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 \(\chi_{784}(205,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1568.cf
\(\chi_{1568}(9,\cdot)\) \(\chi_{1568}(25,\cdot)\) \(\chi_{1568}(121,\cdot)\) \(\chi_{1568}(137,\cdot)\) \(\chi_{1568}(233,\cdot)\) \(\chi_{1568}(249,\cdot)\) \(\chi_{1568}(345,\cdot)\) \(\chi_{1568}(457,\cdot)\) \(\chi_{1568}(473,\cdot)\) \(\chi_{1568}(585,\cdot)\) \(\chi_{1568}(681,\cdot)\) \(\chi_{1568}(697,\cdot)\) \(\chi_{1568}(793,\cdot)\) \(\chi_{1568}(809,\cdot)\) \(\chi_{1568}(905,\cdot)\) \(\chi_{1568}(921,\cdot)\) \(\chi_{1568}(1017,\cdot)\) \(\chi_{1568}(1033,\cdot)\) \(\chi_{1568}(1129,\cdot)\) \(\chi_{1568}(1241,\cdot)\) \(\chi_{1568}(1257,\cdot)\) \(\chi_{1568}(1369,\cdot)\) \(\chi_{1568}(1465,\cdot)\) \(\chi_{1568}(1481,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,197,1473)\) → \((1,-i,e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1568 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) |