Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.ce
\(\chi_{1617}(4,\cdot)\) \(\chi_{1617}(16,\cdot)\) \(\chi_{1617}(25,\cdot)\) \(\chi_{1617}(37,\cdot)\) \(\chi_{1617}(58,\cdot)\) \(\chi_{1617}(130,\cdot)\) \(\chi_{1617}(163,\cdot)\) \(\chi_{1617}(235,\cdot)\) \(\chi_{1617}(247,\cdot)\) \(\chi_{1617}(256,\cdot)\) \(\chi_{1617}(268,\cdot)\) \(\chi_{1617}(289,\cdot)\) \(\chi_{1617}(394,\cdot)\) \(\chi_{1617}(445,\cdot)\) \(\chi_{1617}(466,\cdot)\) \(\chi_{1617}(478,\cdot)\) \(\chi_{1617}(487,\cdot)\) \(\chi_{1617}(499,\cdot)\) \(\chi_{1617}(592,\cdot)\) \(\chi_{1617}(625,\cdot)\) \(\chi_{1617}(676,\cdot)\) \(\chi_{1617}(697,\cdot)\) \(\chi_{1617}(709,\cdot)\) \(\chi_{1617}(718,\cdot)\) \(\chi_{1617}(730,\cdot)\) \(\chi_{1617}(751,\cdot)\) \(\chi_{1617}(823,\cdot)\) \(\chi_{1617}(856,\cdot)\) \(\chi_{1617}(907,\cdot)\) \(\chi_{1617}(928,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((1,e\left(\frac{10}{21}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{34}{35}\right)\) |