Basic properties
| Modulus: | \(2019\) | |
| Conductor: | \(2019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2019.bg
\(\chi_{2019}(95,\cdot)\) \(\chi_{2019}(206,\cdot)\) \(\chi_{2019}(467,\cdot)\) \(\chi_{2019}(578,\cdot)\) \(\chi_{2019}(722,\cdot)\) \(\chi_{2019}(725,\cdot)\) \(\chi_{2019}(758,\cdot)\) \(\chi_{2019}(839,\cdot)\) \(\chi_{2019}(893,\cdot)\) \(\chi_{2019}(1022,\cdot)\) \(\chi_{2019}(1127,\cdot)\) \(\chi_{2019}(1196,\cdot)\) \(\chi_{2019}(1220,\cdot)\) \(\chi_{2019}(1319,\cdot)\) \(\chi_{2019}(1373,\cdot)\) \(\chi_{2019}(1472,\cdot)\) \(\chi_{2019}(1496,\cdot)\) \(\chi_{2019}(1565,\cdot)\) \(\chi_{2019}(1670,\cdot)\) \(\chi_{2019}(1799,\cdot)\) \(\chi_{2019}(1853,\cdot)\) \(\chi_{2019}(1934,\cdot)\) \(\chi_{2019}(1967,\cdot)\) \(\chi_{2019}(1970,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((674,1351)\) → \((-1,e\left(\frac{33}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2019 }(95, a) \) | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(i\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) |