Basic properties
| Modulus: | \(1856\) | |
| Conductor: | \(928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{928}(837,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1856.ck
\(\chi_{1856}(25,\cdot)\) \(\chi_{1856}(169,\cdot)\) \(\chi_{1856}(281,\cdot)\) \(\chi_{1856}(297,\cdot)\) \(\chi_{1856}(313,\cdot)\) \(\chi_{1856}(393,\cdot)\) \(\chi_{1856}(489,\cdot)\) \(\chi_{1856}(633,\cdot)\) \(\chi_{1856}(745,\cdot)\) \(\chi_{1856}(761,\cdot)\) \(\chi_{1856}(777,\cdot)\) \(\chi_{1856}(857,\cdot)\) \(\chi_{1856}(953,\cdot)\) \(\chi_{1856}(1097,\cdot)\) \(\chi_{1856}(1209,\cdot)\) \(\chi_{1856}(1225,\cdot)\) \(\chi_{1856}(1241,\cdot)\) \(\chi_{1856}(1321,\cdot)\) \(\chi_{1856}(1417,\cdot)\) \(\chi_{1856}(1561,\cdot)\) \(\chi_{1856}(1673,\cdot)\) \(\chi_{1856}(1689,\cdot)\) \(\chi_{1856}(1705,\cdot)\) \(\chi_{1856}(1785,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((639,581,321)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1856 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{19}{56}\right)\) |