Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(4608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(384\) | 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 4608.cl
\(\chi_{4608}(43,\cdot)\) \(\chi_{4608}(67,\cdot)\) \(\chi_{4608}(115,\cdot)\) \(\chi_{4608}(139,\cdot)\) \(\chi_{4608}(187,\cdot)\) \(\chi_{4608}(211,\cdot)\) \(\chi_{4608}(259,\cdot)\) \(\chi_{4608}(283,\cdot)\) \(\chi_{4608}(331,\cdot)\) \(\chi_{4608}(355,\cdot)\) \(\chi_{4608}(403,\cdot)\) \(\chi_{4608}(427,\cdot)\) \(\chi_{4608}(475,\cdot)\) \(\chi_{4608}(499,\cdot)\) \(\chi_{4608}(547,\cdot)\) \(\chi_{4608}(571,\cdot)\) \(\chi_{4608}(619,\cdot)\) \(\chi_{4608}(643,\cdot)\) \(\chi_{4608}(691,\cdot)\) \(\chi_{4608}(715,\cdot)\) \(\chi_{4608}(763,\cdot)\) \(\chi_{4608}(787,\cdot)\) \(\chi_{4608}(835,\cdot)\) \(\chi_{4608}(859,\cdot)\) \(\chi_{4608}(907,\cdot)\) \(\chi_{4608}(931,\cdot)\) \(\chi_{4608}(979,\cdot)\) \(\chi_{4608}(1003,\cdot)\) \(\chi_{4608}(1051,\cdot)\) \(\chi_{4608}(1075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{105}{128}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(1051, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{384}\right)\) | \(e\left(\frac{167}{192}\right)\) | \(e\left(\frac{343}{384}\right)\) | \(e\left(\frac{149}{384}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{47}{128}\right)\) | \(e\left(\frac{61}{192}\right)\) | \(e\left(\frac{59}{192}\right)\) | \(e\left(\frac{217}{384}\right)\) | \(e\left(\frac{19}{48}\right)\) |