Basic properties
| Modulus: | \(1049\) | |
| Conductor: | \(1049\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(131\) | 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.e
\(\chi_{1049}(4,\cdot)\) \(\chi_{1049}(16,\cdot)\) \(\chi_{1049}(19,\cdot)\) \(\chi_{1049}(21,\cdot)\) \(\chi_{1049}(26,\cdot)\) \(\chi_{1049}(50,\cdot)\) \(\chi_{1049}(53,\cdot)\) \(\chi_{1049}(58,\cdot)\) \(\chi_{1049}(61,\cdot)\) \(\chi_{1049}(64,\cdot)\) \(\chi_{1049}(76,\cdot)\) \(\chi_{1049}(84,\cdot)\) \(\chi_{1049}(86,\cdot)\) \(\chi_{1049}(90,\cdot)\) \(\chi_{1049}(104,\cdot)\) \(\chi_{1049}(110,\cdot)\) \(\chi_{1049}(131,\cdot)\) \(\chi_{1049}(138,\cdot)\) \(\chi_{1049}(146,\cdot)\) \(\chi_{1049}(162,\cdot)\) \(\chi_{1049}(167,\cdot)\) \(\chi_{1049}(169,\cdot)\) \(\chi_{1049}(194,\cdot)\) \(\chi_{1049}(198,\cdot)\) \(\chi_{1049}(200,\cdot)\) \(\chi_{1049}(212,\cdot)\) \(\chi_{1049}(217,\cdot)\) \(\chi_{1049}(232,\cdot)\) \(\chi_{1049}(238,\cdot)\) \(\chi_{1049}(242,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{131})$ |
| Fixed field: | Number field defined by a degree 131 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{92}{131}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1049 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{74}{131}\right)\) | \(e\left(\frac{92}{131}\right)\) | \(e\left(\frac{17}{131}\right)\) | \(e\left(\frac{108}{131}\right)\) | \(e\left(\frac{35}{131}\right)\) | \(e\left(\frac{11}{131}\right)\) | \(e\left(\frac{91}{131}\right)\) | \(e\left(\frac{53}{131}\right)\) | \(e\left(\frac{51}{131}\right)\) | \(e\left(\frac{73}{131}\right)\) |