Basic properties
| Modulus: | \(1005\) | |
| Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{335}(318,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1005.bt
\(\chi_{1005}(7,\cdot)\) \(\chi_{1005}(13,\cdot)\) \(\chi_{1005}(28,\cdot)\) \(\chi_{1005}(118,\cdot)\) \(\chi_{1005}(178,\cdot)\) \(\chi_{1005}(208,\cdot)\) \(\chi_{1005}(232,\cdot)\) \(\chi_{1005}(247,\cdot)\) \(\chi_{1005}(262,\cdot)\) \(\chi_{1005}(337,\cdot)\) \(\chi_{1005}(367,\cdot)\) \(\chi_{1005}(433,\cdot)\) \(\chi_{1005}(448,\cdot)\) \(\chi_{1005}(463,\cdot)\) \(\chi_{1005}(487,\cdot)\) \(\chi_{1005}(517,\cdot)\) \(\chi_{1005}(532,\cdot)\) \(\chi_{1005}(538,\cdot)\) \(\chi_{1005}(547,\cdot)\) \(\chi_{1005}(568,\cdot)\) \(\chi_{1005}(577,\cdot)\) \(\chi_{1005}(637,\cdot)\) \(\chi_{1005}(682,\cdot)\) \(\chi_{1005}(688,\cdot)\) \(\chi_{1005}(718,\cdot)\) \(\chi_{1005}(727,\cdot)\) \(\chi_{1005}(733,\cdot)\) \(\chi_{1005}(748,\cdot)\) \(\chi_{1005}(757,\cdot)\) \(\chi_{1005}(778,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,202,136)\) → \((1,-i,e\left(\frac{31}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1005 }(988, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) |