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
\(2\) → \(e\left(\frac{1193}{1692}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1193}{1692}\right)\) | \(e\left(\frac{161}{282}\right)\) | \(e\left(\frac{347}{846}\right)\) | \(e\left(\frac{77}{188}\right)\) | \(e\left(\frac{467}{1692}\right)\) | \(e\left(\frac{158}{423}\right)\) | \(e\left(\frac{65}{564}\right)\) | \(e\left(\frac{20}{141}\right)\) | \(e\left(\frac{97}{846}\right)\) | \(e\left(\frac{1489}{1692}\right)\) |