Basic properties
| Modulus: | \(586971\) | |
| Conductor: | \(9317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{9317}(3988,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 586971.oz
\(\chi_{586971}(19,\cdot)\) \(\chi_{586971}(325,\cdot)\) \(\chi_{586971}(2224,\cdot)\) \(\chi_{586971}(3412,\cdot)\) \(\chi_{586971}(3988,\cdot)\) \(\chi_{586971}(4429,\cdot)\) \(\chi_{586971}(4870,\cdot)\) \(\chi_{586971}(5617,\cdot)\) \(\chi_{586971}(6058,\cdot)\) \(\chi_{586971}(7075,\cdot)\) \(\chi_{586971}(8263,\cdot)\) \(\chi_{586971}(8839,\cdot)\) \(\chi_{586971}(9280,\cdot)\) \(\chi_{586971}(9721,\cdot)\) \(\chi_{586971}(10027,\cdot)\) \(\chi_{586971}(10468,\cdot)\) \(\chi_{586971}(10909,\cdot)\) \(\chi_{586971}(11926,\cdot)\) \(\chi_{586971}(13114,\cdot)\) \(\chi_{586971}(13690,\cdot)\) \(\chi_{586971}(14131,\cdot)\) \(\chi_{586971}(14572,\cdot)\) \(\chi_{586971}(14878,\cdot)\) \(\chi_{586971}(15319,\cdot)\) \(\chi_{586971}(15760,\cdot)\) \(\chi_{586971}(16777,\cdot)\) \(\chi_{586971}(17965,\cdot)\) \(\chi_{586971}(18541,\cdot)\) \(\chi_{586971}(18982,\cdot)\) \(\chi_{586971}(19423,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 3630 polynomial (not computed) |
Values on generators
\((130439,179686,73207)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{789}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 586971 }(3988, a) \) | \(1\) | \(1\) | \(e\left(\frac{1157}{3630}\right)\) | \(e\left(\frac{1157}{1815}\right)\) | \(e\left(\frac{533}{3630}\right)\) | \(e\left(\frac{1157}{1210}\right)\) | \(e\left(\frac{169}{363}\right)\) | \(e\left(\frac{382}{605}\right)\) | \(e\left(\frac{499}{1815}\right)\) | \(e\left(\frac{929}{1815}\right)\) | \(e\left(\frac{1513}{1815}\right)\) | \(e\left(\frac{949}{1210}\right)\) |