Basic properties
Modulus: | \(239\) | |
Conductor: | \(239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(119\) | 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 239.g
\(\chi_{239}(2,\cdot)\) \(\chi_{239}(3,\cdot)\) \(\chi_{239}(4,\cdot)\) \(\chi_{239}(5,\cdot)\) \(\chi_{239}(8,\cdot)\) \(\chi_{239}(9,\cdot)\) \(\chi_{239}(11,\cdot)\) \(\chi_{239}(12,\cdot)\) \(\chi_{239}(15,\cdot)\) \(\chi_{239}(16,\cdot)\) \(\chi_{239}(17,\cdot)\) \(\chi_{239}(18,\cdot)\) \(\chi_{239}(20,\cdot)\) \(\chi_{239}(25,\cdot)\) \(\chi_{239}(27,\cdot)\) \(\chi_{239}(29,\cdot)\) \(\chi_{239}(30,\cdot)\) \(\chi_{239}(31,\cdot)\) \(\chi_{239}(32,\cdot)\) \(\chi_{239}(33,\cdot)\) \(\chi_{239}(34,\cdot)\) \(\chi_{239}(45,\cdot)\) \(\chi_{239}(48,\cdot)\) \(\chi_{239}(49,\cdot)\) \(\chi_{239}(50,\cdot)\) \(\chi_{239}(54,\cdot)\) \(\chi_{239}(55,\cdot)\) \(\chi_{239}(58,\cdot)\) \(\chi_{239}(60,\cdot)\) \(\chi_{239}(61,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{119})$ |
Fixed field: | Number field defined by a degree 119 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{69}{119}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 239 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{38}{119}\right)\) |