Basic properties
Modulus: | \(159\) | |
Conductor: | \(159\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | 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 159.k
\(\chi_{159}(2,\cdot)\) \(\chi_{159}(5,\cdot)\) \(\chi_{159}(8,\cdot)\) \(\chi_{159}(14,\cdot)\) \(\chi_{159}(20,\cdot)\) \(\chi_{159}(26,\cdot)\) \(\chi_{159}(32,\cdot)\) \(\chi_{159}(35,\cdot)\) \(\chi_{159}(41,\cdot)\) \(\chi_{159}(50,\cdot)\) \(\chi_{159}(56,\cdot)\) \(\chi_{159}(65,\cdot)\) \(\chi_{159}(71,\cdot)\) \(\chi_{159}(74,\cdot)\) \(\chi_{159}(80,\cdot)\) \(\chi_{159}(86,\cdot)\) \(\chi_{159}(92,\cdot)\) \(\chi_{159}(98,\cdot)\) \(\chi_{159}(101,\cdot)\) \(\chi_{159}(104,\cdot)\) \(\chi_{159}(125,\cdot)\) \(\chi_{159}(128,\cdot)\) \(\chi_{159}(137,\cdot)\) \(\chi_{159}(140,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,55)\) → \((-1,e\left(\frac{1}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 159 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) |