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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.bp
\(\chi_{1859}(8,\cdot)\) \(\chi_{1859}(18,\cdot)\) \(\chi_{1859}(57,\cdot)\) \(\chi_{1859}(73,\cdot)\) \(\chi_{1859}(83,\cdot)\) \(\chi_{1859}(96,\cdot)\) \(\chi_{1859}(112,\cdot)\) \(\chi_{1859}(138,\cdot)\) \(\chi_{1859}(151,\cdot)\) \(\chi_{1859}(161,\cdot)\) \(\chi_{1859}(200,\cdot)\) \(\chi_{1859}(216,\cdot)\) \(\chi_{1859}(226,\cdot)\) \(\chi_{1859}(255,\cdot)\) \(\chi_{1859}(281,\cdot)\) \(\chi_{1859}(294,\cdot)\) \(\chi_{1859}(304,\cdot)\) \(\chi_{1859}(343,\cdot)\) \(\chi_{1859}(359,\cdot)\) \(\chi_{1859}(369,\cdot)\) \(\chi_{1859}(382,\cdot)\) \(\chi_{1859}(398,\cdot)\) \(\chi_{1859}(424,\cdot)\) \(\chi_{1859}(447,\cdot)\) \(\chi_{1859}(486,\cdot)\) \(\chi_{1859}(502,\cdot)\) \(\chi_{1859}(512,\cdot)\) \(\chi_{1859}(525,\cdot)\) \(\chi_{1859}(541,\cdot)\) \(\chi_{1859}(567,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{260}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{97}{260}\right)\) | \(e\left(\frac{27}{260}\right)\) | \(e\left(\frac{41}{260}\right)\) | \(e\left(\frac{249}{260}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) |