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.fb
\(\chi_{4851}(25,\cdot)\) \(\chi_{4851}(58,\cdot)\) \(\chi_{4851}(247,\cdot)\) \(\chi_{4851}(466,\cdot)\) \(\chi_{4851}(499,\cdot)\) \(\chi_{4851}(592,\cdot)\) \(\chi_{4851}(625,\cdot)\) \(\chi_{4851}(718,\cdot)\) \(\chi_{4851}(751,\cdot)\) \(\chi_{4851}(907,\cdot)\) \(\chi_{4851}(940,\cdot)\) \(\chi_{4851}(1159,\cdot)\) \(\chi_{4851}(1192,\cdot)\) \(\chi_{4851}(1285,\cdot)\) \(\chi_{4851}(1318,\cdot)\) \(\chi_{4851}(1411,\cdot)\) \(\chi_{4851}(1444,\cdot)\) \(\chi_{4851}(1600,\cdot)\) \(\chi_{4851}(1633,\cdot)\) \(\chi_{4851}(1852,\cdot)\) \(\chi_{4851}(1885,\cdot)\) \(\chi_{4851}(2011,\cdot)\) \(\chi_{4851}(2104,\cdot)\) \(\chi_{4851}(2293,\cdot)\) \(\chi_{4851}(2326,\cdot)\) \(\chi_{4851}(2545,\cdot)\) \(\chi_{4851}(2671,\cdot)\) \(\chi_{4851}(2704,\cdot)\) \(\chi_{4851}(2797,\cdot)\) \(\chi_{4851}(2830,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{8}{21}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{34}{105}\right)\) |