Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(21952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2352\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{21952}(2069,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43904.fh
\(\chi_{43904}(9,\cdot)\) \(\chi_{43904}(25,\cdot)\) \(\chi_{43904}(121,\cdot)\) \(\chi_{43904}(137,\cdot)\) \(\chi_{43904}(233,\cdot)\) \(\chi_{43904}(249,\cdot)\) \(\chi_{43904}(345,\cdot)\) \(\chi_{43904}(457,\cdot)\) \(\chi_{43904}(473,\cdot)\) \(\chi_{43904}(585,\cdot)\) \(\chi_{43904}(681,\cdot)\) \(\chi_{43904}(697,\cdot)\) \(\chi_{43904}(793,\cdot)\) \(\chi_{43904}(809,\cdot)\) \(\chi_{43904}(905,\cdot)\) \(\chi_{43904}(921,\cdot)\) \(\chi_{43904}(1017,\cdot)\) \(\chi_{43904}(1033,\cdot)\) \(\chi_{43904}(1129,\cdot)\) \(\chi_{43904}(1241,\cdot)\) \(\chi_{43904}(1257,\cdot)\) \(\chi_{43904}(1369,\cdot)\) \(\chi_{43904}(1465,\cdot)\) \(\chi_{43904}(1481,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{2352})$ |
| Fixed field: | Number field defined by a degree 2352 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{104}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(697, a) \) | \(1\) | \(1\) | \(e\left(\frac{341}{2352}\right)\) | \(e\left(\frac{775}{2352}\right)\) | \(e\left(\frac{341}{1176}\right)\) | \(e\left(\frac{515}{2352}\right)\) | \(e\left(\frac{643}{784}\right)\) | \(e\left(\frac{93}{196}\right)\) | \(e\left(\frac{257}{588}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{473}{1176}\right)\) | \(e\left(\frac{775}{1176}\right)\) |