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.cs
\(\chi_{2432}(5,\cdot)\) \(\chi_{2432}(61,\cdot)\) \(\chi_{2432}(85,\cdot)\) \(\chi_{2432}(93,\cdot)\) \(\chi_{2432}(101,\cdot)\) \(\chi_{2432}(149,\cdot)\) \(\chi_{2432}(157,\cdot)\) \(\chi_{2432}(213,\cdot)\) \(\chi_{2432}(237,\cdot)\) \(\chi_{2432}(245,\cdot)\) \(\chi_{2432}(253,\cdot)\) \(\chi_{2432}(301,\cdot)\) \(\chi_{2432}(309,\cdot)\) \(\chi_{2432}(365,\cdot)\) \(\chi_{2432}(389,\cdot)\) \(\chi_{2432}(397,\cdot)\) \(\chi_{2432}(405,\cdot)\) \(\chi_{2432}(453,\cdot)\) \(\chi_{2432}(461,\cdot)\) \(\chi_{2432}(517,\cdot)\) \(\chi_{2432}(541,\cdot)\) \(\chi_{2432}(549,\cdot)\) \(\chi_{2432}(557,\cdot)\) \(\chi_{2432}(605,\cdot)\) \(\chi_{2432}(613,\cdot)\) \(\chi_{2432}(669,\cdot)\) \(\chi_{2432}(693,\cdot)\) \(\chi_{2432}(701,\cdot)\) \(\chi_{2432}(709,\cdot)\) \(\chi_{2432}(757,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((1407,2053,1921)\) → \((1,e\left(\frac{19}{32}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{288}\right)\) | \(e\left(\frac{107}{288}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{133}{288}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{239}{288}\right)\) | \(e\left(\frac{77}{144}\right)\) |