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 \(\chi_{896}(803,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.bx
\(\chi_{3584}(47,\cdot)\) \(\chi_{3584}(143,\cdot)\) \(\chi_{3584}(271,\cdot)\) \(\chi_{3584}(367,\cdot)\) \(\chi_{3584}(495,\cdot)\) \(\chi_{3584}(591,\cdot)\) \(\chi_{3584}(719,\cdot)\) \(\chi_{3584}(815,\cdot)\) \(\chi_{3584}(943,\cdot)\) \(\chi_{3584}(1039,\cdot)\) \(\chi_{3584}(1167,\cdot)\) \(\chi_{3584}(1263,\cdot)\) \(\chi_{3584}(1391,\cdot)\) \(\chi_{3584}(1487,\cdot)\) \(\chi_{3584}(1615,\cdot)\) \(\chi_{3584}(1711,\cdot)\) \(\chi_{3584}(1839,\cdot)\) \(\chi_{3584}(1935,\cdot)\) \(\chi_{3584}(2063,\cdot)\) \(\chi_{3584}(2159,\cdot)\) \(\chi_{3584}(2287,\cdot)\) \(\chi_{3584}(2383,\cdot)\) \(\chi_{3584}(2511,\cdot)\) \(\chi_{3584}(2607,\cdot)\) \(\chi_{3584}(2735,\cdot)\) \(\chi_{3584}(2831,\cdot)\) \(\chi_{3584}(2959,\cdot)\) \(\chi_{3584}(3055,\cdot)\) \(\chi_{3584}(3183,\cdot)\) \(\chi_{3584}(3279,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{11}{32}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 3584 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{1}{48}\right)\) |