Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6019.ec
\(\chi_{6019}(25,\cdot)\) \(\chi_{6019}(103,\cdot)\) \(\chi_{6019}(116,\cdot)\) \(\chi_{6019}(168,\cdot)\) \(\chi_{6019}(181,\cdot)\) \(\chi_{6019}(220,\cdot)\) \(\chi_{6019}(246,\cdot)\) \(\chi_{6019}(259,\cdot)\) \(\chi_{6019}(298,\cdot)\) \(\chi_{6019}(311,\cdot)\) \(\chi_{6019}(415,\cdot)\) \(\chi_{6019}(467,\cdot)\) \(\chi_{6019}(480,\cdot)\) \(\chi_{6019}(493,\cdot)\) \(\chi_{6019}(506,\cdot)\) \(\chi_{6019}(532,\cdot)\) \(\chi_{6019}(584,\cdot)\) \(\chi_{6019}(636,\cdot)\) \(\chi_{6019}(727,\cdot)\) \(\chi_{6019}(766,\cdot)\) \(\chi_{6019}(779,\cdot)\) \(\chi_{6019}(818,\cdot)\) \(\chi_{6019}(935,\cdot)\) \(\chi_{6019}(961,\cdot)\) \(\chi_{6019}(987,\cdot)\) \(\chi_{6019}(1039,\cdot)\) \(\chi_{6019}(1182,\cdot)\) \(\chi_{6019}(1247,\cdot)\) \(\chi_{6019}(1468,\cdot)\) \(\chi_{6019}(1520,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((-1,e\left(\frac{125}{231}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{415}{462}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{65}{462}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{355}{462}\right)\) |