Basic properties
| Modulus: | \(16384\) | |
| Conductor: | \(4096\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1024\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4096}(3309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16384.u
\(\chi_{16384}(17,\cdot)\) \(\chi_{16384}(49,\cdot)\) \(\chi_{16384}(81,\cdot)\) \(\chi_{16384}(113,\cdot)\) \(\chi_{16384}(145,\cdot)\) \(\chi_{16384}(177,\cdot)\) \(\chi_{16384}(209,\cdot)\) \(\chi_{16384}(241,\cdot)\) \(\chi_{16384}(273,\cdot)\) \(\chi_{16384}(305,\cdot)\) \(\chi_{16384}(337,\cdot)\) \(\chi_{16384}(369,\cdot)\) \(\chi_{16384}(401,\cdot)\) \(\chi_{16384}(433,\cdot)\) \(\chi_{16384}(465,\cdot)\) \(\chi_{16384}(497,\cdot)\) \(\chi_{16384}(529,\cdot)\) \(\chi_{16384}(561,\cdot)\) \(\chi_{16384}(593,\cdot)\) \(\chi_{16384}(625,\cdot)\) \(\chi_{16384}(657,\cdot)\) \(\chi_{16384}(689,\cdot)\) \(\chi_{16384}(721,\cdot)\) \(\chi_{16384}(753,\cdot)\) \(\chi_{16384}(785,\cdot)\) \(\chi_{16384}(817,\cdot)\) \(\chi_{16384}(849,\cdot)\) \(\chi_{16384}(881,\cdot)\) \(\chi_{16384}(913,\cdot)\) \(\chi_{16384}(945,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1024})$ |
| Fixed field: | Number field defined by a degree 1024 polynomial (not computed) |
Values on generators
\((16383,5)\) → \((1,e\left(\frac{855}{1024}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 16384 }(273, a) \) | \(1\) | \(1\) | \(e\left(\frac{613}{1024}\right)\) | \(e\left(\frac{855}{1024}\right)\) | \(e\left(\frac{83}{512}\right)\) | \(e\left(\frac{101}{512}\right)\) | \(e\left(\frac{867}{1024}\right)\) | \(e\left(\frac{825}{1024}\right)\) | \(e\left(\frac{111}{256}\right)\) | \(e\left(\frac{1}{256}\right)\) | \(e\left(\frac{337}{1024}\right)\) | \(e\left(\frac{779}{1024}\right)\) |