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 \(\chi_{2873}(2716,\cdot)\) | 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
\((5747,5917,2536)\) → \((1,e\left(\frac{21}{26}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
\( \chi_{ 8619 }(2716, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(1\) |