Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1600\) | 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 8005.cz
\(\chi_{8005}(14,\cdot)\) \(\chi_{8005}(24,\cdot)\) \(\chi_{8005}(44,\cdot)\) \(\chi_{8005}(59,\cdot)\) \(\chi_{8005}(104,\cdot)\) \(\chi_{8005}(129,\cdot)\) \(\chi_{8005}(149,\cdot)\) \(\chi_{8005}(159,\cdot)\) \(\chi_{8005}(174,\cdot)\) \(\chi_{8005}(214,\cdot)\) \(\chi_{8005}(224,\cdot)\) \(\chi_{8005}(234,\cdot)\) \(\chi_{8005}(239,\cdot)\) \(\chi_{8005}(254,\cdot)\) \(\chi_{8005}(259,\cdot)\) \(\chi_{8005}(274,\cdot)\) \(\chi_{8005}(294,\cdot)\) \(\chi_{8005}(309,\cdot)\) \(\chi_{8005}(319,\cdot)\) \(\chi_{8005}(329,\cdot)\) \(\chi_{8005}(379,\cdot)\) \(\chi_{8005}(404,\cdot)\) \(\chi_{8005}(409,\cdot)\) \(\chi_{8005}(414,\cdot)\) \(\chi_{8005}(429,\cdot)\) \(\chi_{8005}(434,\cdot)\) \(\chi_{8005}(444,\cdot)\) \(\chi_{8005}(469,\cdot)\) \(\chi_{8005}(474,\cdot)\) \(\chi_{8005}(479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1600})$ |
| Fixed field: | Number field defined by a degree 1600 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-1,e\left(\frac{639}{1600}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{400}\right)\) | \(e\left(\frac{1439}{1600}\right)\) | \(e\left(\frac{107}{200}\right)\) | \(e\left(\frac{267}{1600}\right)\) | \(e\left(\frac{1493}{1600}\right)\) | \(e\left(\frac{321}{400}\right)\) | \(e\left(\frac{639}{800}\right)\) | \(e\left(\frac{1287}{1600}\right)\) | \(e\left(\frac{139}{320}\right)\) | \(e\left(\frac{23}{64}\right)\) |