Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.dl
\(\chi_{8619}(200,\cdot)\) \(\chi_{8619}(242,\cdot)\) \(\chi_{8619}(863,\cdot)\) \(\chi_{8619}(905,\cdot)\) \(\chi_{8619}(1526,\cdot)\) \(\chi_{8619}(1568,\cdot)\) \(\chi_{8619}(2189,\cdot)\) \(\chi_{8619}(2231,\cdot)\) \(\chi_{8619}(2852,\cdot)\) \(\chi_{8619}(2894,\cdot)\) \(\chi_{8619}(3515,\cdot)\) \(\chi_{8619}(3557,\cdot)\) \(\chi_{8619}(4178,\cdot)\) \(\chi_{8619}(4220,\cdot)\) \(\chi_{8619}(4841,\cdot)\) \(\chi_{8619}(4883,\cdot)\) \(\chi_{8619}(5504,\cdot)\) \(\chi_{8619}(5546,\cdot)\) \(\chi_{8619}(6167,\cdot)\) \(\chi_{8619}(6209,\cdot)\) \(\chi_{8619}(6872,\cdot)\) \(\chi_{8619}(7493,\cdot)\) \(\chi_{8619}(8156,\cdot)\) \(\chi_{8619}(8198,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{7}{52}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(200, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(i\) |