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.bx
\(\chi_{2873}(16,\cdot)\) \(\chi_{2873}(152,\cdot)\) \(\chi_{2873}(237,\cdot)\) \(\chi_{2873}(373,\cdot)\) \(\chi_{2873}(458,\cdot)\) \(\chi_{2873}(594,\cdot)\) \(\chi_{2873}(679,\cdot)\) \(\chi_{2873}(815,\cdot)\) \(\chi_{2873}(900,\cdot)\) \(\chi_{2873}(1121,\cdot)\) \(\chi_{2873}(1257,\cdot)\) \(\chi_{2873}(1342,\cdot)\) \(\chi_{2873}(1478,\cdot)\) \(\chi_{2873}(1563,\cdot)\) \(\chi_{2873}(1699,\cdot)\) \(\chi_{2873}(1784,\cdot)\) \(\chi_{2873}(1920,\cdot)\) \(\chi_{2873}(2141,\cdot)\) \(\chi_{2873}(2226,\cdot)\) \(\chi_{2873}(2362,\cdot)\) \(\chi_{2873}(2447,\cdot)\) \(\chi_{2873}(2583,\cdot)\) \(\chi_{2873}(2668,\cdot)\) \(\chi_{2873}(2804,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{1}{39}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) |