Basic properties
| Modulus: | \(1503\) | |
| Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1503.n
\(\chi_{1503}(2,\cdot)\) \(\chi_{1503}(11,\cdot)\) \(\chi_{1503}(14,\cdot)\) \(\chi_{1503}(29,\cdot)\) \(\chi_{1503}(32,\cdot)\) \(\chi_{1503}(38,\cdot)\) \(\chi_{1503}(47,\cdot)\) \(\chi_{1503}(50,\cdot)\) \(\chi_{1503}(56,\cdot)\) \(\chi_{1503}(65,\cdot)\) \(\chi_{1503}(77,\cdot)\) \(\chi_{1503}(122,\cdot)\) \(\chi_{1503}(128,\cdot)\) \(\chi_{1503}(137,\cdot)\) \(\chi_{1503}(173,\cdot)\) \(\chi_{1503}(176,\cdot)\) \(\chi_{1503}(185,\cdot)\) \(\chi_{1503}(191,\cdot)\) \(\chi_{1503}(194,\cdot)\) \(\chi_{1503}(200,\cdot)\) \(\chi_{1503}(203,\cdot)\) \(\chi_{1503}(209,\cdot)\) \(\chi_{1503}(221,\cdot)\) \(\chi_{1503}(230,\cdot)\) \(\chi_{1503}(239,\cdot)\) \(\chi_{1503}(248,\cdot)\) \(\chi_{1503}(254,\cdot)\) \(\chi_{1503}(263,\cdot)\) \(\chi_{1503}(266,\cdot)\) \(\chi_{1503}(275,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{249})$ |
| Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((335,172)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{29}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1503 }(353, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{498}\right)\) | \(e\left(\frac{71}{249}\right)\) | \(e\left(\frac{91}{498}\right)\) | \(e\left(\frac{223}{249}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{473}{498}\right)\) | \(e\left(\frac{80}{249}\right)\) | \(e\left(\frac{19}{498}\right)\) | \(e\left(\frac{142}{249}\right)\) |