Basic properties
Modulus: | \(1859\) | |
Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | 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.bj
\(\chi_{1859}(25,\cdot)\) \(\chi_{1859}(38,\cdot)\) \(\chi_{1859}(64,\cdot)\) \(\chi_{1859}(103,\cdot)\) \(\chi_{1859}(181,\cdot)\) \(\chi_{1859}(207,\cdot)\) \(\chi_{1859}(246,\cdot)\) \(\chi_{1859}(311,\cdot)\) \(\chi_{1859}(324,\cdot)\) \(\chi_{1859}(350,\cdot)\) \(\chi_{1859}(389,\cdot)\) \(\chi_{1859}(454,\cdot)\) \(\chi_{1859}(467,\cdot)\) \(\chi_{1859}(493,\cdot)\) \(\chi_{1859}(532,\cdot)\) \(\chi_{1859}(597,\cdot)\) \(\chi_{1859}(610,\cdot)\) \(\chi_{1859}(636,\cdot)\) \(\chi_{1859}(740,\cdot)\) \(\chi_{1859}(753,\cdot)\) \(\chi_{1859}(779,\cdot)\) \(\chi_{1859}(818,\cdot)\) \(\chi_{1859}(883,\cdot)\) \(\chi_{1859}(896,\cdot)\) \(\chi_{1859}(922,\cdot)\) \(\chi_{1859}(961,\cdot)\) \(\chi_{1859}(1026,\cdot)\) \(\chi_{1859}(1039,\cdot)\) \(\chi_{1859}(1065,\cdot)\) \(\chi_{1859}(1104,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) |