Basic properties
| Modulus: | \(1319\) | |
| Conductor: | \(1319\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1318\) | 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 1319.d
\(\chi_{1319}(13,\cdot)\) \(\chi_{1319}(17,\cdot)\) \(\chi_{1319}(23,\cdot)\) \(\chi_{1319}(26,\cdot)\) \(\chi_{1319}(29,\cdot)\) \(\chi_{1319}(34,\cdot)\) \(\chi_{1319}(37,\cdot)\) \(\chi_{1319}(39,\cdot)\) \(\chi_{1319}(41,\cdot)\) \(\chi_{1319}(46,\cdot)\) \(\chi_{1319}(47,\cdot)\) \(\chi_{1319}(51,\cdot)\) \(\chi_{1319}(52,\cdot)\) \(\chi_{1319}(58,\cdot)\) \(\chi_{1319}(59,\cdot)\) \(\chi_{1319}(61,\cdot)\) \(\chi_{1319}(65,\cdot)\) \(\chi_{1319}(68,\cdot)\) \(\chi_{1319}(69,\cdot)\) \(\chi_{1319}(73,\cdot)\) \(\chi_{1319}(74,\cdot)\) \(\chi_{1319}(78,\cdot)\) \(\chi_{1319}(79,\cdot)\) \(\chi_{1319}(82,\cdot)\) \(\chi_{1319}(85,\cdot)\) \(\chi_{1319}(87,\cdot)\) \(\chi_{1319}(91,\cdot)\) \(\chi_{1319}(92,\cdot)\) \(\chi_{1319}(94,\cdot)\) \(\chi_{1319}(97,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{659})$ |
| Fixed field: | Number field defined by a degree 1318 polynomial (not computed) |
Values on generators
\(13\) → \(e\left(\frac{677}{1318}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1319 }(1317, a) \) | \(-1\) | \(1\) | \(e\left(\frac{162}{659}\right)\) | \(e\left(\frac{297}{659}\right)\) | \(e\left(\frac{324}{659}\right)\) | \(e\left(\frac{328}{659}\right)\) | \(e\left(\frac{459}{659}\right)\) | \(e\left(\frac{46}{659}\right)\) | \(e\left(\frac{486}{659}\right)\) | \(e\left(\frac{594}{659}\right)\) | \(e\left(\frac{490}{659}\right)\) | \(e\left(\frac{207}{659}\right)\) |