Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | 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 2873.cj
\(\chi_{2873}(5,\cdot)\) \(\chi_{2873}(31,\cdot)\) \(\chi_{2873}(112,\cdot)\) \(\chi_{2873}(122,\cdot)\) \(\chi_{2873}(125,\cdot)\) \(\chi_{2873}(148,\cdot)\) \(\chi_{2873}(164,\cdot)\) \(\chi_{2873}(177,\cdot)\) \(\chi_{2873}(226,\cdot)\) \(\chi_{2873}(252,\cdot)\) \(\chi_{2873}(333,\cdot)\) \(\chi_{2873}(343,\cdot)\) \(\chi_{2873}(346,\cdot)\) \(\chi_{2873}(369,\cdot)\) \(\chi_{2873}(385,\cdot)\) \(\chi_{2873}(398,\cdot)\) \(\chi_{2873}(447,\cdot)\) \(\chi_{2873}(473,\cdot)\) \(\chi_{2873}(554,\cdot)\) \(\chi_{2873}(564,\cdot)\) \(\chi_{2873}(567,\cdot)\) \(\chi_{2873}(590,\cdot)\) \(\chi_{2873}(619,\cdot)\) \(\chi_{2873}(668,\cdot)\) \(\chi_{2873}(694,\cdot)\) \(\chi_{2873}(785,\cdot)\) \(\chi_{2873}(788,\cdot)\) \(\chi_{2873}(811,\cdot)\) \(\chi_{2873}(827,\cdot)\) \(\chi_{2873}(840,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((171,2536)\) → \((e\left(\frac{3}{52}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{104}\right)\) | \(e\left(\frac{97}{208}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{17}{208}\right)\) | \(e\left(\frac{187}{208}\right)\) | \(e\left(\frac{127}{208}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{107}{208}\right)\) | \(e\left(\frac{27}{208}\right)\) |