Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | 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.cg
\(\chi_{8005}(4,\cdot)\) \(\chi_{8005}(29,\cdot)\) \(\chi_{8005}(64,\cdot)\) \(\chi_{8005}(124,\cdot)\) \(\chi_{8005}(154,\cdot)\) \(\chi_{8005}(244,\cdot)\) \(\chi_{8005}(374,\cdot)\) \(\chi_{8005}(464,\cdot)\) \(\chi_{8005}(514,\cdot)\) \(\chi_{8005}(949,\cdot)\) \(\chi_{8005}(959,\cdot)\) \(\chi_{8005}(1214,\cdot)\) \(\chi_{8005}(1299,\cdot)\) \(\chi_{8005}(1434,\cdot)\) \(\chi_{8005}(1439,\cdot)\) \(\chi_{8005}(1444,\cdot)\) \(\chi_{8005}(1769,\cdot)\) \(\chi_{8005}(1854,\cdot)\) \(\chi_{8005}(1984,\cdot)\) \(\chi_{8005}(2329,\cdot)\) \(\chi_{8005}(2474,\cdot)\) \(\chi_{8005}(2819,\cdot)\) \(\chi_{8005}(2949,\cdot)\) \(\chi_{8005}(3034,\cdot)\) \(\chi_{8005}(3359,\cdot)\) \(\chi_{8005}(3364,\cdot)\) \(\chi_{8005}(3369,\cdot)\) \(\chi_{8005}(3504,\cdot)\) \(\chi_{8005}(3589,\cdot)\) \(\chi_{8005}(3844,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-1,e\left(\frac{97}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{197}{200}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{141}{200}\right)\) | \(e\left(\frac{39}{200}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{1}{200}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |