Basic properties
| Modulus: | \(10009\) | |
| Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2502\) | 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 10009.u
\(\chi_{10009}(5,\cdot)\) \(\chi_{10009}(9,\cdot)\) \(\chi_{10009}(24,\cdot)\) \(\chi_{10009}(34,\cdot)\) \(\chi_{10009}(39,\cdot)\) \(\chi_{10009}(73,\cdot)\) \(\chi_{10009}(77,\cdot)\) \(\chi_{10009}(80,\cdot)\) \(\chi_{10009}(97,\cdot)\) \(\chi_{10009}(100,\cdot)\) \(\chi_{10009}(116,\cdot)\) \(\chi_{10009}(123,\cdot)\) \(\chi_{10009}(130,\cdot)\) \(\chi_{10009}(144,\cdot)\) \(\chi_{10009}(147,\cdot)\) \(\chi_{10009}(180,\cdot)\) \(\chi_{10009}(184,\cdot)\) \(\chi_{10009}(201,\cdot)\) \(\chi_{10009}(230,\cdot)\) \(\chi_{10009}(234,\cdot)\) \(\chi_{10009}(242,\cdot)\) \(\chi_{10009}(255,\cdot)\) \(\chi_{10009}(278,\cdot)\) \(\chi_{10009}(289,\cdot)\) \(\chi_{10009}(299,\cdot)\) \(\chi_{10009}(309,\cdot)\) \(\chi_{10009}(316,\cdot)\) \(\chi_{10009}(317,\cdot)\) \(\chi_{10009}(324,\cdot)\) \(\chi_{10009}(341,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1251})$ |
| Fixed field: | Number field defined by a degree 2502 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{2063}{2502}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10009 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{417}\right)\) | \(e\left(\frac{67}{1251}\right)\) | \(e\left(\frac{158}{417}\right)\) | \(e\left(\frac{422}{1251}\right)\) | \(e\left(\frac{304}{1251}\right)\) | \(e\left(\frac{151}{278}\right)\) | \(e\left(\frac{79}{139}\right)\) | \(e\left(\frac{134}{1251}\right)\) | \(e\left(\frac{659}{1251}\right)\) | \(e\left(\frac{2063}{2502}\right)\) |