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.bd
\(\chi_{539}(3,\cdot)\) \(\chi_{539}(5,\cdot)\) \(\chi_{539}(26,\cdot)\) \(\chi_{539}(38,\cdot)\) \(\chi_{539}(47,\cdot)\) \(\chi_{539}(59,\cdot)\) \(\chi_{539}(75,\cdot)\) \(\chi_{539}(82,\cdot)\) \(\chi_{539}(103,\cdot)\) \(\chi_{539}(108,\cdot)\) \(\chi_{539}(115,\cdot)\) \(\chi_{539}(124,\cdot)\) \(\chi_{539}(136,\cdot)\) \(\chi_{539}(152,\cdot)\) \(\chi_{539}(157,\cdot)\) \(\chi_{539}(159,\cdot)\) \(\chi_{539}(180,\cdot)\) \(\chi_{539}(185,\cdot)\) \(\chi_{539}(192,\cdot)\) \(\chi_{539}(201,\cdot)\) \(\chi_{539}(213,\cdot)\) \(\chi_{539}(229,\cdot)\) \(\chi_{539}(234,\cdot)\) \(\chi_{539}(236,\cdot)\) \(\chi_{539}(257,\cdot)\) \(\chi_{539}(262,\cdot)\) \(\chi_{539}(269,\cdot)\) \(\chi_{539}(278,\cdot)\) \(\chi_{539}(290,\cdot)\) \(\chi_{539}(306,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,442)\) → \((e\left(\frac{19}{42}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{23}{70}\right)\) |