Basic properties
| Modulus: | \(9216\) | |
| Conductor: | \(4608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(384\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4608}(2003,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.cn
\(\chi_{9216}(23,\cdot)\) \(\chi_{9216}(119,\cdot)\) \(\chi_{9216}(167,\cdot)\) \(\chi_{9216}(263,\cdot)\) \(\chi_{9216}(311,\cdot)\) \(\chi_{9216}(407,\cdot)\) \(\chi_{9216}(455,\cdot)\) \(\chi_{9216}(551,\cdot)\) \(\chi_{9216}(599,\cdot)\) \(\chi_{9216}(695,\cdot)\) \(\chi_{9216}(743,\cdot)\) \(\chi_{9216}(839,\cdot)\) \(\chi_{9216}(887,\cdot)\) \(\chi_{9216}(983,\cdot)\) \(\chi_{9216}(1031,\cdot)\) \(\chi_{9216}(1127,\cdot)\) \(\chi_{9216}(1175,\cdot)\) \(\chi_{9216}(1271,\cdot)\) \(\chi_{9216}(1319,\cdot)\) \(\chi_{9216}(1415,\cdot)\) \(\chi_{9216}(1463,\cdot)\) \(\chi_{9216}(1559,\cdot)\) \(\chi_{9216}(1607,\cdot)\) \(\chi_{9216}(1703,\cdot)\) \(\chi_{9216}(1751,\cdot)\) \(\chi_{9216}(1847,\cdot)\) \(\chi_{9216}(1895,\cdot)\) \(\chi_{9216}(1991,\cdot)\) \(\chi_{9216}(2039,\cdot)\) \(\chi_{9216}(2135,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((8191,2053,4097)\) → \((-1,e\left(\frac{71}{128}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{384}\right)\) | \(e\left(\frac{169}{192}\right)\) | \(e\left(\frac{185}{384}\right)\) | \(e\left(\frac{91}{384}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{33}{128}\right)\) | \(e\left(\frac{83}{192}\right)\) | \(e\left(\frac{85}{192}\right)\) | \(e\left(\frac{23}{384}\right)\) | \(e\left(\frac{29}{48}\right)\) |