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.dl
\(\chi_{3312}(13,\cdot)\) \(\chi_{3312}(85,\cdot)\) \(\chi_{3312}(133,\cdot)\) \(\chi_{3312}(301,\cdot)\) \(\chi_{3312}(349,\cdot)\) \(\chi_{3312}(445,\cdot)\) \(\chi_{3312}(565,\cdot)\) \(\chi_{3312}(637,\cdot)\) \(\chi_{3312}(853,\cdot)\) \(\chi_{3312}(877,\cdot)\) \(\chi_{3312}(949,\cdot)\) \(\chi_{3312}(997,\cdot)\) \(\chi_{3312}(1021,\cdot)\) \(\chi_{3312}(1093,\cdot)\) \(\chi_{3312}(1237,\cdot)\) \(\chi_{3312}(1429,\cdot)\) \(\chi_{3312}(1453,\cdot)\) \(\chi_{3312}(1501,\cdot)\) \(\chi_{3312}(1573,\cdot)\) \(\chi_{3312}(1645,\cdot)\) \(\chi_{3312}(1669,\cdot)\) \(\chi_{3312}(1741,\cdot)\) \(\chi_{3312}(1789,\cdot)\) \(\chi_{3312}(1957,\cdot)\) \(\chi_{3312}(2005,\cdot)\) \(\chi_{3312}(2101,\cdot)\) \(\chi_{3312}(2221,\cdot)\) \(\chi_{3312}(2293,\cdot)\) \(\chi_{3312}(2509,\cdot)\) \(\chi_{3312}(2533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((415,2485,2945,2305)\) → \((1,-i,e\left(\frac{1}{3}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3312 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) |