Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(5929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | 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.cd
\(\chi_{5929}(10,\cdot)\) \(\chi_{5929}(54,\cdot)\) \(\chi_{5929}(87,\cdot)\) \(\chi_{5929}(131,\cdot)\) \(\chi_{5929}(164,\cdot)\) \(\chi_{5929}(208,\cdot)\) \(\chi_{5929}(285,\cdot)\) \(\chi_{5929}(318,\cdot)\) \(\chi_{5929}(395,\cdot)\) \(\chi_{5929}(439,\cdot)\) \(\chi_{5929}(516,\cdot)\) \(\chi_{5929}(549,\cdot)\) \(\chi_{5929}(593,\cdot)\) \(\chi_{5929}(626,\cdot)\) \(\chi_{5929}(670,\cdot)\) \(\chi_{5929}(703,\cdot)\) \(\chi_{5929}(747,\cdot)\) \(\chi_{5929}(780,\cdot)\) \(\chi_{5929}(824,\cdot)\) \(\chi_{5929}(857,\cdot)\) \(\chi_{5929}(934,\cdot)\) \(\chi_{5929}(978,\cdot)\) \(\chi_{5929}(1055,\cdot)\) \(\chi_{5929}(1132,\cdot)\) \(\chi_{5929}(1165,\cdot)\) \(\chi_{5929}(1242,\cdot)\) \(\chi_{5929}(1286,\cdot)\) \(\chi_{5929}(1319,\cdot)\) \(\chi_{5929}(1363,\cdot)\) \(\chi_{5929}(1396,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{13}{42}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{337}{462}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{6}{77}\right)\) |