Basic properties
| Modulus: | \(1049\) | |
| Conductor: | \(1049\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(262\) | 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 1049.f
\(\chi_{1049}(2,\cdot)\) \(\chi_{1049}(8,\cdot)\) \(\chi_{1049}(13,\cdot)\) \(\chi_{1049}(25,\cdot)\) \(\chi_{1049}(29,\cdot)\) \(\chi_{1049}(32,\cdot)\) \(\chi_{1049}(38,\cdot)\) \(\chi_{1049}(42,\cdot)\) \(\chi_{1049}(43,\cdot)\) \(\chi_{1049}(45,\cdot)\) \(\chi_{1049}(52,\cdot)\) \(\chi_{1049}(55,\cdot)\) \(\chi_{1049}(69,\cdot)\) \(\chi_{1049}(73,\cdot)\) \(\chi_{1049}(81,\cdot)\) \(\chi_{1049}(97,\cdot)\) \(\chi_{1049}(99,\cdot)\) \(\chi_{1049}(100,\cdot)\) \(\chi_{1049}(106,\cdot)\) \(\chi_{1049}(116,\cdot)\) \(\chi_{1049}(119,\cdot)\) \(\chi_{1049}(121,\cdot)\) \(\chi_{1049}(122,\cdot)\) \(\chi_{1049}(128,\cdot)\) \(\chi_{1049}(152,\cdot)\) \(\chi_{1049}(163,\cdot)\) \(\chi_{1049}(168,\cdot)\) \(\chi_{1049}(172,\cdot)\) \(\chi_{1049}(180,\cdot)\) \(\chi_{1049}(181,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{131})$ |
| Fixed field: | Number field defined by a degree 262 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{61}{262}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1049 }(180, a) \) | \(1\) | \(1\) | \(e\left(\frac{100}{131}\right)\) | \(e\left(\frac{61}{262}\right)\) | \(e\left(\frac{69}{131}\right)\) | \(e\left(\frac{107}{131}\right)\) | \(e\left(\frac{261}{262}\right)\) | \(e\left(\frac{97}{262}\right)\) | \(e\left(\frac{38}{131}\right)\) | \(e\left(\frac{61}{131}\right)\) | \(e\left(\frac{76}{131}\right)\) | \(e\left(\frac{42}{131}\right)\) |