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 \(\chi_{2464}(317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.ft
\(\chi_{4928}(9,\cdot)\) \(\chi_{4928}(25,\cdot)\) \(\chi_{4928}(137,\cdot)\) \(\chi_{4928}(345,\cdot)\) \(\chi_{4928}(361,\cdot)\) \(\chi_{4928}(697,\cdot)\) \(\chi_{4928}(905,\cdot)\) \(\chi_{4928}(1017,\cdot)\) \(\chi_{4928}(1241,\cdot)\) \(\chi_{4928}(1257,\cdot)\) \(\chi_{4928}(1369,\cdot)\) \(\chi_{4928}(1577,\cdot)\) \(\chi_{4928}(1593,\cdot)\) \(\chi_{4928}(1929,\cdot)\) \(\chi_{4928}(2137,\cdot)\) \(\chi_{4928}(2249,\cdot)\) \(\chi_{4928}(2473,\cdot)\) \(\chi_{4928}(2489,\cdot)\) \(\chi_{4928}(2601,\cdot)\) \(\chi_{4928}(2809,\cdot)\) \(\chi_{4928}(2825,\cdot)\) \(\chi_{4928}(3161,\cdot)\) \(\chi_{4928}(3369,\cdot)\) \(\chi_{4928}(3481,\cdot)\) \(\chi_{4928}(3705,\cdot)\) \(\chi_{4928}(3721,\cdot)\) \(\chi_{4928}(3833,\cdot)\) \(\chi_{4928}(4041,\cdot)\) \(\chi_{4928}(4057,\cdot)\) \(\chi_{4928}(4393,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,1541,2817,3137)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) |