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.cx
\(\chi_{4864}(45,\cdot)\) \(\chi_{4864}(125,\cdot)\) \(\chi_{4864}(197,\cdot)\) \(\chi_{4864}(277,\cdot)\) \(\chi_{4864}(349,\cdot)\) \(\chi_{4864}(429,\cdot)\) \(\chi_{4864}(501,\cdot)\) \(\chi_{4864}(581,\cdot)\) \(\chi_{4864}(653,\cdot)\) \(\chi_{4864}(733,\cdot)\) \(\chi_{4864}(805,\cdot)\) \(\chi_{4864}(885,\cdot)\) \(\chi_{4864}(957,\cdot)\) \(\chi_{4864}(1037,\cdot)\) \(\chi_{4864}(1109,\cdot)\) \(\chi_{4864}(1189,\cdot)\) \(\chi_{4864}(1261,\cdot)\) \(\chi_{4864}(1341,\cdot)\) \(\chi_{4864}(1413,\cdot)\) \(\chi_{4864}(1493,\cdot)\) \(\chi_{4864}(1565,\cdot)\) \(\chi_{4864}(1645,\cdot)\) \(\chi_{4864}(1717,\cdot)\) \(\chi_{4864}(1797,\cdot)\) \(\chi_{4864}(1869,\cdot)\) \(\chi_{4864}(1949,\cdot)\) \(\chi_{4864}(2021,\cdot)\) \(\chi_{4864}(2101,\cdot)\) \(\chi_{4864}(2173,\cdot)\) \(\chi_{4864}(2253,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((3839,2053,4353)\) → \((1,e\left(\frac{7}{64}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{192}\right)\) | \(e\left(\frac{85}{192}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{155}{192}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{49}{192}\right)\) | \(e\left(\frac{19}{96}\right)\) |