Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(4005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 4005.du
\(\chi_{4005}(67,\cdot)\) \(\chi_{4005}(97,\cdot)\) \(\chi_{4005}(223,\cdot)\) \(\chi_{4005}(283,\cdot)\) \(\chi_{4005}(358,\cdot)\) \(\chi_{4005}(538,\cdot)\) \(\chi_{4005}(598,\cdot)\) \(\chi_{4005}(817,\cdot)\) \(\chi_{4005}(868,\cdot)\) \(\chi_{4005}(898,\cdot)\) \(\chi_{4005}(922,\cdot)\) \(\chi_{4005}(1057,\cdot)\) \(\chi_{4005}(1132,\cdot)\) \(\chi_{4005}(1402,\cdot)\) \(\chi_{4005}(1552,\cdot)\) \(\chi_{4005}(1618,\cdot)\) \(\chi_{4005}(1723,\cdot)\) \(\chi_{4005}(1858,\cdot)\) \(\chi_{4005}(1933,\cdot)\) \(\chi_{4005}(2092,\cdot)\) \(\chi_{4005}(2203,\cdot)\) \(\chi_{4005}(2227,\cdot)\) \(\chi_{4005}(2257,\cdot)\) \(\chi_{4005}(2353,\cdot)\) \(\chi_{4005}(2392,\cdot)\) \(\chi_{4005}(2407,\cdot)\) \(\chi_{4005}(2767,\cdot)\) \(\chi_{4005}(2887,\cdot)\) \(\chi_{4005}(2893,\cdot)\) \(\chi_{4005}(3028,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(2092, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) |