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.em
\(\chi_{8281}(45,\cdot)\) \(\chi_{8281}(54,\cdot)\) \(\chi_{8281}(59,\cdot)\) \(\chi_{8281}(136,\cdot)\) \(\chi_{8281}(145,\cdot)\) \(\chi_{8281}(180,\cdot)\) \(\chi_{8281}(236,\cdot)\) \(\chi_{8281}(241,\cdot)\) \(\chi_{8281}(271,\cdot)\) \(\chi_{8281}(318,\cdot)\) \(\chi_{8281}(327,\cdot)\) \(\chi_{8281}(332,\cdot)\) \(\chi_{8281}(409,\cdot)\) \(\chi_{8281}(453,\cdot)\) \(\chi_{8281}(500,\cdot)\) \(\chi_{8281}(514,\cdot)\) \(\chi_{8281}(544,\cdot)\) \(\chi_{8281}(591,\cdot)\) \(\chi_{8281}(600,\cdot)\) \(\chi_{8281}(605,\cdot)\) \(\chi_{8281}(635,\cdot)\) \(\chi_{8281}(682,\cdot)\) \(\chi_{8281}(691,\cdot)\) \(\chi_{8281}(696,\cdot)\) \(\chi_{8281}(726,\cdot)\) \(\chi_{8281}(773,\cdot)\) \(\chi_{8281}(782,\cdot)\) \(\chi_{8281}(787,\cdot)\) \(\chi_{8281}(817,\cdot)\) \(\chi_{8281}(873,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{31}{42}\right),e\left(\frac{101}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{305}{364}\right)\) | \(e\left(\frac{11}{546}\right)\) | \(e\left(\frac{123}{182}\right)\) | \(e\left(\frac{253}{1092}\right)\) | \(e\left(\frac{937}{1092}\right)\) | \(e\left(\frac{187}{364}\right)\) | \(e\left(\frac{11}{273}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{229}{1092}\right)\) | \(e\left(\frac{190}{273}\right)\) |