Basic properties
| Modulus: | \(2541\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(718,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.ce
\(\chi_{2541}(4,\cdot)\) \(\chi_{2541}(16,\cdot)\) \(\chi_{2541}(25,\cdot)\) \(\chi_{2541}(37,\cdot)\) \(\chi_{2541}(58,\cdot)\) \(\chi_{2541}(163,\cdot)\) \(\chi_{2541}(214,\cdot)\) \(\chi_{2541}(235,\cdot)\) \(\chi_{2541}(247,\cdot)\) \(\chi_{2541}(256,\cdot)\) \(\chi_{2541}(268,\cdot)\) \(\chi_{2541}(289,\cdot)\) \(\chi_{2541}(361,\cdot)\) \(\chi_{2541}(394,\cdot)\) \(\chi_{2541}(445,\cdot)\) \(\chi_{2541}(466,\cdot)\) \(\chi_{2541}(478,\cdot)\) \(\chi_{2541}(499,\cdot)\) \(\chi_{2541}(520,\cdot)\) \(\chi_{2541}(592,\cdot)\) \(\chi_{2541}(625,\cdot)\) \(\chi_{2541}(676,\cdot)\) \(\chi_{2541}(697,\cdot)\) \(\chi_{2541}(709,\cdot)\) \(\chi_{2541}(718,\cdot)\) \(\chi_{2541}(730,\cdot)\) \(\chi_{2541}(751,\cdot)\) \(\chi_{2541}(823,\cdot)\) \(\chi_{2541}(907,\cdot)\) \(\chi_{2541}(940,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,1816,2059)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{29}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 2541 }(718, a) \) | \(1\) | \(1\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{4}{55}\right)\) |