Basic properties
| Modulus: | \(859\) | |
| Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 859.j
\(\chi_{859}(33,\cdot)\) \(\chi_{859}(112,\cdot)\) \(\chi_{859}(120,\cdot)\) \(\chi_{859}(144,\cdot)\) \(\chi_{859}(173,\cdot)\) \(\chi_{859}(212,\cdot)\) \(\chi_{859}(230,\cdot)\) \(\chi_{859}(276,\cdot)\) \(\chi_{859}(277,\cdot)\) \(\chi_{859}(278,\cdot)\) \(\chi_{859}(312,\cdot)\) \(\chi_{859}(316,\cdot)\) \(\chi_{859}(457,\cdot)\) \(\chi_{859}(501,\cdot)\) \(\chi_{859}(518,\cdot)\) \(\chi_{859}(529,\cdot)\) \(\chi_{859}(584,\cdot)\) \(\chi_{859}(656,\cdot)\) \(\chi_{859}(666,\cdot)\) \(\chi_{859}(676,\cdot)\) \(\chi_{859}(723,\cdot)\) \(\chi_{859}(833,\cdot)\) \(\chi_{859}(836,\cdot)\) \(\chi_{859}(847,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\(2\) → \(e\left(\frac{22}{39}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 859 }(120, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) |