Basic properties
| Modulus: | \(3381\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1127}(676,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.ce
\(\chi_{3381}(4,\cdot)\) \(\chi_{3381}(16,\cdot)\) \(\chi_{3381}(25,\cdot)\) \(\chi_{3381}(58,\cdot)\) \(\chi_{3381}(100,\cdot)\) \(\chi_{3381}(121,\cdot)\) \(\chi_{3381}(142,\cdot)\) \(\chi_{3381}(151,\cdot)\) \(\chi_{3381}(163,\cdot)\) \(\chi_{3381}(193,\cdot)\) \(\chi_{3381}(256,\cdot)\) \(\chi_{3381}(289,\cdot)\) \(\chi_{3381}(331,\cdot)\) \(\chi_{3381}(340,\cdot)\) \(\chi_{3381}(394,\cdot)\) \(\chi_{3381}(403,\cdot)\) \(\chi_{3381}(445,\cdot)\) \(\chi_{3381}(466,\cdot)\) \(\chi_{3381}(478,\cdot)\) \(\chi_{3381}(487,\cdot)\) \(\chi_{3381}(499,\cdot)\) \(\chi_{3381}(541,\cdot)\) \(\chi_{3381}(583,\cdot)\) \(\chi_{3381}(604,\cdot)\) \(\chi_{3381}(625,\cdot)\) \(\chi_{3381}(634,\cdot)\) \(\chi_{3381}(646,\cdot)\) \(\chi_{3381}(676,\cdot)\) \(\chi_{3381}(739,\cdot)\) \(\chi_{3381}(772,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{17}{21}\right),e\left(\frac{5}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3381 }(676, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{5}{33}\right)\) |