Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(196,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.dz
\(\chi_{8619}(196,\cdot)\) \(\chi_{8619}(274,\cdot)\) \(\chi_{8619}(586,\cdot)\) \(\chi_{8619}(859,\cdot)\) \(\chi_{8619}(937,\cdot)\) \(\chi_{8619}(1171,\cdot)\) \(\chi_{8619}(1249,\cdot)\) \(\chi_{8619}(1600,\cdot)\) \(\chi_{8619}(1834,\cdot)\) \(\chi_{8619}(1912,\cdot)\) \(\chi_{8619}(2185,\cdot)\) \(\chi_{8619}(2263,\cdot)\) \(\chi_{8619}(2497,\cdot)\) \(\chi_{8619}(2575,\cdot)\) \(\chi_{8619}(2848,\cdot)\) \(\chi_{8619}(2926,\cdot)\) \(\chi_{8619}(3160,\cdot)\) \(\chi_{8619}(3238,\cdot)\) \(\chi_{8619}(3511,\cdot)\) \(\chi_{8619}(3589,\cdot)\) \(\chi_{8619}(3823,\cdot)\) \(\chi_{8619}(3901,\cdot)\) \(\chi_{8619}(4174,\cdot)\) \(\chi_{8619}(4252,\cdot)\) \(\chi_{8619}(4486,\cdot)\) \(\chi_{8619}(4837,\cdot)\) \(\chi_{8619}(4915,\cdot)\) \(\chi_{8619}(5149,\cdot)\) \(\chi_{8619}(5227,\cdot)\) \(\chi_{8619}(5500,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{5}{13}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(196, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{55}{104}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{69}{104}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(-i\) |