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.fl
\(\chi_{43904}(5,\cdot)\) \(\chi_{43904}(45,\cdot)\) \(\chi_{43904}(61,\cdot)\) \(\chi_{43904}(101,\cdot)\) \(\chi_{43904}(157,\cdot)\) \(\chi_{43904}(173,\cdot)\) \(\chi_{43904}(213,\cdot)\) \(\chi_{43904}(229,\cdot)\) \(\chi_{43904}(269,\cdot)\) \(\chi_{43904}(285,\cdot)\) \(\chi_{43904}(341,\cdot)\) \(\chi_{43904}(381,\cdot)\) \(\chi_{43904}(397,\cdot)\) \(\chi_{43904}(437,\cdot)\) \(\chi_{43904}(453,\cdot)\) \(\chi_{43904}(493,\cdot)\) \(\chi_{43904}(549,\cdot)\) \(\chi_{43904}(565,\cdot)\) \(\chi_{43904}(605,\cdot)\) \(\chi_{43904}(621,\cdot)\) \(\chi_{43904}(661,\cdot)\) \(\chi_{43904}(677,\cdot)\) \(\chi_{43904}(733,\cdot)\) \(\chi_{43904}(773,\cdot)\) \(\chi_{43904}(789,\cdot)\) \(\chi_{43904}(829,\cdot)\) \(\chi_{43904}(845,\cdot)\) \(\chi_{43904}(885,\cdot)\) \(\chi_{43904}(941,\cdot)\) \(\chi_{43904}(957,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4704})$ |
| Fixed field: | Number field defined by a degree 4704 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((1,e\left(\frac{21}{32}\right),e\left(\frac{43}{294}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(885, a) \) | \(-1\) | \(1\) | \(e\left(\frac{541}{4704}\right)\) | \(e\left(\frac{4223}{4704}\right)\) | \(e\left(\frac{541}{2352}\right)\) | \(e\left(\frac{955}{4704}\right)\) | \(e\left(\frac{827}{1568}\right)\) | \(e\left(\frac{5}{392}\right)\) | \(e\left(\frac{37}{1176}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{409}{2352}\right)\) | \(e\left(\frac{1871}{2352}\right)\) |