Basic properties
| Modulus: | \(1024\) | |
| Conductor: | \(1024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(256\) | 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 1024.q
\(\chi_{1024}(5,\cdot)\) \(\chi_{1024}(13,\cdot)\) \(\chi_{1024}(21,\cdot)\) \(\chi_{1024}(29,\cdot)\) \(\chi_{1024}(37,\cdot)\) \(\chi_{1024}(45,\cdot)\) \(\chi_{1024}(53,\cdot)\) \(\chi_{1024}(61,\cdot)\) \(\chi_{1024}(69,\cdot)\) \(\chi_{1024}(77,\cdot)\) \(\chi_{1024}(85,\cdot)\) \(\chi_{1024}(93,\cdot)\) \(\chi_{1024}(101,\cdot)\) \(\chi_{1024}(109,\cdot)\) \(\chi_{1024}(117,\cdot)\) \(\chi_{1024}(125,\cdot)\) \(\chi_{1024}(133,\cdot)\) \(\chi_{1024}(141,\cdot)\) \(\chi_{1024}(149,\cdot)\) \(\chi_{1024}(157,\cdot)\) \(\chi_{1024}(165,\cdot)\) \(\chi_{1024}(173,\cdot)\) \(\chi_{1024}(181,\cdot)\) \(\chi_{1024}(189,\cdot)\) \(\chi_{1024}(197,\cdot)\) \(\chi_{1024}(205,\cdot)\) \(\chi_{1024}(213,\cdot)\) \(\chi_{1024}(221,\cdot)\) \(\chi_{1024}(229,\cdot)\) \(\chi_{1024}(237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((1023,5)\) → \((1,e\left(\frac{251}{256}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1024 }(541, a) \) | \(1\) | \(1\) | \(e\left(\frac{209}{256}\right)\) | \(e\left(\frac{251}{256}\right)\) | \(e\left(\frac{7}{128}\right)\) | \(e\left(\frac{81}{128}\right)\) | \(e\left(\frac{215}{256}\right)\) | \(e\left(\frac{85}{256}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{13}{256}\right)\) | \(e\left(\frac{223}{256}\right)\) |