Basic properties
| Modulus: | \(16384\) | |
| Conductor: | \(16384\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4096\) | 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 16384.y
\(\chi_{16384}(5,\cdot)\) \(\chi_{16384}(13,\cdot)\) \(\chi_{16384}(21,\cdot)\) \(\chi_{16384}(29,\cdot)\) \(\chi_{16384}(37,\cdot)\) \(\chi_{16384}(45,\cdot)\) \(\chi_{16384}(53,\cdot)\) \(\chi_{16384}(61,\cdot)\) \(\chi_{16384}(69,\cdot)\) \(\chi_{16384}(77,\cdot)\) \(\chi_{16384}(85,\cdot)\) \(\chi_{16384}(93,\cdot)\) \(\chi_{16384}(101,\cdot)\) \(\chi_{16384}(109,\cdot)\) \(\chi_{16384}(117,\cdot)\) \(\chi_{16384}(125,\cdot)\) \(\chi_{16384}(133,\cdot)\) \(\chi_{16384}(141,\cdot)\) \(\chi_{16384}(149,\cdot)\) \(\chi_{16384}(157,\cdot)\) \(\chi_{16384}(165,\cdot)\) \(\chi_{16384}(173,\cdot)\) \(\chi_{16384}(181,\cdot)\) \(\chi_{16384}(189,\cdot)\) \(\chi_{16384}(197,\cdot)\) \(\chi_{16384}(205,\cdot)\) \(\chi_{16384}(213,\cdot)\) \(\chi_{16384}(221,\cdot)\) \(\chi_{16384}(229,\cdot)\) \(\chi_{16384}(237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4096})$ |
| Fixed field: | Number field defined by a degree 4096 polynomial (not computed) |
Values on generators
\((16383,5)\) → \((1,e\left(\frac{339}{4096}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 16384 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{2521}{4096}\right)\) | \(e\left(\frac{339}{4096}\right)\) | \(e\left(\frac{703}{2048}\right)\) | \(e\left(\frac{473}{2048}\right)\) | \(e\left(\frac{3599}{4096}\right)\) | \(e\left(\frac{381}{4096}\right)\) | \(e\left(\frac{715}{1024}\right)\) | \(e\left(\frac{101}{1024}\right)\) | \(e\left(\frac{2293}{4096}\right)\) | \(e\left(\frac{3927}{4096}\right)\) |