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 \(\chi_{896}(795,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bw
\(\chi_{1792}(23,\cdot)\) \(\chi_{1792}(39,\cdot)\) \(\chi_{1792}(135,\cdot)\) \(\chi_{1792}(151,\cdot)\) \(\chi_{1792}(247,\cdot)\) \(\chi_{1792}(263,\cdot)\) \(\chi_{1792}(359,\cdot)\) \(\chi_{1792}(375,\cdot)\) \(\chi_{1792}(471,\cdot)\) \(\chi_{1792}(487,\cdot)\) \(\chi_{1792}(583,\cdot)\) \(\chi_{1792}(599,\cdot)\) \(\chi_{1792}(695,\cdot)\) \(\chi_{1792}(711,\cdot)\) \(\chi_{1792}(807,\cdot)\) \(\chi_{1792}(823,\cdot)\) \(\chi_{1792}(919,\cdot)\) \(\chi_{1792}(935,\cdot)\) \(\chi_{1792}(1031,\cdot)\) \(\chi_{1792}(1047,\cdot)\) \(\chi_{1792}(1143,\cdot)\) \(\chi_{1792}(1159,\cdot)\) \(\chi_{1792}(1255,\cdot)\) \(\chi_{1792}(1271,\cdot)\) \(\chi_{1792}(1367,\cdot)\) \(\chi_{1792}(1383,\cdot)\) \(\chi_{1792}(1479,\cdot)\) \(\chi_{1792}(1495,\cdot)\) \(\chi_{1792}(1591,\cdot)\) \(\chi_{1792}(1607,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{9}{32}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) |