Basic properties
| Modulus: | \(1856\) | |
| Conductor: | \(1856\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1856.cr
\(\chi_{1856}(35,\cdot)\) \(\chi_{1856}(51,\cdot)\) \(\chi_{1856}(67,\cdot)\) \(\chi_{1856}(91,\cdot)\) \(\chi_{1856}(179,\cdot)\) \(\chi_{1856}(187,\cdot)\) \(\chi_{1856}(267,\cdot)\) \(\chi_{1856}(283,\cdot)\) \(\chi_{1856}(299,\cdot)\) \(\chi_{1856}(323,\cdot)\) \(\chi_{1856}(411,\cdot)\) \(\chi_{1856}(419,\cdot)\) \(\chi_{1856}(499,\cdot)\) \(\chi_{1856}(515,\cdot)\) \(\chi_{1856}(531,\cdot)\) \(\chi_{1856}(555,\cdot)\) \(\chi_{1856}(643,\cdot)\) \(\chi_{1856}(651,\cdot)\) \(\chi_{1856}(731,\cdot)\) \(\chi_{1856}(747,\cdot)\) \(\chi_{1856}(763,\cdot)\) \(\chi_{1856}(787,\cdot)\) \(\chi_{1856}(875,\cdot)\) \(\chi_{1856}(883,\cdot)\) \(\chi_{1856}(963,\cdot)\) \(\chi_{1856}(979,\cdot)\) \(\chi_{1856}(995,\cdot)\) \(\chi_{1856}(1019,\cdot)\) \(\chi_{1856}(1107,\cdot)\) \(\chi_{1856}(1115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((639,581,321)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1856 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{112}\right)\) | \(e\left(\frac{45}{112}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(-i\) | \(e\left(\frac{27}{112}\right)\) | \(e\left(\frac{65}{112}\right)\) |