Basic properties
Modulus: | \(131\) | |
Conductor: | \(131\) | 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 131.g
\(\chi_{131}(3,\cdot)\) \(\chi_{131}(4,\cdot)\) \(\chi_{131}(5,\cdot)\) \(\chi_{131}(7,\cdot)\) \(\chi_{131}(9,\cdot)\) \(\chi_{131}(11,\cdot)\) \(\chi_{131}(12,\cdot)\) \(\chi_{131}(13,\cdot)\) \(\chi_{131}(15,\cdot)\) \(\chi_{131}(16,\cdot)\) \(\chi_{131}(20,\cdot)\) \(\chi_{131}(21,\cdot)\) \(\chi_{131}(25,\cdot)\) \(\chi_{131}(27,\cdot)\) \(\chi_{131}(28,\cdot)\) \(\chi_{131}(33,\cdot)\) \(\chi_{131}(34,\cdot)\) \(\chi_{131}(35,\cdot)\) \(\chi_{131}(36,\cdot)\) \(\chi_{131}(38,\cdot)\) \(\chi_{131}(41,\cdot)\) \(\chi_{131}(43,\cdot)\) \(\chi_{131}(44,\cdot)\) \(\chi_{131}(46,\cdot)\) \(\chi_{131}(48,\cdot)\) \(\chi_{131}(49,\cdot)\) \(\chi_{131}(55,\cdot)\) \(\chi_{131}(59,\cdot)\) \(\chi_{131}(64,\cdot)\) \(\chi_{131}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\(2\) → \(e\left(\frac{32}{65}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 131 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) |