Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | 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.dt
\(\chi_{6019}(29,\cdot)\) \(\chi_{6019}(42,\cdot)\) \(\chi_{6019}(61,\cdot)\) \(\chi_{6019}(321,\cdot)\) \(\chi_{6019}(458,\cdot)\) \(\chi_{6019}(523,\cdot)\) \(\chi_{6019}(536,\cdot)\) \(\chi_{6019}(601,\cdot)\) \(\chi_{6019}(685,\cdot)\) \(\chi_{6019}(711,\cdot)\) \(\chi_{6019}(718,\cdot)\) \(\chi_{6019}(724,\cdot)\) \(\chi_{6019}(841,\cdot)\) \(\chi_{6019}(880,\cdot)\) \(\chi_{6019}(900,\cdot)\) \(\chi_{6019}(906,\cdot)\) \(\chi_{6019}(1036,\cdot)\) \(\chi_{6019}(1166,\cdot)\) \(\chi_{6019}(1179,\cdot)\) \(\chi_{6019}(1186,\cdot)\) \(\chi_{6019}(1218,\cdot)\) \(\chi_{6019}(1238,\cdot)\) \(\chi_{6019}(1335,\cdot)\) \(\chi_{6019}(1478,\cdot)\) \(\chi_{6019}(1524,\cdot)\) \(\chi_{6019}(1628,\cdot)\) \(\chi_{6019}(1660,\cdot)\) \(\chi_{6019}(1686,\cdot)\) \(\chi_{6019}(1764,\cdot)\) \(\chi_{6019}(1868,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{163}{231}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{75}{77}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{52}{77}\right)\) |