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 \(\chi_{3381}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6762.cf
\(\chi_{6762}(11,\cdot)\) \(\chi_{6762}(53,\cdot)\) \(\chi_{6762}(65,\cdot)\) \(\chi_{6762}(107,\cdot)\) \(\chi_{6762}(149,\cdot)\) \(\chi_{6762}(191,\cdot)\) \(\chi_{6762}(221,\cdot)\) \(\chi_{6762}(359,\cdot)\) \(\chi_{6762}(389,\cdot)\) \(\chi_{6762}(401,\cdot)\) \(\chi_{6762}(431,\cdot)\) \(\chi_{6762}(527,\cdot)\) \(\chi_{6762}(641,\cdot)\) \(\chi_{6762}(695,\cdot)\) \(\chi_{6762}(779,\cdot)\) \(\chi_{6762}(893,\cdot)\) \(\chi_{6762}(935,\cdot)\) \(\chi_{6762}(977,\cdot)\) \(\chi_{6762}(1019,\cdot)\) \(\chi_{6762}(1031,\cdot)\) \(\chi_{6762}(1073,\cdot)\) \(\chi_{6762}(1115,\cdot)\) \(\chi_{6762}(1187,\cdot)\) \(\chi_{6762}(1229,\cdot)\) \(\chi_{6762}(1325,\cdot)\) \(\chi_{6762}(1355,\cdot)\) \(\chi_{6762}(1367,\cdot)\) \(\chi_{6762}(1397,\cdot)\) \(\chi_{6762}(1493,\cdot)\) \(\chi_{6762}(1523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,3727,3823)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6762 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{31}{462}\right)\) | \(e\left(\frac{107}{154}\right)\) |