Basic properties
| Modulus: | \(5082\) | |
| 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 \(\chi_{847}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5082.ck
\(\chi_{5082}(19,\cdot)\) \(\chi_{5082}(61,\cdot)\) \(\chi_{5082}(73,\cdot)\) \(\chi_{5082}(145,\cdot)\) \(\chi_{5082}(271,\cdot)\) \(\chi_{5082}(283,\cdot)\) \(\chi_{5082}(325,\cdot)\) \(\chi_{5082}(409,\cdot)\) \(\chi_{5082}(523,\cdot)\) \(\chi_{5082}(535,\cdot)\) \(\chi_{5082}(607,\cdot)\) \(\chi_{5082}(733,\cdot)\) \(\chi_{5082}(745,\cdot)\) \(\chi_{5082}(787,\cdot)\) \(\chi_{5082}(871,\cdot)\) \(\chi_{5082}(943,\cdot)\) \(\chi_{5082}(985,\cdot)\) \(\chi_{5082}(997,\cdot)\) \(\chi_{5082}(1069,\cdot)\) \(\chi_{5082}(1195,\cdot)\) \(\chi_{5082}(1249,\cdot)\) \(\chi_{5082}(1333,\cdot)\) \(\chi_{5082}(1405,\cdot)\) \(\chi_{5082}(1447,\cdot)\) \(\chi_{5082}(1459,\cdot)\) \(\chi_{5082}(1531,\cdot)\) \(\chi_{5082}(1657,\cdot)\) \(\chi_{5082}(1669,\cdot)\) \(\chi_{5082}(1711,\cdot)\) \(\chi_{5082}(1795,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3389,4357,2059)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5082 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{47}{55}\right)\) |