Basic properties
| Modulus: | \(2432\) | |
| Conductor: | \(2432\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(288\) | 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 2432.cr
\(\chi_{2432}(3,\cdot)\) \(\chi_{2432}(51,\cdot)\) \(\chi_{2432}(59,\cdot)\) \(\chi_{2432}(67,\cdot)\) \(\chi_{2432}(91,\cdot)\) \(\chi_{2432}(147,\cdot)\) \(\chi_{2432}(155,\cdot)\) \(\chi_{2432}(203,\cdot)\) \(\chi_{2432}(211,\cdot)\) \(\chi_{2432}(219,\cdot)\) \(\chi_{2432}(243,\cdot)\) \(\chi_{2432}(299,\cdot)\) \(\chi_{2432}(307,\cdot)\) \(\chi_{2432}(355,\cdot)\) \(\chi_{2432}(363,\cdot)\) \(\chi_{2432}(371,\cdot)\) \(\chi_{2432}(395,\cdot)\) \(\chi_{2432}(451,\cdot)\) \(\chi_{2432}(459,\cdot)\) \(\chi_{2432}(507,\cdot)\) \(\chi_{2432}(515,\cdot)\) \(\chi_{2432}(523,\cdot)\) \(\chi_{2432}(547,\cdot)\) \(\chi_{2432}(603,\cdot)\) \(\chi_{2432}(611,\cdot)\) \(\chi_{2432}(659,\cdot)\) \(\chi_{2432}(667,\cdot)\) \(\chi_{2432}(675,\cdot)\) \(\chi_{2432}(699,\cdot)\) \(\chi_{2432}(755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((1407,2053,1921)\) → \((-1,e\left(\frac{19}{32}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{288}\right)\) | \(e\left(\frac{203}{288}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{17}{144}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{181}{288}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{191}{288}\right)\) | \(e\left(\frac{101}{144}\right)\) |