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.fp
\(\chi_{4851}(61,\cdot)\) \(\chi_{4851}(94,\cdot)\) \(\chi_{4851}(250,\cdot)\) \(\chi_{4851}(283,\cdot)\) \(\chi_{4851}(376,\cdot)\) \(\chi_{4851}(409,\cdot)\) \(\chi_{4851}(502,\cdot)\) \(\chi_{4851}(535,\cdot)\) \(\chi_{4851}(787,\cdot)\) \(\chi_{4851}(943,\cdot)\) \(\chi_{4851}(976,\cdot)\) \(\chi_{4851}(1069,\cdot)\) \(\chi_{4851}(1102,\cdot)\) \(\chi_{4851}(1228,\cdot)\) \(\chi_{4851}(1447,\cdot)\) \(\chi_{4851}(1480,\cdot)\) \(\chi_{4851}(1669,\cdot)\) \(\chi_{4851}(1762,\cdot)\) \(\chi_{4851}(1888,\cdot)\) \(\chi_{4851}(1921,\cdot)\) \(\chi_{4851}(2140,\cdot)\) \(\chi_{4851}(2173,\cdot)\) \(\chi_{4851}(2329,\cdot)\) \(\chi_{4851}(2362,\cdot)\) \(\chi_{4851}(2455,\cdot)\) \(\chi_{4851}(2488,\cdot)\) \(\chi_{4851}(2581,\cdot)\) \(\chi_{4851}(2614,\cdot)\) \(\chi_{4851}(2833,\cdot)\) \(\chi_{4851}(2866,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{210}\right)\) |