Basic properties
Modulus: | \(1859\) | |
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 \(\chi_{169}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.ba
\(\chi_{1859}(100,\cdot)\) \(\chi_{1859}(133,\cdot)\) \(\chi_{1859}(243,\cdot)\) \(\chi_{1859}(276,\cdot)\) \(\chi_{1859}(386,\cdot)\) \(\chi_{1859}(419,\cdot)\) \(\chi_{1859}(562,\cdot)\) \(\chi_{1859}(672,\cdot)\) \(\chi_{1859}(705,\cdot)\) \(\chi_{1859}(815,\cdot)\) \(\chi_{1859}(848,\cdot)\) \(\chi_{1859}(958,\cdot)\) \(\chi_{1859}(1101,\cdot)\) \(\chi_{1859}(1134,\cdot)\) \(\chi_{1859}(1244,\cdot)\) \(\chi_{1859}(1277,\cdot)\) \(\chi_{1859}(1387,\cdot)\) \(\chi_{1859}(1420,\cdot)\) \(\chi_{1859}(1530,\cdot)\) \(\chi_{1859}(1563,\cdot)\) \(\chi_{1859}(1673,\cdot)\) \(\chi_{1859}(1706,\cdot)\) \(\chi_{1859}(1816,\cdot)\) \(\chi_{1859}(1849,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((508,1354)\) → \((1,e\left(\frac{7}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(419, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) |