Basic properties
Modulus: | \(371\) | |
Conductor: | \(371\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 371.v
\(\chi_{371}(10,\cdot)\) \(\chi_{371}(24,\cdot)\) \(\chi_{371}(47,\cdot)\) \(\chi_{371}(66,\cdot)\) \(\chi_{371}(68,\cdot)\) \(\chi_{371}(89,\cdot)\) \(\chi_{371}(122,\cdot)\) \(\chi_{371}(150,\cdot)\) \(\chi_{371}(152,\cdot)\) \(\chi_{371}(187,\cdot)\) \(\chi_{371}(201,\cdot)\) \(\chi_{371}(206,\cdot)\) \(\chi_{371}(208,\cdot)\) \(\chi_{371}(222,\cdot)\) \(\chi_{371}(227,\cdot)\) \(\chi_{371}(236,\cdot)\) \(\chi_{371}(248,\cdot)\) \(\chi_{371}(278,\cdot)\) \(\chi_{371}(311,\cdot)\) \(\chi_{371}(334,\cdot)\) \(\chi_{371}(346,\cdot)\) \(\chi_{371}(360,\cdot)\) \(\chi_{371}(362,\cdot)\) \(\chi_{371}(367,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((213,267)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{11}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 371 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) |