Basic properties
| Modulus: | \(3484\) | |
| Conductor: | \(3484\) | 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 3484.ek
\(\chi_{3484}(119,\cdot)\) \(\chi_{3484}(271,\cdot)\) \(\chi_{3484}(527,\cdot)\) \(\chi_{3484}(539,\cdot)\) \(\chi_{3484}(579,\cdot)\) \(\chi_{3484}(795,\cdot)\) \(\chi_{3484}(847,\cdot)\) \(\chi_{3484}(943,\cdot)\) \(\chi_{3484}(1047,\cdot)\) \(\chi_{3484}(1099,\cdot)\) \(\chi_{3484}(1211,\cdot)\) \(\chi_{3484}(1259,\cdot)\) \(\chi_{3484}(1315,\cdot)\) \(\chi_{3484}(1367,\cdot)\) \(\chi_{3484}(1415,\cdot)\) \(\chi_{3484}(1519,\cdot)\) \(\chi_{3484}(1527,\cdot)\) \(\chi_{3484}(1683,\cdot)\) \(\chi_{3484}(1727,\cdot)\) \(\chi_{3484}(1787,\cdot)\) \(\chi_{3484}(1879,\cdot)\) \(\chi_{3484}(1995,\cdot)\) \(\chi_{3484}(2147,\cdot)\) \(\chi_{3484}(2403,\cdot)\) \(\chi_{3484}(2455,\cdot)\) \(\chi_{3484}(2671,\cdot)\) \(\chi_{3484}(2723,\cdot)\) \(\chi_{3484}(2819,\cdot)\) \(\chi_{3484}(2867,\cdot)\) \(\chi_{3484}(2923,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((-1,e\left(\frac{1}{12}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3484 }(119, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) |