Basic properties
| Modulus: | \(1610\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{805}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1610.bv
\(\chi_{1610}(3,\cdot)\) \(\chi_{1610}(73,\cdot)\) \(\chi_{1610}(87,\cdot)\) \(\chi_{1610}(117,\cdot)\) \(\chi_{1610}(173,\cdot)\) \(\chi_{1610}(187,\cdot)\) \(\chi_{1610}(213,\cdot)\) \(\chi_{1610}(243,\cdot)\) \(\chi_{1610}(257,\cdot)\) \(\chi_{1610}(353,\cdot)\) \(\chi_{1610}(397,\cdot)\) \(\chi_{1610}(423,\cdot)\) \(\chi_{1610}(453,\cdot)\) \(\chi_{1610}(537,\cdot)\) \(\chi_{1610}(577,\cdot)\) \(\chi_{1610}(593,\cdot)\) \(\chi_{1610}(607,\cdot)\) \(\chi_{1610}(633,\cdot)\) \(\chi_{1610}(647,\cdot)\) \(\chi_{1610}(703,\cdot)\) \(\chi_{1610}(717,\cdot)\) \(\chi_{1610}(817,\cdot)\) \(\chi_{1610}(857,\cdot)\) \(\chi_{1610}(887,\cdot)\) \(\chi_{1610}(913,\cdot)\) \(\chi_{1610}(997,\cdot)\) \(\chi_{1610}(1053,\cdot)\) \(\chi_{1610}(1067,\cdot)\) \(\chi_{1610}(1083,\cdot)\) \(\chi_{1610}(1097,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((967,1151,281)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 1610 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{35}{132}\right)\) |