Basic properties
| Modulus: | \(1568\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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 1568.cj
\(\chi_{1568}(3,\cdot)\) \(\chi_{1568}(59,\cdot)\) \(\chi_{1568}(75,\cdot)\) \(\chi_{1568}(115,\cdot)\) \(\chi_{1568}(131,\cdot)\) \(\chi_{1568}(171,\cdot)\) \(\chi_{1568}(187,\cdot)\) \(\chi_{1568}(243,\cdot)\) \(\chi_{1568}(283,\cdot)\) \(\chi_{1568}(299,\cdot)\) \(\chi_{1568}(339,\cdot)\) \(\chi_{1568}(355,\cdot)\) \(\chi_{1568}(395,\cdot)\) \(\chi_{1568}(451,\cdot)\) \(\chi_{1568}(467,\cdot)\) \(\chi_{1568}(507,\cdot)\) \(\chi_{1568}(523,\cdot)\) \(\chi_{1568}(563,\cdot)\) \(\chi_{1568}(579,\cdot)\) \(\chi_{1568}(635,\cdot)\) \(\chi_{1568}(675,\cdot)\) \(\chi_{1568}(691,\cdot)\) \(\chi_{1568}(731,\cdot)\) \(\chi_{1568}(747,\cdot)\) \(\chi_{1568}(787,\cdot)\) \(\chi_{1568}(843,\cdot)\) \(\chi_{1568}(859,\cdot)\) \(\chi_{1568}(899,\cdot)\) \(\chi_{1568}(915,\cdot)\) \(\chi_{1568}(955,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{55}{168}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) |