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.bp
\(\chi_{2873}(38,\cdot)\) \(\chi_{2873}(64,\cdot)\) \(\chi_{2873}(259,\cdot)\) \(\chi_{2873}(285,\cdot)\) \(\chi_{2873}(480,\cdot)\) \(\chi_{2873}(701,\cdot)\) \(\chi_{2873}(727,\cdot)\) \(\chi_{2873}(922,\cdot)\) \(\chi_{2873}(948,\cdot)\) \(\chi_{2873}(1143,\cdot)\) \(\chi_{2873}(1169,\cdot)\) \(\chi_{2873}(1364,\cdot)\) \(\chi_{2873}(1390,\cdot)\) \(\chi_{2873}(1585,\cdot)\) \(\chi_{2873}(1611,\cdot)\) \(\chi_{2873}(1806,\cdot)\) \(\chi_{2873}(1832,\cdot)\) \(\chi_{2873}(2053,\cdot)\) \(\chi_{2873}(2248,\cdot)\) \(\chi_{2873}(2274,\cdot)\) \(\chi_{2873}(2469,\cdot)\) \(\chi_{2873}(2495,\cdot)\) \(\chi_{2873}(2690,\cdot)\) \(\chi_{2873}(2716,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{11}{26}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) |