Basic properties
| Modulus: | \(539\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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 539.bc
\(\chi_{539}(4,\cdot)\) \(\chi_{539}(9,\cdot)\) \(\chi_{539}(16,\cdot)\) \(\chi_{539}(25,\cdot)\) \(\chi_{539}(37,\cdot)\) \(\chi_{539}(53,\cdot)\) \(\chi_{539}(58,\cdot)\) \(\chi_{539}(60,\cdot)\) \(\chi_{539}(81,\cdot)\) \(\chi_{539}(86,\cdot)\) \(\chi_{539}(93,\cdot)\) \(\chi_{539}(102,\cdot)\) \(\chi_{539}(114,\cdot)\) \(\chi_{539}(130,\cdot)\) \(\chi_{539}(135,\cdot)\) \(\chi_{539}(137,\cdot)\) \(\chi_{539}(158,\cdot)\) \(\chi_{539}(163,\cdot)\) \(\chi_{539}(170,\cdot)\) \(\chi_{539}(179,\cdot)\) \(\chi_{539}(191,\cdot)\) \(\chi_{539}(207,\cdot)\) \(\chi_{539}(212,\cdot)\) \(\chi_{539}(235,\cdot)\) \(\chi_{539}(240,\cdot)\) \(\chi_{539}(247,\cdot)\) \(\chi_{539}(256,\cdot)\) \(\chi_{539}(268,\cdot)\) \(\chi_{539}(284,\cdot)\) \(\chi_{539}(289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((199,442)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{35}\right)\) |