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 \(\chi_{1792}(723,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.ch
\(\chi_{3584}(23,\cdot)\) \(\chi_{3584}(39,\cdot)\) \(\chi_{3584}(135,\cdot)\) \(\chi_{3584}(151,\cdot)\) \(\chi_{3584}(247,\cdot)\) \(\chi_{3584}(263,\cdot)\) \(\chi_{3584}(359,\cdot)\) \(\chi_{3584}(375,\cdot)\) \(\chi_{3584}(471,\cdot)\) \(\chi_{3584}(487,\cdot)\) \(\chi_{3584}(583,\cdot)\) \(\chi_{3584}(599,\cdot)\) \(\chi_{3584}(695,\cdot)\) \(\chi_{3584}(711,\cdot)\) \(\chi_{3584}(807,\cdot)\) \(\chi_{3584}(823,\cdot)\) \(\chi_{3584}(919,\cdot)\) \(\chi_{3584}(935,\cdot)\) \(\chi_{3584}(1031,\cdot)\) \(\chi_{3584}(1047,\cdot)\) \(\chi_{3584}(1143,\cdot)\) \(\chi_{3584}(1159,\cdot)\) \(\chi_{3584}(1255,\cdot)\) \(\chi_{3584}(1271,\cdot)\) \(\chi_{3584}(1367,\cdot)\) \(\chi_{3584}(1383,\cdot)\) \(\chi_{3584}(1479,\cdot)\) \(\chi_{3584}(1495,\cdot)\) \(\chi_{3584}(1591,\cdot)\) \(\chi_{3584}(1607,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{7}{64}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{192}\right)\) | \(e\left(\frac{149}{192}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{25}{192}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{131}{192}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{53}{96}\right)\) |