Basic properties
Modulus: | \(1859\) | |
Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(390\) | 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 1859.bs
\(\chi_{1859}(4,\cdot)\) \(\chi_{1859}(36,\cdot)\) \(\chi_{1859}(49,\cdot)\) \(\chi_{1859}(69,\cdot)\) \(\chi_{1859}(75,\cdot)\) \(\chi_{1859}(82,\cdot)\) \(\chi_{1859}(108,\cdot)\) \(\chi_{1859}(114,\cdot)\) \(\chi_{1859}(179,\cdot)\) \(\chi_{1859}(212,\cdot)\) \(\chi_{1859}(218,\cdot)\) \(\chi_{1859}(225,\cdot)\) \(\chi_{1859}(251,\cdot)\) \(\chi_{1859}(257,\cdot)\) \(\chi_{1859}(290,\cdot)\) \(\chi_{1859}(322,\cdot)\) \(\chi_{1859}(335,\cdot)\) \(\chi_{1859}(355,\cdot)\) \(\chi_{1859}(368,\cdot)\) \(\chi_{1859}(394,\cdot)\) \(\chi_{1859}(400,\cdot)\) \(\chi_{1859}(433,\cdot)\) \(\chi_{1859}(465,\cdot)\) \(\chi_{1859}(478,\cdot)\) \(\chi_{1859}(498,\cdot)\) \(\chi_{1859}(504,\cdot)\) \(\chi_{1859}(511,\cdot)\) \(\chi_{1859}(537,\cdot)\) \(\chi_{1859}(543,\cdot)\) \(\chi_{1859}(576,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{7}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(498, a) \) | \(1\) | \(1\) | \(e\left(\frac{347}{390}\right)\) | \(e\left(\frac{103}{195}\right)\) | \(e\left(\frac{152}{195}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{163}{390}\right)\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) |