Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(800\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1601}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cs
\(\chi_{8005}(36,\cdot)\) \(\chi_{8005}(41,\cdot)\) \(\chi_{8005}(66,\cdot)\) \(\chi_{8005}(86,\cdot)\) \(\chi_{8005}(121,\cdot)\) \(\chi_{8005}(161,\cdot)\) \(\chi_{8005}(171,\cdot)\) \(\chi_{8005}(196,\cdot)\) \(\chi_{8005}(261,\cdot)\) \(\chi_{8005}(281,\cdot)\) \(\chi_{8005}(296,\cdot)\) \(\chi_{8005}(376,\cdot)\) \(\chi_{8005}(391,\cdot)\) \(\chi_{8005}(411,\cdot)\) \(\chi_{8005}(426,\cdot)\) \(\chi_{8005}(436,\cdot)\) \(\chi_{8005}(466,\cdot)\) \(\chi_{8005}(476,\cdot)\) \(\chi_{8005}(511,\cdot)\) \(\chi_{8005}(526,\cdot)\) \(\chi_{8005}(536,\cdot)\) \(\chi_{8005}(571,\cdot)\) \(\chi_{8005}(576,\cdot)\) \(\chi_{8005}(621,\cdot)\) \(\chi_{8005}(626,\cdot)\) \(\chi_{8005}(631,\cdot)\) \(\chi_{8005}(656,\cdot)\) \(\chi_{8005}(661,\cdot)\) \(\chi_{8005}(676,\cdot)\) \(\chi_{8005}(701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{800})$ |
| Fixed field: | Number field defined by a degree 800 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((1,e\left(\frac{53}{800}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{200}\right)\) | \(e\left(\frac{53}{800}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{409}{800}\right)\) | \(e\left(\frac{711}{800}\right)\) | \(e\left(\frac{67}{200}\right)\) | \(e\left(\frac{53}{400}\right)\) | \(e\left(\frac{749}{800}\right)\) | \(e\left(\frac{153}{160}\right)\) | \(e\left(\frac{29}{32}\right)\) |