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.ch
\(\chi_{1323}(29,\cdot)\) \(\chi_{1323}(92,\cdot)\) \(\chi_{1323}(113,\cdot)\) \(\chi_{1323}(155,\cdot)\) \(\chi_{1323}(176,\cdot)\) \(\chi_{1323}(218,\cdot)\) \(\chi_{1323}(239,\cdot)\) \(\chi_{1323}(281,\cdot)\) \(\chi_{1323}(302,\cdot)\) \(\chi_{1323}(365,\cdot)\) \(\chi_{1323}(407,\cdot)\) \(\chi_{1323}(428,\cdot)\) \(\chi_{1323}(470,\cdot)\) \(\chi_{1323}(533,\cdot)\) \(\chi_{1323}(554,\cdot)\) \(\chi_{1323}(596,\cdot)\) \(\chi_{1323}(617,\cdot)\) \(\chi_{1323}(659,\cdot)\) \(\chi_{1323}(680,\cdot)\) \(\chi_{1323}(722,\cdot)\) \(\chi_{1323}(743,\cdot)\) \(\chi_{1323}(806,\cdot)\) \(\chi_{1323}(848,\cdot)\) \(\chi_{1323}(869,\cdot)\) \(\chi_{1323}(911,\cdot)\) \(\chi_{1323}(974,\cdot)\) \(\chi_{1323}(995,\cdot)\) \(\chi_{1323}(1037,\cdot)\) \(\chi_{1323}(1058,\cdot)\) \(\chi_{1323}(1100,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1323 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) |