Basic properties
| Modulus: | \(1441\) | |
| Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | 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 1441.bi
\(\chi_{1441}(4,\cdot)\) \(\chi_{1441}(16,\cdot)\) \(\chi_{1441}(59,\cdot)\) \(\chi_{1441}(64,\cdot)\) \(\chi_{1441}(146,\cdot)\) \(\chi_{1441}(180,\cdot)\) \(\chi_{1441}(212,\cdot)\) \(\chi_{1441}(236,\cdot)\) \(\chi_{1441}(245,\cdot)\) \(\chi_{1441}(256,\cdot)\) \(\chi_{1441}(273,\cdot)\) \(\chi_{1441}(421,\cdot)\) \(\chi_{1441}(510,\cdot)\) \(\chi_{1441}(533,\cdot)\) \(\chi_{1441}(598,\cdot)\) \(\chi_{1441}(599,\cdot)\) \(\chi_{1441}(691,\cdot)\) \(\chi_{1441}(698,\cdot)\) \(\chi_{1441}(720,\cdot)\) \(\chi_{1441}(757,\cdot)\) \(\chi_{1441}(806,\cdot)\) \(\chi_{1441}(834,\cdot)\) \(\chi_{1441}(894,\cdot)\) \(\chi_{1441}(895,\cdot)\) \(\chi_{1441}(922,\cdot)\) \(\chi_{1441}(929,\cdot)\) \(\chi_{1441}(938,\cdot)\) \(\chi_{1441}(944,\cdot)\) \(\chi_{1441}(951,\cdot)\) \(\chi_{1441}(955,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{56}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1441 }(1038, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) |