Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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 2873.bu
\(\chi_{2873}(157,\cdot)\) \(\chi_{2873}(183,\cdot)\) \(\chi_{2873}(378,\cdot)\) \(\chi_{2873}(404,\cdot)\) \(\chi_{2873}(599,\cdot)\) \(\chi_{2873}(625,\cdot)\) \(\chi_{2873}(820,\cdot)\) \(\chi_{2873}(1041,\cdot)\) \(\chi_{2873}(1067,\cdot)\) \(\chi_{2873}(1262,\cdot)\) \(\chi_{2873}(1288,\cdot)\) \(\chi_{2873}(1483,\cdot)\) \(\chi_{2873}(1509,\cdot)\) \(\chi_{2873}(1704,\cdot)\) \(\chi_{2873}(1730,\cdot)\) \(\chi_{2873}(1925,\cdot)\) \(\chi_{2873}(1951,\cdot)\) \(\chi_{2873}(2146,\cdot)\) \(\chi_{2873}(2172,\cdot)\) \(\chi_{2873}(2393,\cdot)\) \(\chi_{2873}(2588,\cdot)\) \(\chi_{2873}(2614,\cdot)\) \(\chi_{2873}(2809,\cdot)\) \(\chi_{2873}(2835,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{4}{13}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) |