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.ci
\(\chi_{3584}(5,\cdot)\) \(\chi_{3584}(45,\cdot)\) \(\chi_{3584}(61,\cdot)\) \(\chi_{3584}(101,\cdot)\) \(\chi_{3584}(117,\cdot)\) \(\chi_{3584}(157,\cdot)\) \(\chi_{3584}(173,\cdot)\) \(\chi_{3584}(213,\cdot)\) \(\chi_{3584}(229,\cdot)\) \(\chi_{3584}(269,\cdot)\) \(\chi_{3584}(285,\cdot)\) \(\chi_{3584}(325,\cdot)\) \(\chi_{3584}(341,\cdot)\) \(\chi_{3584}(381,\cdot)\) \(\chi_{3584}(397,\cdot)\) \(\chi_{3584}(437,\cdot)\) \(\chi_{3584}(453,\cdot)\) \(\chi_{3584}(493,\cdot)\) \(\chi_{3584}(509,\cdot)\) \(\chi_{3584}(549,\cdot)\) \(\chi_{3584}(565,\cdot)\) \(\chi_{3584}(605,\cdot)\) \(\chi_{3584}(621,\cdot)\) \(\chi_{3584}(661,\cdot)\) \(\chi_{3584}(677,\cdot)\) \(\chi_{3584}(717,\cdot)\) \(\chi_{3584}(733,\cdot)\) \(\chi_{3584}(773,\cdot)\) \(\chi_{3584}(789,\cdot)\) \(\chi_{3584}(829,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{1}{128}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{384}\right)\) | \(e\left(\frac{67}{384}\right)\) | \(e\left(\frac{41}{192}\right)\) | \(e\left(\frac{383}{384}\right)\) | \(e\left(\frac{47}{128}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{133}{384}\right)\) | \(e\left(\frac{149}{192}\right)\) | \(e\left(\frac{67}{192}\right)\) |