Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cw
\(\chi_{3332}(9,\cdot)\) \(\chi_{3332}(25,\cdot)\) \(\chi_{3332}(53,\cdot)\) \(\chi_{3332}(93,\cdot)\) \(\chi_{3332}(121,\cdot)\) \(\chi_{3332}(389,\cdot)\) \(\chi_{3332}(417,\cdot)\) \(\chi_{3332}(457,\cdot)\) \(\chi_{3332}(485,\cdot)\) \(\chi_{3332}(501,\cdot)\) \(\chi_{3332}(529,\cdot)\) \(\chi_{3332}(597,\cdot)\) \(\chi_{3332}(865,\cdot)\) \(\chi_{3332}(893,\cdot)\) \(\chi_{3332}(933,\cdot)\) \(\chi_{3332}(977,\cdot)\) \(\chi_{3332}(1005,\cdot)\) \(\chi_{3332}(1045,\cdot)\) \(\chi_{3332}(1073,\cdot)\) \(\chi_{3332}(1369,\cdot)\) \(\chi_{3332}(1409,\cdot)\) \(\chi_{3332}(1437,\cdot)\) \(\chi_{3332}(1453,\cdot)\) \(\chi_{3332}(1481,\cdot)\) \(\chi_{3332}(1521,\cdot)\) \(\chi_{3332}(1817,\cdot)\) \(\chi_{3332}(1845,\cdot)\) \(\chi_{3332}(1885,\cdot)\) \(\chi_{3332}(1913,\cdot)\) \(\chi_{3332}(1957,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{1}{21}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{131}{168}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{56}\right)\) |