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 \(\chi_{928}(651,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1856.cl
\(\chi_{1856}(71,\cdot)\) \(\chi_{1856}(151,\cdot)\) \(\chi_{1856}(167,\cdot)\) \(\chi_{1856}(183,\cdot)\) \(\chi_{1856}(295,\cdot)\) \(\chi_{1856}(439,\cdot)\) \(\chi_{1856}(535,\cdot)\) \(\chi_{1856}(615,\cdot)\) \(\chi_{1856}(631,\cdot)\) \(\chi_{1856}(647,\cdot)\) \(\chi_{1856}(759,\cdot)\) \(\chi_{1856}(903,\cdot)\) \(\chi_{1856}(999,\cdot)\) \(\chi_{1856}(1079,\cdot)\) \(\chi_{1856}(1095,\cdot)\) \(\chi_{1856}(1111,\cdot)\) \(\chi_{1856}(1223,\cdot)\) \(\chi_{1856}(1367,\cdot)\) \(\chi_{1856}(1463,\cdot)\) \(\chi_{1856}(1543,\cdot)\) \(\chi_{1856}(1559,\cdot)\) \(\chi_{1856}(1575,\cdot)\) \(\chi_{1856}(1687,\cdot)\) \(\chi_{1856}(1831,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((639,581,321)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1856 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(1\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{3}{56}\right)\) |