Basic properties
Modulus: | \(3584\) | |
Conductor: | \(3584\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(384\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.cj
\(\chi_{3584}(11,\cdot)\) \(\chi_{3584}(51,\cdot)\) \(\chi_{3584}(67,\cdot)\) \(\chi_{3584}(107,\cdot)\) \(\chi_{3584}(123,\cdot)\) \(\chi_{3584}(163,\cdot)\) \(\chi_{3584}(179,\cdot)\) \(\chi_{3584}(219,\cdot)\) \(\chi_{3584}(235,\cdot)\) \(\chi_{3584}(275,\cdot)\) \(\chi_{3584}(291,\cdot)\) \(\chi_{3584}(331,\cdot)\) \(\chi_{3584}(347,\cdot)\) \(\chi_{3584}(387,\cdot)\) \(\chi_{3584}(403,\cdot)\) \(\chi_{3584}(443,\cdot)\) \(\chi_{3584}(459,\cdot)\) \(\chi_{3584}(499,\cdot)\) \(\chi_{3584}(515,\cdot)\) \(\chi_{3584}(555,\cdot)\) \(\chi_{3584}(571,\cdot)\) \(\chi_{3584}(611,\cdot)\) \(\chi_{3584}(627,\cdot)\) \(\chi_{3584}(667,\cdot)\) \(\chi_{3584}(683,\cdot)\) \(\chi_{3584}(723,\cdot)\) \(\chi_{3584}(739,\cdot)\) \(\chi_{3584}(779,\cdot)\) \(\chi_{3584}(795,\cdot)\) \(\chi_{3584}(835,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{384})$ |
Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{85}{128}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 3584 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{157}{384}\right)\) | \(e\left(\frac{383}{384}\right)\) | \(e\left(\frac{157}{192}\right)\) | \(e\left(\frac{235}{384}\right)\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{41}{384}\right)\) | \(e\left(\frac{25}{192}\right)\) | \(e\left(\frac{191}{192}\right)\) |