Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.de
\(\chi_{8619}(64,\cdot)\) \(\chi_{8619}(259,\cdot)\) \(\chi_{8619}(727,\cdot)\) \(\chi_{8619}(922,\cdot)\) \(\chi_{8619}(1390,\cdot)\) \(\chi_{8619}(1585,\cdot)\) \(\chi_{8619}(2053,\cdot)\) \(\chi_{8619}(2248,\cdot)\) \(\chi_{8619}(2716,\cdot)\) \(\chi_{8619}(2911,\cdot)\) \(\chi_{8619}(3574,\cdot)\) \(\chi_{8619}(4042,\cdot)\) \(\chi_{8619}(4237,\cdot)\) \(\chi_{8619}(4705,\cdot)\) \(\chi_{8619}(5368,\cdot)\) \(\chi_{8619}(5563,\cdot)\) \(\chi_{8619}(6031,\cdot)\) \(\chi_{8619}(6226,\cdot)\) \(\chi_{8619}(6694,\cdot)\) \(\chi_{8619}(6889,\cdot)\) \(\chi_{8619}(7357,\cdot)\) \(\chi_{8619}(7552,\cdot)\) \(\chi_{8619}(8020,\cdot)\) \(\chi_{8619}(8215,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{1}{26}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(1\) |