Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(197\) | 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.i
\(\chi_{4729}(16,\cdot)\) \(\chi_{4729}(24,\cdot)\) \(\chi_{4729}(36,\cdot)\) \(\chi_{4729}(54,\cdot)\) \(\chi_{4729}(81,\cdot)\) \(\chi_{4729}(250,\cdot)\) \(\chi_{4729}(251,\cdot)\) \(\chi_{4729}(253,\cdot)\) \(\chi_{4729}(256,\cdot)\) \(\chi_{4729}(295,\cdot)\) \(\chi_{4729}(314,\cdot)\) \(\chi_{4729}(319,\cdot)\) \(\chi_{4729}(325,\cdot)\) \(\chi_{4729}(375,\cdot)\) \(\chi_{4729}(384,\cdot)\) \(\chi_{4729}(471,\cdot)\) \(\chi_{4729}(490,\cdot)\) \(\chi_{4729}(497,\cdot)\) \(\chi_{4729}(576,\cdot)\) \(\chi_{4729}(637,\cdot)\) \(\chi_{4729}(665,\cdot)\) \(\chi_{4729}(682,\cdot)\) \(\chi_{4729}(734,\cdot)\) \(\chi_{4729}(735,\cdot)\) \(\chi_{4729}(739,\cdot)\) \(\chi_{4729}(746,\cdot)\) \(\chi_{4729}(788,\cdot)\) \(\chi_{4729}(821,\cdot)\) \(\chi_{4729}(857,\cdot)\) \(\chi_{4729}(864,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{197})$ |
| Fixed field: | Number field defined by a degree 197 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{146}{197}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(490, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{197}\right)\) | \(e\left(\frac{195}{197}\right)\) | \(e\left(\frac{69}{197}\right)\) | \(e\left(\frac{37}{197}\right)\) | \(e\left(\frac{131}{197}\right)\) | \(e\left(\frac{1}{197}\right)\) | \(e\left(\frac{5}{197}\right)\) | \(e\left(\frac{193}{197}\right)\) | \(e\left(\frac{170}{197}\right)\) | \(e\left(\frac{104}{197}\right)\) |