Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.bv
\(\chi_{2873}(101,\cdot)\) \(\chi_{2873}(186,\cdot)\) \(\chi_{2873}(322,\cdot)\) \(\chi_{2873}(407,\cdot)\) \(\chi_{2873}(543,\cdot)\) \(\chi_{2873}(628,\cdot)\) \(\chi_{2873}(764,\cdot)\) \(\chi_{2873}(849,\cdot)\) \(\chi_{2873}(985,\cdot)\) \(\chi_{2873}(1070,\cdot)\) \(\chi_{2873}(1291,\cdot)\) \(\chi_{2873}(1427,\cdot)\) \(\chi_{2873}(1512,\cdot)\) \(\chi_{2873}(1648,\cdot)\) \(\chi_{2873}(1733,\cdot)\) \(\chi_{2873}(1869,\cdot)\) \(\chi_{2873}(1954,\cdot)\) \(\chi_{2873}(2090,\cdot)\) \(\chi_{2873}(2311,\cdot)\) \(\chi_{2873}(2396,\cdot)\) \(\chi_{2873}(2532,\cdot)\) \(\chi_{2873}(2617,\cdot)\) \(\chi_{2873}(2753,\cdot)\) \(\chi_{2873}(2838,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{35}{78}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) |