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 \(\chi_{1792}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.cg
\(\chi_{3584}(87,\cdot)\) \(\chi_{3584}(103,\cdot)\) \(\chi_{3584}(199,\cdot)\) \(\chi_{3584}(215,\cdot)\) \(\chi_{3584}(311,\cdot)\) \(\chi_{3584}(327,\cdot)\) \(\chi_{3584}(423,\cdot)\) \(\chi_{3584}(439,\cdot)\) \(\chi_{3584}(535,\cdot)\) \(\chi_{3584}(551,\cdot)\) \(\chi_{3584}(647,\cdot)\) \(\chi_{3584}(663,\cdot)\) \(\chi_{3584}(759,\cdot)\) \(\chi_{3584}(775,\cdot)\) \(\chi_{3584}(871,\cdot)\) \(\chi_{3584}(887,\cdot)\) \(\chi_{3584}(983,\cdot)\) \(\chi_{3584}(999,\cdot)\) \(\chi_{3584}(1095,\cdot)\) \(\chi_{3584}(1111,\cdot)\) \(\chi_{3584}(1207,\cdot)\) \(\chi_{3584}(1223,\cdot)\) \(\chi_{3584}(1319,\cdot)\) \(\chi_{3584}(1335,\cdot)\) \(\chi_{3584}(1431,\cdot)\) \(\chi_{3584}(1447,\cdot)\) \(\chi_{3584}(1543,\cdot)\) \(\chi_{3584}(1559,\cdot)\) \(\chi_{3584}(1655,\cdot)\) \(\chi_{3584}(1671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{15}{64}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{192}\right)\) | \(e\left(\frac{13}{192}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{17}{192}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{139}{192}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{13}{96}\right)\) |