Basic properties
Modulus: | \(1792\) | |
Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{896}(549,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bz
\(\chi_{1792}(73,\cdot)\) \(\chi_{1792}(89,\cdot)\) \(\chi_{1792}(185,\cdot)\) \(\chi_{1792}(201,\cdot)\) \(\chi_{1792}(297,\cdot)\) \(\chi_{1792}(313,\cdot)\) \(\chi_{1792}(409,\cdot)\) \(\chi_{1792}(425,\cdot)\) \(\chi_{1792}(521,\cdot)\) \(\chi_{1792}(537,\cdot)\) \(\chi_{1792}(633,\cdot)\) \(\chi_{1792}(649,\cdot)\) \(\chi_{1792}(745,\cdot)\) \(\chi_{1792}(761,\cdot)\) \(\chi_{1792}(857,\cdot)\) \(\chi_{1792}(873,\cdot)\) \(\chi_{1792}(969,\cdot)\) \(\chi_{1792}(985,\cdot)\) \(\chi_{1792}(1081,\cdot)\) \(\chi_{1792}(1097,\cdot)\) \(\chi_{1792}(1193,\cdot)\) \(\chi_{1792}(1209,\cdot)\) \(\chi_{1792}(1305,\cdot)\) \(\chi_{1792}(1321,\cdot)\) \(\chi_{1792}(1417,\cdot)\) \(\chi_{1792}(1433,\cdot)\) \(\chi_{1792}(1529,\cdot)\) \(\chi_{1792}(1545,\cdot)\) \(\chi_{1792}(1641,\cdot)\) \(\chi_{1792}(1657,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{25}{32}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(857, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) |