Basic properties
Modulus: | \(896\) | |
Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | 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 896.bs
\(\chi_{896}(11,\cdot)\) \(\chi_{896}(51,\cdot)\) \(\chi_{896}(67,\cdot)\) \(\chi_{896}(107,\cdot)\) \(\chi_{896}(123,\cdot)\) \(\chi_{896}(163,\cdot)\) \(\chi_{896}(179,\cdot)\) \(\chi_{896}(219,\cdot)\) \(\chi_{896}(235,\cdot)\) \(\chi_{896}(275,\cdot)\) \(\chi_{896}(291,\cdot)\) \(\chi_{896}(331,\cdot)\) \(\chi_{896}(347,\cdot)\) \(\chi_{896}(387,\cdot)\) \(\chi_{896}(403,\cdot)\) \(\chi_{896}(443,\cdot)\) \(\chi_{896}(459,\cdot)\) \(\chi_{896}(499,\cdot)\) \(\chi_{896}(515,\cdot)\) \(\chi_{896}(555,\cdot)\) \(\chi_{896}(571,\cdot)\) \(\chi_{896}(611,\cdot)\) \(\chi_{896}(627,\cdot)\) \(\chi_{896}(667,\cdot)\) \(\chi_{896}(683,\cdot)\) \(\chi_{896}(723,\cdot)\) \(\chi_{896}(739,\cdot)\) \(\chi_{896}(779,\cdot)\) \(\chi_{896}(795,\cdot)\) \(\chi_{896}(835,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,645,129)\) → \((-1,e\left(\frac{25}{32}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 896 }(219, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{43}{48}\right)\) |