Basic properties
Modulus: | \(1859\) | |
Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | 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.bu
\(\chi_{1859}(15,\cdot)\) \(\chi_{1859}(20,\cdot)\) \(\chi_{1859}(37,\cdot)\) \(\chi_{1859}(58,\cdot)\) \(\chi_{1859}(59,\cdot)\) \(\chi_{1859}(71,\cdot)\) \(\chi_{1859}(93,\cdot)\) \(\chi_{1859}(97,\cdot)\) \(\chi_{1859}(102,\cdot)\) \(\chi_{1859}(115,\cdot)\) \(\chi_{1859}(119,\cdot)\) \(\chi_{1859}(124,\cdot)\) \(\chi_{1859}(136,\cdot)\) \(\chi_{1859}(137,\cdot)\) \(\chi_{1859}(141,\cdot)\) \(\chi_{1859}(158,\cdot)\) \(\chi_{1859}(163,\cdot)\) \(\chi_{1859}(180,\cdot)\) \(\chi_{1859}(201,\cdot)\) \(\chi_{1859}(202,\cdot)\) \(\chi_{1859}(214,\cdot)\) \(\chi_{1859}(223,\cdot)\) \(\chi_{1859}(236,\cdot)\) \(\chi_{1859}(240,\cdot)\) \(\chi_{1859}(245,\cdot)\) \(\chi_{1859}(262,\cdot)\) \(\chi_{1859}(267,\cdot)\) \(\chi_{1859}(279,\cdot)\) \(\chi_{1859}(280,\cdot)\) \(\chi_{1859}(284,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{11}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{523}{780}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{133}{390}\right)\) | \(e\left(\frac{9}{260}\right)\) | \(e\left(\frac{167}{780}\right)\) | \(e\left(\frac{581}{780}\right)\) | \(e\left(\frac{3}{260}\right)\) | \(e\left(\frac{17}{195}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) |