Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(788\) | 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.l
\(\chi_{4729}(2,\cdot)\) \(\chi_{4729}(3,\cdot)\) \(\chi_{4729}(8,\cdot)\) \(\chi_{4729}(12,\cdot)\) \(\chi_{4729}(18,\cdot)\) \(\chi_{4729}(27,\cdot)\) \(\chi_{4729}(32,\cdot)\) \(\chi_{4729}(48,\cdot)\) \(\chi_{4729}(72,\cdot)\) \(\chi_{4729}(108,\cdot)\) \(\chi_{4729}(121,\cdot)\) \(\chi_{4729}(125,\cdot)\) \(\chi_{4729}(127,\cdot)\) \(\chi_{4729}(128,\cdot)\) \(\chi_{4729}(157,\cdot)\) \(\chi_{4729}(162,\cdot)\) \(\chi_{4729}(175,\cdot)\) \(\chi_{4729}(192,\cdot)\) \(\chi_{4729}(211,\cdot)\) \(\chi_{4729}(227,\cdot)\) \(\chi_{4729}(229,\cdot)\) \(\chi_{4729}(243,\cdot)\) \(\chi_{4729}(245,\cdot)\) \(\chi_{4729}(288,\cdot)\) \(\chi_{4729}(317,\cdot)\) \(\chi_{4729}(335,\cdot)\) \(\chi_{4729}(341,\cdot)\) \(\chi_{4729}(343,\cdot)\) \(\chi_{4729}(367,\cdot)\) \(\chi_{4729}(373,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{788})$ |
| Fixed field: | Number field defined by a degree 788 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{111}{788}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(1037, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{394}\right)\) | \(e\left(\frac{373}{394}\right)\) | \(e\left(\frac{116}{197}\right)\) | \(e\left(\frac{93}{394}\right)\) | \(e\left(\frac{146}{197}\right)\) | \(e\left(\frac{109}{394}\right)\) | \(e\left(\frac{151}{394}\right)\) | \(e\left(\frac{176}{197}\right)\) | \(e\left(\frac{6}{197}\right)\) | \(e\left(\frac{17}{788}\right)\) |