Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(1573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1573}(1099,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.da
\(\chi_{4719}(76,\cdot)\) \(\chi_{4719}(175,\cdot)\) \(\chi_{4719}(340,\cdot)\) \(\chi_{4719}(505,\cdot)\) \(\chi_{4719}(670,\cdot)\) \(\chi_{4719}(769,\cdot)\) \(\chi_{4719}(934,\cdot)\) \(\chi_{4719}(1033,\cdot)\) \(\chi_{4719}(1099,\cdot)\) \(\chi_{4719}(1198,\cdot)\) \(\chi_{4719}(1363,\cdot)\) \(\chi_{4719}(1462,\cdot)\) \(\chi_{4719}(1528,\cdot)\) \(\chi_{4719}(1627,\cdot)\) \(\chi_{4719}(1792,\cdot)\) \(\chi_{4719}(1891,\cdot)\) \(\chi_{4719}(1957,\cdot)\) \(\chi_{4719}(2221,\cdot)\) \(\chi_{4719}(2320,\cdot)\) \(\chi_{4719}(2386,\cdot)\) \(\chi_{4719}(2485,\cdot)\) \(\chi_{4719}(2650,\cdot)\) \(\chi_{4719}(2749,\cdot)\) \(\chi_{4719}(2815,\cdot)\) \(\chi_{4719}(2914,\cdot)\) \(\chi_{4719}(3079,\cdot)\) \(\chi_{4719}(3178,\cdot)\) \(\chi_{4719}(3244,\cdot)\) \(\chi_{4719}(3343,\cdot)\) \(\chi_{4719}(3607,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((1,e\left(\frac{15}{22}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(1099, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{23}{132}\right)\) |