Basic properties
| Modulus: | \(3584\) | |
| Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{896}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.bz
\(\chi_{3584}(17,\cdot)\) \(\chi_{3584}(145,\cdot)\) \(\chi_{3584}(241,\cdot)\) \(\chi_{3584}(369,\cdot)\) \(\chi_{3584}(465,\cdot)\) \(\chi_{3584}(593,\cdot)\) \(\chi_{3584}(689,\cdot)\) \(\chi_{3584}(817,\cdot)\) \(\chi_{3584}(913,\cdot)\) \(\chi_{3584}(1041,\cdot)\) \(\chi_{3584}(1137,\cdot)\) \(\chi_{3584}(1265,\cdot)\) \(\chi_{3584}(1361,\cdot)\) \(\chi_{3584}(1489,\cdot)\) \(\chi_{3584}(1585,\cdot)\) \(\chi_{3584}(1713,\cdot)\) \(\chi_{3584}(1809,\cdot)\) \(\chi_{3584}(1937,\cdot)\) \(\chi_{3584}(2033,\cdot)\) \(\chi_{3584}(2161,\cdot)\) \(\chi_{3584}(2257,\cdot)\) \(\chi_{3584}(2385,\cdot)\) \(\chi_{3584}(2481,\cdot)\) \(\chi_{3584}(2609,\cdot)\) \(\chi_{3584}(2705,\cdot)\) \(\chi_{3584}(2833,\cdot)\) \(\chi_{3584}(2929,\cdot)\) \(\chi_{3584}(3057,\cdot)\) \(\chi_{3584}(3153,\cdot)\) \(\chi_{3584}(3281,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) |