Basic properties
| Modulus: | \(1568\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1568.ce
\(\chi_{1568}(73,\cdot)\) \(\chi_{1568}(89,\cdot)\) \(\chi_{1568}(185,\cdot)\) \(\chi_{1568}(201,\cdot)\) \(\chi_{1568}(297,\cdot)\) \(\chi_{1568}(409,\cdot)\) \(\chi_{1568}(425,\cdot)\) \(\chi_{1568}(537,\cdot)\) \(\chi_{1568}(633,\cdot)\) \(\chi_{1568}(649,\cdot)\) \(\chi_{1568}(745,\cdot)\) \(\chi_{1568}(761,\cdot)\) \(\chi_{1568}(857,\cdot)\) \(\chi_{1568}(873,\cdot)\) \(\chi_{1568}(969,\cdot)\) \(\chi_{1568}(985,\cdot)\) \(\chi_{1568}(1081,\cdot)\) \(\chi_{1568}(1193,\cdot)\) \(\chi_{1568}(1209,\cdot)\) \(\chi_{1568}(1321,\cdot)\) \(\chi_{1568}(1417,\cdot)\) \(\chi_{1568}(1433,\cdot)\) \(\chi_{1568}(1529,\cdot)\) \(\chi_{1568}(1545,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,-i,e\left(\frac{37}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) |