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.bk
\(\chi_{1339}(9,\cdot)\) \(\chi_{1339}(61,\cdot)\) \(\chi_{1339}(81,\cdot)\) \(\chi_{1339}(100,\cdot)\) \(\chi_{1339}(126,\cdot)\) \(\chi_{1339}(133,\cdot)\) \(\chi_{1339}(282,\cdot)\) \(\chi_{1339}(373,\cdot)\) \(\chi_{1339}(425,\cdot)\) \(\chi_{1339}(484,\cdot)\) \(\chi_{1339}(523,\cdot)\) \(\chi_{1339}(529,\cdot)\) \(\chi_{1339}(549,\cdot)\) \(\chi_{1339}(581,\cdot)\) \(\chi_{1339}(594,\cdot)\) \(\chi_{1339}(627,\cdot)\) \(\chi_{1339}(679,\cdot)\) \(\chi_{1339}(711,\cdot)\) \(\chi_{1339}(718,\cdot)\) \(\chi_{1339}(744,\cdot)\) \(\chi_{1339}(802,\cdot)\) \(\chi_{1339}(854,\cdot)\) \(\chi_{1339}(900,\cdot)\) \(\chi_{1339}(991,\cdot)\) \(\chi_{1339}(1043,\cdot)\) \(\chi_{1339}(1147,\cdot)\) \(\chi_{1339}(1199,\cdot)\) \(\chi_{1339}(1205,\cdot)\) \(\chi_{1339}(1212,\cdot)\) \(\chi_{1339}(1244,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{13}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1339 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) |