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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dq
\(\chi_{4005}(47,\cdot)\) \(\chi_{4005}(158,\cdot)\) \(\chi_{4005}(173,\cdot)\) \(\chi_{4005}(272,\cdot)\) \(\chi_{4005}(347,\cdot)\) \(\chi_{4005}(398,\cdot)\) \(\chi_{4005}(428,\cdot)\) \(\chi_{4005}(587,\cdot)\) \(\chi_{4005}(722,\cdot)\) \(\chi_{4005}(752,\cdot)\) \(\chi_{4005}(1028,\cdot)\) \(\chi_{4005}(1058,\cdot)\) \(\chi_{4005}(1193,\cdot)\) \(\chi_{4005}(1352,\cdot)\) \(\chi_{4005}(1382,\cdot)\) \(\chi_{4005}(1433,\cdot)\) \(\chi_{4005}(1508,\cdot)\) \(\chi_{4005}(1607,\cdot)\) \(\chi_{4005}(1622,\cdot)\) \(\chi_{4005}(1733,\cdot)\) \(\chi_{4005}(1922,\cdot)\) \(\chi_{4005}(1937,\cdot)\) \(\chi_{4005}(2057,\cdot)\) \(\chi_{4005}(2207,\cdot)\) \(\chi_{4005}(2243,\cdot)\) \(\chi_{4005}(2363,\cdot)\) \(\chi_{4005}(2513,\cdot)\) \(\chi_{4005}(2687,\cdot)\) \(\chi_{4005}(2768,\cdot)\) \(\chi_{4005}(2828,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{27}{44}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) |