Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(4719\) | 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 4719.cz
\(\chi_{4719}(89,\cdot)\) \(\chi_{4719}(188,\cdot)\) \(\chi_{4719}(254,\cdot)\) \(\chi_{4719}(353,\cdot)\) \(\chi_{4719}(518,\cdot)\) \(\chi_{4719}(617,\cdot)\) \(\chi_{4719}(683,\cdot)\) \(\chi_{4719}(782,\cdot)\) \(\chi_{4719}(947,\cdot)\) \(\chi_{4719}(1046,\cdot)\) \(\chi_{4719}(1112,\cdot)\) \(\chi_{4719}(1376,\cdot)\) \(\chi_{4719}(1475,\cdot)\) \(\chi_{4719}(1541,\cdot)\) \(\chi_{4719}(1640,\cdot)\) \(\chi_{4719}(1805,\cdot)\) \(\chi_{4719}(1904,\cdot)\) \(\chi_{4719}(1970,\cdot)\) \(\chi_{4719}(2069,\cdot)\) \(\chi_{4719}(2234,\cdot)\) \(\chi_{4719}(2333,\cdot)\) \(\chi_{4719}(2399,\cdot)\) \(\chi_{4719}(2498,\cdot)\) \(\chi_{4719}(2762,\cdot)\) \(\chi_{4719}(2828,\cdot)\) \(\chi_{4719}(2927,\cdot)\) \(\chi_{4719}(3092,\cdot)\) \(\chi_{4719}(3191,\cdot)\) \(\chi_{4719}(3257,\cdot)\) \(\chi_{4719}(3356,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((-1,e\left(\frac{6}{11}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{25}{132}\right)\) |