Basic properties
Modulus: | \(1805\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(258,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1805.w
\(\chi_{1805}(11,\cdot)\) \(\chi_{1805}(26,\cdot)\) \(\chi_{1805}(106,\cdot)\) \(\chi_{1805}(121,\cdot)\) \(\chi_{1805}(201,\cdot)\) \(\chi_{1805}(216,\cdot)\) \(\chi_{1805}(296,\cdot)\) \(\chi_{1805}(311,\cdot)\) \(\chi_{1805}(391,\cdot)\) \(\chi_{1805}(406,\cdot)\) \(\chi_{1805}(486,\cdot)\) \(\chi_{1805}(501,\cdot)\) \(\chi_{1805}(581,\cdot)\) \(\chi_{1805}(596,\cdot)\) \(\chi_{1805}(676,\cdot)\) \(\chi_{1805}(691,\cdot)\) \(\chi_{1805}(771,\cdot)\) \(\chi_{1805}(786,\cdot)\) \(\chi_{1805}(866,\cdot)\) \(\chi_{1805}(881,\cdot)\) \(\chi_{1805}(961,\cdot)\) \(\chi_{1805}(976,\cdot)\) \(\chi_{1805}(1056,\cdot)\) \(\chi_{1805}(1071,\cdot)\) \(\chi_{1805}(1166,\cdot)\) \(\chi_{1805}(1246,\cdot)\) \(\chi_{1805}(1261,\cdot)\) \(\chi_{1805}(1341,\cdot)\) \(\chi_{1805}(1356,\cdot)\) \(\chi_{1805}(1436,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((362,1446)\) → \((1,e\left(\frac{32}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1805 }(1341, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) |