Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | 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.bf
\(\chi_{1859}(14,\cdot)\) \(\chi_{1859}(27,\cdot)\) \(\chi_{1859}(53,\cdot)\) \(\chi_{1859}(92,\cdot)\) \(\chi_{1859}(157,\cdot)\) \(\chi_{1859}(196,\cdot)\) \(\chi_{1859}(235,\cdot)\) \(\chi_{1859}(300,\cdot)\) \(\chi_{1859}(313,\cdot)\) \(\chi_{1859}(378,\cdot)\) \(\chi_{1859}(443,\cdot)\) \(\chi_{1859}(456,\cdot)\) \(\chi_{1859}(482,\cdot)\) \(\chi_{1859}(521,\cdot)\) \(\chi_{1859}(586,\cdot)\) \(\chi_{1859}(599,\cdot)\) \(\chi_{1859}(625,\cdot)\) \(\chi_{1859}(664,\cdot)\) \(\chi_{1859}(729,\cdot)\) \(\chi_{1859}(742,\cdot)\) \(\chi_{1859}(768,\cdot)\) \(\chi_{1859}(807,\cdot)\) \(\chi_{1859}(872,\cdot)\) \(\chi_{1859}(885,\cdot)\) \(\chi_{1859}(911,\cdot)\) \(\chi_{1859}(950,\cdot)\) \(\chi_{1859}(1028,\cdot)\) \(\chi_{1859}(1054,\cdot)\) \(\chi_{1859}(1093,\cdot)\) \(\chi_{1859}(1158,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((508,1354)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) |