Basic properties
| Modulus: | \(8043\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1146\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2681}(535,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8043.be
\(\chi_{8043}(19,\cdot)\) \(\chi_{8043}(31,\cdot)\) \(\chi_{8043}(73,\cdot)\) \(\chi_{8043}(103,\cdot)\) \(\chi_{8043}(124,\cdot)\) \(\chi_{8043}(136,\cdot)\) \(\chi_{8043}(220,\cdot)\) \(\chi_{8043}(229,\cdot)\) \(\chi_{8043}(292,\cdot)\) \(\chi_{8043}(304,\cdot)\) \(\chi_{8043}(313,\cdot)\) \(\chi_{8043}(346,\cdot)\) \(\chi_{8043}(397,\cdot)\) \(\chi_{8043}(439,\cdot)\) \(\chi_{8043}(451,\cdot)\) \(\chi_{8043}(481,\cdot)\) \(\chi_{8043}(493,\cdot)\) \(\chi_{8043}(502,\cdot)\) \(\chi_{8043}(535,\cdot)\) \(\chi_{8043}(544,\cdot)\) \(\chi_{8043}(556,\cdot)\) \(\chi_{8043}(586,\cdot)\) \(\chi_{8043}(607,\cdot)\) \(\chi_{8043}(649,\cdot)\) \(\chi_{8043}(661,\cdot)\) \(\chi_{8043}(733,\cdot)\) \(\chi_{8043}(775,\cdot)\) \(\chi_{8043}(787,\cdot)\) \(\chi_{8043}(808,\cdot)\) \(\chi_{8043}(817,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{573})$ |
| Fixed field: | Number field defined by a degree 1146 polynomial (not computed) |
Values on generators
\((5363,2299,6133)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{75}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8043 }(535, a) \) | \(-1\) | \(1\) | \(e\left(\frac{545}{573}\right)\) | \(e\left(\frac{517}{573}\right)\) | \(e\left(\frac{259}{1146}\right)\) | \(e\left(\frac{163}{191}\right)\) | \(e\left(\frac{203}{1146}\right)\) | \(e\left(\frac{82}{573}\right)\) | \(e\left(\frac{215}{382}\right)\) | \(e\left(\frac{461}{573}\right)\) | \(e\left(\frac{485}{1146}\right)\) | \(e\left(\frac{1009}{1146}\right)\) |