Basic properties
| Modulus: | \(539\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 539.be
\(\chi_{539}(2,\cdot)\) \(\chi_{539}(39,\cdot)\) \(\chi_{539}(46,\cdot)\) \(\chi_{539}(51,\cdot)\) \(\chi_{539}(72,\cdot)\) \(\chi_{539}(74,\cdot)\) \(\chi_{539}(95,\cdot)\) \(\chi_{539}(107,\cdot)\) \(\chi_{539}(123,\cdot)\) \(\chi_{539}(149,\cdot)\) \(\chi_{539}(151,\cdot)\) \(\chi_{539}(156,\cdot)\) \(\chi_{539}(172,\cdot)\) \(\chi_{539}(184,\cdot)\) \(\chi_{539}(193,\cdot)\) \(\chi_{539}(200,\cdot)\) \(\chi_{539}(205,\cdot)\) \(\chi_{539}(228,\cdot)\) \(\chi_{539}(233,\cdot)\) \(\chi_{539}(249,\cdot)\) \(\chi_{539}(261,\cdot)\) \(\chi_{539}(270,\cdot)\) \(\chi_{539}(277,\cdot)\) \(\chi_{539}(282,\cdot)\) \(\chi_{539}(303,\cdot)\) \(\chi_{539}(305,\cdot)\) \(\chi_{539}(310,\cdot)\) \(\chi_{539}(326,\cdot)\) \(\chi_{539}(338,\cdot)\) \(\chi_{539}(347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,442)\) → \((e\left(\frac{17}{21}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{43}{70}\right)\) |