Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1692\) | 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 5077.v
\(\chi_{5077}(8,\cdot)\) \(\chi_{5077}(13,\cdot)\) \(\chi_{5077}(15,\cdot)\) \(\chi_{5077}(23,\cdot)\) \(\chi_{5077}(29,\cdot)\) \(\chi_{5077}(38,\cdot)\) \(\chi_{5077}(45,\cdot)\) \(\chi_{5077}(69,\cdot)\) \(\chi_{5077}(72,\cdot)\) \(\chi_{5077}(77,\cdot)\) \(\chi_{5077}(114,\cdot)\) \(\chi_{5077}(117,\cdot)\) \(\chi_{5077}(124,\cdot)\) \(\chi_{5077}(140,\cdot)\) \(\chi_{5077}(164,\cdot)\) \(\chi_{5077}(172,\cdot)\) \(\chi_{5077}(176,\cdot)\) \(\chi_{5077}(200,\cdot)\) \(\chi_{5077}(204,\cdot)\) \(\chi_{5077}(216,\cdot)\) \(\chi_{5077}(219,\cdot)\) \(\chi_{5077}(259,\cdot)\) \(\chi_{5077}(262,\cdot)\) \(\chi_{5077}(265,\cdot)\) \(\chi_{5077}(286,\cdot)\) \(\chi_{5077}(294,\cdot)\) \(\chi_{5077}(320,\cdot)\) \(\chi_{5077}(323,\cdot)\) \(\chi_{5077}(325,\cdot)\) \(\chi_{5077}(330,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1692})$ |
| Fixed field: | Number field defined by a degree 1692 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{191}{1692}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{1692}\right)\) | \(e\left(\frac{113}{282}\right)\) | \(e\left(\frac{191}{846}\right)\) | \(e\left(\frac{99}{188}\right)\) | \(e\left(\frac{869}{1692}\right)\) | \(e\left(\frac{371}{423}\right)\) | \(e\left(\frac{191}{564}\right)\) | \(e\left(\frac{113}{141}\right)\) | \(e\left(\frac{541}{846}\right)\) | \(e\left(\frac{115}{1692}\right)\) |