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.bv
\(\chi_{896}(5,\cdot)\) \(\chi_{896}(45,\cdot)\) \(\chi_{896}(61,\cdot)\) \(\chi_{896}(101,\cdot)\) \(\chi_{896}(117,\cdot)\) \(\chi_{896}(157,\cdot)\) \(\chi_{896}(173,\cdot)\) \(\chi_{896}(213,\cdot)\) \(\chi_{896}(229,\cdot)\) \(\chi_{896}(269,\cdot)\) \(\chi_{896}(285,\cdot)\) \(\chi_{896}(325,\cdot)\) \(\chi_{896}(341,\cdot)\) \(\chi_{896}(381,\cdot)\) \(\chi_{896}(397,\cdot)\) \(\chi_{896}(437,\cdot)\) \(\chi_{896}(453,\cdot)\) \(\chi_{896}(493,\cdot)\) \(\chi_{896}(509,\cdot)\) \(\chi_{896}(549,\cdot)\) \(\chi_{896}(565,\cdot)\) \(\chi_{896}(605,\cdot)\) \(\chi_{896}(621,\cdot)\) \(\chi_{896}(661,\cdot)\) \(\chi_{896}(677,\cdot)\) \(\chi_{896}(717,\cdot)\) \(\chi_{896}(733,\cdot)\) \(\chi_{896}(773,\cdot)\) \(\chi_{896}(789,\cdot)\) \(\chi_{896}(829,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,645,129)\) → \((1,e\left(\frac{15}{32}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 896 }(397, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) |