Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(2304\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2304}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.cg
\(\chi_{4608}(7,\cdot)\) \(\chi_{4608}(103,\cdot)\) \(\chi_{4608}(151,\cdot)\) \(\chi_{4608}(247,\cdot)\) \(\chi_{4608}(295,\cdot)\) \(\chi_{4608}(391,\cdot)\) \(\chi_{4608}(439,\cdot)\) \(\chi_{4608}(535,\cdot)\) \(\chi_{4608}(583,\cdot)\) \(\chi_{4608}(679,\cdot)\) \(\chi_{4608}(727,\cdot)\) \(\chi_{4608}(823,\cdot)\) \(\chi_{4608}(871,\cdot)\) \(\chi_{4608}(967,\cdot)\) \(\chi_{4608}(1015,\cdot)\) \(\chi_{4608}(1111,\cdot)\) \(\chi_{4608}(1159,\cdot)\) \(\chi_{4608}(1255,\cdot)\) \(\chi_{4608}(1303,\cdot)\) \(\chi_{4608}(1399,\cdot)\) \(\chi_{4608}(1447,\cdot)\) \(\chi_{4608}(1543,\cdot)\) \(\chi_{4608}(1591,\cdot)\) \(\chi_{4608}(1687,\cdot)\) \(\chi_{4608}(1735,\cdot)\) \(\chi_{4608}(1831,\cdot)\) \(\chi_{4608}(1879,\cdot)\) \(\chi_{4608}(1975,\cdot)\) \(\chi_{4608}(2023,\cdot)\) \(\chi_{4608}(2119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{49}{64}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(871, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{192}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{47}{192}\right)\) | \(e\left(\frac{61}{192}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{53}{96}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{23}{24}\right)\) |