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.eo
\(\chi_{8281}(6,\cdot)\) \(\chi_{8281}(20,\cdot)\) \(\chi_{8281}(41,\cdot)\) \(\chi_{8281}(76,\cdot)\) \(\chi_{8281}(111,\cdot)\) \(\chi_{8281}(132,\cdot)\) \(\chi_{8281}(167,\cdot)\) \(\chi_{8281}(202,\cdot)\) \(\chi_{8281}(223,\cdot)\) \(\chi_{8281}(279,\cdot)\) \(\chi_{8281}(314,\cdot)\) \(\chi_{8281}(349,\cdot)\) \(\chi_{8281}(370,\cdot)\) \(\chi_{8281}(384,\cdot)\) \(\chi_{8281}(405,\cdot)\) \(\chi_{8281}(461,\cdot)\) \(\chi_{8281}(475,\cdot)\) \(\chi_{8281}(496,\cdot)\) \(\chi_{8281}(531,\cdot)\) \(\chi_{8281}(552,\cdot)\) \(\chi_{8281}(566,\cdot)\) \(\chi_{8281}(622,\cdot)\) \(\chi_{8281}(643,\cdot)\) \(\chi_{8281}(678,\cdot)\) \(\chi_{8281}(713,\cdot)\) \(\chi_{8281}(748,\cdot)\) \(\chi_{8281}(769,\cdot)\) \(\chi_{8281}(804,\cdot)\) \(\chi_{8281}(825,\cdot)\) \(\chi_{8281}(839,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{125}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{563}{1092}\right)\) | \(e\left(\frac{1}{546}\right)\) | \(e\left(\frac{17}{546}\right)\) | \(e\left(\frac{311}{364}\right)\) | \(e\left(\frac{565}{1092}\right)\) | \(e\left(\frac{199}{364}\right)\) | \(e\left(\frac{1}{273}\right)\) | \(e\left(\frac{101}{273}\right)\) | \(e\left(\frac{269}{1092}\right)\) | \(e\left(\frac{3}{91}\right)\) |