Basic properties
| Modulus: | \(3312\) | |
| Conductor: | \(3312\) | 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 3312.dq
\(\chi_{3312}(59,\cdot)\) \(\chi_{3312}(131,\cdot)\) \(\chi_{3312}(347,\cdot)\) \(\chi_{3312}(371,\cdot)\) \(\chi_{3312}(443,\cdot)\) \(\chi_{3312}(491,\cdot)\) \(\chi_{3312}(515,\cdot)\) \(\chi_{3312}(587,\cdot)\) \(\chi_{3312}(731,\cdot)\) \(\chi_{3312}(923,\cdot)\) \(\chi_{3312}(947,\cdot)\) \(\chi_{3312}(995,\cdot)\) \(\chi_{3312}(1067,\cdot)\) \(\chi_{3312}(1139,\cdot)\) \(\chi_{3312}(1163,\cdot)\) \(\chi_{3312}(1235,\cdot)\) \(\chi_{3312}(1283,\cdot)\) \(\chi_{3312}(1451,\cdot)\) \(\chi_{3312}(1499,\cdot)\) \(\chi_{3312}(1595,\cdot)\) \(\chi_{3312}(1715,\cdot)\) \(\chi_{3312}(1787,\cdot)\) \(\chi_{3312}(2003,\cdot)\) \(\chi_{3312}(2027,\cdot)\) \(\chi_{3312}(2099,\cdot)\) \(\chi_{3312}(2147,\cdot)\) \(\chi_{3312}(2171,\cdot)\) \(\chi_{3312}(2243,\cdot)\) \(\chi_{3312}(2387,\cdot)\) \(\chi_{3312}(2579,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((415,2485,2945,2305)\) → \((-1,i,e\left(\frac{5}{6}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3312 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{21}{44}\right)\) |