Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(43904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4704\) | 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 43904.fm
\(\chi_{43904}(11,\cdot)\) \(\chi_{43904}(51,\cdot)\) \(\chi_{43904}(107,\cdot)\) \(\chi_{43904}(123,\cdot)\) \(\chi_{43904}(163,\cdot)\) \(\chi_{43904}(179,\cdot)\) \(\chi_{43904}(219,\cdot)\) \(\chi_{43904}(235,\cdot)\) \(\chi_{43904}(291,\cdot)\) \(\chi_{43904}(331,\cdot)\) \(\chi_{43904}(347,\cdot)\) \(\chi_{43904}(387,\cdot)\) \(\chi_{43904}(403,\cdot)\) \(\chi_{43904}(443,\cdot)\) \(\chi_{43904}(499,\cdot)\) \(\chi_{43904}(515,\cdot)\) \(\chi_{43904}(555,\cdot)\) \(\chi_{43904}(571,\cdot)\) \(\chi_{43904}(611,\cdot)\) \(\chi_{43904}(627,\cdot)\) \(\chi_{43904}(683,\cdot)\) \(\chi_{43904}(723,\cdot)\) \(\chi_{43904}(739,\cdot)\) \(\chi_{43904}(779,\cdot)\) \(\chi_{43904}(795,\cdot)\) \(\chi_{43904}(835,\cdot)\) \(\chi_{43904}(891,\cdot)\) \(\chi_{43904}(907,\cdot)\) \(\chi_{43904}(947,\cdot)\) \(\chi_{43904}(963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4704})$ |
| Fixed field: | Number field defined by a degree 4704 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((-1,e\left(\frac{31}{32}\right),e\left(\frac{65}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(179, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3991}{4704}\right)\) | \(e\left(\frac{3725}{4704}\right)\) | \(e\left(\frac{1639}{2352}\right)\) | \(e\left(\frac{3841}{4704}\right)\) | \(e\left(\frac{865}{1568}\right)\) | \(e\left(\frac{251}{392}\right)\) | \(e\left(\frac{211}{1176}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{1363}{2352}\right)\) | \(e\left(\frac{1373}{2352}\right)\) |