Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(800\) | 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.ct
\(\chi_{8005}(18,\cdot)\) \(\chi_{8005}(37,\cdot)\) \(\chi_{8005}(47,\cdot)\) \(\chi_{8005}(78,\cdot)\) \(\chi_{8005}(132,\cdot)\) \(\chi_{8005}(177,\cdot)\) \(\chi_{8005}(178,\cdot)\) \(\chi_{8005}(213,\cdot)\) \(\chi_{8005}(218,\cdot)\) \(\chi_{8005}(268,\cdot)\) \(\chi_{8005}(288,\cdot)\) \(\chi_{8005}(303,\cdot)\) \(\chi_{8005}(307,\cdot)\) \(\chi_{8005}(313,\cdot)\) \(\chi_{8005}(328,\cdot)\) \(\chi_{8005}(338,\cdot)\) \(\chi_{8005}(353,\cdot)\) \(\chi_{8005}(412,\cdot)\) \(\chi_{8005}(477,\cdot)\) \(\chi_{8005}(503,\cdot)\) \(\chi_{8005}(557,\cdot)\) \(\chi_{8005}(558,\cdot)\) \(\chi_{8005}(572,\cdot)\) \(\chi_{8005}(592,\cdot)\) \(\chi_{8005}(627,\cdot)\) \(\chi_{8005}(633,\cdot)\) \(\chi_{8005}(678,\cdot)\) \(\chi_{8005}(687,\cdot)\) \(\chi_{8005}(688,\cdot)\) \(\chi_{8005}(693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{800})$ |
| Fixed field: | Number field defined by a degree 800 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{27}{800}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{200}\right)\) | \(e\left(\frac{227}{800}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{631}{800}\right)\) | \(e\left(\frac{449}{800}\right)\) | \(e\left(\frac{103}{200}\right)\) | \(e\left(\frac{227}{400}\right)\) | \(e\left(\frac{291}{800}\right)\) | \(e\left(\frac{47}{160}\right)\) | \(e\left(\frac{27}{32}\right)\) |