Basic properties
| Modulus: | \(1805\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | 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.bg
\(\chi_{1805}(14,\cdot)\) \(\chi_{1805}(29,\cdot)\) \(\chi_{1805}(34,\cdot)\) \(\chi_{1805}(59,\cdot)\) \(\chi_{1805}(79,\cdot)\) \(\chi_{1805}(89,\cdot)\) \(\chi_{1805}(109,\cdot)\) \(\chi_{1805}(124,\cdot)\) \(\chi_{1805}(129,\cdot)\) \(\chi_{1805}(154,\cdot)\) \(\chi_{1805}(174,\cdot)\) \(\chi_{1805}(184,\cdot)\) \(\chi_{1805}(204,\cdot)\) \(\chi_{1805}(219,\cdot)\) \(\chi_{1805}(224,\cdot)\) \(\chi_{1805}(249,\cdot)\) \(\chi_{1805}(269,\cdot)\) \(\chi_{1805}(279,\cdot)\) \(\chi_{1805}(314,\cdot)\) \(\chi_{1805}(319,\cdot)\) \(\chi_{1805}(344,\cdot)\) \(\chi_{1805}(364,\cdot)\) \(\chi_{1805}(374,\cdot)\) \(\chi_{1805}(394,\cdot)\) \(\chi_{1805}(409,\cdot)\) \(\chi_{1805}(414,\cdot)\) \(\chi_{1805}(439,\cdot)\) \(\chi_{1805}(459,\cdot)\) \(\chi_{1805}(469,\cdot)\) \(\chi_{1805}(489,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((-1,e\left(\frac{151}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{161}{171}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{151}{171}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{127}{171}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{130}{171}\right)\) |