Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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.da
\(\chi_{6019}(345,\cdot)\) \(\chi_{6019}(514,\cdot)\) \(\chi_{6019}(618,\cdot)\) \(\chi_{6019}(696,\cdot)\) \(\chi_{6019}(808,\cdot)\) \(\chi_{6019}(977,\cdot)\) \(\chi_{6019}(1081,\cdot)\) \(\chi_{6019}(1103,\cdot)\) \(\chi_{6019}(1159,\cdot)\) \(\chi_{6019}(1566,\cdot)\) \(\chi_{6019}(1818,\cdot)\) \(\chi_{6019}(2281,\cdot)\) \(\chi_{6019}(3586,\cdot)\) \(\chi_{6019}(3755,\cdot)\) \(\chi_{6019}(3859,\cdot)\) \(\chi_{6019}(3881,\cdot)\) \(\chi_{6019}(3937,\cdot)\) \(\chi_{6019}(4049,\cdot)\) \(\chi_{6019}(4218,\cdot)\) \(\chi_{6019}(4322,\cdot)\) \(\chi_{6019}(4344,\cdot)\) \(\chi_{6019}(4400,\cdot)\) \(\chi_{6019}(4596,\cdot)\) \(\chi_{6019}(5059,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2316,1392)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(345, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{65}{84}\right)\) |