Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 1859.bn
\(\chi_{1859}(32,\cdot)\) \(\chi_{1859}(54,\cdot)\) \(\chi_{1859}(76,\cdot)\) \(\chi_{1859}(98,\cdot)\) \(\chi_{1859}(175,\cdot)\) \(\chi_{1859}(197,\cdot)\) \(\chi_{1859}(219,\cdot)\) \(\chi_{1859}(241,\cdot)\) \(\chi_{1859}(318,\cdot)\) \(\chi_{1859}(340,\cdot)\) \(\chi_{1859}(362,\cdot)\) \(\chi_{1859}(384,\cdot)\) \(\chi_{1859}(461,\cdot)\) \(\chi_{1859}(483,\cdot)\) \(\chi_{1859}(505,\cdot)\) \(\chi_{1859}(527,\cdot)\) \(\chi_{1859}(604,\cdot)\) \(\chi_{1859}(626,\cdot)\) \(\chi_{1859}(648,\cdot)\) \(\chi_{1859}(670,\cdot)\) \(\chi_{1859}(747,\cdot)\) \(\chi_{1859}(769,\cdot)\) \(\chi_{1859}(791,\cdot)\) \(\chi_{1859}(813,\cdot)\) \(\chi_{1859}(890,\cdot)\) \(\chi_{1859}(912,\cdot)\) \(\chi_{1859}(956,\cdot)\) \(\chi_{1859}(1055,\cdot)\) \(\chi_{1859}(1077,\cdot)\) \(\chi_{1859}(1099,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((-1,e\left(\frac{31}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(648, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) |