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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cy
\(\chi_{8005}(3,\cdot)\) \(\chi_{8005}(7,\cdot)\) \(\chi_{8005}(17,\cdot)\) \(\chi_{8005}(27,\cdot)\) \(\chi_{8005}(48,\cdot)\) \(\chi_{8005}(63,\cdot)\) \(\chi_{8005}(88,\cdot)\) \(\chi_{8005}(92,\cdot)\) \(\chi_{8005}(107,\cdot)\) \(\chi_{8005}(113,\cdot)\) \(\chi_{8005}(117,\cdot)\) \(\chi_{8005}(183,\cdot)\) \(\chi_{8005}(193,\cdot)\) \(\chi_{8005}(208,\cdot)\) \(\chi_{8005}(217,\cdot)\) \(\chi_{8005}(222,\cdot)\) \(\chi_{8005}(223,\cdot)\) \(\chi_{8005}(228,\cdot)\) \(\chi_{8005}(262,\cdot)\) \(\chi_{8005}(267,\cdot)\) \(\chi_{8005}(272,\cdot)\) \(\chi_{8005}(273,\cdot)\) \(\chi_{8005}(278,\cdot)\) \(\chi_{8005}(282,\cdot)\) \(\chi_{8005}(283,\cdot)\) \(\chi_{8005}(292,\cdot)\) \(\chi_{8005}(318,\cdot)\) \(\chi_{8005}(327,\cdot)\) \(\chi_{8005}(343,\cdot)\) \(\chi_{8005}(348,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1600})$ |
| Fixed field: | Number field defined by a degree 1600 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{1}{1600}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{400}\right)\) | \(e\left(\frac{401}{1600}\right)\) | \(e\left(\frac{113}{200}\right)\) | \(e\left(\frac{53}{1600}\right)\) | \(e\left(\frac{187}{1600}\right)\) | \(e\left(\frac{139}{400}\right)\) | \(e\left(\frac{401}{800}\right)\) | \(e\left(\frac{633}{1600}\right)\) | \(e\left(\frac{261}{320}\right)\) | \(e\left(\frac{25}{64}\right)\) |