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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1805.bj
\(\chi_{1805}(17,\cdot)\) \(\chi_{1805}(23,\cdot)\) \(\chi_{1805}(42,\cdot)\) \(\chi_{1805}(43,\cdot)\) \(\chi_{1805}(47,\cdot)\) \(\chi_{1805}(63,\cdot)\) \(\chi_{1805}(73,\cdot)\) \(\chi_{1805}(82,\cdot)\) \(\chi_{1805}(92,\cdot)\) \(\chi_{1805}(93,\cdot)\) \(\chi_{1805}(112,\cdot)\) \(\chi_{1805}(118,\cdot)\) \(\chi_{1805}(123,\cdot)\) \(\chi_{1805}(137,\cdot)\) \(\chi_{1805}(138,\cdot)\) \(\chi_{1805}(142,\cdot)\) \(\chi_{1805}(157,\cdot)\) \(\chi_{1805}(158,\cdot)\) \(\chi_{1805}(168,\cdot)\) \(\chi_{1805}(177,\cdot)\) \(\chi_{1805}(187,\cdot)\) \(\chi_{1805}(188,\cdot)\) \(\chi_{1805}(207,\cdot)\) \(\chi_{1805}(213,\cdot)\) \(\chi_{1805}(218,\cdot)\) \(\chi_{1805}(232,\cdot)\) \(\chi_{1805}(233,\cdot)\) \(\chi_{1805}(237,\cdot)\) \(\chi_{1805}(252,\cdot)\) \(\chi_{1805}(253,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{684})$ |
| Fixed field: | Number field defined by a degree 684 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((-i,e\left(\frac{169}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(158, a) \) | \(-1\) | \(1\) | \(e\left(\frac{505}{684}\right)\) | \(e\left(\frac{427}{684}\right)\) | \(e\left(\frac{163}{342}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{227}{228}\right)\) | \(e\left(\frac{49}{228}\right)\) | \(e\left(\frac{85}{342}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{23}{228}\right)\) | \(e\left(\frac{275}{684}\right)\) |