Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | 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 1339.bl
\(\chi_{1339}(16,\cdot)\) \(\chi_{1339}(29,\cdot)\) \(\chi_{1339}(55,\cdot)\) \(\chi_{1339}(68,\cdot)\) \(\chi_{1339}(139,\cdot)\) \(\chi_{1339}(224,\cdot)\) \(\chi_{1339}(256,\cdot)\) \(\chi_{1339}(269,\cdot)\) \(\chi_{1339}(289,\cdot)\) \(\chi_{1339}(328,\cdot)\) \(\chi_{1339}(347,\cdot)\) \(\chi_{1339}(406,\cdot)\) \(\chi_{1339}(464,\cdot)\) \(\chi_{1339}(471,\cdot)\) \(\chi_{1339}(503,\cdot)\) \(\chi_{1339}(575,\cdot)\) \(\chi_{1339}(607,\cdot)\) \(\chi_{1339}(633,\cdot)\) \(\chi_{1339}(770,\cdot)\) \(\chi_{1339}(828,\cdot)\) \(\chi_{1339}(841,\cdot)\) \(\chi_{1339}(906,\cdot)\) \(\chi_{1339}(952,\cdot)\) \(\chi_{1339}(1056,\cdot)\) \(\chi_{1339}(1062,\cdot)\) \(\chi_{1339}(1088,\cdot)\) \(\chi_{1339}(1140,\cdot)\) \(\chi_{1339}(1166,\cdot)\) \(\chi_{1339}(1231,\cdot)\) \(\chi_{1339}(1238,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{31}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{7}{17}\right)\) |