Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1182\) | 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.m
\(\chi_{4729}(10,\cdot)\) \(\chi_{4729}(13,\cdot)\) \(\chi_{4729}(15,\cdot)\) \(\chi_{4729}(25,\cdot)\) \(\chi_{4729}(49,\cdot)\) \(\chi_{4729}(56,\cdot)\) \(\chi_{4729}(76,\cdot)\) \(\chi_{4729}(84,\cdot)\) \(\chi_{4729}(97,\cdot)\) \(\chi_{4729}(114,\cdot)\) \(\chi_{4729}(126,\cdot)\) \(\chi_{4729}(140,\cdot)\) \(\chi_{4729}(142,\cdot)\) \(\chi_{4729}(146,\cdot)\) \(\chi_{4729}(148,\cdot)\) \(\chi_{4729}(149,\cdot)\) \(\chi_{4729}(160,\cdot)\) \(\chi_{4729}(171,\cdot)\) \(\chi_{4729}(179,\cdot)\) \(\chi_{4729}(182,\cdot)\) \(\chi_{4729}(189,\cdot)\) \(\chi_{4729}(190,\cdot)\) \(\chi_{4729}(208,\cdot)\) \(\chi_{4729}(210,\cdot)\) \(\chi_{4729}(213,\cdot)\) \(\chi_{4729}(219,\cdot)\) \(\chi_{4729}(222,\cdot)\) \(\chi_{4729}(240,\cdot)\) \(\chi_{4729}(241,\cdot)\) \(\chi_{4729}(247,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{591})$ |
| Fixed field: | Number field defined by a degree 1182 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{685}{1182}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(126, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{197}\right)\) | \(e\left(\frac{168}{197}\right)\) | \(e\left(\frac{114}{197}\right)\) | \(e\left(\frac{329}{591}\right)\) | \(e\left(\frac{28}{197}\right)\) | \(e\left(\frac{536}{591}\right)\) | \(e\left(\frac{171}{197}\right)\) | \(e\left(\frac{139}{197}\right)\) | \(e\left(\frac{500}{591}\right)\) | \(e\left(\frac{61}{394}\right)\) |