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.fc
\(\chi_{4851}(5,\cdot)\) \(\chi_{4851}(38,\cdot)\) \(\chi_{4851}(257,\cdot)\) \(\chi_{4851}(290,\cdot)\) \(\chi_{4851}(383,\cdot)\) \(\chi_{4851}(416,\cdot)\) \(\chi_{4851}(542,\cdot)\) \(\chi_{4851}(698,\cdot)\) \(\chi_{4851}(731,\cdot)\) \(\chi_{4851}(983,\cdot)\) \(\chi_{4851}(1076,\cdot)\) \(\chi_{4851}(1202,\cdot)\) \(\chi_{4851}(1235,\cdot)\) \(\chi_{4851}(1424,\cdot)\) \(\chi_{4851}(1643,\cdot)\) \(\chi_{4851}(1676,\cdot)\) \(\chi_{4851}(1769,\cdot)\) \(\chi_{4851}(1802,\cdot)\) \(\chi_{4851}(1895,\cdot)\) \(\chi_{4851}(1928,\cdot)\) \(\chi_{4851}(2084,\cdot)\) \(\chi_{4851}(2117,\cdot)\) \(\chi_{4851}(2336,\cdot)\) \(\chi_{4851}(2369,\cdot)\) \(\chi_{4851}(2462,\cdot)\) \(\chi_{4851}(2495,\cdot)\) \(\chi_{4851}(2588,\cdot)\) \(\chi_{4851}(2621,\cdot)\) \(\chi_{4851}(2777,\cdot)\) \(\chi_{4851}(2810,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{29}{42}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{105}\right)\) |