Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(2464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2464}(347,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.fq
\(\chi_{4928}(39,\cdot)\) \(\chi_{4928}(151,\cdot)\) \(\chi_{4928}(359,\cdot)\) \(\chi_{4928}(695,\cdot)\) \(\chi_{4928}(711,\cdot)\) \(\chi_{4928}(919,\cdot)\) \(\chi_{4928}(1031,\cdot)\) \(\chi_{4928}(1047,\cdot)\) \(\chi_{4928}(1271,\cdot)\) \(\chi_{4928}(1383,\cdot)\) \(\chi_{4928}(1591,\cdot)\) \(\chi_{4928}(1927,\cdot)\) \(\chi_{4928}(1943,\cdot)\) \(\chi_{4928}(2151,\cdot)\) \(\chi_{4928}(2263,\cdot)\) \(\chi_{4928}(2279,\cdot)\) \(\chi_{4928}(2503,\cdot)\) \(\chi_{4928}(2615,\cdot)\) \(\chi_{4928}(2823,\cdot)\) \(\chi_{4928}(3159,\cdot)\) \(\chi_{4928}(3175,\cdot)\) \(\chi_{4928}(3383,\cdot)\) \(\chi_{4928}(3495,\cdot)\) \(\chi_{4928}(3511,\cdot)\) \(\chi_{4928}(3735,\cdot)\) \(\chi_{4928}(3847,\cdot)\) \(\chi_{4928}(4055,\cdot)\) \(\chi_{4928}(4391,\cdot)\) \(\chi_{4928}(4407,\cdot)\) \(\chi_{4928}(4615,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{2}{3}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) |