Basic properties
| Modulus: | \(3584\) | |
| Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1792}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.ce
\(\chi_{3584}(73,\cdot)\) \(\chi_{3584}(89,\cdot)\) \(\chi_{3584}(185,\cdot)\) \(\chi_{3584}(201,\cdot)\) \(\chi_{3584}(297,\cdot)\) \(\chi_{3584}(313,\cdot)\) \(\chi_{3584}(409,\cdot)\) \(\chi_{3584}(425,\cdot)\) \(\chi_{3584}(521,\cdot)\) \(\chi_{3584}(537,\cdot)\) \(\chi_{3584}(633,\cdot)\) \(\chi_{3584}(649,\cdot)\) \(\chi_{3584}(745,\cdot)\) \(\chi_{3584}(761,\cdot)\) \(\chi_{3584}(857,\cdot)\) \(\chi_{3584}(873,\cdot)\) \(\chi_{3584}(969,\cdot)\) \(\chi_{3584}(985,\cdot)\) \(\chi_{3584}(1081,\cdot)\) \(\chi_{3584}(1097,\cdot)\) \(\chi_{3584}(1193,\cdot)\) \(\chi_{3584}(1209,\cdot)\) \(\chi_{3584}(1305,\cdot)\) \(\chi_{3584}(1321,\cdot)\) \(\chi_{3584}(1417,\cdot)\) \(\chi_{3584}(1433,\cdot)\) \(\chi_{3584}(1529,\cdot)\) \(\chi_{3584}(1545,\cdot)\) \(\chi_{3584}(1641,\cdot)\) \(\chi_{3584}(1657,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{27}{64}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{179}{192}\right)\) | \(e\left(\frac{49}{192}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{101}{192}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{103}{192}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{49}{96}\right)\) |