Basic properties
| Modulus: | \(1048\) | |
| Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{131}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1048.y
\(\chi_{1048}(9,\cdot)\) \(\chi_{1048}(25,\cdot)\) \(\chi_{1048}(33,\cdot)\) \(\chi_{1048}(41,\cdot)\) \(\chi_{1048}(49,\cdot)\) \(\chi_{1048}(65,\cdot)\) \(\chi_{1048}(81,\cdot)\) \(\chi_{1048}(105,\cdot)\) \(\chi_{1048}(121,\cdot)\) \(\chi_{1048}(129,\cdot)\) \(\chi_{1048}(169,\cdot)\) \(\chi_{1048}(177,\cdot)\) \(\chi_{1048}(225,\cdot)\) \(\chi_{1048}(233,\cdot)\) \(\chi_{1048}(265,\cdot)\) \(\chi_{1048}(273,\cdot)\) \(\chi_{1048}(289,\cdot)\) \(\chi_{1048}(297,\cdot)\) \(\chi_{1048}(305,\cdot)\) \(\chi_{1048}(321,\cdot)\) \(\chi_{1048}(337,\cdot)\) \(\chi_{1048}(353,\cdot)\) \(\chi_{1048}(385,\cdot)\) \(\chi_{1048}(409,\cdot)\) \(\chi_{1048}(441,\cdot)\) \(\chi_{1048}(457,\cdot)\) \(\chi_{1048}(529,\cdot)\) \(\chi_{1048}(537,\cdot)\) \(\chi_{1048}(545,\cdot)\) \(\chi_{1048}(601,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((263,525,657)\) → \((1,1,e\left(\frac{7}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1048 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{6}{65}\right)\) |