Basic properties
Modulus: | \(1805\) | |
Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(684\) | 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 1805.bi
\(\chi_{1805}(2,\cdot)\) \(\chi_{1805}(3,\cdot)\) \(\chi_{1805}(13,\cdot)\) \(\chi_{1805}(22,\cdot)\) \(\chi_{1805}(32,\cdot)\) \(\chi_{1805}(33,\cdot)\) \(\chi_{1805}(48,\cdot)\) \(\chi_{1805}(52,\cdot)\) \(\chi_{1805}(53,\cdot)\) \(\chi_{1805}(67,\cdot)\) \(\chi_{1805}(72,\cdot)\) \(\chi_{1805}(78,\cdot)\) \(\chi_{1805}(97,\cdot)\) \(\chi_{1805}(98,\cdot)\) \(\chi_{1805}(108,\cdot)\) \(\chi_{1805}(117,\cdot)\) \(\chi_{1805}(128,\cdot)\) \(\chi_{1805}(143,\cdot)\) \(\chi_{1805}(147,\cdot)\) \(\chi_{1805}(148,\cdot)\) \(\chi_{1805}(162,\cdot)\) \(\chi_{1805}(167,\cdot)\) \(\chi_{1805}(173,\cdot)\) \(\chi_{1805}(192,\cdot)\) \(\chi_{1805}(193,\cdot)\) \(\chi_{1805}(203,\cdot)\) \(\chi_{1805}(212,\cdot)\) \(\chi_{1805}(222,\cdot)\) \(\chi_{1805}(223,\cdot)\) \(\chi_{1805}(238,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{684})$ |
Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((-i,e\left(\frac{329}{342}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1805 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{487}{684}\right)\) | \(e\left(\frac{661}{684}\right)\) | \(e\left(\frac{145}{342}\right)\) | \(e\left(\frac{116}{171}\right)\) | \(e\left(\frac{11}{228}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{89}{228}\right)\) | \(e\left(\frac{509}{684}\right)\) |