Basic properties
Modulus: | \(1152\) | |
Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1152.bu
\(\chi_{1152}(43,\cdot)\) \(\chi_{1152}(67,\cdot)\) \(\chi_{1152}(115,\cdot)\) \(\chi_{1152}(139,\cdot)\) \(\chi_{1152}(187,\cdot)\) \(\chi_{1152}(211,\cdot)\) \(\chi_{1152}(259,\cdot)\) \(\chi_{1152}(283,\cdot)\) \(\chi_{1152}(331,\cdot)\) \(\chi_{1152}(355,\cdot)\) \(\chi_{1152}(403,\cdot)\) \(\chi_{1152}(427,\cdot)\) \(\chi_{1152}(475,\cdot)\) \(\chi_{1152}(499,\cdot)\) \(\chi_{1152}(547,\cdot)\) \(\chi_{1152}(571,\cdot)\) \(\chi_{1152}(619,\cdot)\) \(\chi_{1152}(643,\cdot)\) \(\chi_{1152}(691,\cdot)\) \(\chi_{1152}(715,\cdot)\) \(\chi_{1152}(763,\cdot)\) \(\chi_{1152}(787,\cdot)\) \(\chi_{1152}(835,\cdot)\) \(\chi_{1152}(859,\cdot)\) \(\chi_{1152}(907,\cdot)\) \(\chi_{1152}(931,\cdot)\) \(\chi_{1152}(979,\cdot)\) \(\chi_{1152}(1003,\cdot)\) \(\chi_{1152}(1051,\cdot)\) \(\chi_{1152}(1075,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,901,641)\) → \((-1,e\left(\frac{11}{32}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1152 }(547, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{7}{12}\right)\) |