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
\((199,442)\) → \((e\left(\frac{29}{42}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
\( \chi_{ 539 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{70}\right)\) |