Basic properties
| Modulus: | \(4851\) | |
| Conductor: | \(4851\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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.fa
\(\chi_{4851}(4,\cdot)\) \(\chi_{4851}(16,\cdot)\) \(\chi_{4851}(130,\cdot)\) \(\chi_{4851}(256,\cdot)\) \(\chi_{4851}(268,\cdot)\) \(\chi_{4851}(394,\cdot)\) \(\chi_{4851}(445,\cdot)\) \(\chi_{4851}(697,\cdot)\) \(\chi_{4851}(709,\cdot)\) \(\chi_{4851}(823,\cdot)\) \(\chi_{4851}(1087,\cdot)\) \(\chi_{4851}(1138,\cdot)\) \(\chi_{4851}(1213,\cdot)\) \(\chi_{4851}(1516,\cdot)\) \(\chi_{4851}(1642,\cdot)\) \(\chi_{4851}(1654,\cdot)\) \(\chi_{4851}(1780,\cdot)\) \(\chi_{4851}(1906,\cdot)\) \(\chi_{4851}(2083,\cdot)\) \(\chi_{4851}(2095,\cdot)\) \(\chi_{4851}(2209,\cdot)\) \(\chi_{4851}(2335,\cdot)\) \(\chi_{4851}(2347,\cdot)\) \(\chi_{4851}(2473,\cdot)\) \(\chi_{4851}(2524,\cdot)\) \(\chi_{4851}(2599,\cdot)\) \(\chi_{4851}(2776,\cdot)\) \(\chi_{4851}(2788,\cdot)\) \(\chi_{4851}(2902,\cdot)\) \(\chi_{4851}(3028,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{21}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{86}{105}\right)\) |