Basic properties
Modulus: | \(1859\) | |
Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(260\) | 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 1859.bq
\(\chi_{1859}(5,\cdot)\) \(\chi_{1859}(31,\cdot)\) \(\chi_{1859}(47,\cdot)\) \(\chi_{1859}(60,\cdot)\) \(\chi_{1859}(86,\cdot)\) \(\chi_{1859}(125,\cdot)\) \(\chi_{1859}(135,\cdot)\) \(\chi_{1859}(148,\cdot)\) \(\chi_{1859}(174,\cdot)\) \(\chi_{1859}(190,\cdot)\) \(\chi_{1859}(203,\cdot)\) \(\chi_{1859}(213,\cdot)\) \(\chi_{1859}(229,\cdot)\) \(\chi_{1859}(278,\cdot)\) \(\chi_{1859}(291,\cdot)\) \(\chi_{1859}(317,\cdot)\) \(\chi_{1859}(333,\cdot)\) \(\chi_{1859}(346,\cdot)\) \(\chi_{1859}(356,\cdot)\) \(\chi_{1859}(372,\cdot)\) \(\chi_{1859}(411,\cdot)\) \(\chi_{1859}(421,\cdot)\) \(\chi_{1859}(434,\cdot)\) \(\chi_{1859}(460,\cdot)\) \(\chi_{1859}(476,\cdot)\) \(\chi_{1859}(489,\cdot)\) \(\chi_{1859}(499,\cdot)\) \(\chi_{1859}(515,\cdot)\) \(\chi_{1859}(554,\cdot)\) \(\chi_{1859}(564,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{7}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{260}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{159}{260}\right)\) | \(e\left(\frac{59}{260}\right)\) | \(e\left(\frac{157}{260}\right)\) | \(e\left(\frac{53}{260}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) |