Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(3136\) | 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 3136.db
\(\chi_{3136}(3,\cdot)\) \(\chi_{3136}(59,\cdot)\) \(\chi_{3136}(75,\cdot)\) \(\chi_{3136}(115,\cdot)\) \(\chi_{3136}(131,\cdot)\) \(\chi_{3136}(171,\cdot)\) \(\chi_{3136}(187,\cdot)\) \(\chi_{3136}(243,\cdot)\) \(\chi_{3136}(283,\cdot)\) \(\chi_{3136}(299,\cdot)\) \(\chi_{3136}(339,\cdot)\) \(\chi_{3136}(355,\cdot)\) \(\chi_{3136}(395,\cdot)\) \(\chi_{3136}(451,\cdot)\) \(\chi_{3136}(467,\cdot)\) \(\chi_{3136}(507,\cdot)\) \(\chi_{3136}(523,\cdot)\) \(\chi_{3136}(563,\cdot)\) \(\chi_{3136}(579,\cdot)\) \(\chi_{3136}(635,\cdot)\) \(\chi_{3136}(675,\cdot)\) \(\chi_{3136}(691,\cdot)\) \(\chi_{3136}(731,\cdot)\) \(\chi_{3136}(747,\cdot)\) \(\chi_{3136}(787,\cdot)\) \(\chi_{3136}(843,\cdot)\) \(\chi_{3136}(859,\cdot)\) \(\chi_{3136}(899,\cdot)\) \(\chi_{3136}(915,\cdot)\) \(\chi_{3136}(955,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{336}\right)\) | \(e\left(\frac{295}{336}\right)\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{131}{336}\right)\) | \(e\left(\frac{67}{112}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{5}{168}\right)\) | \(e\left(\frac{127}{168}\right)\) |