Basic properties
| Modulus: | \(4864\) | |
| Conductor: | \(4864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | 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 4864.cw
\(\chi_{4864}(27,\cdot)\) \(\chi_{4864}(107,\cdot)\) \(\chi_{4864}(179,\cdot)\) \(\chi_{4864}(259,\cdot)\) \(\chi_{4864}(331,\cdot)\) \(\chi_{4864}(411,\cdot)\) \(\chi_{4864}(483,\cdot)\) \(\chi_{4864}(563,\cdot)\) \(\chi_{4864}(635,\cdot)\) \(\chi_{4864}(715,\cdot)\) \(\chi_{4864}(787,\cdot)\) \(\chi_{4864}(867,\cdot)\) \(\chi_{4864}(939,\cdot)\) \(\chi_{4864}(1019,\cdot)\) \(\chi_{4864}(1091,\cdot)\) \(\chi_{4864}(1171,\cdot)\) \(\chi_{4864}(1243,\cdot)\) \(\chi_{4864}(1323,\cdot)\) \(\chi_{4864}(1395,\cdot)\) \(\chi_{4864}(1475,\cdot)\) \(\chi_{4864}(1547,\cdot)\) \(\chi_{4864}(1627,\cdot)\) \(\chi_{4864}(1699,\cdot)\) \(\chi_{4864}(1779,\cdot)\) \(\chi_{4864}(1851,\cdot)\) \(\chi_{4864}(1931,\cdot)\) \(\chi_{4864}(2003,\cdot)\) \(\chi_{4864}(2083,\cdot)\) \(\chi_{4864}(2155,\cdot)\) \(\chi_{4864}(2235,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((3839,2053,4353)\) → \((-1,e\left(\frac{41}{64}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{192}\right)\) | \(e\left(\frac{59}{192}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{181}{192}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{191}{192}\right)\) | \(e\left(\frac{77}{96}\right)\) |