Basic properties
| Modulus: | \(21952\) | |
| Conductor: | \(21952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(784\) | 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 21952.ee
\(\chi_{21952}(13,\cdot)\) \(\chi_{21952}(69,\cdot)\) \(\chi_{21952}(125,\cdot)\) \(\chi_{21952}(181,\cdot)\) \(\chi_{21952}(237,\cdot)\) \(\chi_{21952}(349,\cdot)\) \(\chi_{21952}(405,\cdot)\) \(\chi_{21952}(461,\cdot)\) \(\chi_{21952}(517,\cdot)\) \(\chi_{21952}(573,\cdot)\) \(\chi_{21952}(629,\cdot)\) \(\chi_{21952}(741,\cdot)\) \(\chi_{21952}(797,\cdot)\) \(\chi_{21952}(853,\cdot)\) \(\chi_{21952}(909,\cdot)\) \(\chi_{21952}(965,\cdot)\) \(\chi_{21952}(1021,\cdot)\) \(\chi_{21952}(1133,\cdot)\) \(\chi_{21952}(1189,\cdot)\) \(\chi_{21952}(1245,\cdot)\) \(\chi_{21952}(1301,\cdot)\) \(\chi_{21952}(1357,\cdot)\) \(\chi_{21952}(1413,\cdot)\) \(\chi_{21952}(1525,\cdot)\) \(\chi_{21952}(1581,\cdot)\) \(\chi_{21952}(1637,\cdot)\) \(\chi_{21952}(1693,\cdot)\) \(\chi_{21952}(1749,\cdot)\) \(\chi_{21952}(1805,\cdot)\) \(\chi_{21952}(1917,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{784})$ |
| Fixed field: | Number field defined by a degree 784 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{13}{98}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 21952 }(15357, a) \) | \(-1\) | \(1\) | \(e\left(\frac{545}{784}\right)\) | \(e\left(\frac{27}{784}\right)\) | \(e\left(\frac{153}{392}\right)\) | \(e\left(\frac{415}{784}\right)\) | \(e\left(\frac{485}{784}\right)\) | \(e\left(\frac{143}{196}\right)\) | \(e\left(\frac{111}{196}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{149}{392}\right)\) | \(e\left(\frac{27}{392}\right)\) |