Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(92,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1339.bj
\(\chi_{1339}(92,\cdot)\) \(\chi_{1339}(105,\cdot)\) \(\chi_{1339}(118,\cdot)\) \(\chi_{1339}(131,\cdot)\) \(\chi_{1339}(144,\cdot)\) \(\chi_{1339}(222,\cdot)\) \(\chi_{1339}(235,\cdot)\) \(\chi_{1339}(261,\cdot)\) \(\chi_{1339}(274,\cdot)\) \(\chi_{1339}(313,\cdot)\) \(\chi_{1339}(326,\cdot)\) \(\chi_{1339}(391,\cdot)\) \(\chi_{1339}(430,\cdot)\) \(\chi_{1339}(495,\cdot)\) \(\chi_{1339}(534,\cdot)\) \(\chi_{1339}(547,\cdot)\) \(\chi_{1339}(573,\cdot)\) \(\chi_{1339}(612,\cdot)\) \(\chi_{1339}(625,\cdot)\) \(\chi_{1339}(651,\cdot)\) \(\chi_{1339}(677,\cdot)\) \(\chi_{1339}(716,\cdot)\) \(\chi_{1339}(781,\cdot)\) \(\chi_{1339}(963,\cdot)\) \(\chi_{1339}(976,\cdot)\) \(\chi_{1339}(1080,\cdot)\) \(\chi_{1339}(1093,\cdot)\) \(\chi_{1339}(1158,\cdot)\) \(\chi_{1339}(1171,\cdot)\) \(\chi_{1339}(1262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((1,e\left(\frac{5}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) |