from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35937, base_ring=CyclotomicField(10890))
M = H._module
chi = DirichletCharacter(H, M([605,9]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,35937))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(35937\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(10890\) | 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: | $\Q(\zeta_{5445})$ |
| Fixed field: | Number field defined by a degree 10890 polynomial (not computed) |
First 31 of 2640 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{35937}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{5445}\right)\) | \(e\left(\frac{614}{5445}\right)\) | \(e\left(\frac{4681}{10890}\right)\) | \(e\left(\frac{3803}{10890}\right)\) | \(e\left(\frac{307}{1815}\right)\) | \(e\left(\frac{353}{726}\right)\) | \(e\left(\frac{4759}{10890}\right)\) | \(e\left(\frac{4417}{10890}\right)\) | \(e\left(\frac{1228}{5445}\right)\) | \(e\left(\frac{1751}{1815}\right)\) |
| \(\chi_{35937}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1864}{5445}\right)\) | \(e\left(\frac{3728}{5445}\right)\) | \(e\left(\frac{487}{10890}\right)\) | \(e\left(\frac{6791}{10890}\right)\) | \(e\left(\frac{49}{1815}\right)\) | \(e\left(\frac{281}{726}\right)\) | \(e\left(\frac{9403}{10890}\right)\) | \(e\left(\frac{10519}{10890}\right)\) | \(e\left(\frac{2011}{5445}\right)\) | \(e\left(\frac{782}{1815}\right)\) |
| \(\chi_{35937}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1781}{5445}\right)\) | \(e\left(\frac{3562}{5445}\right)\) | \(e\left(\frac{1403}{10890}\right)\) | \(e\left(\frac{2659}{10890}\right)\) | \(e\left(\frac{1781}{1815}\right)\) | \(e\left(\frac{331}{726}\right)\) | \(e\left(\frac{1217}{10890}\right)\) | \(e\left(\frac{6221}{10890}\right)\) | \(e\left(\frac{1679}{5445}\right)\) | \(e\left(\frac{13}{1815}\right)\) |
| \(\chi_{35937}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4988}{5445}\right)\) | \(e\left(\frac{4531}{5445}\right)\) | \(e\left(\frac{1829}{10890}\right)\) | \(e\left(\frac{6967}{10890}\right)\) | \(e\left(\frac{1358}{1815}\right)\) | \(e\left(\frac{61}{726}\right)\) | \(e\left(\frac{1571}{10890}\right)\) | \(e\left(\frac{6053}{10890}\right)\) | \(e\left(\frac{3617}{5445}\right)\) | \(e\left(\frac{1189}{1815}\right)\) |
| \(\chi_{35937}(68,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{422}{5445}\right)\) | \(e\left(\frac{844}{5445}\right)\) | \(e\left(\frac{2231}{10890}\right)\) | \(e\left(\frac{2443}{10890}\right)\) | \(e\left(\frac{422}{1815}\right)\) | \(e\left(\frac{205}{726}\right)\) | \(e\left(\frac{3899}{10890}\right)\) | \(e\left(\frac{3287}{10890}\right)\) | \(e\left(\frac{1688}{5445}\right)\) | \(e\left(\frac{586}{1815}\right)\) |
| \(\chi_{35937}(74,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1816}{5445}\right)\) | \(e\left(\frac{3632}{5445}\right)\) | \(e\left(\frac{8233}{10890}\right)\) | \(e\left(\frac{4139}{10890}\right)\) | \(e\left(\frac{1}{1815}\right)\) | \(e\left(\frac{65}{726}\right)\) | \(e\left(\frac{6637}{10890}\right)\) | \(e\left(\frac{7771}{10890}\right)\) | \(e\left(\frac{1819}{5445}\right)\) | \(e\left(\frac{53}{1815}\right)\) |
| \(\chi_{35937}(83,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{433}{5445}\right)\) | \(e\left(\frac{866}{5445}\right)\) | \(e\left(\frac{7489}{10890}\right)\) | \(e\left(\frac{2597}{10890}\right)\) | \(e\left(\frac{433}{1815}\right)\) | \(e\left(\frac{557}{726}\right)\) | \(e\left(\frac{2491}{10890}\right)\) | \(e\left(\frac{3463}{10890}\right)\) | \(e\left(\frac{1732}{5445}\right)\) | \(e\left(\frac{1169}{1815}\right)\) |
