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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 896.bt
\(\chi_{896}(3,\cdot)\) \(\chi_{896}(19,\cdot)\) \(\chi_{896}(59,\cdot)\) \(\chi_{896}(75,\cdot)\) \(\chi_{896}(115,\cdot)\) \(\chi_{896}(131,\cdot)\) \(\chi_{896}(171,\cdot)\) \(\chi_{896}(187,\cdot)\) \(\chi_{896}(227,\cdot)\) \(\chi_{896}(243,\cdot)\) \(\chi_{896}(283,\cdot)\) \(\chi_{896}(299,\cdot)\) \(\chi_{896}(339,\cdot)\) \(\chi_{896}(355,\cdot)\) \(\chi_{896}(395,\cdot)\) \(\chi_{896}(411,\cdot)\) \(\chi_{896}(451,\cdot)\) \(\chi_{896}(467,\cdot)\) \(\chi_{896}(507,\cdot)\) \(\chi_{896}(523,\cdot)\) \(\chi_{896}(563,\cdot)\) \(\chi_{896}(579,\cdot)\) \(\chi_{896}(619,\cdot)\) \(\chi_{896}(635,\cdot)\) \(\chi_{896}(675,\cdot)\) \(\chi_{896}(691,\cdot)\) \(\chi_{896}(731,\cdot)\) \(\chi_{896}(747,\cdot)\) \(\chi_{896}(787,\cdot)\) \(\chi_{896}(803,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,645,129)\) → \((-1,e\left(\frac{17}{32}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 896 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) |