Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(21952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(784\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{21952}(21419,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43904.ew
\(\chi_{43904}(55,\cdot)\) \(\chi_{43904}(167,\cdot)\) \(\chi_{43904}(279,\cdot)\) \(\chi_{43904}(503,\cdot)\) \(\chi_{43904}(615,\cdot)\) \(\chi_{43904}(727,\cdot)\) \(\chi_{43904}(839,\cdot)\) \(\chi_{43904}(951,\cdot)\) \(\chi_{43904}(1063,\cdot)\) \(\chi_{43904}(1287,\cdot)\) \(\chi_{43904}(1399,\cdot)\) \(\chi_{43904}(1511,\cdot)\) \(\chi_{43904}(1623,\cdot)\) \(\chi_{43904}(1735,\cdot)\) \(\chi_{43904}(1847,\cdot)\) \(\chi_{43904}(2071,\cdot)\) \(\chi_{43904}(2183,\cdot)\) \(\chi_{43904}(2295,\cdot)\) \(\chi_{43904}(2407,\cdot)\) \(\chi_{43904}(2519,\cdot)\) \(\chi_{43904}(2631,\cdot)\) \(\chi_{43904}(2855,\cdot)\) \(\chi_{43904}(2967,\cdot)\) \(\chi_{43904}(3079,\cdot)\) \(\chi_{43904}(3191,\cdot)\) \(\chi_{43904}(3303,\cdot)\) \(\chi_{43904}(3415,\cdot)\) \(\chi_{43904}(3639,\cdot)\) \(\chi_{43904}(3751,\cdot)\) \(\chi_{43904}(3863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{784})$ |
| Fixed field: | Number field defined by a degree 784 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{9}{98}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(839, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{784}\right)\) | \(e\left(\frac{373}{784}\right)\) | \(e\left(\frac{23}{392}\right)\) | \(e\left(\frac{521}{784}\right)\) | \(e\left(\frac{283}{784}\right)\) | \(e\left(\frac{99}{196}\right)\) | \(e\left(\frac{9}{196}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{367}{392}\right)\) | \(e\left(\frac{373}{392}\right)\) |