Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.bi
\(\chi_{1859}(10,\cdot)\) \(\chi_{1859}(43,\cdot)\) \(\chi_{1859}(153,\cdot)\) \(\chi_{1859}(186,\cdot)\) \(\chi_{1859}(296,\cdot)\) \(\chi_{1859}(329,\cdot)\) \(\chi_{1859}(439,\cdot)\) \(\chi_{1859}(472,\cdot)\) \(\chi_{1859}(582,\cdot)\) \(\chi_{1859}(615,\cdot)\) \(\chi_{1859}(725,\cdot)\) \(\chi_{1859}(758,\cdot)\) \(\chi_{1859}(901,\cdot)\) \(\chi_{1859}(1011,\cdot)\) \(\chi_{1859}(1044,\cdot)\) \(\chi_{1859}(1154,\cdot)\) \(\chi_{1859}(1187,\cdot)\) \(\chi_{1859}(1297,\cdot)\) \(\chi_{1859}(1440,\cdot)\) \(\chi_{1859}(1473,\cdot)\) \(\chi_{1859}(1583,\cdot)\) \(\chi_{1859}(1616,\cdot)\) \(\chi_{1859}(1726,\cdot)\) \(\chi_{1859}(1759,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((508,1354)\) → \((-1,e\left(\frac{5}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) |