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.eb
\(\chi_{6019}(49,\cdot)\) \(\chi_{6019}(244,\cdot)\) \(\chi_{6019}(270,\cdot)\) \(\chi_{6019}(277,\cdot)\) \(\chi_{6019}(283,\cdot)\) \(\chi_{6019}(381,\cdot)\) \(\chi_{6019}(407,\cdot)\) \(\chi_{6019}(563,\cdot)\) \(\chi_{6019}(725,\cdot)\) \(\chi_{6019}(797,\cdot)\) \(\chi_{6019}(855,\cdot)\) \(\chi_{6019}(914,\cdot)\) \(\chi_{6019}(992,\cdot)\) \(\chi_{6019}(1037,\cdot)\) \(\chi_{6019}(1050,\cdot)\) \(\chi_{6019}(1070,\cdot)\) \(\chi_{6019}(1115,\cdot)\) \(\chi_{6019}(1135,\cdot)\) \(\chi_{6019}(1239,\cdot)\) \(\chi_{6019}(1284,\cdot)\) \(\chi_{6019}(1362,\cdot)\) \(\chi_{6019}(1382,\cdot)\) \(\chi_{6019}(1447,\cdot)\) \(\chi_{6019}(1453,\cdot)\) \(\chi_{6019}(1473,\cdot)\) \(\chi_{6019}(1486,\cdot)\) \(\chi_{6019}(1512,\cdot)\) \(\chi_{6019}(1538,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{51}{77}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{462}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{233}{462}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{229}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{145}{462}\right)\) |