| \(\chi_{35937}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5354}{5445}\right)\) | \(e\left(\frac{5263}{5445}\right)\) | \(e\left(\frac{9467}{10890}\right)\) | \(e\left(\frac{8131}{10890}\right)\) | \(e\left(\frac{1724}{1815}\right)\) | \(e\left(\frac{619}{726}\right)\) | \(e\left(\frac{2243}{10890}\right)\) | \(e\left(\frac{7949}{10890}\right)\) | \(e\left(\frac{5081}{5445}\right)\) | \(e\left(\frac{622}{1815}\right)\) |
| \(\chi_{35937}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5182}{5445}\right)\) | \(e\left(\frac{4919}{5445}\right)\) | \(e\left(\frac{5461}{10890}\right)\) | \(e\left(\frac{7703}{10890}\right)\) | \(e\left(\frac{1552}{1815}\right)\) | \(e\left(\frac{329}{726}\right)\) | \(e\left(\frac{499}{10890}\right)\) | \(e\left(\frac{7177}{10890}\right)\) | \(e\left(\frac{4393}{5445}\right)\) | \(e\left(\frac{581}{1815}\right)\) |
| \(\chi_{35937}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2149}{5445}\right)\) | \(e\left(\frac{4298}{5445}\right)\) | \(e\left(\frac{97}{10890}\right)\) | \(e\left(\frac{4841}{10890}\right)\) | \(e\left(\frac{334}{1815}\right)\) | \(e\left(\frac{293}{726}\right)\) | \(e\left(\frac{643}{10890}\right)\) | \(e\left(\frac{9139}{10890}\right)\) | \(e\left(\frac{3151}{5445}\right)\) | \(e\left(\frac{1367}{1815}\right)\) |
| \(\chi_{35937}(140,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4856}{5445}\right)\) | \(e\left(\frac{4267}{5445}\right)\) | \(e\left(\frac{4073}{10890}\right)\) | \(e\left(\frac{5119}{10890}\right)\) | \(e\left(\frac{1226}{1815}\right)\) | \(e\left(\frac{193}{726}\right)\) | \(e\left(\frac{7577}{10890}\right)\) | \(e\left(\frac{3941}{10890}\right)\) | \(e\left(\frac{3089}{5445}\right)\) | \(e\left(\frac{1453}{1815}\right)\) |
| \(\chi_{35937}(149,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{5445}\right)\) | \(e\left(\frac{466}{5445}\right)\) | \(e\left(\frac{8909}{10890}\right)\) | \(e\left(\frac{9697}{10890}\right)\) | \(e\left(\frac{233}{1815}\right)\) | \(e\left(\frac{625}{726}\right)\) | \(e\left(\frac{7301}{10890}\right)\) | \(e\left(\frac{10163}{10890}\right)\) | \(e\left(\frac{932}{5445}\right)\) | \(e\left(\frac{1459}{1815}\right)\) |
| \(\chi_{35937}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2327}{5445}\right)\) | \(e\left(\frac{4654}{5445}\right)\) | \(e\left(\frac{9941}{10890}\right)\) | \(e\left(\frac{8323}{10890}\right)\) | \(e\left(\frac{512}{1815}\right)\) | \(e\left(\frac{247}{726}\right)\) | \(e\left(\frac{9539}{10890}\right)\) | \(e\left(\frac{2087}{10890}\right)\) | \(e\left(\frac{3863}{5445}\right)\) | \(e\left(\frac{1726}{1815}\right)\) |
| \(\chi_{35937}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2416}{5445}\right)\) | \(e\left(\frac{4832}{5445}\right)\) | \(e\left(\frac{3973}{10890}\right)\) | \(e\left(\frac{4619}{10890}\right)\) | \(e\left(\frac{601}{1815}\right)\) | \(e\left(\frac{587}{726}\right)\) | \(e\left(\frac{3097}{10890}\right)\) | \(e\left(\frac{9451}{10890}\right)\) | \(e\left(\frac{4219}{5445}\right)\) | \(e\left(\frac{998}{1815}\right)\) |
| \(\chi_{35937}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4588}{5445}\right)\) | \(e\left(\frac{3731}{5445}\right)\) | \(e\left(\frac{4669}{10890}\right)\) | \(e\left(\frac{10277}{10890}\right)\) | \(e\left(\frac{958}{1815}\right)\) | \(e\left(\frac{197}{726}\right)\) | \(e\left(\frac{301}{10890}\right)\) | \(e\left(\frac{8563}{10890}\right)\) | \(e\left(\frac{2017}{5445}\right)\) | \(e\left(\frac{1769}{1815}\right)\) |
