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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43904.fn
\(\chi_{43904}(37,\cdot)\) \(\chi_{43904}(53,\cdot)\) \(\chi_{43904}(93,\cdot)\) \(\chi_{43904}(109,\cdot)\) \(\chi_{43904}(149,\cdot)\) \(\chi_{43904}(205,\cdot)\) \(\chi_{43904}(221,\cdot)\) \(\chi_{43904}(261,\cdot)\) \(\chi_{43904}(277,\cdot)\) \(\chi_{43904}(317,\cdot)\) \(\chi_{43904}(333,\cdot)\) \(\chi_{43904}(389,\cdot)\) \(\chi_{43904}(429,\cdot)\) \(\chi_{43904}(445,\cdot)\) \(\chi_{43904}(485,\cdot)\) \(\chi_{43904}(501,\cdot)\) \(\chi_{43904}(541,\cdot)\) \(\chi_{43904}(597,\cdot)\) \(\chi_{43904}(613,\cdot)\) \(\chi_{43904}(653,\cdot)\) \(\chi_{43904}(669,\cdot)\) \(\chi_{43904}(709,\cdot)\) \(\chi_{43904}(725,\cdot)\) \(\chi_{43904}(781,\cdot)\) \(\chi_{43904}(821,\cdot)\) \(\chi_{43904}(837,\cdot)\) \(\chi_{43904}(877,\cdot)\) \(\chi_{43904}(893,\cdot)\) \(\chi_{43904}(933,\cdot)\) \(\chi_{43904}(989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4704})$ |
| Fixed field: | Number field defined by a degree 4704 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((1,e\left(\frac{9}{32}\right),e\left(\frac{130}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(485, a) \) | \(1\) | \(1\) | \(e\left(\frac{3425}{4704}\right)\) | \(e\left(\frac{4363}{4704}\right)\) | \(e\left(\frac{1073}{2352}\right)\) | \(e\left(\frac{4007}{4704}\right)\) | \(e\left(\frac{407}{1568}\right)\) | \(e\left(\frac{257}{392}\right)\) | \(e\left(\frac{1157}{1176}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{2285}{2352}\right)\) | \(e\left(\frac{2011}{2352}\right)\) |