Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(56,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.bh
\(\chi_{1859}(56,\cdot)\) \(\chi_{1859}(166,\cdot)\) \(\chi_{1859}(199,\cdot)\) \(\chi_{1859}(309,\cdot)\) \(\chi_{1859}(342,\cdot)\) \(\chi_{1859}(452,\cdot)\) \(\chi_{1859}(595,\cdot)\) \(\chi_{1859}(628,\cdot)\) \(\chi_{1859}(738,\cdot)\) \(\chi_{1859}(771,\cdot)\) \(\chi_{1859}(881,\cdot)\) \(\chi_{1859}(914,\cdot)\) \(\chi_{1859}(1024,\cdot)\) \(\chi_{1859}(1057,\cdot)\) \(\chi_{1859}(1167,\cdot)\) \(\chi_{1859}(1200,\cdot)\) \(\chi_{1859}(1310,\cdot)\) \(\chi_{1859}(1343,\cdot)\) \(\chi_{1859}(1453,\cdot)\) \(\chi_{1859}(1486,\cdot)\) \(\chi_{1859}(1596,\cdot)\) \(\chi_{1859}(1629,\cdot)\) \(\chi_{1859}(1739,\cdot)\) \(\chi_{1859}(1772,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((508,1354)\) → \((1,e\left(\frac{55}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(56, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) |