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 \(\chi_{1152}(893,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bx
\(\chi_{2304}(41,\cdot)\) \(\chi_{2304}(137,\cdot)\) \(\chi_{2304}(185,\cdot)\) \(\chi_{2304}(281,\cdot)\) \(\chi_{2304}(329,\cdot)\) \(\chi_{2304}(425,\cdot)\) \(\chi_{2304}(473,\cdot)\) \(\chi_{2304}(569,\cdot)\) \(\chi_{2304}(617,\cdot)\) \(\chi_{2304}(713,\cdot)\) \(\chi_{2304}(761,\cdot)\) \(\chi_{2304}(857,\cdot)\) \(\chi_{2304}(905,\cdot)\) \(\chi_{2304}(1001,\cdot)\) \(\chi_{2304}(1049,\cdot)\) \(\chi_{2304}(1145,\cdot)\) \(\chi_{2304}(1193,\cdot)\) \(\chi_{2304}(1289,\cdot)\) \(\chi_{2304}(1337,\cdot)\) \(\chi_{2304}(1433,\cdot)\) \(\chi_{2304}(1481,\cdot)\) \(\chi_{2304}(1577,\cdot)\) \(\chi_{2304}(1625,\cdot)\) \(\chi_{2304}(1721,\cdot)\) \(\chi_{2304}(1769,\cdot)\) \(\chi_{2304}(1865,\cdot)\) \(\chi_{2304}(1913,\cdot)\) \(\chi_{2304}(2009,\cdot)\) \(\chi_{2304}(2057,\cdot)\) \(\chi_{2304}(2153,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{3}{32}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(1289, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |