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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.cj
\(\chi_{4608}(11,\cdot)\) \(\chi_{4608}(59,\cdot)\) \(\chi_{4608}(83,\cdot)\) \(\chi_{4608}(131,\cdot)\) \(\chi_{4608}(155,\cdot)\) \(\chi_{4608}(203,\cdot)\) \(\chi_{4608}(227,\cdot)\) \(\chi_{4608}(275,\cdot)\) \(\chi_{4608}(299,\cdot)\) \(\chi_{4608}(347,\cdot)\) \(\chi_{4608}(371,\cdot)\) \(\chi_{4608}(419,\cdot)\) \(\chi_{4608}(443,\cdot)\) \(\chi_{4608}(491,\cdot)\) \(\chi_{4608}(515,\cdot)\) \(\chi_{4608}(563,\cdot)\) \(\chi_{4608}(587,\cdot)\) \(\chi_{4608}(635,\cdot)\) \(\chi_{4608}(659,\cdot)\) \(\chi_{4608}(707,\cdot)\) \(\chi_{4608}(731,\cdot)\) \(\chi_{4608}(779,\cdot)\) \(\chi_{4608}(803,\cdot)\) \(\chi_{4608}(851,\cdot)\) \(\chi_{4608}(875,\cdot)\) \(\chi_{4608}(923,\cdot)\) \(\chi_{4608}(947,\cdot)\) \(\chi_{4608}(995,\cdot)\) \(\chi_{4608}(1019,\cdot)\) \(\chi_{4608}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{103}{128}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{245}{384}\right)\) | \(e\left(\frac{137}{192}\right)\) | \(e\left(\frac{25}{384}\right)\) | \(e\left(\frac{251}{384}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{1}{128}\right)\) | \(e\left(\frac{115}{192}\right)\) | \(e\left(\frac{53}{192}\right)\) | \(e\left(\frac{55}{384}\right)\) | \(e\left(\frac{13}{48}\right)\) |