Basic properties
Modulus: | \(2304\) | |
Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1152}(371,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bw
\(\chi_{2304}(23,\cdot)\) \(\chi_{2304}(119,\cdot)\) \(\chi_{2304}(167,\cdot)\) \(\chi_{2304}(263,\cdot)\) \(\chi_{2304}(311,\cdot)\) \(\chi_{2304}(407,\cdot)\) \(\chi_{2304}(455,\cdot)\) \(\chi_{2304}(551,\cdot)\) \(\chi_{2304}(599,\cdot)\) \(\chi_{2304}(695,\cdot)\) \(\chi_{2304}(743,\cdot)\) \(\chi_{2304}(839,\cdot)\) \(\chi_{2304}(887,\cdot)\) \(\chi_{2304}(983,\cdot)\) \(\chi_{2304}(1031,\cdot)\) \(\chi_{2304}(1127,\cdot)\) \(\chi_{2304}(1175,\cdot)\) \(\chi_{2304}(1271,\cdot)\) \(\chi_{2304}(1319,\cdot)\) \(\chi_{2304}(1415,\cdot)\) \(\chi_{2304}(1463,\cdot)\) \(\chi_{2304}(1559,\cdot)\) \(\chi_{2304}(1607,\cdot)\) \(\chi_{2304}(1703,\cdot)\) \(\chi_{2304}(1751,\cdot)\) \(\chi_{2304}(1847,\cdot)\) \(\chi_{2304}(1895,\cdot)\) \(\chi_{2304}(1991,\cdot)\) \(\chi_{2304}(2039,\cdot)\) \(\chi_{2304}(2135,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{15}{32}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(2135, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{7}{12}\right)\) |