Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(1573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1573}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4719.cr
\(\chi_{4719}(25,\cdot)\) \(\chi_{4719}(64,\cdot)\) \(\chi_{4719}(103,\cdot)\) \(\chi_{4719}(181,\cdot)\) \(\chi_{4719}(454,\cdot)\) \(\chi_{4719}(532,\cdot)\) \(\chi_{4719}(610,\cdot)\) \(\chi_{4719}(883,\cdot)\) \(\chi_{4719}(922,\cdot)\) \(\chi_{4719}(961,\cdot)\) \(\chi_{4719}(1039,\cdot)\) \(\chi_{4719}(1312,\cdot)\) \(\chi_{4719}(1351,\cdot)\) \(\chi_{4719}(1390,\cdot)\) \(\chi_{4719}(1468,\cdot)\) \(\chi_{4719}(1741,\cdot)\) \(\chi_{4719}(1780,\cdot)\) \(\chi_{4719}(1819,\cdot)\) \(\chi_{4719}(1897,\cdot)\) \(\chi_{4719}(2170,\cdot)\) \(\chi_{4719}(2209,\cdot)\) \(\chi_{4719}(2248,\cdot)\) \(\chi_{4719}(2599,\cdot)\) \(\chi_{4719}(2638,\cdot)\) \(\chi_{4719}(2677,\cdot)\) \(\chi_{4719}(2755,\cdot)\) \(\chi_{4719}(3067,\cdot)\) \(\chi_{4719}(3184,\cdot)\) \(\chi_{4719}(3457,\cdot)\) \(\chi_{4719}(3496,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((1,e\left(\frac{19}{55}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) |