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.ct
\(\chi_{2432}(35,\cdot)\) \(\chi_{2432}(43,\cdot)\) \(\chi_{2432}(99,\cdot)\) \(\chi_{2432}(123,\cdot)\) \(\chi_{2432}(131,\cdot)\) \(\chi_{2432}(139,\cdot)\) \(\chi_{2432}(187,\cdot)\) \(\chi_{2432}(195,\cdot)\) \(\chi_{2432}(251,\cdot)\) \(\chi_{2432}(275,\cdot)\) \(\chi_{2432}(283,\cdot)\) \(\chi_{2432}(291,\cdot)\) \(\chi_{2432}(339,\cdot)\) \(\chi_{2432}(347,\cdot)\) \(\chi_{2432}(403,\cdot)\) \(\chi_{2432}(427,\cdot)\) \(\chi_{2432}(435,\cdot)\) \(\chi_{2432}(443,\cdot)\) \(\chi_{2432}(491,\cdot)\) \(\chi_{2432}(499,\cdot)\) \(\chi_{2432}(555,\cdot)\) \(\chi_{2432}(579,\cdot)\) \(\chi_{2432}(587,\cdot)\) \(\chi_{2432}(595,\cdot)\) \(\chi_{2432}(643,\cdot)\) \(\chi_{2432}(651,\cdot)\) \(\chi_{2432}(707,\cdot)\) \(\chi_{2432}(731,\cdot)\) \(\chi_{2432}(739,\cdot)\) \(\chi_{2432}(747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((1407,2053,1921)\) → \((-1,e\left(\frac{29}{32}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{223}{288}\right)\) | \(e\left(\frac{37}{288}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{79}{144}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{11}{288}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{193}{288}\right)\) | \(e\left(\frac{139}{144}\right)\) |