135}{322}\right)\) | \(e\left(\frac{419}{966}\right)\) | \(e\left(\frac{967}{1932}\right)\) | \(e\left(\frac{197}{966}\right)\) |
| \(\chi_{8033}(288,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{322}\right)\) | \(e\left(\frac{863}{1932}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{1567}{1932}\right)\) | \(e\left(\frac{1373}{1932}\right)\) | \(e\left(\frac{953}{966}\right)\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{863}{966}\right)\) | \(e\left(\frac{145}{1932}\right)\) | \(e\left(\frac{551}{966}\right)\) |
| \(\chi_{8033}(301,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{291}{322}\right)\) | \(e\left(\frac{1765}{1932}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{1781}{1932}\right)\) | \(e\left(\frac{1579}{1932}\right)\) | \(e\left(\frac{823}{966}\right)\) | \(e\left(\frac{229}{322}\right)\) | \(e\left(\frac{799}{966}\right)\) | \(e\left(\frac{1595}{1932}\right)\) | \(e\left(\frac{265}{966}\right)\) |
| \(\chi_{8033}(308,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{322}\right)\) | \(e\left(\frac{1891}{1932}\right)\) | \(e\left(\frac{137}{161}\right)\) | \(e\left(\frac{1571}{1932}\right)\) | \(e\left(\frac{781}{1932}\right)\) | \(e\left(\frac{445}{966}\right)\) | \(e\left(\frac{89}{322}\right)\) | \(e\left(\frac{925}{966}\right)\) | \(e\left(\frac{461}{1932}\right)\) | \(e\left(\frac{13}{966}\right)\) |
| \(\chi_{8033}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{322}\right)\) | \(e\left(\frac{401}{1932}\right)\) | \(e\left(\frac{113}{161}\right)\) | \(e\left(\frac{1693}{1932}\right)\) | \(e\left(\frac{1079}{1932}\right)\) | \(e\left(\frac{407}{966}\right)\) | \(e\left(\frac{17}{322}\right)\) | \(e\left(\frac{401}{966}\right)\) | \(e\left(\frac{439}{1932}\right)\) | \(e\left(\frac{509}{966}\right)\) |
| \(\chi_{8033}(322,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{313}{322}\right)\) | \(e\left(\frac{1333}{1932}\right)\) | \(e\left(\frac{152}{161}\right)\) | \(e\left(\frac{569}{1932}\right)\) | \(e\left(\frac{1279}{1932}\right)\) | \(e\left(\frac{187}{966}\right)\) | \(e\left(\frac{295}{322}\right)\) | \(e\left(\frac{367}{966}\right)\) | \(e\left(\frac{515}{1932}\right)\) | \(e\left(\frac{25}{966}\right)\) |
| \(\chi_{8033}(375,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{322}\right)\) | \(e\left(\frac{1507}{1932}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{923}{1932}\right)\) | \(e\left(\frac{85}{1932}\right)\) | \(e\left(\frac{631}{966}\right)\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{541}{966}\right)\) | \(e\left(\frac{1433}{1932}\right)\) | \(e\left(\frac{229}{966}\right)\) |
| \(\chi_{8033}(387,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{121}{322}\right)\) | \(e\left(\frac{1327}{1932}\right)\) | \(e\left(\frac{121}{161}\right)\) | \(e\left(\frac{1223}{1932}\right)\) | \(e\left(\frac{121}{1932}\right)\) | \(e\left(\frac{205}{966}\right)\) | \(e\left(\frac{41}{322}\right)\) | \(e\left(\frac{361}{966}\right)\) | \(e\left(\frac{17}{1932}\right)\) | \(e\left(\frac{451}{966}\right)\) |
| \(\chi_{8033}(396,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{322}\right)\) | \(e\left(\frac{1453}{1932}\right)\) | \(e\left(\frac{128}{161}\right)\) | \(e\left(\frac{1013}{1932}\right)\) | \(e\left(\frac{1255}{1932}\right)\) | \(e\left(\frac{793}{966}\right)\) | \(e\left(\frac{223}{322}\right)\) | \(e\left(\frac{487}{966}\right)\) | \(e\left(\frac{815}{1932}\right)\) | \(e\left(\frac{199}{966}\right)\) |
| \(\chi_{8033}(404,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{322}\right)\) | \(e\left(\frac{443}{1932}\right)\) | \(e\left(\frac{8}{161}\right)\) | \(e\left(\frac{979}{1932}\right)\) | \(e\left(\frac{1457}{1932}\right)\) | \(e\left(\frac{281}{966}\right)\) | \(e\left(\frac{185}{322}\right)\) | \(e\left(\frac{443}{966}\right)\) | \(e\left(\frac{61}{1932}\right)\) | \(e\left(\frac{425}{966}\right)\) |
| \(\chi_{8033}(414,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{322}\right)\) | \(e\left(\frac{895}{1932}\right)\) | \(e\left(\frac{143}{161}\right)\) | \(e\left(\frac{11}{1932}\right)\) | \(e\left(\frac{1753}{1932}\right)\) | \(e\left(\frac{535}{966}\right)\) | \(e\left(\frac{107}{322}\right)\) | \(e\left(\frac{895}{966}\right)\) | \(e\left(\frac{869}{1932}\right)\) | \(e\left(\frac{211}{966}\right)\) |
| \(\chi_{8033}(417,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{322}\right)\) | \(e\left(\frac{757}{1932}\right)\) | \(e\left(\frac{74}{161}\right)\) | \(e\left(\frac{1529}{1932}\right)\) | \(e\left(\frac{235}{1932}\right)\) | \(e\left(\frac{949}{966}\right)\) | \(e\left(\frac{61}{322}\right)\) | \(e\left(\frac{757}{966}\right)\) | \(e\left(\frac{1007}{1932}\right)\) | \(e\left(\frac{349}{966}\right)\) |