Basic properties
| Modulus: | \(2541\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.ck
\(\chi_{2541}(19,\cdot)\) \(\chi_{2541}(52,\cdot)\) \(\chi_{2541}(61,\cdot)\) \(\chi_{2541}(73,\cdot)\) \(\chi_{2541}(145,\cdot)\) \(\chi_{2541}(178,\cdot)\) \(\chi_{2541}(250,\cdot)\) \(\chi_{2541}(271,\cdot)\) \(\chi_{2541}(283,\cdot)\) \(\chi_{2541}(292,\cdot)\) \(\chi_{2541}(304,\cdot)\) \(\chi_{2541}(325,\cdot)\) \(\chi_{2541}(376,\cdot)\) \(\chi_{2541}(409,\cdot)\) \(\chi_{2541}(502,\cdot)\) \(\chi_{2541}(514,\cdot)\) \(\chi_{2541}(523,\cdot)\) \(\chi_{2541}(535,\cdot)\) \(\chi_{2541}(556,\cdot)\) \(\chi_{2541}(607,\cdot)\) \(\chi_{2541}(640,\cdot)\) \(\chi_{2541}(712,\cdot)\) \(\chi_{2541}(733,\cdot)\) \(\chi_{2541}(745,\cdot)\) \(\chi_{2541}(754,\cdot)\) \(\chi_{2541}(787,\cdot)\) \(\chi_{2541}(871,\cdot)\) \(\chi_{2541}(943,\cdot)\) \(\chi_{2541}(964,\cdot)\) \(\chi_{2541}(976,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,1816,2059)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{37}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 2541 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{330}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{112}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{7}{110}\right)\) |