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.cx
\(\chi_{8005}(23,\cdot)\) \(\chi_{8005}(28,\cdot)\) \(\chi_{8005}(52,\cdot)\) \(\chi_{8005}(57,\cdot)\) \(\chi_{8005}(68,\cdot)\) \(\chi_{8005}(73,\cdot)\) \(\chi_{8005}(87,\cdot)\) \(\chi_{8005}(108,\cdot)\) \(\chi_{8005}(123,\cdot)\) \(\chi_{8005}(133,\cdot)\) \(\chi_{8005}(142,\cdot)\) \(\chi_{8005}(192,\cdot)\) \(\chi_{8005}(198,\cdot)\) \(\chi_{8005}(202,\cdot)\) \(\chi_{8005}(203,\cdot)\) \(\chi_{8005}(207,\cdot)\) \(\chi_{8005}(237,\cdot)\) \(\chi_{8005}(247,\cdot)\) \(\chi_{8005}(252,\cdot)\) \(\chi_{8005}(258,\cdot)\) \(\chi_{8005}(287,\cdot)\) \(\chi_{8005}(298,\cdot)\) \(\chi_{8005}(332,\cdot)\) \(\chi_{8005}(352,\cdot)\) \(\chi_{8005}(362,\cdot)\) \(\chi_{8005}(363,\cdot)\) \(\chi_{8005}(368,\cdot)\) \(\chi_{8005}(372,\cdot)\) \(\chi_{8005}(377,\cdot)\) \(\chi_{8005}(397,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1600})$ |
| Fixed field: | Number field defined by a degree 1600 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{691}{1600}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{400}\right)\) | \(e\left(\frac{1091}{1600}\right)\) | \(e\left(\frac{83}{200}\right)\) | \(e\left(\frac{1423}{1600}\right)\) | \(e\left(\frac{417}{1600}\right)\) | \(e\left(\frac{249}{400}\right)\) | \(e\left(\frac{291}{800}\right)\) | \(e\left(\frac{603}{1600}\right)\) | \(e\left(\frac{31}{320}\right)\) | \(e\left(\frac{27}{64}\right)\) |