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.dp
\(\chi_{4005}(49,\cdot)\) \(\chi_{4005}(79,\cdot)\) \(\chi_{4005}(94,\cdot)\) \(\chi_{4005}(169,\cdot)\) \(\chi_{4005}(214,\cdot)\) \(\chi_{4005}(409,\cdot)\) \(\chi_{4005}(454,\cdot)\) \(\chi_{4005}(529,\cdot)\) \(\chi_{4005}(544,\cdot)\) \(\chi_{4005}(574,\cdot)\) \(\chi_{4005}(754,\cdot)\) \(\chi_{4005}(1174,\cdot)\) \(\chi_{4005}(1204,\cdot)\) \(\chi_{4005}(1264,\cdot)\) \(\chi_{4005}(1384,\cdot)\) \(\chi_{4005}(1429,\cdot)\) \(\chi_{4005}(1444,\cdot)\) \(\chi_{4005}(1534,\cdot)\) \(\chi_{4005}(1744,\cdot)\) \(\chi_{4005}(1759,\cdot)\) \(\chi_{4005}(1789,\cdot)\) \(\chi_{4005}(1849,\cdot)\) \(\chi_{4005}(1879,\cdot)\) \(\chi_{4005}(2029,\cdot)\) \(\chi_{4005}(2119,\cdot)\) \(\chi_{4005}(2509,\cdot)\) \(\chi_{4005}(2599,\cdot)\) \(\chi_{4005}(2749,\cdot)\) \(\chi_{4005}(2779,\cdot)\) \(\chi_{4005}(2839,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{37}{44}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) |