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.bk
\(\chi_{1441}(60,\cdot)\) \(\chi_{1441}(80,\cdot)\) \(\chi_{1441}(113,\cdot)\) \(\chi_{1441}(170,\cdot)\) \(\chi_{1441}(191,\cdot)\) \(\chi_{1441}(301,\cdot)\) \(\chi_{1441}(322,\cdot)\) \(\chi_{1441}(324,\cdot)\) \(\chi_{1441}(346,\cdot)\) \(\chi_{1441}(361,\cdot)\) \(\chi_{1441}(432,\cdot)\) \(\chi_{1441}(438,\cdot)\) \(\chi_{1441}(445,\cdot)\) \(\chi_{1441}(455,\cdot)\) \(\chi_{1441}(456,\cdot)\) \(\chi_{1441}(477,\cdot)\) \(\chi_{1441}(500,\cdot)\) \(\chi_{1441}(576,\cdot)\) \(\chi_{1441}(586,\cdot)\) \(\chi_{1441}(587,\cdot)\) \(\chi_{1441}(608,\cdot)\) \(\chi_{1441}(631,\cdot)\) \(\chi_{1441}(636,\cdot)\) \(\chi_{1441}(707,\cdot)\) \(\chi_{1441}(718,\cdot)\) \(\chi_{1441}(735,\cdot)\) \(\chi_{1441}(762,\cdot)\) \(\chi_{1441}(768,\cdot)\) \(\chi_{1441}(885,\cdot)\) \(\chi_{1441}(962,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{7}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1441 }(1016, a) \) | \(1\) | \(1\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) |