| \(\chi_{35937}(194,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2174}{5445}\right)\) | \(e\left(\frac{4348}{5445}\right)\) | \(e\left(\frac{8087}{10890}\right)\) | \(e\left(\frac{1231}{10890}\right)\) | \(e\left(\frac{359}{1815}\right)\) | \(e\left(\frac{103}{726}\right)\) | \(e\left(\frac{1403}{10890}\right)\) | \(e\left(\frac{5579}{10890}\right)\) | \(e\left(\frac{3251}{5445}\right)\) | \(e\left(\frac{877}{1815}\right)\) |
| \(\chi_{35937}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{5445}\right)\) | \(e\left(\frac{314}{5445}\right)\) | \(e\left(\frac{301}{10890}\right)\) | \(e\left(\frac{3683}{10890}\right)\) | \(e\left(\frac{157}{1815}\right)\) | \(e\left(\frac{41}{726}\right)\) | \(e\left(\frac{199}{10890}\right)\) | \(e\left(\frac{3997}{10890}\right)\) | \(e\left(\frac{628}{5445}\right)\) | \(e\left(\frac{1061}{1815}\right)\) |
| \(\chi_{35937}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5404}{5445}\right)\) | \(e\left(\frac{5363}{5445}\right)\) | \(e\left(\frac{3667}{10890}\right)\) | \(e\left(\frac{911}{10890}\right)\) | \(e\left(\frac{1774}{1815}\right)\) | \(e\left(\frac{239}{726}\right)\) | \(e\left(\frac{3763}{10890}\right)\) | \(e\left(\frac{829}{10890}\right)\) | \(e\left(\frac{5281}{5445}\right)\) | \(e\left(\frac{1457}{1815}\right)\) |
| \(\chi_{35937}(248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{428}{5445}\right)\) | \(e\left(\frac{856}{5445}\right)\) | \(e\left(\frac{8069}{10890}\right)\) | \(e\left(\frac{5497}{10890}\right)\) | \(e\left(\frac{428}{1815}\right)\) | \(e\left(\frac{595}{726}\right)\) | \(e\left(\frac{161}{10890}\right)\) | \(e\left(\frac{6353}{10890}\right)\) | \(e\left(\frac{1712}{5445}\right)\) | \(e\left(\frac{904}{1815}\right)\) |
| \(\chi_{35937}(266,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5222}{5445}\right)\) | \(e\left(\frac{4999}{5445}\right)\) | \(e\left(\frac{821}{10890}\right)\) | \(e\left(\frac{6283}{10890}\right)\) | \(e\left(\frac{1592}{1815}\right)\) | \(e\left(\frac{25}{726}\right)\) | \(e\left(\frac{8249}{10890}\right)\) | \(e\left(\frac{5837}{10890}\right)\) | \(e\left(\frac{4553}{5445}\right)\) | \(e\left(\frac{886}{1815}\right)\) |
| \(\chi_{35937}(272,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1036}{5445}\right)\) | \(e\left(\frac{2072}{5445}\right)\) | \(e\left(\frac{703}{10890}\right)\) | \(e\left(\frac{10049}{10890}\right)\) | \(e\left(\frac{1036}{1815}\right)\) | \(e\left(\frac{185}{726}\right)\) | \(e\left(\frac{2527}{10890}\right)\) | \(e\left(\frac{1231}{10890}\right)\) | \(e\left(\frac{4144}{5445}\right)\) | \(e\left(\frac{458}{1815}\right)\) |
| \(\chi_{35937}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2803}{5445}\right)\) | \(e\left(\frac{161}{5445}\right)\) | \(e\left(\frac{4819}{10890}\right)\) | \(e\left(\frac{137}{10890}\right)\) | \(e\left(\frac{988}{1815}\right)\) | \(e\left(\frac{695}{726}\right)\) | \(e\left(\frac{7021}{10890}\right)\) | \(e\left(\frac{5743}{10890}\right)\) | \(e\left(\frac{322}{5445}\right)\) | \(e\left(\frac{1544}{1815}\right)\) |
| \(\chi_{35937}(293,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1964}{5445}\right)\) | \(e\left(\frac{3928}{5445}\right)\) | \(e\left(\frac{10667}{10890}\right)\) | \(e\left(\frac{3241}{10890}\right)\) | \(e\left(\frac{149}{1815}\right)\) | \(e\left(\frac{247}{726}\right)\) | \(e\left(\frac{1553}{10890}\right)\) | \(e\left(\frac{7169}{10890}\right)\) | \(e\left(\frac{2411}{5445}\right)\) | \(e\left(\frac{637}{1815}\right)\) |
