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.en
\(\chi_{3484}(7,\cdot)\) \(\chi_{3484}(115,\cdot)\) \(\chi_{3484}(175,\cdot)\) \(\chi_{3484}(219,\cdot)\) \(\chi_{3484}(279,\cdot)\) \(\chi_{3484}(331,\cdot)\) \(\chi_{3484}(379,\cdot)\) \(\chi_{3484}(587,\cdot)\) \(\chi_{3484}(739,\cdot)\) \(\chi_{3484}(891,\cdot)\) \(\chi_{3484}(899,\cdot)\) \(\chi_{3484}(903,\cdot)\) \(\chi_{3484}(951,\cdot)\) \(\chi_{3484}(999,\cdot)\) \(\chi_{3484}(1055,\cdot)\) \(\chi_{3484}(1151,\cdot)\) \(\chi_{3484}(1263,\cdot)\) \(\chi_{3484}(1307,\cdot)\) \(\chi_{3484}(1319,\cdot)\) \(\chi_{3484}(1371,\cdot)\) \(\chi_{3484}(1515,\cdot)\) \(\chi_{3484}(1619,\cdot)\) \(\chi_{3484}(1671,\cdot)\) \(\chi_{3484}(1987,\cdot)\) \(\chi_{3484}(1991,\cdot)\) \(\chi_{3484}(2095,\cdot)\) \(\chi_{3484}(2151,\cdot)\) \(\chi_{3484}(2195,\cdot)\) \(\chi_{3484}(2243,\cdot)\) \(\chi_{3484}(2507,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{23}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3484 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) |