Basic properties
| Modulus: | \(4851\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4851.fy
\(\chi_{4851}(53,\cdot)\) \(\chi_{4851}(170,\cdot)\) \(\chi_{4851}(179,\cdot)\) \(\chi_{4851}(368,\cdot)\) \(\chi_{4851}(548,\cdot)\) \(\chi_{4851}(620,\cdot)\) \(\chi_{4851}(674,\cdot)\) \(\chi_{4851}(746,\cdot)\) \(\chi_{4851}(872,\cdot)\) \(\chi_{4851}(1061,\cdot)\) \(\chi_{4851}(1115,\cdot)\) \(\chi_{4851}(1241,\cdot)\) \(\chi_{4851}(1313,\cdot)\) \(\chi_{4851}(1367,\cdot)\) \(\chi_{4851}(1556,\cdot)\) \(\chi_{4851}(1565,\cdot)\) \(\chi_{4851}(1754,\cdot)\) \(\chi_{4851}(1808,\cdot)\) \(\chi_{4851}(1934,\cdot)\) \(\chi_{4851}(2006,\cdot)\) \(\chi_{4851}(2060,\cdot)\) \(\chi_{4851}(2132,\cdot)\) \(\chi_{4851}(2249,\cdot)\) \(\chi_{4851}(2258,\cdot)\) \(\chi_{4851}(2447,\cdot)\) \(\chi_{4851}(2501,\cdot)\) \(\chi_{4851}(2699,\cdot)\) \(\chi_{4851}(2753,\cdot)\) \(\chi_{4851}(2825,\cdot)\) \(\chi_{4851}(2942,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((-1,e\left(\frac{5}{21}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{27}{70}\right)\) |