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.cn
\(\chi_{8005}(83,\cdot)\) \(\chi_{8005}(93,\cdot)\) \(\chi_{8005}(112,\cdot)\) \(\chi_{8005}(118,\cdot)\) \(\chi_{8005}(127,\cdot)\) \(\chi_{8005}(153,\cdot)\) \(\chi_{8005}(243,\cdot)\) \(\chi_{8005}(277,\cdot)\) \(\chi_{8005}(367,\cdot)\) \(\chi_{8005}(382,\cdot)\) \(\chi_{8005}(427,\cdot)\) \(\chi_{8005}(502,\cdot)\) \(\chi_{8005}(518,\cdot)\) \(\chi_{8005}(537,\cdot)\) \(\chi_{8005}(653,\cdot)\) \(\chi_{8005}(658,\cdot)\) \(\chi_{8005}(667,\cdot)\) \(\chi_{8005}(797,\cdot)\) \(\chi_{8005}(943,\cdot)\) \(\chi_{8005}(948,\cdot)\) \(\chi_{8005}(982,\cdot)\) \(\chi_{8005}(1017,\cdot)\) \(\chi_{8005}(1042,\cdot)\) \(\chi_{8005}(1083,\cdot)\) \(\chi_{8005}(1358,\cdot)\) \(\chi_{8005}(1448,\cdot)\) \(\chi_{8005}(1483,\cdot)\) \(\chi_{8005}(1502,\cdot)\) \(\chi_{8005}(1508,\cdot)\) \(\chi_{8005}(1518,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{281}{320}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{41}{320}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{173}{320}\right)\) | \(e\left(\frac{67}{320}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{41}{160}\right)\) | \(e\left(\frac{273}{320}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{53}{64}\right)\) |