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 \(\chi_{131}(37,\cdot)\) | 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
\(133\) → \(e\left(\frac{41}{130}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 262 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{64}{65}\right)\) |