Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(320\) | 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.cm
\(\chi_{8005}(12,\cdot)\) \(\chi_{8005}(22,\cdot)\) \(\chi_{8005}(173,\cdot)\) \(\chi_{8005}(293,\cdot)\) \(\chi_{8005}(323,\cdot)\) \(\chi_{8005}(513,\cdot)\) \(\chi_{8005}(733,\cdot)\) \(\chi_{8005}(758,\cdot)\) \(\chi_{8005}(843,\cdot)\) \(\chi_{8005}(868,\cdot)\) \(\chi_{8005}(897,\cdot)\) \(\chi_{8005}(1027,\cdot)\) \(\chi_{8005}(1088,\cdot)\) \(\chi_{8005}(1097,\cdot)\) \(\chi_{8005}(1182,\cdot)\) \(\chi_{8005}(1217,\cdot)\) \(\chi_{8005}(1278,\cdot)\) \(\chi_{8005}(1308,\cdot)\) \(\chi_{8005}(1317,\cdot)\) \(\chi_{8005}(1372,\cdot)\) \(\chi_{8005}(1392,\cdot)\) \(\chi_{8005}(1428,\cdot)\) \(\chi_{8005}(1487,\cdot)\) \(\chi_{8005}(1713,\cdot)\) \(\chi_{8005}(1728,\cdot)\) \(\chi_{8005}(1827,\cdot)\) \(\chi_{8005}(1878,\cdot)\) \(\chi_{8005}(1968,\cdot)\) \(\chi_{8005}(1983,\cdot)\) \(\chi_{8005}(2017,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((i,e\left(\frac{21}{320}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{261}{320}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{153}{320}\right)\) | \(e\left(\frac{247}{320}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{101}{160}\right)\) | \(e\left(\frac{173}{320}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) |