Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1092\) | 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 8281.ei
\(\chi_{8281}(24,\cdot)\) \(\chi_{8281}(33,\cdot)\) \(\chi_{8281}(110,\cdot)\) \(\chi_{8281}(115,\cdot)\) \(\chi_{8281}(124,\cdot)\) \(\chi_{8281}(171,\cdot)\) \(\chi_{8281}(201,\cdot)\) \(\chi_{8281}(206,\cdot)\) \(\chi_{8281}(262,\cdot)\) \(\chi_{8281}(292,\cdot)\) \(\chi_{8281}(297,\cdot)\) \(\chi_{8281}(306,\cdot)\) \(\chi_{8281}(353,\cdot)\) \(\chi_{8281}(383,\cdot)\) \(\chi_{8281}(388,\cdot)\) \(\chi_{8281}(397,\cdot)\) \(\chi_{8281}(444,\cdot)\) \(\chi_{8281}(474,\cdot)\) \(\chi_{8281}(479,\cdot)\) \(\chi_{8281}(535,\cdot)\) \(\chi_{8281}(565,\cdot)\) \(\chi_{8281}(579,\cdot)\) \(\chi_{8281}(626,\cdot)\) \(\chi_{8281}(661,\cdot)\) \(\chi_{8281}(670,\cdot)\) \(\chi_{8281}(747,\cdot)\) \(\chi_{8281}(752,\cdot)\) \(\chi_{8281}(761,\cdot)\) \(\chi_{8281}(808,\cdot)\) \(\chi_{8281}(838,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{41}{42}\right),e\left(\frac{71}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{913}{1092}\right)\) | \(e\left(\frac{75}{182}\right)\) | \(e\left(\frac{367}{546}\right)\) | \(e\left(\frac{443}{1092}\right)\) | \(e\left(\frac{271}{1092}\right)\) | \(e\left(\frac{185}{364}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{22}{91}\right)\) | \(e\left(\frac{337}{364}\right)\) | \(e\left(\frac{23}{273}\right)\) |