Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(3332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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.cx
\(\chi_{3332}(151,\cdot)\) \(\chi_{3332}(179,\cdot)\) \(\chi_{3332}(219,\cdot)\) \(\chi_{3332}(247,\cdot)\) \(\chi_{3332}(291,\cdot)\) \(\chi_{3332}(331,\cdot)\) \(\chi_{3332}(359,\cdot)\) \(\chi_{3332}(627,\cdot)\) \(\chi_{3332}(695,\cdot)\) \(\chi_{3332}(723,\cdot)\) \(\chi_{3332}(739,\cdot)\) \(\chi_{3332}(767,\cdot)\) \(\chi_{3332}(807,\cdot)\) \(\chi_{3332}(835,\cdot)\) \(\chi_{3332}(1103,\cdot)\) \(\chi_{3332}(1131,\cdot)\) \(\chi_{3332}(1171,\cdot)\) \(\chi_{3332}(1199,\cdot)\) \(\chi_{3332}(1215,\cdot)\) \(\chi_{3332}(1283,\cdot)\) \(\chi_{3332}(1311,\cdot)\) \(\chi_{3332}(1579,\cdot)\) \(\chi_{3332}(1607,\cdot)\) \(\chi_{3332}(1675,\cdot)\) \(\chi_{3332}(1691,\cdot)\) \(\chi_{3332}(1719,\cdot)\) \(\chi_{3332}(1759,\cdot)\) \(\chi_{3332}(1787,\cdot)\) \(\chi_{3332}(2055,\cdot)\) \(\chi_{3332}(2083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{5}{21}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(151, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{131}{168}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{19}{56}\right)\) |