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.ci
\(\chi_{4608}(5,\cdot)\) \(\chi_{4608}(29,\cdot)\) \(\chi_{4608}(77,\cdot)\) \(\chi_{4608}(101,\cdot)\) \(\chi_{4608}(149,\cdot)\) \(\chi_{4608}(173,\cdot)\) \(\chi_{4608}(221,\cdot)\) \(\chi_{4608}(245,\cdot)\) \(\chi_{4608}(293,\cdot)\) \(\chi_{4608}(317,\cdot)\) \(\chi_{4608}(365,\cdot)\) \(\chi_{4608}(389,\cdot)\) \(\chi_{4608}(437,\cdot)\) \(\chi_{4608}(461,\cdot)\) \(\chi_{4608}(509,\cdot)\) \(\chi_{4608}(533,\cdot)\) \(\chi_{4608}(581,\cdot)\) \(\chi_{4608}(605,\cdot)\) \(\chi_{4608}(653,\cdot)\) \(\chi_{4608}(677,\cdot)\) \(\chi_{4608}(725,\cdot)\) \(\chi_{4608}(749,\cdot)\) \(\chi_{4608}(797,\cdot)\) \(\chi_{4608}(821,\cdot)\) \(\chi_{4608}(869,\cdot)\) \(\chi_{4608}(893,\cdot)\) \(\chi_{4608}(941,\cdot)\) \(\chi_{4608}(965,\cdot)\) \(\chi_{4608}(1013,\cdot)\) \(\chi_{4608}(1037,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{1}{128}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{384}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{191}{384}\right)\) | \(e\left(\frac{205}{384}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{23}{128}\right)\) | \(e\left(\frac{53}{192}\right)\) | \(e\left(\frac{67}{192}\right)\) | \(e\left(\frac{305}{384}\right)\) | \(e\left(\frac{35}{48}\right)\) |