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.cs
\(\chi_{1856}(21,\cdot)\) \(\chi_{1856}(69,\cdot)\) \(\chi_{1856}(101,\cdot)\) \(\chi_{1856}(189,\cdot)\) \(\chi_{1856}(221,\cdot)\) \(\chi_{1856}(269,\cdot)\) \(\chi_{1856}(293,\cdot)\) \(\chi_{1856}(309,\cdot)\) \(\chi_{1856}(317,\cdot)\) \(\chi_{1856}(437,\cdot)\) \(\chi_{1856}(445,\cdot)\) \(\chi_{1856}(461,\cdot)\) \(\chi_{1856}(485,\cdot)\) \(\chi_{1856}(533,\cdot)\) \(\chi_{1856}(565,\cdot)\) \(\chi_{1856}(653,\cdot)\) \(\chi_{1856}(685,\cdot)\) \(\chi_{1856}(733,\cdot)\) \(\chi_{1856}(757,\cdot)\) \(\chi_{1856}(773,\cdot)\) \(\chi_{1856}(781,\cdot)\) \(\chi_{1856}(901,\cdot)\) \(\chi_{1856}(909,\cdot)\) \(\chi_{1856}(925,\cdot)\) \(\chi_{1856}(949,\cdot)\) \(\chi_{1856}(997,\cdot)\) \(\chi_{1856}(1029,\cdot)\) \(\chi_{1856}(1117,\cdot)\) \(\chi_{1856}(1149,\cdot)\) \(\chi_{1856}(1197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((639,581,321)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{17}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1856 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{112}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{27}{112}\right)\) | \(e\left(\frac{13}{112}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(-1\) | \(e\left(\frac{17}{112}\right)\) | \(e\left(\frac{99}{112}\right)\) |