Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(394\) | 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 4729.j
\(\chi_{4729}(4,\cdot)\) \(\chi_{4729}(6,\cdot)\) \(\chi_{4729}(9,\cdot)\) \(\chi_{4729}(64,\cdot)\) \(\chi_{4729}(96,\cdot)\) \(\chi_{4729}(144,\cdot)\) \(\chi_{4729}(197,\cdot)\) \(\chi_{4729}(216,\cdot)\) \(\chi_{4729}(242,\cdot)\) \(\chi_{4729}(254,\cdot)\) \(\chi_{4729}(324,\cdot)\) \(\chi_{4729}(350,\cdot)\) \(\chi_{4729}(355,\cdot)\) \(\chi_{4729}(363,\cdot)\) \(\chi_{4729}(381,\cdot)\) \(\chi_{4729}(413,\cdot)\) \(\chi_{4729}(422,\cdot)\) \(\chi_{4729}(451,\cdot)\) \(\chi_{4729}(454,\cdot)\) \(\chi_{4729}(455,\cdot)\) \(\chi_{4729}(458,\cdot)\) \(\chi_{4729}(475,\cdot)\) \(\chi_{4729}(486,\cdot)\) \(\chi_{4729}(525,\cdot)\) \(\chi_{4729}(607,\cdot)\) \(\chi_{4729}(613,\cdot)\) \(\chi_{4729}(633,\cdot)\) \(\chi_{4729}(634,\cdot)\) \(\chi_{4729}(643,\cdot)\) \(\chi_{4729}(670,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{197})$ |
| Fixed field: | Number field defined by a degree 394 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{195}{394}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(1087, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{197}\right)\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{152}{197}\right)\) | \(e\left(\frac{190}{197}\right)\) | \(e\left(\frac{103}{197}\right)\) | \(e\left(\frac{85}{197}\right)\) | \(e\left(\frac{31}{197}\right)\) | \(e\left(\frac{54}{197}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{147}{394}\right)\) |