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.bg
\(\chi_{1859}(87,\cdot)\) \(\chi_{1859}(120,\cdot)\) \(\chi_{1859}(230,\cdot)\) \(\chi_{1859}(263,\cdot)\) \(\chi_{1859}(373,\cdot)\) \(\chi_{1859}(406,\cdot)\) \(\chi_{1859}(516,\cdot)\) \(\chi_{1859}(549,\cdot)\) \(\chi_{1859}(659,\cdot)\) \(\chi_{1859}(692,\cdot)\) \(\chi_{1859}(802,\cdot)\) \(\chi_{1859}(835,\cdot)\) \(\chi_{1859}(945,\cdot)\) \(\chi_{1859}(978,\cdot)\) \(\chi_{1859}(1088,\cdot)\) \(\chi_{1859}(1121,\cdot)\) \(\chi_{1859}(1231,\cdot)\) \(\chi_{1859}(1264,\cdot)\) \(\chi_{1859}(1407,\cdot)\) \(\chi_{1859}(1517,\cdot)\) \(\chi_{1859}(1550,\cdot)\) \(\chi_{1859}(1660,\cdot)\) \(\chi_{1859}(1693,\cdot)\) \(\chi_{1859}(1803,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((508,1354)\) → \((-1,e\left(\frac{2}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(87, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) |