| \(\chi_{35937}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1567}{5445}\right)\) | \(e\left(\frac{3134}{5445}\right)\) | \(e\left(\frac{91}{10890}\right)\) | \(e\left(\frac{2633}{10890}\right)\) | \(e\left(\frac{1567}{1815}\right)\) | \(e\left(\frac{215}{726}\right)\) | \(e\left(\frac{3859}{10890}\right)\) | \(e\left(\frac{5767}{10890}\right)\) | \(e\left(\frac{823}{5445}\right)\) | \(e\left(\frac{1376}{1815}\right)\) |
| \(\chi_{35937}(326,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{739}{5445}\right)\) | \(e\left(\frac{1478}{5445}\right)\) | \(e\left(\frac{307}{10890}\right)\) | \(e\left(\frac{5891}{10890}\right)\) | \(e\left(\frac{739}{1815}\right)\) | \(e\left(\frac{119}{726}\right)\) | \(e\left(\frac{7873}{10890}\right)\) | \(e\left(\frac{7369}{10890}\right)\) | \(e\left(\frac{2956}{5445}\right)\) | \(e\left(\frac{1052}{1815}\right)\) |
| \(\chi_{35937}(338,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5066}{5445}\right)\) | \(e\left(\frac{4687}{5445}\right)\) | \(e\left(\frac{1493}{10890}\right)\) | \(e\left(\frac{3109}{10890}\right)\) | \(e\left(\frac{1436}{1815}\right)\) | \(e\left(\frac{49}{726}\right)\) | \(e\left(\frac{7427}{10890}\right)\) | \(e\left(\frac{2351}{10890}\right)\) | \(e\left(\frac{3929}{5445}\right)\) | \(e\left(\frac{1693}{1815}\right)\) |
| \(\chi_{35937}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{128}{5445}\right)\) | \(e\left(\frac{256}{5445}\right)\) | \(e\left(\frac{10199}{10890}\right)\) | \(e\left(\frac{5257}{10890}\right)\) | \(e\left(\frac{128}{1815}\right)\) | \(e\left(\frac{697}{726}\right)\) | \(e\left(\frac{1931}{10890}\right)\) | \(e\left(\frac{5513}{10890}\right)\) | \(e\left(\frac{512}{5445}\right)\) | \(e\left(\frac{1339}{1815}\right)\) |
| \(\chi_{35937}(365,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3662}{5445}\right)\) | \(e\left(\frac{1879}{5445}\right)\) | \(e\left(\frac{7541}{10890}\right)\) | \(e\left(\frac{7213}{10890}\right)\) | \(e\left(\frac{32}{1815}\right)\) | \(e\left(\frac{265}{726}\right)\) | \(e\left(\frac{29}{10890}\right)\) | \(e\left(\frac{3647}{10890}\right)\) | \(e\left(\frac{3758}{5445}\right)\) | \(e\left(\frac{1696}{1815}\right)\) |
| \(\chi_{35937}(371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3121}{5445}\right)\) | \(e\left(\frac{797}{5445}\right)\) | \(e\left(\frac{9313}{10890}\right)\) | \(e\left(\frac{9539}{10890}\right)\) | \(e\left(\frac{1306}{1815}\right)\) | \(e\left(\frac{311}{726}\right)\) | \(e\left(\frac{4927}{10890}\right)\) | \(e\left(\frac{4891}{10890}\right)\) | \(e\left(\frac{1594}{5445}\right)\) | \(e\left(\frac{248}{1815}\right)\) |
| \(\chi_{35937}(380,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{523}{5445}\right)\) | \(e\left(\frac{1046}{5445}\right)\) | \(e\left(\frac{7939}{10890}\right)\) | \(e\left(\frac{4847}{10890}\right)\) | \(e\left(\frac{523}{1815}\right)\) | \(e\left(\frac{599}{726}\right)\) | \(e\left(\frac{871}{10890}\right)\) | \(e\left(\frac{5893}{10890}\right)\) | \(e\left(\frac{2092}{5445}\right)\) | \(e\left(\frac{494}{1815}\right)\) |
| \(\chi_{35937}(392,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4724}{5445}\right)\) | \(e\left(\frac{4003}{5445}\right)\) | \(e\left(\frac{6317}{10890}\right)\) | \(e\left(\frac{3271}{10890}\right)\) | \(e\left(\frac{1094}{1815}\right)\) | \(e\left(\frac{325}{726}\right)\) | \(e\left(\frac{2693}{10890}\right)\) | \(e\left(\frac{1829}{10890}\right)\) | \(e\left(\frac{2561}{5445}\right)\) | \(e\left(\frac{1717}{1815}\right)\) |