Basic properties
Modulus: | \(131\) | |
Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 131.h
\(\chi_{131}(2,\cdot)\) \(\chi_{131}(6,\cdot)\) \(\chi_{131}(8,\cdot)\) \(\chi_{131}(10,\cdot)\) \(\chi_{131}(14,\cdot)\) \(\chi_{131}(17,\cdot)\) \(\chi_{131}(22,\cdot)\) \(\chi_{131}(23,\cdot)\) \(\chi_{131}(26,\cdot)\) \(\chi_{131}(29,\cdot)\) \(\chi_{131}(30,\cdot)\) \(\chi_{131}(31,\cdot)\) \(\chi_{131}(37,\cdot)\) \(\chi_{131}(40,\cdot)\) \(\chi_{131}(50,\cdot)\) \(\chi_{131}(54,\cdot)\) \(\chi_{131}(56,\cdot)\) \(\chi_{131}(57,\cdot)\) \(\chi_{131}(66,\cdot)\) \(\chi_{131}(67,\cdot)\) \(\chi_{131}(72,\cdot)\) \(\chi_{131}(76,\cdot)\) \(\chi_{131}(82,\cdot)\) \(\chi_{131}(83,\cdot)\) \(\chi_{131}(85,\cdot)\) \(\chi_{131}(87,\cdot)\) \(\chi_{131}(88,\cdot)\) \(\chi_{131}(90,\cdot)\) \(\chi_{131}(93,\cdot)\) \(\chi_{131}(95,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{51}{130}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 131 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{63}{65}\right)\) |