Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(3332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 3332.da
\(\chi_{3332}(3,\cdot)\) \(\chi_{3332}(75,\cdot)\) \(\chi_{3332}(131,\cdot)\) \(\chi_{3332}(143,\cdot)\) \(\chi_{3332}(159,\cdot)\) \(\chi_{3332}(199,\cdot)\) \(\chi_{3332}(243,\cdot)\) \(\chi_{3332}(283,\cdot)\) \(\chi_{3332}(299,\cdot)\) \(\chi_{3332}(311,\cdot)\) \(\chi_{3332}(367,\cdot)\) \(\chi_{3332}(439,\cdot)\) \(\chi_{3332}(479,\cdot)\) \(\chi_{3332}(507,\cdot)\) \(\chi_{3332}(551,\cdot)\) \(\chi_{3332}(635,\cdot)\) \(\chi_{3332}(675,\cdot)\) \(\chi_{3332}(691,\cdot)\) \(\chi_{3332}(703,\cdot)\) \(\chi_{3332}(719,\cdot)\) \(\chi_{3332}(759,\cdot)\) \(\chi_{3332}(775,\cdot)\) \(\chi_{3332}(787,\cdot)\) \(\chi_{3332}(843,\cdot)\) \(\chi_{3332}(887,\cdot)\) \(\chi_{3332}(915,\cdot)\) \(\chi_{3332}(955,\cdot)\) \(\chi_{3332}(983,\cdot)\) \(\chi_{3332}(1027,\cdot)\) \(\chi_{3332}(1083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{1}{42}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{197}{336}\right)\) | \(e\left(\frac{1}{336}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{299}{336}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{115}{336}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{85}{112}\right)\) |