Basic properties
| Modulus: | \(4019\) | |
| Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2009\) | 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 4019.k
\(\chi_{4019}(4,\cdot)\) \(\chi_{4019}(5,\cdot)\) \(\chi_{4019}(12,\cdot)\) \(\chi_{4019}(14,\cdot)\) \(\chi_{4019}(15,\cdot)\) \(\chi_{4019}(16,\cdot)\) \(\chi_{4019}(19,\cdot)\) \(\chi_{4019}(22,\cdot)\) \(\chi_{4019}(23,\cdot)\) \(\chi_{4019}(25,\cdot)\) \(\chi_{4019}(26,\cdot)\) \(\chi_{4019}(36,\cdot)\) \(\chi_{4019}(43,\cdot)\) \(\chi_{4019}(45,\cdot)\) \(\chi_{4019}(49,\cdot)\) \(\chi_{4019}(53,\cdot)\) \(\chi_{4019}(57,\cdot)\) \(\chi_{4019}(58,\cdot)\) \(\chi_{4019}(60,\cdot)\) \(\chi_{4019}(62,\cdot)\) \(\chi_{4019}(64,\cdot)\) \(\chi_{4019}(66,\cdot)\) \(\chi_{4019}(67,\cdot)\) \(\chi_{4019}(69,\cdot)\) \(\chi_{4019}(70,\cdot)\) \(\chi_{4019}(73,\cdot)\) \(\chi_{4019}(74,\cdot)\) \(\chi_{4019}(75,\cdot)\) \(\chi_{4019}(76,\cdot)\) \(\chi_{4019}(77,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2009})$ |
| Fixed field: | Number field defined by a degree 2009 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{2009}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4019 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{2009}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{2}{2009}\right)\) | \(e\left(\frac{796}{2009}\right)\) | \(e\left(\frac{1026}{2009}\right)\) | \(e\left(\frac{1760}{2009}\right)\) | \(e\left(\frac{3}{2009}\right)\) | \(e\left(\frac{1}{49}\right)\) | \(e\left(\frac{797}{2009}\right)\) | \(e\left(\frac{261}{2009}\right)\) |