Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2873.bk
\(\chi_{2873}(35,\cdot)\) \(\chi_{2873}(120,\cdot)\) \(\chi_{2873}(256,\cdot)\) \(\chi_{2873}(341,\cdot)\) \(\chi_{2873}(477,\cdot)\) \(\chi_{2873}(562,\cdot)\) \(\chi_{2873}(783,\cdot)\) \(\chi_{2873}(919,\cdot)\) \(\chi_{2873}(1004,\cdot)\) \(\chi_{2873}(1140,\cdot)\) \(\chi_{2873}(1225,\cdot)\) \(\chi_{2873}(1361,\cdot)\) \(\chi_{2873}(1446,\cdot)\) \(\chi_{2873}(1582,\cdot)\) \(\chi_{2873}(1803,\cdot)\) \(\chi_{2873}(1888,\cdot)\) \(\chi_{2873}(2024,\cdot)\) \(\chi_{2873}(2109,\cdot)\) \(\chi_{2873}(2245,\cdot)\) \(\chi_{2873}(2330,\cdot)\) \(\chi_{2873}(2466,\cdot)\) \(\chi_{2873}(2551,\cdot)\) \(\chi_{2873}(2687,\cdot)\) \(\chi_{2873}(2772,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{29}{39}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) |