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 \(\chi_{539}(334,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.ck
\(\chi_{2156}(5,\cdot)\) \(\chi_{2156}(157,\cdot)\) \(\chi_{2156}(185,\cdot)\) \(\chi_{2156}(201,\cdot)\) \(\chi_{2156}(213,\cdot)\) \(\chi_{2156}(229,\cdot)\) \(\chi_{2156}(257,\cdot)\) \(\chi_{2156}(269,\cdot)\) \(\chi_{2156}(465,\cdot)\) \(\chi_{2156}(493,\cdot)\) \(\chi_{2156}(537,\cdot)\) \(\chi_{2156}(565,\cdot)\) \(\chi_{2156}(577,\cdot)\) \(\chi_{2156}(621,\cdot)\) \(\chi_{2156}(773,\cdot)\) \(\chi_{2156}(801,\cdot)\) \(\chi_{2156}(817,\cdot)\) \(\chi_{2156}(829,\cdot)\) \(\chi_{2156}(845,\cdot)\) \(\chi_{2156}(873,\cdot)\) \(\chi_{2156}(885,\cdot)\) \(\chi_{2156}(929,\cdot)\) \(\chi_{2156}(1081,\cdot)\) \(\chi_{2156}(1125,\cdot)\) \(\chi_{2156}(1137,\cdot)\) \(\chi_{2156}(1153,\cdot)\) \(\chi_{2156}(1181,\cdot)\) \(\chi_{2156}(1193,\cdot)\) \(\chi_{2156}(1237,\cdot)\) \(\chi_{2156}(1389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,1277,981)\) → \((1,e\left(\frac{23}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(873, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{31}{70}\right)\) |