Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(501,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.cf
\(\chi_{2156}(149,\cdot)\) \(\chi_{2156}(193,\cdot)\) \(\chi_{2156}(205,\cdot)\) \(\chi_{2156}(233,\cdot)\) \(\chi_{2156}(249,\cdot)\) \(\chi_{2156}(261,\cdot)\) \(\chi_{2156}(277,\cdot)\) \(\chi_{2156}(305,\cdot)\) \(\chi_{2156}(457,\cdot)\) \(\chi_{2156}(501,\cdot)\) \(\chi_{2156}(513,\cdot)\) \(\chi_{2156}(541,\cdot)\) \(\chi_{2156}(585,\cdot)\) \(\chi_{2156}(613,\cdot)\) \(\chi_{2156}(809,\cdot)\) \(\chi_{2156}(821,\cdot)\) \(\chi_{2156}(849,\cdot)\) \(\chi_{2156}(865,\cdot)\) \(\chi_{2156}(877,\cdot)\) \(\chi_{2156}(893,\cdot)\) \(\chi_{2156}(921,\cdot)\) \(\chi_{2156}(1073,\cdot)\) \(\chi_{2156}(1117,\cdot)\) \(\chi_{2156}(1129,\cdot)\) \(\chi_{2156}(1173,\cdot)\) \(\chi_{2156}(1185,\cdot)\) \(\chi_{2156}(1201,\cdot)\) \(\chi_{2156}(1229,\cdot)\) \(\chi_{2156}(1381,\cdot)\) \(\chi_{2156}(1425,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,1277,981)\) → \((1,e\left(\frac{20}{21}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(501, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{16}{35}\right)\) |