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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1568.ci
\(\chi_{1568}(11,\cdot)\) \(\chi_{1568}(51,\cdot)\) \(\chi_{1568}(107,\cdot)\) \(\chi_{1568}(123,\cdot)\) \(\chi_{1568}(163,\cdot)\) \(\chi_{1568}(179,\cdot)\) \(\chi_{1568}(219,\cdot)\) \(\chi_{1568}(235,\cdot)\) \(\chi_{1568}(291,\cdot)\) \(\chi_{1568}(331,\cdot)\) \(\chi_{1568}(347,\cdot)\) \(\chi_{1568}(387,\cdot)\) \(\chi_{1568}(403,\cdot)\) \(\chi_{1568}(443,\cdot)\) \(\chi_{1568}(499,\cdot)\) \(\chi_{1568}(515,\cdot)\) \(\chi_{1568}(555,\cdot)\) \(\chi_{1568}(571,\cdot)\) \(\chi_{1568}(611,\cdot)\) \(\chi_{1568}(627,\cdot)\) \(\chi_{1568}(683,\cdot)\) \(\chi_{1568}(723,\cdot)\) \(\chi_{1568}(739,\cdot)\) \(\chi_{1568}(779,\cdot)\) \(\chi_{1568}(795,\cdot)\) \(\chi_{1568}(835,\cdot)\) \(\chi_{1568}(891,\cdot)\) \(\chi_{1568}(907,\cdot)\) \(\chi_{1568}(947,\cdot)\) \(\chi_{1568}(963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{168}\right)\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{121}{168}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) |