Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(2156\) | 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 2156.ch
\(\chi_{2156}(171,\cdot)\) \(\chi_{2156}(255,\cdot)\) \(\chi_{2156}(271,\cdot)\) \(\chi_{2156}(283,\cdot)\) \(\chi_{2156}(299,\cdot)\) \(\chi_{2156}(327,\cdot)\) \(\chi_{2156}(479,\cdot)\) \(\chi_{2156}(523,\cdot)\) \(\chi_{2156}(535,\cdot)\) \(\chi_{2156}(563,\cdot)\) \(\chi_{2156}(579,\cdot)\) \(\chi_{2156}(591,\cdot)\) \(\chi_{2156}(635,\cdot)\) \(\chi_{2156}(787,\cdot)\) \(\chi_{2156}(831,\cdot)\) \(\chi_{2156}(843,\cdot)\) \(\chi_{2156}(871,\cdot)\) \(\chi_{2156}(887,\cdot)\) \(\chi_{2156}(899,\cdot)\) \(\chi_{2156}(915,\cdot)\) \(\chi_{2156}(943,\cdot)\) \(\chi_{2156}(1095,\cdot)\) \(\chi_{2156}(1139,\cdot)\) \(\chi_{2156}(1151,\cdot)\) \(\chi_{2156}(1179,\cdot)\) \(\chi_{2156}(1223,\cdot)\) \(\chi_{2156}(1251,\cdot)\) \(\chi_{2156}(1447,\cdot)\) \(\chi_{2156}(1459,\cdot)\) \(\chi_{2156}(1487,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{41}{42}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(327, a) \) | \(-1\) | \(1\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) |