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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2432.cq
\(\chi_{2432}(13,\cdot)\) \(\chi_{2432}(21,\cdot)\) \(\chi_{2432}(29,\cdot)\) \(\chi_{2432}(53,\cdot)\) \(\chi_{2432}(109,\cdot)\) \(\chi_{2432}(117,\cdot)\) \(\chi_{2432}(165,\cdot)\) \(\chi_{2432}(173,\cdot)\) \(\chi_{2432}(181,\cdot)\) \(\chi_{2432}(205,\cdot)\) \(\chi_{2432}(261,\cdot)\) \(\chi_{2432}(269,\cdot)\) \(\chi_{2432}(317,\cdot)\) \(\chi_{2432}(325,\cdot)\) \(\chi_{2432}(333,\cdot)\) \(\chi_{2432}(357,\cdot)\) \(\chi_{2432}(413,\cdot)\) \(\chi_{2432}(421,\cdot)\) \(\chi_{2432}(469,\cdot)\) \(\chi_{2432}(477,\cdot)\) \(\chi_{2432}(485,\cdot)\) \(\chi_{2432}(509,\cdot)\) \(\chi_{2432}(565,\cdot)\) \(\chi_{2432}(573,\cdot)\) \(\chi_{2432}(621,\cdot)\) \(\chi_{2432}(629,\cdot)\) \(\chi_{2432}(637,\cdot)\) \(\chi_{2432}(661,\cdot)\) \(\chi_{2432}(717,\cdot)\) \(\chi_{2432}(725,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((1407,2053,1921)\) → \((1,e\left(\frac{13}{32}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{271}{288}\right)\) | \(e\left(\frac{85}{288}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{127}{144}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{107}{288}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{97}{288}\right)\) | \(e\left(\frac{115}{144}\right)\) |