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.dv
\(\chi_{4005}(22,\cdot)\) \(\chi_{4005}(133,\cdot)\) \(\chi_{4005}(292,\cdot)\) \(\chi_{4005}(367,\cdot)\) \(\chi_{4005}(502,\cdot)\) \(\chi_{4005}(607,\cdot)\) \(\chi_{4005}(673,\cdot)\) \(\chi_{4005}(823,\cdot)\) \(\chi_{4005}(1093,\cdot)\) \(\chi_{4005}(1168,\cdot)\) \(\chi_{4005}(1303,\cdot)\) \(\chi_{4005}(1327,\cdot)\) \(\chi_{4005}(1357,\cdot)\) \(\chi_{4005}(1408,\cdot)\) \(\chi_{4005}(1627,\cdot)\) \(\chi_{4005}(1687,\cdot)\) \(\chi_{4005}(1867,\cdot)\) \(\chi_{4005}(1942,\cdot)\) \(\chi_{4005}(2002,\cdot)\) \(\chi_{4005}(2128,\cdot)\) \(\chi_{4005}(2158,\cdot)\) \(\chi_{4005}(2428,\cdot)\) \(\chi_{4005}(2488,\cdot)\) \(\chi_{4005}(2542,\cdot)\) \(\chi_{4005}(2662,\cdot)\) \(\chi_{4005}(2668,\cdot)\) \(\chi_{4005}(2743,\cdot)\) \(\chi_{4005}(2803,\cdot)\) \(\chi_{4005}(3022,\cdot)\) \(\chi_{4005}(3037,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) |