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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cy
\(\chi_{3332}(11,\cdot)\) \(\chi_{3332}(23,\cdot)\) \(\chi_{3332}(39,\cdot)\) \(\chi_{3332}(95,\cdot)\) \(\chi_{3332}(107,\cdot)\) \(\chi_{3332}(163,\cdot)\) \(\chi_{3332}(207,\cdot)\) \(\chi_{3332}(235,\cdot)\) \(\chi_{3332}(303,\cdot)\) \(\chi_{3332}(347,\cdot)\) \(\chi_{3332}(403,\cdot)\) \(\chi_{3332}(415,\cdot)\) \(\chi_{3332}(431,\cdot)\) \(\chi_{3332}(487,\cdot)\) \(\chi_{3332}(499,\cdot)\) \(\chi_{3332}(515,\cdot)\) \(\chi_{3332}(555,\cdot)\) \(\chi_{3332}(571,\cdot)\) \(\chi_{3332}(583,\cdot)\) \(\chi_{3332}(639,\cdot)\) \(\chi_{3332}(683,\cdot)\) \(\chi_{3332}(711,\cdot)\) \(\chi_{3332}(751,\cdot)\) \(\chi_{3332}(779,\cdot)\) \(\chi_{3332}(823,\cdot)\) \(\chi_{3332}(879,\cdot)\) \(\chi_{3332}(891,\cdot)\) \(\chi_{3332}(907,\cdot)\) \(\chi_{3332}(947,\cdot)\) \(\chi_{3332}(963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((-1,e\left(\frac{19}{21}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{115}{336}\right)\) | \(e\left(\frac{311}{336}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{85}{336}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{317}{336}\right)\) | \(e\left(\frac{143}{168}\right)\) | \(e\left(\frac{3}{112}\right)\) |