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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1323.cf
\(\chi_{1323}(47,\cdot)\) \(\chi_{1323}(59,\cdot)\) \(\chi_{1323}(110,\cdot)\) \(\chi_{1323}(122,\cdot)\) \(\chi_{1323}(173,\cdot)\) \(\chi_{1323}(185,\cdot)\) \(\chi_{1323}(236,\cdot)\) \(\chi_{1323}(248,\cdot)\) \(\chi_{1323}(299,\cdot)\) \(\chi_{1323}(311,\cdot)\) \(\chi_{1323}(425,\cdot)\) \(\chi_{1323}(437,\cdot)\) \(\chi_{1323}(488,\cdot)\) \(\chi_{1323}(500,\cdot)\) \(\chi_{1323}(551,\cdot)\) \(\chi_{1323}(563,\cdot)\) \(\chi_{1323}(614,\cdot)\) \(\chi_{1323}(626,\cdot)\) \(\chi_{1323}(677,\cdot)\) \(\chi_{1323}(689,\cdot)\) \(\chi_{1323}(740,\cdot)\) \(\chi_{1323}(752,\cdot)\) \(\chi_{1323}(866,\cdot)\) \(\chi_{1323}(878,\cdot)\) \(\chi_{1323}(929,\cdot)\) \(\chi_{1323}(941,\cdot)\) \(\chi_{1323}(992,\cdot)\) \(\chi_{1323}(1004,\cdot)\) \(\chi_{1323}(1055,\cdot)\) \(\chi_{1323}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{37}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1323 }(563, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |