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 \(\chi_{2304}(1229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.cf
\(\chi_{4608}(41,\cdot)\) \(\chi_{4608}(137,\cdot)\) \(\chi_{4608}(185,\cdot)\) \(\chi_{4608}(281,\cdot)\) \(\chi_{4608}(329,\cdot)\) \(\chi_{4608}(425,\cdot)\) \(\chi_{4608}(473,\cdot)\) \(\chi_{4608}(569,\cdot)\) \(\chi_{4608}(617,\cdot)\) \(\chi_{4608}(713,\cdot)\) \(\chi_{4608}(761,\cdot)\) \(\chi_{4608}(857,\cdot)\) \(\chi_{4608}(905,\cdot)\) \(\chi_{4608}(1001,\cdot)\) \(\chi_{4608}(1049,\cdot)\) \(\chi_{4608}(1145,\cdot)\) \(\chi_{4608}(1193,\cdot)\) \(\chi_{4608}(1289,\cdot)\) \(\chi_{4608}(1337,\cdot)\) \(\chi_{4608}(1433,\cdot)\) \(\chi_{4608}(1481,\cdot)\) \(\chi_{4608}(1577,\cdot)\) \(\chi_{4608}(1625,\cdot)\) \(\chi_{4608}(1721,\cdot)\) \(\chi_{4608}(1769,\cdot)\) \(\chi_{4608}(1865,\cdot)\) \(\chi_{4608}(1913,\cdot)\) \(\chi_{4608}(2009,\cdot)\) \(\chi_{4608}(2057,\cdot)\) \(\chi_{4608}(2153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{63}{64}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{192}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{97}{192}\right)\) | \(e\left(\frac{179}{192}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{13}{24}\right)\) |