Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(4928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 4928.gc
\(\chi_{4928}(51,\cdot)\) \(\chi_{4928}(107,\cdot)\) \(\chi_{4928}(123,\cdot)\) \(\chi_{4928}(347,\cdot)\) \(\chi_{4928}(387,\cdot)\) \(\chi_{4928}(403,\cdot)\) \(\chi_{4928}(459,\cdot)\) \(\chi_{4928}(611,\cdot)\) \(\chi_{4928}(667,\cdot)\) \(\chi_{4928}(723,\cdot)\) \(\chi_{4928}(739,\cdot)\) \(\chi_{4928}(963,\cdot)\) \(\chi_{4928}(1003,\cdot)\) \(\chi_{4928}(1019,\cdot)\) \(\chi_{4928}(1075,\cdot)\) \(\chi_{4928}(1227,\cdot)\) \(\chi_{4928}(1283,\cdot)\) \(\chi_{4928}(1339,\cdot)\) \(\chi_{4928}(1355,\cdot)\) \(\chi_{4928}(1579,\cdot)\) \(\chi_{4928}(1619,\cdot)\) \(\chi_{4928}(1635,\cdot)\) \(\chi_{4928}(1691,\cdot)\) \(\chi_{4928}(1843,\cdot)\) \(\chi_{4928}(1899,\cdot)\) \(\chi_{4928}(1955,\cdot)\) \(\chi_{4928}(1971,\cdot)\) \(\chi_{4928}(2195,\cdot)\) \(\chi_{4928}(2235,\cdot)\) \(\chi_{4928}(2251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(1691, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{161}{240}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{61}{80}\right)\) |