Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(1617\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.ci
\(\chi_{1617}(5,\cdot)\) \(\chi_{1617}(26,\cdot)\) \(\chi_{1617}(38,\cdot)\) \(\chi_{1617}(47,\cdot)\) \(\chi_{1617}(59,\cdot)\) \(\chi_{1617}(152,\cdot)\) \(\chi_{1617}(185,\cdot)\) \(\chi_{1617}(236,\cdot)\) \(\chi_{1617}(257,\cdot)\) \(\chi_{1617}(269,\cdot)\) \(\chi_{1617}(278,\cdot)\) \(\chi_{1617}(290,\cdot)\) \(\chi_{1617}(311,\cdot)\) \(\chi_{1617}(383,\cdot)\) \(\chi_{1617}(416,\cdot)\) \(\chi_{1617}(467,\cdot)\) \(\chi_{1617}(488,\cdot)\) \(\chi_{1617}(500,\cdot)\) \(\chi_{1617}(542,\cdot)\) \(\chi_{1617}(614,\cdot)\) \(\chi_{1617}(647,\cdot)\) \(\chi_{1617}(698,\cdot)\) \(\chi_{1617}(719,\cdot)\) \(\chi_{1617}(731,\cdot)\) \(\chi_{1617}(740,\cdot)\) \(\chi_{1617}(752,\cdot)\) \(\chi_{1617}(773,\cdot)\) \(\chi_{1617}(845,\cdot)\) \(\chi_{1617}(878,\cdot)\) \(\chi_{1617}(929,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{5}{42}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{33}{35}\right)\) |