Basic properties
| Modulus: | \(1019\) | |
| Conductor: | \(1019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1018\) | 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 1019.d
\(\chi_{1019}(2,\cdot)\) \(\chi_{1019}(6,\cdot)\) \(\chi_{1019}(7,\cdot)\) \(\chi_{1019}(8,\cdot)\) \(\chi_{1019}(10,\cdot)\) \(\chi_{1019}(13,\cdot)\) \(\chi_{1019}(18,\cdot)\) \(\chi_{1019}(21,\cdot)\) \(\chi_{1019}(22,\cdot)\) \(\chi_{1019}(24,\cdot)\) \(\chi_{1019}(28,\cdot)\) \(\chi_{1019}(30,\cdot)\) \(\chi_{1019}(32,\cdot)\) \(\chi_{1019}(34,\cdot)\) \(\chi_{1019}(35,\cdot)\) \(\chi_{1019}(37,\cdot)\) \(\chi_{1019}(38,\cdot)\) \(\chi_{1019}(39,\cdot)\) \(\chi_{1019}(40,\cdot)\) \(\chi_{1019}(41,\cdot)\) \(\chi_{1019}(46,\cdot)\) \(\chi_{1019}(47,\cdot)\) \(\chi_{1019}(50,\cdot)\) \(\chi_{1019}(52,\cdot)\) \(\chi_{1019}(53,\cdot)\) \(\chi_{1019}(54,\cdot)\) \(\chi_{1019}(58,\cdot)\) \(\chi_{1019}(59,\cdot)\) \(\chi_{1019}(61,\cdot)\) \(\chi_{1019}(62,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{509})$ |
| Fixed field: | Number field defined by a degree 1018 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1018}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1019 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1018}\right)\) | \(e\left(\frac{479}{509}\right)\) | \(e\left(\frac{1}{509}\right)\) | \(e\left(\frac{5}{509}\right)\) | \(e\left(\frac{959}{1018}\right)\) | \(e\left(\frac{363}{1018}\right)\) | \(e\left(\frac{3}{1018}\right)\) | \(e\left(\frac{449}{509}\right)\) | \(e\left(\frac{11}{1018}\right)\) | \(e\left(\frac{378}{509}\right)\) |