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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.ej
\(\chi_{8281}(2,\cdot)\) \(\chi_{8281}(32,\cdot)\) \(\chi_{8281}(37,\cdot)\) \(\chi_{8281}(46,\cdot)\) \(\chi_{8281}(93,\cdot)\) \(\chi_{8281}(123,\cdot)\) \(\chi_{8281}(137,\cdot)\) \(\chi_{8281}(184,\cdot)\) \(\chi_{8281}(219,\cdot)\) \(\chi_{8281}(228,\cdot)\) \(\chi_{8281}(305,\cdot)\) \(\chi_{8281}(310,\cdot)\) \(\chi_{8281}(366,\cdot)\) \(\chi_{8281}(396,\cdot)\) \(\chi_{8281}(401,\cdot)\) \(\chi_{8281}(457,\cdot)\) \(\chi_{8281}(487,\cdot)\) \(\chi_{8281}(492,\cdot)\) \(\chi_{8281}(501,\cdot)\) \(\chi_{8281}(548,\cdot)\) \(\chi_{8281}(578,\cdot)\) \(\chi_{8281}(583,\cdot)\) \(\chi_{8281}(592,\cdot)\) \(\chi_{8281}(639,\cdot)\) \(\chi_{8281}(669,\cdot)\) \(\chi_{8281}(674,\cdot)\) \(\chi_{8281}(683,\cdot)\) \(\chi_{8281}(730,\cdot)\) \(\chi_{8281}(760,\cdot)\) \(\chi_{8281}(774,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{16}{21}\right),e\left(\frac{151}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{283}{364}\right)\) | \(e\left(\frac{215}{273}\right)\) | \(e\left(\frac{101}{182}\right)\) | \(e\left(\frac{881}{1092}\right)\) | \(e\left(\frac{617}{1092}\right)\) | \(e\left(\frac{121}{364}\right)\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{319}{546}\right)\) | \(e\left(\frac{191}{1092}\right)\) | \(e\left(\frac{187}{546}\right)\) |