Basic properties
| Modulus: | \(262\) | |
| 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 \(\chi_{131}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 262.g
\(\chi_{262}(3,\cdot)\) \(\chi_{262}(5,\cdot)\) \(\chi_{262}(7,\cdot)\) \(\chi_{262}(9,\cdot)\) \(\chi_{262}(11,\cdot)\) \(\chi_{262}(13,\cdot)\) \(\chi_{262}(15,\cdot)\) \(\chi_{262}(21,\cdot)\) \(\chi_{262}(25,\cdot)\) \(\chi_{262}(27,\cdot)\) \(\chi_{262}(33,\cdot)\) \(\chi_{262}(35,\cdot)\) \(\chi_{262}(41,\cdot)\) \(\chi_{262}(43,\cdot)\) \(\chi_{262}(49,\cdot)\) \(\chi_{262}(55,\cdot)\) \(\chi_{262}(59,\cdot)\) \(\chi_{262}(65,\cdot)\) \(\chi_{262}(75,\cdot)\) \(\chi_{262}(77,\cdot)\) \(\chi_{262}(81,\cdot)\) \(\chi_{262}(91,\cdot)\) \(\chi_{262}(101,\cdot)\) \(\chi_{262}(105,\cdot)\) \(\chi_{262}(109,\cdot)\) \(\chi_{262}(117,\cdot)\) \(\chi_{262}(121,\cdot)\) \(\chi_{262}(123,\cdot)\) \(\chi_{262}(125,\cdot)\) \(\chi_{262}(129,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\(133\) → \(e\left(\frac{36}{65}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 262 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) |