Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.cf
\(\chi_{4719}(157,\cdot)\) \(\chi_{4719}(196,\cdot)\) \(\chi_{4719}(235,\cdot)\) \(\chi_{4719}(313,\cdot)\) \(\chi_{4719}(586,\cdot)\) \(\chi_{4719}(625,\cdot)\) \(\chi_{4719}(664,\cdot)\) \(\chi_{4719}(742,\cdot)\) \(\chi_{4719}(1015,\cdot)\) \(\chi_{4719}(1054,\cdot)\) \(\chi_{4719}(1093,\cdot)\) \(\chi_{4719}(1171,\cdot)\) \(\chi_{4719}(1444,\cdot)\) \(\chi_{4719}(1483,\cdot)\) \(\chi_{4719}(1522,\cdot)\) \(\chi_{4719}(1873,\cdot)\) \(\chi_{4719}(1912,\cdot)\) \(\chi_{4719}(1951,\cdot)\) \(\chi_{4719}(2029,\cdot)\) \(\chi_{4719}(2341,\cdot)\) \(\chi_{4719}(2458,\cdot)\) \(\chi_{4719}(2731,\cdot)\) \(\chi_{4719}(2770,\cdot)\) \(\chi_{4719}(2809,\cdot)\) \(\chi_{4719}(2887,\cdot)\) \(\chi_{4719}(3160,\cdot)\) \(\chi_{4719}(3199,\cdot)\) \(\chi_{4719}(3238,\cdot)\) \(\chi_{4719}(3316,\cdot)\) \(\chi_{4719}(3589,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((1574,3511,4357)\) → \((1,e\left(\frac{34}{55}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) |