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.bi
\(\chi_{1339}(107,\cdot)\) \(\chi_{1339}(120,\cdot)\) \(\chi_{1339}(152,\cdot)\) \(\chi_{1339}(185,\cdot)\) \(\chi_{1339}(334,\cdot)\) \(\chi_{1339}(341,\cdot)\) \(\chi_{1339}(367,\cdot)\) \(\chi_{1339}(419,\cdot)\) \(\chi_{1339}(438,\cdot)\) \(\chi_{1339}(445,\cdot)\) \(\chi_{1339}(510,\cdot)\) \(\chi_{1339}(620,\cdot)\) \(\chi_{1339}(646,\cdot)\) \(\chi_{1339}(659,\cdot)\) \(\chi_{1339}(737,\cdot)\) \(\chi_{1339}(750,\cdot)\) \(\chi_{1339}(757,\cdot)\) \(\chi_{1339}(776,\cdot)\) \(\chi_{1339}(789,\cdot)\) \(\chi_{1339}(874,\cdot)\) \(\chi_{1339}(887,\cdot)\) \(\chi_{1339}(945,\cdot)\) \(\chi_{1339}(965,\cdot)\) \(\chi_{1339}(1010,\cdot)\) \(\chi_{1339}(1049,\cdot)\) \(\chi_{1339}(1082,\cdot)\) \(\chi_{1339}(1121,\cdot)\) \(\chi_{1339}(1127,\cdot)\) \(\chi_{1339}(1192,\cdot)\) \(\chi_{1339}(1225,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{44}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{49}{51}\right)\) |