Basic properties
Modulus: | \(859\) | |
Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(286\) | 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 859.n
\(\chi_{859}(8,\cdot)\) \(\chi_{859}(11,\cdot)\) \(\chi_{859}(21,\cdot)\) \(\chi_{859}(27,\cdot)\) \(\chi_{859}(34,\cdot)\) \(\chi_{859}(48,\cdot)\) \(\chi_{859}(60,\cdot)\) \(\chi_{859}(75,\cdot)\) \(\chi_{859}(92,\cdot)\) \(\chi_{859}(93,\cdot)\) \(\chi_{859}(98,\cdot)\) \(\chi_{859}(104,\cdot)\) \(\chi_{859}(106,\cdot)\) \(\chi_{859}(109,\cdot)\) \(\chi_{859}(113,\cdot)\) \(\chi_{859}(115,\cdot)\) \(\chi_{859}(116,\cdot)\) \(\chi_{859}(123,\cdot)\) \(\chi_{859}(126,\cdot)\) \(\chi_{859}(130,\cdot)\) \(\chi_{859}(133,\cdot)\) \(\chi_{859}(143,\cdot)\) \(\chi_{859}(145,\cdot)\) \(\chi_{859}(162,\cdot)\) \(\chi_{859}(167,\cdot)\) \(\chi_{859}(171,\cdot)\) \(\chi_{859}(199,\cdot)\) \(\chi_{859}(204,\cdot)\) \(\chi_{859}(224,\cdot)\) \(\chi_{859}(241,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{143})$ |
Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{119}{286}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 859 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{119}{286}\right)\) | \(e\left(\frac{147}{286}\right)\) | \(e\left(\frac{119}{143}\right)\) | \(e\left(\frac{89}{143}\right)\) | \(e\left(\frac{133}{143}\right)\) | \(e\left(\frac{114}{143}\right)\) | \(e\left(\frac{71}{286}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{7}{286}\right)\) |