Basic properties
Modulus: | \(859\) | |
Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(858\) | 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.p
\(\chi_{859}(2,\cdot)\) \(\chi_{859}(3,\cdot)\) \(\chi_{859}(14,\cdot)\) \(\chi_{859}(18,\cdot)\) \(\chi_{859}(29,\cdot)\) \(\chi_{859}(32,\cdot)\) \(\chi_{859}(37,\cdot)\) \(\chi_{859}(39,\cdot)\) \(\chi_{859}(40,\cdot)\) \(\chi_{859}(44,\cdot)\) \(\chi_{859}(50,\cdot)\) \(\chi_{859}(51,\cdot)\) \(\chi_{859}(55,\cdot)\) \(\chi_{859}(62,\cdot)\) \(\chi_{859}(67,\cdot)\) \(\chi_{859}(70,\cdot)\) \(\chi_{859}(72,\cdot)\) \(\chi_{859}(73,\cdot)\) \(\chi_{859}(76,\cdot)\) \(\chi_{859}(77,\cdot)\) \(\chi_{859}(82,\cdot)\) \(\chi_{859}(83,\cdot)\) \(\chi_{859}(84,\cdot)\) \(\chi_{859}(89,\cdot)\) \(\chi_{859}(90,\cdot)\) \(\chi_{859}(94,\cdot)\) \(\chi_{859}(95,\cdot)\) \(\chi_{859}(97,\cdot)\) \(\chi_{859}(99,\cdot)\) \(\chi_{859}(101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{429})$ |
Fixed field: | Number field defined by a degree 858 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{199}{858}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 859 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{858}\right)\) | \(e\left(\frac{515}{858}\right)\) | \(e\left(\frac{199}{429}\right)\) | \(e\left(\frac{412}{429}\right)\) | \(e\left(\frac{119}{143}\right)\) | \(e\left(\frac{20}{429}\right)\) | \(e\left(\frac{199}{286}\right)\) | \(e\left(\frac{86}{429}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{217}{286}\right)\) |