Basic properties
| Modulus: | \(4034\) | |
| Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2017}(313,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.t
\(\chi_{4034}(313,\cdot)\) \(\chi_{4034}(523,\cdot)\) \(\chi_{4034}(537,\cdot)\) \(\chi_{4034}(837,\cdot)\) \(\chi_{4034}(935,\cdot)\) \(\chi_{4034}(977,\cdot)\) \(\chi_{4034}(995,\cdot)\) \(\chi_{4034}(1253,\cdot)\) \(\chi_{4034}(1863,\cdot)\) \(\chi_{4034}(1951,\cdot)\) \(\chi_{4034}(1953,\cdot)\) \(\chi_{4034}(1959,\cdot)\) \(\chi_{4034}(2075,\cdot)\) \(\chi_{4034}(2081,\cdot)\) \(\chi_{4034}(2083,\cdot)\) \(\chi_{4034}(2171,\cdot)\) \(\chi_{4034}(2781,\cdot)\) \(\chi_{4034}(3039,\cdot)\) \(\chi_{4034}(3057,\cdot)\) \(\chi_{4034}(3099,\cdot)\) \(\chi_{4034}(3197,\cdot)\) \(\chi_{4034}(3497,\cdot)\) \(\chi_{4034}(3511,\cdot)\) \(\chi_{4034}(3721,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\(5\) → \(e\left(\frac{3}{56}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4034 }(313, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{11}{14}\right)\) |