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.bg
\(\chi_{1441}(36,\cdot)\) \(\chi_{1441}(102,\cdot)\) \(\chi_{1441}(147,\cdot)\) \(\chi_{1441}(159,\cdot)\) \(\chi_{1441}(179,\cdot)\) \(\chi_{1441}(240,\cdot)\) \(\chi_{1441}(267,\cdot)\) \(\chi_{1441}(289,\cdot)\) \(\chi_{1441}(300,\cdot)\) \(\chi_{1441}(317,\cdot)\) \(\chi_{1441}(339,\cdot)\) \(\chi_{1441}(367,\cdot)\) \(\chi_{1441}(383,\cdot)\) \(\chi_{1441}(487,\cdot)\) \(\chi_{1441}(531,\cdot)\) \(\chi_{1441}(544,\cdot)\) \(\chi_{1441}(559,\cdot)\) \(\chi_{1441}(632,\cdot)\) \(\chi_{1441}(658,\cdot)\) \(\chi_{1441}(664,\cdot)\) \(\chi_{1441}(676,\cdot)\) \(\chi_{1441}(680,\cdot)\) \(\chi_{1441}(696,\cdot)\) \(\chi_{1441}(730,\cdot)\) \(\chi_{1441}(784,\cdot)\) \(\chi_{1441}(790,\cdot)\) \(\chi_{1441}(819,\cdot)\) \(\chi_{1441}(829,\cdot)\) \(\chi_{1441}(830,\cdot)\) \(\chi_{1441}(845,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{46}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(680, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) |