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.fx
\(\chi_{4928}(3,\cdot)\) \(\chi_{4928}(59,\cdot)\) \(\chi_{4928}(75,\cdot)\) \(\chi_{4928}(115,\cdot)\) \(\chi_{4928}(339,\cdot)\) \(\chi_{4928}(355,\cdot)\) \(\chi_{4928}(411,\cdot)\) \(\chi_{4928}(467,\cdot)\) \(\chi_{4928}(619,\cdot)\) \(\chi_{4928}(675,\cdot)\) \(\chi_{4928}(691,\cdot)\) \(\chi_{4928}(731,\cdot)\) \(\chi_{4928}(955,\cdot)\) \(\chi_{4928}(971,\cdot)\) \(\chi_{4928}(1027,\cdot)\) \(\chi_{4928}(1083,\cdot)\) \(\chi_{4928}(1235,\cdot)\) \(\chi_{4928}(1291,\cdot)\) \(\chi_{4928}(1307,\cdot)\) \(\chi_{4928}(1347,\cdot)\) \(\chi_{4928}(1571,\cdot)\) \(\chi_{4928}(1587,\cdot)\) \(\chi_{4928}(1643,\cdot)\) \(\chi_{4928}(1699,\cdot)\) \(\chi_{4928}(1851,\cdot)\) \(\chi_{4928}(1907,\cdot)\) \(\chi_{4928}(1923,\cdot)\) \(\chi_{4928}(1963,\cdot)\) \(\chi_{4928}(2187,\cdot)\) \(\chi_{4928}(2203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{1}{6}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{240}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{71}{80}\right)\) |