Basic properties
Modulus: | \(859\) | |
Conductor: | \(859\) | 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 859.l
\(\chi_{859}(12,\cdot)\) \(\chi_{859}(23,\cdot)\) \(\chi_{859}(26,\cdot)\) \(\chi_{859}(136,\cdot)\) \(\chi_{859}(183,\cdot)\) \(\chi_{859}(193,\cdot)\) \(\chi_{859}(203,\cdot)\) \(\chi_{859}(275,\cdot)\) \(\chi_{859}(330,\cdot)\) \(\chi_{859}(341,\cdot)\) \(\chi_{859}(358,\cdot)\) \(\chi_{859}(402,\cdot)\) \(\chi_{859}(543,\cdot)\) \(\chi_{859}(547,\cdot)\) \(\chi_{859}(581,\cdot)\) \(\chi_{859}(582,\cdot)\) \(\chi_{859}(583,\cdot)\) \(\chi_{859}(629,\cdot)\) \(\chi_{859}(647,\cdot)\) \(\chi_{859}(686,\cdot)\) \(\chi_{859}(715,\cdot)\) \(\chi_{859}(739,\cdot)\) \(\chi_{859}(747,\cdot)\) \(\chi_{859}(826,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\(2\) → \(e\left(\frac{11}{78}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 859 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{15}{26}\right)\) |