Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(591\) | 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.k
\(\chi_{4729}(14,\cdot)\) \(\chi_{4729}(19,\cdot)\) \(\chi_{4729}(21,\cdot)\) \(\chi_{4729}(35,\cdot)\) \(\chi_{4729}(37,\cdot)\) \(\chi_{4729}(40,\cdot)\) \(\chi_{4729}(52,\cdot)\) \(\chi_{4729}(60,\cdot)\) \(\chi_{4729}(67,\cdot)\) \(\chi_{4729}(78,\cdot)\) \(\chi_{4729}(83,\cdot)\) \(\chi_{4729}(90,\cdot)\) \(\chi_{4729}(100,\cdot)\) \(\chi_{4729}(117,\cdot)\) \(\chi_{4729}(118,\cdot)\) \(\chi_{4729}(130,\cdot)\) \(\chi_{4729}(131,\cdot)\) \(\chi_{4729}(135,\cdot)\) \(\chi_{4729}(150,\cdot)\) \(\chi_{4729}(169,\cdot)\) \(\chi_{4729}(177,\cdot)\) \(\chi_{4729}(187,\cdot)\) \(\chi_{4729}(193,\cdot)\) \(\chi_{4729}(195,\cdot)\) \(\chi_{4729}(196,\cdot)\) \(\chi_{4729}(224,\cdot)\) \(\chi_{4729}(225,\cdot)\) \(\chi_{4729}(266,\cdot)\) \(\chi_{4729}(294,\cdot)\) \(\chi_{4729}(304,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{591})$ |
| Fixed field: | Number field defined by a degree 591 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{391}{591}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(1047, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{197}\right)\) | \(e\left(\frac{27}{197}\right)\) | \(e\left(\frac{152}{197}\right)\) | \(e\left(\frac{373}{591}\right)\) | \(e\left(\frac{103}{197}\right)\) | \(e\left(\frac{58}{591}\right)\) | \(e\left(\frac{31}{197}\right)\) | \(e\left(\frac{54}{197}\right)\) | \(e\left(\frac{10}{591}\right)\) | \(e\left(\frac{172}{197}\right)\) |