Basic properties
| Modulus: | \(1339\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | 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.bn
\(\chi_{1339}(31,\cdot)\) \(\chi_{1339}(73,\cdot)\) \(\chi_{1339}(125,\cdot)\) \(\chi_{1339}(216,\cdot)\) \(\chi_{1339}(333,\cdot)\) \(\chi_{1339}(346,\cdot)\) \(\chi_{1339}(382,\cdot)\) \(\chi_{1339}(398,\cdot)\) \(\chi_{1339}(434,\cdot)\) \(\chi_{1339}(502,\cdot)\) \(\chi_{1339}(525,\cdot)\) \(\chi_{1339}(554,\cdot)\) \(\chi_{1339}(642,\cdot)\) \(\chi_{1339}(645,\cdot)\) \(\chi_{1339}(655,\cdot)\) \(\chi_{1339}(707,\cdot)\) \(\chi_{1339}(801,\cdot)\) \(\chi_{1339}(811,\cdot)\) \(\chi_{1339}(827,\cdot)\) \(\chi_{1339}(863,\cdot)\) \(\chi_{1339}(866,\cdot)\) \(\chi_{1339}(918,\cdot)\) \(\chi_{1339}(954,\cdot)\) \(\chi_{1339}(996,\cdot)\) \(\chi_{1339}(1022,\cdot)\) \(\chi_{1339}(1061,\cdot)\) \(\chi_{1339}(1110,\cdot)\) \(\chi_{1339}(1136,\cdot)\) \(\chi_{1339}(1175,\cdot)\) \(\chi_{1339}(1227,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((1237,417)\) → \((-i,e\left(\frac{19}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{23}{68}\right)\) |