Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(5929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2310\) | 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 5929.ck
\(\chi_{5929}(17,\cdot)\) \(\chi_{5929}(24,\cdot)\) \(\chi_{5929}(52,\cdot)\) \(\chi_{5929}(61,\cdot)\) \(\chi_{5929}(73,\cdot)\) \(\chi_{5929}(96,\cdot)\) \(\chi_{5929}(101,\cdot)\) \(\chi_{5929}(138,\cdot)\) \(\chi_{5929}(145,\cdot)\) \(\chi_{5929}(150,\cdot)\) \(\chi_{5929}(171,\cdot)\) \(\chi_{5929}(173,\cdot)\) \(\chi_{5929}(194,\cdot)\) \(\chi_{5929}(206,\cdot)\) \(\chi_{5929}(222,\cdot)\) \(\chi_{5929}(248,\cdot)\) \(\chi_{5929}(250,\cdot)\) \(\chi_{5929}(255,\cdot)\) \(\chi_{5929}(271,\cdot)\) \(\chi_{5929}(283,\cdot)\) \(\chi_{5929}(292,\cdot)\) \(\chi_{5929}(299,\cdot)\) \(\chi_{5929}(304,\cdot)\) \(\chi_{5929}(327,\cdot)\) \(\chi_{5929}(332,\cdot)\) \(\chi_{5929}(348,\cdot)\) \(\chi_{5929}(369,\cdot)\) \(\chi_{5929}(376,\cdot)\) \(\chi_{5929}(381,\cdot)\) \(\chi_{5929}(402,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1155})$ |
| Fixed field: | Number field defined by a degree 2310 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{25}{42}\right),e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{2129}{2310}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{974}{1155}\right)\) | \(e\left(\frac{521}{2310}\right)\) | \(e\left(\frac{276}{385}\right)\) | \(e\left(\frac{589}{770}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{244}{385}\right)\) |