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 \(\chi_{2873}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.dy
\(\chi_{8619}(25,\cdot)\) \(\chi_{8619}(298,\cdot)\) \(\chi_{8619}(376,\cdot)\) \(\chi_{8619}(610,\cdot)\) \(\chi_{8619}(688,\cdot)\) \(\chi_{8619}(961,\cdot)\) \(\chi_{8619}(1039,\cdot)\) \(\chi_{8619}(1273,\cdot)\) \(\chi_{8619}(1624,\cdot)\) \(\chi_{8619}(1702,\cdot)\) \(\chi_{8619}(1936,\cdot)\) \(\chi_{8619}(2014,\cdot)\) \(\chi_{8619}(2287,\cdot)\) \(\chi_{8619}(2599,\cdot)\) \(\chi_{8619}(2677,\cdot)\) \(\chi_{8619}(2950,\cdot)\) \(\chi_{8619}(3028,\cdot)\) \(\chi_{8619}(3262,\cdot)\) \(\chi_{8619}(3340,\cdot)\) \(\chi_{8619}(3613,\cdot)\) \(\chi_{8619}(3691,\cdot)\) \(\chi_{8619}(3925,\cdot)\) \(\chi_{8619}(4003,\cdot)\) \(\chi_{8619}(4276,\cdot)\) \(\chi_{8619}(4354,\cdot)\) \(\chi_{8619}(4588,\cdot)\) \(\chi_{8619}(4666,\cdot)\) \(\chi_{8619}(4939,\cdot)\) \(\chi_{8619}(5017,\cdot)\) \(\chi_{8619}(5251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{3}{26}\right),e\left(\frac{5}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{17}{104}\right)\) | \(e\left(\frac{23}{104}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{27}{104}\right)\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(i\) |