Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1576\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4729.n
\(\chi_{4729}(11,\cdot)\) \(\chi_{4729}(22,\cdot)\) \(\chi_{4729}(23,\cdot)\) \(\chi_{4729}(29,\cdot)\) \(\chi_{4729}(31,\cdot)\) \(\chi_{4729}(33,\cdot)\) \(\chi_{4729}(41,\cdot)\) \(\chi_{4729}(44,\cdot)\) \(\chi_{4729}(46,\cdot)\) \(\chi_{4729}(62,\cdot)\) \(\chi_{4729}(66,\cdot)\) \(\chi_{4729}(69,\cdot)\) \(\chi_{4729}(82,\cdot)\) \(\chi_{4729}(87,\cdot)\) \(\chi_{4729}(88,\cdot)\) \(\chi_{4729}(92,\cdot)\) \(\chi_{4729}(93,\cdot)\) \(\chi_{4729}(99,\cdot)\) \(\chi_{4729}(103,\cdot)\) \(\chi_{4729}(113,\cdot)\) \(\chi_{4729}(116,\cdot)\) \(\chi_{4729}(123,\cdot)\) \(\chi_{4729}(124,\cdot)\) \(\chi_{4729}(132,\cdot)\) \(\chi_{4729}(138,\cdot)\) \(\chi_{4729}(151,\cdot)\) \(\chi_{4729}(163,\cdot)\) \(\chi_{4729}(164,\cdot)\) \(\chi_{4729}(173,\cdot)\) \(\chi_{4729}(174,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1576})$ |
| Fixed field: | Number field defined by a degree 1576 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{159}{1576}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(2330, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{788}\right)\) | \(e\left(\frac{513}{788}\right)\) | \(e\left(\frac{65}{394}\right)\) | \(e\left(\frac{261}{788}\right)\) | \(e\left(\frac{289}{394}\right)\) | \(e\left(\frac{39}{788}\right)\) | \(e\left(\frac{195}{788}\right)\) | \(e\left(\frac{119}{394}\right)\) | \(e\left(\frac{163}{394}\right)\) | \(e\left(\frac{1217}{1576}\right)\) |