Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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 1859.bb
\(\chi_{1859}(21,\cdot)\) \(\chi_{1859}(109,\cdot)\) \(\chi_{1859}(164,\cdot)\) \(\chi_{1859}(252,\cdot)\) \(\chi_{1859}(307,\cdot)\) \(\chi_{1859}(395,\cdot)\) \(\chi_{1859}(450,\cdot)\) \(\chi_{1859}(538,\cdot)\) \(\chi_{1859}(593,\cdot)\) \(\chi_{1859}(681,\cdot)\) \(\chi_{1859}(736,\cdot)\) \(\chi_{1859}(824,\cdot)\) \(\chi_{1859}(879,\cdot)\) \(\chi_{1859}(967,\cdot)\) \(\chi_{1859}(1022,\cdot)\) \(\chi_{1859}(1110,\cdot)\) \(\chi_{1859}(1165,\cdot)\) \(\chi_{1859}(1308,\cdot)\) \(\chi_{1859}(1396,\cdot)\) \(\chi_{1859}(1539,\cdot)\) \(\chi_{1859}(1594,\cdot)\) \(\chi_{1859}(1682,\cdot)\) \(\chi_{1859}(1737,\cdot)\) \(\chi_{1859}(1825,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((508,1354)\) → \((-1,e\left(\frac{25}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) |