Basic properties
| Modulus: | \(5635\) | |
| Conductor: | \(5635\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | 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)
|
Galois orbit 5635.dl
\(\chi_{5635}(89,\cdot)\) \(\chi_{5635}(159,\cdot)\) \(\chi_{5635}(194,\cdot)\) \(\chi_{5635}(199,\cdot)\) \(\chi_{5635}(304,\cdot)\) \(\chi_{5635}(339,\cdot)\) \(\chi_{5635}(444,\cdot)\) \(\chi_{5635}(474,\cdot)\) \(\chi_{5635}(479,\cdot)\) \(\chi_{5635}(544,\cdot)\) \(\chi_{5635}(549,\cdot)\) \(\chi_{5635}(649,\cdot)\) \(\chi_{5635}(654,\cdot)\) \(\chi_{5635}(684,\cdot)\) \(\chi_{5635}(724,\cdot)\) \(\chi_{5635}(789,\cdot)\) \(\chi_{5635}(824,\cdot)\) \(\chi_{5635}(894,\cdot)\) \(\chi_{5635}(934,\cdot)\) \(\chi_{5635}(964,\cdot)\) \(\chi_{5635}(1004,\cdot)\) \(\chi_{5635}(1069,\cdot)\) \(\chi_{5635}(1144,\cdot)\) \(\chi_{5635}(1249,\cdot)\) \(\chi_{5635}(1279,\cdot)\) \(\chi_{5635}(1284,\cdot)\) \(\chi_{5635}(1349,\cdot)\) \(\chi_{5635}(1424,\cdot)\) \(\chi_{5635}(1454,\cdot)\) \(\chi_{5635}(1459,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((3382,346,2696)\) → \((-1,e\left(\frac{23}{42}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 5635 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{178}{231}\right)\) |