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.ck
\(\chi_{4608}(13,\cdot)\) \(\chi_{4608}(61,\cdot)\) \(\chi_{4608}(85,\cdot)\) \(\chi_{4608}(133,\cdot)\) \(\chi_{4608}(157,\cdot)\) \(\chi_{4608}(205,\cdot)\) \(\chi_{4608}(229,\cdot)\) \(\chi_{4608}(277,\cdot)\) \(\chi_{4608}(301,\cdot)\) \(\chi_{4608}(349,\cdot)\) \(\chi_{4608}(373,\cdot)\) \(\chi_{4608}(421,\cdot)\) \(\chi_{4608}(445,\cdot)\) \(\chi_{4608}(493,\cdot)\) \(\chi_{4608}(517,\cdot)\) \(\chi_{4608}(565,\cdot)\) \(\chi_{4608}(589,\cdot)\) \(\chi_{4608}(637,\cdot)\) \(\chi_{4608}(661,\cdot)\) \(\chi_{4608}(709,\cdot)\) \(\chi_{4608}(733,\cdot)\) \(\chi_{4608}(781,\cdot)\) \(\chi_{4608}(805,\cdot)\) \(\chi_{4608}(853,\cdot)\) \(\chi_{4608}(877,\cdot)\) \(\chi_{4608}(925,\cdot)\) \(\chi_{4608}(949,\cdot)\) \(\chi_{4608}(997,\cdot)\) \(\chi_{4608}(1021,\cdot)\) \(\chi_{4608}(1069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{29}{128}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{343}{384}\right)\) | \(e\left(\frac{19}{192}\right)\) | \(e\left(\frac{227}{384}\right)\) | \(e\left(\frac{313}{384}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{27}{128}\right)\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{151}{192}\right)\) | \(e\left(\frac{77}{384}\right)\) | \(e\left(\frac{23}{48}\right)\) |