Basic properties
| Modulus: | \(7942\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7942.z
\(\chi_{7942}(45,\cdot)\) \(\chi_{7942}(353,\cdot)\) \(\chi_{7942}(463,\cdot)\) \(\chi_{7942}(771,\cdot)\) \(\chi_{7942}(881,\cdot)\) \(\chi_{7942}(1189,\cdot)\) \(\chi_{7942}(1299,\cdot)\) \(\chi_{7942}(1607,\cdot)\) \(\chi_{7942}(1717,\cdot)\) \(\chi_{7942}(2025,\cdot)\) \(\chi_{7942}(2135,\cdot)\) \(\chi_{7942}(2443,\cdot)\) \(\chi_{7942}(2553,\cdot)\) \(\chi_{7942}(2861,\cdot)\) \(\chi_{7942}(2971,\cdot)\) \(\chi_{7942}(3279,\cdot)\) \(\chi_{7942}(3389,\cdot)\) \(\chi_{7942}(3697,\cdot)\) \(\chi_{7942}(3807,\cdot)\) \(\chi_{7942}(4115,\cdot)\) \(\chi_{7942}(4225,\cdot)\) \(\chi_{7942}(4533,\cdot)\) \(\chi_{7942}(4643,\cdot)\) \(\chi_{7942}(4951,\cdot)\) \(\chi_{7942}(5061,\cdot)\) \(\chi_{7942}(5369,\cdot)\) \(\chi_{7942}(5479,\cdot)\) \(\chi_{7942}(5787,\cdot)\) \(\chi_{7942}(5897,\cdot)\) \(\chi_{7942}(6315,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((5777,6139)\) → \((1,e\left(\frac{28}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 7942 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) |