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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1805.bf
\(\chi_{1805}(4,\cdot)\) \(\chi_{1805}(9,\cdot)\) \(\chi_{1805}(24,\cdot)\) \(\chi_{1805}(44,\cdot)\) \(\chi_{1805}(74,\cdot)\) \(\chi_{1805}(104,\cdot)\) \(\chi_{1805}(119,\cdot)\) \(\chi_{1805}(139,\cdot)\) \(\chi_{1805}(149,\cdot)\) \(\chi_{1805}(169,\cdot)\) \(\chi_{1805}(194,\cdot)\) \(\chi_{1805}(199,\cdot)\) \(\chi_{1805}(214,\cdot)\) \(\chi_{1805}(244,\cdot)\) \(\chi_{1805}(264,\cdot)\) \(\chi_{1805}(289,\cdot)\) \(\chi_{1805}(294,\cdot)\) \(\chi_{1805}(309,\cdot)\) \(\chi_{1805}(329,\cdot)\) \(\chi_{1805}(339,\cdot)\) \(\chi_{1805}(359,\cdot)\) \(\chi_{1805}(384,\cdot)\) \(\chi_{1805}(404,\cdot)\) \(\chi_{1805}(424,\cdot)\) \(\chi_{1805}(434,\cdot)\) \(\chi_{1805}(454,\cdot)\) \(\chi_{1805}(479,\cdot)\) \(\chi_{1805}(484,\cdot)\) \(\chi_{1805}(499,\cdot)\) \(\chi_{1805}(519,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((-1,e\left(\frac{47}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(244, a) \) | \(1\) | \(1\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{241}{342}\right)\) | \(e\left(\frac{94}{171}\right)\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{317}{342}\right)\) |