Basic properties
| Modulus: | \(1323\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 1323.ck
\(\chi_{1323}(13,\cdot)\) \(\chi_{1323}(34,\cdot)\) \(\chi_{1323}(76,\cdot)\) \(\chi_{1323}(139,\cdot)\) \(\chi_{1323}(160,\cdot)\) \(\chi_{1323}(202,\cdot)\) \(\chi_{1323}(223,\cdot)\) \(\chi_{1323}(265,\cdot)\) \(\chi_{1323}(286,\cdot)\) \(\chi_{1323}(328,\cdot)\) \(\chi_{1323}(349,\cdot)\) \(\chi_{1323}(412,\cdot)\) \(\chi_{1323}(454,\cdot)\) \(\chi_{1323}(475,\cdot)\) \(\chi_{1323}(517,\cdot)\) \(\chi_{1323}(580,\cdot)\) \(\chi_{1323}(601,\cdot)\) \(\chi_{1323}(643,\cdot)\) \(\chi_{1323}(664,\cdot)\) \(\chi_{1323}(706,\cdot)\) \(\chi_{1323}(727,\cdot)\) \(\chi_{1323}(769,\cdot)\) \(\chi_{1323}(790,\cdot)\) \(\chi_{1323}(853,\cdot)\) \(\chi_{1323}(895,\cdot)\) \(\chi_{1323}(916,\cdot)\) \(\chi_{1323}(958,\cdot)\) \(\chi_{1323}(1021,\cdot)\) \(\chi_{1323}(1042,\cdot)\) \(\chi_{1323}(1084,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1323 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) |