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.cz
\(\chi_{6019}(145,\cdot)\) \(\chi_{6019}(267,\cdot)\) \(\chi_{6019}(726,\cdot)\) \(\chi_{6019}(748,\cdot)\) \(\chi_{6019}(1402,\cdot)\) \(\chi_{6019}(1601,\cdot)\) \(\chi_{6019}(1670,\cdot)\) \(\chi_{6019}(1683,\cdot)\) \(\chi_{6019}(2125,\cdot)\) \(\chi_{6019}(2282,\cdot)\) \(\chi_{6019}(2329,\cdot)\) \(\chi_{6019}(2615,\cdot)\) \(\chi_{6019}(2923,\cdot)\) \(\chi_{6019}(3967,\cdot)\) \(\chi_{6019}(3971,\cdot)\) \(\chi_{6019}(3985,\cdot)\) \(\chi_{6019}(3998,\cdot)\) \(\chi_{6019}(4379,\cdot)\) \(\chi_{6019}(4440,\cdot)\) \(\chi_{6019}(4452,\cdot)\) \(\chi_{6019}(4643,\cdot)\) \(\chi_{6019}(5107,\cdot)\) \(\chi_{6019}(5393,\cdot)\) \(\chi_{6019}(5986,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2316,1392)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) |