Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(273\) | 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.dq
\(\chi_{8281}(53,\cdot)\) \(\chi_{8281}(144,\cdot)\) \(\chi_{8281}(235,\cdot)\) \(\chi_{8281}(261,\cdot)\) \(\chi_{8281}(326,\cdot)\) \(\chi_{8281}(352,\cdot)\) \(\chi_{8281}(417,\cdot)\) \(\chi_{8281}(443,\cdot)\) \(\chi_{8281}(534,\cdot)\) \(\chi_{8281}(599,\cdot)\) \(\chi_{8281}(625,\cdot)\) \(\chi_{8281}(690,\cdot)\) \(\chi_{8281}(781,\cdot)\) \(\chi_{8281}(807,\cdot)\) \(\chi_{8281}(872,\cdot)\) \(\chi_{8281}(898,\cdot)\) \(\chi_{8281}(963,\cdot)\) \(\chi_{8281}(989,\cdot)\) \(\chi_{8281}(1054,\cdot)\) \(\chi_{8281}(1080,\cdot)\) \(\chi_{8281}(1171,\cdot)\) \(\chi_{8281}(1236,\cdot)\) \(\chi_{8281}(1262,\cdot)\) \(\chi_{8281}(1327,\cdot)\) \(\chi_{8281}(1418,\cdot)\) \(\chi_{8281}(1444,\cdot)\) \(\chi_{8281}(1509,\cdot)\) \(\chi_{8281}(1535,\cdot)\) \(\chi_{8281}(1600,\cdot)\) \(\chi_{8281}(1626,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{10}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{262}{273}\right)\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{251}{273}\right)\) | \(e\left(\frac{226}{273}\right)\) | \(e\left(\frac{53}{91}\right)\) | \(e\left(\frac{80}{91}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{215}{273}\right)\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{148}{273}\right)\) |