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.ck
\(\chi_{1568}(37,\cdot)\) \(\chi_{1568}(53,\cdot)\) \(\chi_{1568}(93,\cdot)\) \(\chi_{1568}(109,\cdot)\) \(\chi_{1568}(149,\cdot)\) \(\chi_{1568}(205,\cdot)\) \(\chi_{1568}(221,\cdot)\) \(\chi_{1568}(261,\cdot)\) \(\chi_{1568}(277,\cdot)\) \(\chi_{1568}(317,\cdot)\) \(\chi_{1568}(333,\cdot)\) \(\chi_{1568}(389,\cdot)\) \(\chi_{1568}(429,\cdot)\) \(\chi_{1568}(445,\cdot)\) \(\chi_{1568}(485,\cdot)\) \(\chi_{1568}(501,\cdot)\) \(\chi_{1568}(541,\cdot)\) \(\chi_{1568}(597,\cdot)\) \(\chi_{1568}(613,\cdot)\) \(\chi_{1568}(653,\cdot)\) \(\chi_{1568}(669,\cdot)\) \(\chi_{1568}(709,\cdot)\) \(\chi_{1568}(725,\cdot)\) \(\chi_{1568}(781,\cdot)\) \(\chi_{1568}(821,\cdot)\) \(\chi_{1568}(837,\cdot)\) \(\chi_{1568}(877,\cdot)\) \(\chi_{1568}(893,\cdot)\) \(\chi_{1568}(933,\cdot)\) \(\chi_{1568}(989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{168}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{168}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) |