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
\(17\) → \(e\left(\frac{545}{591}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4729 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{197}\right)\) | \(e\left(\frac{20}{197}\right)\) | \(e\left(\frac{98}{197}\right)\) | \(e\left(\frac{269}{591}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{167}{591}\right)\) | \(e\left(\frac{147}{197}\right)\) | \(e\left(\frac{40}{197}\right)\) | \(e\left(\frac{416}{591}\right)\) | \(e\left(\frac{142}{197}\right)\) |