Basic properties
| Modulus: | \(262\) | |
| Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{131}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 262.h
\(\chi_{262}(17,\cdot)\) \(\chi_{262}(23,\cdot)\) \(\chi_{262}(29,\cdot)\) \(\chi_{262}(31,\cdot)\) \(\chi_{262}(37,\cdot)\) \(\chi_{262}(57,\cdot)\) \(\chi_{262}(67,\cdot)\) \(\chi_{262}(83,\cdot)\) \(\chi_{262}(85,\cdot)\) \(\chi_{262}(87,\cdot)\) \(\chi_{262}(93,\cdot)\) \(\chi_{262}(95,\cdot)\) \(\chi_{262}(97,\cdot)\) \(\chi_{262}(103,\cdot)\) \(\chi_{262}(111,\cdot)\) \(\chi_{262}(115,\cdot)\) \(\chi_{262}(119,\cdot)\) \(\chi_{262}(127,\cdot)\) \(\chi_{262}(133,\cdot)\) \(\chi_{262}(137,\cdot)\) \(\chi_{262}(139,\cdot)\) \(\chi_{262}(141,\cdot)\) \(\chi_{262}(145,\cdot)\) \(\chi_{262}(153,\cdot)\) \(\chi_{262}(157,\cdot)\) \(\chi_{262}(161,\cdot)\) \(\chi_{262}(171,\cdot)\) \(\chi_{262}(181,\cdot)\) \(\chi_{262}(185,\cdot)\) \(\chi_{262}(187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\(133\) → \(e\left(\frac{107}{130}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 262 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{18}{65}\right)\) |