Basic properties
| Modulus: | \(6762\) | |
| Conductor: | \(3381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3381}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6762.cg
\(\chi_{6762}(59,\cdot)\) \(\chi_{6762}(101,\cdot)\) \(\chi_{6762}(131,\cdot)\) \(\chi_{6762}(173,\cdot)\) \(\chi_{6762}(257,\cdot)\) \(\chi_{6762}(269,\cdot)\) \(\chi_{6762}(311,\cdot)\) \(\chi_{6762}(353,\cdot)\) \(\chi_{6762}(395,\cdot)\) \(\chi_{6762}(593,\cdot)\) \(\chi_{6762}(647,\cdot)\) \(\chi_{6762}(719,\cdot)\) \(\chi_{6762}(731,\cdot)\) \(\chi_{6762}(761,\cdot)\) \(\chi_{6762}(857,\cdot)\) \(\chi_{6762}(887,\cdot)\) \(\chi_{6762}(899,\cdot)\) \(\chi_{6762}(929,\cdot)\) \(\chi_{6762}(1025,\cdot)\) \(\chi_{6762}(1067,\cdot)\) \(\chi_{6762}(1139,\cdot)\) \(\chi_{6762}(1181,\cdot)\) \(\chi_{6762}(1223,\cdot)\) \(\chi_{6762}(1235,\cdot)\) \(\chi_{6762}(1277,\cdot)\) \(\chi_{6762}(1319,\cdot)\) \(\chi_{6762}(1361,\cdot)\) \(\chi_{6762}(1475,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,3727,3823)\) → \((-1,e\left(\frac{13}{42}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6762 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{60}{77}\right)\) |