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 \(\chi_{1152}(331,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.by
\(\chi_{2304}(7,\cdot)\) \(\chi_{2304}(103,\cdot)\) \(\chi_{2304}(151,\cdot)\) \(\chi_{2304}(247,\cdot)\) \(\chi_{2304}(295,\cdot)\) \(\chi_{2304}(391,\cdot)\) \(\chi_{2304}(439,\cdot)\) \(\chi_{2304}(535,\cdot)\) \(\chi_{2304}(583,\cdot)\) \(\chi_{2304}(679,\cdot)\) \(\chi_{2304}(727,\cdot)\) \(\chi_{2304}(823,\cdot)\) \(\chi_{2304}(871,\cdot)\) \(\chi_{2304}(967,\cdot)\) \(\chi_{2304}(1015,\cdot)\) \(\chi_{2304}(1111,\cdot)\) \(\chi_{2304}(1159,\cdot)\) \(\chi_{2304}(1255,\cdot)\) \(\chi_{2304}(1303,\cdot)\) \(\chi_{2304}(1399,\cdot)\) \(\chi_{2304}(1447,\cdot)\) \(\chi_{2304}(1543,\cdot)\) \(\chi_{2304}(1591,\cdot)\) \(\chi_{2304}(1687,\cdot)\) \(\chi_{2304}(1735,\cdot)\) \(\chi_{2304}(1831,\cdot)\) \(\chi_{2304}(1879,\cdot)\) \(\chi_{2304}(1975,\cdot)\) \(\chi_{2304}(2023,\cdot)\) \(\chi_{2304}(2119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{5}{32}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |