Basic properties
| Modulus: | \(4851\) | |
| Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 4851.fg
\(\chi_{4851}(2,\cdot)\) \(\chi_{4851}(95,\cdot)\) \(\chi_{4851}(347,\cdot)\) \(\chi_{4851}(380,\cdot)\) \(\chi_{4851}(536,\cdot)\) \(\chi_{4851}(662,\cdot)\) \(\chi_{4851}(695,\cdot)\) \(\chi_{4851}(788,\cdot)\) \(\chi_{4851}(821,\cdot)\) \(\chi_{4851}(1040,\cdot)\) \(\chi_{4851}(1073,\cdot)\) \(\chi_{4851}(1229,\cdot)\) \(\chi_{4851}(1262,\cdot)\) \(\chi_{4851}(1355,\cdot)\) \(\chi_{4851}(1388,\cdot)\) \(\chi_{4851}(1481,\cdot)\) \(\chi_{4851}(1514,\cdot)\) \(\chi_{4851}(1766,\cdot)\) \(\chi_{4851}(1922,\cdot)\) \(\chi_{4851}(1955,\cdot)\) \(\chi_{4851}(2048,\cdot)\) \(\chi_{4851}(2081,\cdot)\) \(\chi_{4851}(2207,\cdot)\) \(\chi_{4851}(2426,\cdot)\) \(\chi_{4851}(2459,\cdot)\) \(\chi_{4851}(2648,\cdot)\) \(\chi_{4851}(2741,\cdot)\) \(\chi_{4851}(2867,\cdot)\) \(\chi_{4851}(2900,\cdot)\) \(\chi_{4851}(3119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{13}{21}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{191}{210}\right)\) |