Basic properties
| Modulus: | \(1805\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1805.bh
\(\chi_{1805}(21,\cdot)\) \(\chi_{1805}(41,\cdot)\) \(\chi_{1805}(51,\cdot)\) \(\chi_{1805}(71,\cdot)\) \(\chi_{1805}(86,\cdot)\) \(\chi_{1805}(91,\cdot)\) \(\chi_{1805}(136,\cdot)\) \(\chi_{1805}(146,\cdot)\) \(\chi_{1805}(166,\cdot)\) \(\chi_{1805}(181,\cdot)\) \(\chi_{1805}(186,\cdot)\) \(\chi_{1805}(211,\cdot)\) \(\chi_{1805}(231,\cdot)\) \(\chi_{1805}(241,\cdot)\) \(\chi_{1805}(261,\cdot)\) \(\chi_{1805}(276,\cdot)\) \(\chi_{1805}(281,\cdot)\) \(\chi_{1805}(306,\cdot)\) \(\chi_{1805}(326,\cdot)\) \(\chi_{1805}(336,\cdot)\) \(\chi_{1805}(356,\cdot)\) \(\chi_{1805}(371,\cdot)\) \(\chi_{1805}(376,\cdot)\) \(\chi_{1805}(401,\cdot)\) \(\chi_{1805}(421,\cdot)\) \(\chi_{1805}(431,\cdot)\) \(\chi_{1805}(451,\cdot)\) \(\chi_{1805}(466,\cdot)\) \(\chi_{1805}(471,\cdot)\) \(\chi_{1805}(496,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((1,e\left(\frac{289}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{157}{342}\right)\) | \(e\left(\frac{118}{171}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{5}{342}\right)\) |