Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.di
\(\chi_{8281}(227,\cdot)\) \(\chi_{8281}(362,\cdot)\) \(\chi_{8281}(423,\cdot)\) \(\chi_{8281}(509,\cdot)\) \(\chi_{8281}(999,\cdot)\) \(\chi_{8281}(1060,\cdot)\) \(\chi_{8281}(1146,\cdot)\) \(\chi_{8281}(1501,\cdot)\) \(\chi_{8281}(1636,\cdot)\) \(\chi_{8281}(1697,\cdot)\) \(\chi_{8281}(1783,\cdot)\) \(\chi_{8281}(2138,\cdot)\) \(\chi_{8281}(2273,\cdot)\) \(\chi_{8281}(2334,\cdot)\) \(\chi_{8281}(2420,\cdot)\) \(\chi_{8281}(2775,\cdot)\) \(\chi_{8281}(2910,\cdot)\) \(\chi_{8281}(2971,\cdot)\) \(\chi_{8281}(3057,\cdot)\) \(\chi_{8281}(3412,\cdot)\) \(\chi_{8281}(3547,\cdot)\) \(\chi_{8281}(3608,\cdot)\) \(\chi_{8281}(3694,\cdot)\) \(\chi_{8281}(4049,\cdot)\) \(\chi_{8281}(4184,\cdot)\) \(\chi_{8281}(4245,\cdot)\) \(\chi_{8281}(4331,\cdot)\) \(\chi_{8281}(4686,\cdot)\) \(\chi_{8281}(4968,\cdot)\) \(\chi_{8281}(5323,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{41}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(227, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{37}{39}\right)\) |