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.fn
\(\chi_{4851}(29,\cdot)\) \(\chi_{4851}(239,\cdot)\) \(\chi_{4851}(281,\cdot)\) \(\chi_{4851}(365,\cdot)\) \(\chi_{4851}(470,\cdot)\) \(\chi_{4851}(596,\cdot)\) \(\chi_{4851}(722,\cdot)\) \(\chi_{4851}(743,\cdot)\) \(\chi_{4851}(974,\cdot)\) \(\chi_{4851}(1058,\cdot)\) \(\chi_{4851}(1163,\cdot)\) \(\chi_{4851}(1184,\cdot)\) \(\chi_{4851}(1289,\cdot)\) \(\chi_{4851}(1415,\cdot)\) \(\chi_{4851}(1436,\cdot)\) \(\chi_{4851}(1625,\cdot)\) \(\chi_{4851}(1751,\cdot)\) \(\chi_{4851}(1856,\cdot)\) \(\chi_{4851}(1877,\cdot)\) \(\chi_{4851}(1982,\cdot)\) \(\chi_{4851}(2129,\cdot)\) \(\chi_{4851}(2318,\cdot)\) \(\chi_{4851}(2360,\cdot)\) \(\chi_{4851}(2444,\cdot)\) \(\chi_{4851}(2570,\cdot)\) \(\chi_{4851}(2675,\cdot)\) \(\chi_{4851}(2801,\cdot)\) \(\chi_{4851}(2822,\cdot)\) \(\chi_{4851}(3011,\cdot)\) \(\chi_{4851}(3053,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{7}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{13}{210}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{210}\right)\) |