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.fw
\(\chi_{4851}(13,\cdot)\) \(\chi_{4851}(139,\cdot)\) \(\chi_{4851}(160,\cdot)\) \(\chi_{4851}(349,\cdot)\) \(\chi_{4851}(475,\cdot)\) \(\chi_{4851}(580,\cdot)\) \(\chi_{4851}(601,\cdot)\) \(\chi_{4851}(706,\cdot)\) \(\chi_{4851}(853,\cdot)\) \(\chi_{4851}(1042,\cdot)\) \(\chi_{4851}(1084,\cdot)\) \(\chi_{4851}(1168,\cdot)\) \(\chi_{4851}(1294,\cdot)\) \(\chi_{4851}(1399,\cdot)\) \(\chi_{4851}(1525,\cdot)\) \(\chi_{4851}(1546,\cdot)\) \(\chi_{4851}(1735,\cdot)\) \(\chi_{4851}(1777,\cdot)\) \(\chi_{4851}(1966,\cdot)\) \(\chi_{4851}(1987,\cdot)\) \(\chi_{4851}(2092,\cdot)\) \(\chi_{4851}(2218,\cdot)\) \(\chi_{4851}(2239,\cdot)\) \(\chi_{4851}(2428,\cdot)\) \(\chi_{4851}(2470,\cdot)\) \(\chi_{4851}(2554,\cdot)\) \(\chi_{4851}(2659,\cdot)\) \(\chi_{4851}(2680,\cdot)\) \(\chi_{4851}(2785,\cdot)\) \(\chi_{4851}(2911,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{121}{210}\right)\) |