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 \(\chi_{2464}(411,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.fr
\(\chi_{4928}(103,\cdot)\) \(\chi_{4928}(311,\cdot)\) \(\chi_{4928}(423,\cdot)\) \(\chi_{4928}(647,\cdot)\) \(\chi_{4928}(663,\cdot)\) \(\chi_{4928}(775,\cdot)\) \(\chi_{4928}(983,\cdot)\) \(\chi_{4928}(999,\cdot)\) \(\chi_{4928}(1335,\cdot)\) \(\chi_{4928}(1543,\cdot)\) \(\chi_{4928}(1655,\cdot)\) \(\chi_{4928}(1879,\cdot)\) \(\chi_{4928}(1895,\cdot)\) \(\chi_{4928}(2007,\cdot)\) \(\chi_{4928}(2215,\cdot)\) \(\chi_{4928}(2231,\cdot)\) \(\chi_{4928}(2567,\cdot)\) \(\chi_{4928}(2775,\cdot)\) \(\chi_{4928}(2887,\cdot)\) \(\chi_{4928}(3111,\cdot)\) \(\chi_{4928}(3127,\cdot)\) \(\chi_{4928}(3239,\cdot)\) \(\chi_{4928}(3447,\cdot)\) \(\chi_{4928}(3463,\cdot)\) \(\chi_{4928}(3799,\cdot)\) \(\chi_{4928}(4007,\cdot)\) \(\chi_{4928}(4119,\cdot)\) \(\chi_{4928}(4343,\cdot)\) \(\chi_{4928}(4359,\cdot)\) \(\chi_{4928}(4471,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) |