Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | 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.ev
\(\chi_{8619}(14,\cdot)\) \(\chi_{8619}(92,\cdot)\) \(\chi_{8619}(131,\cdot)\) \(\chi_{8619}(209,\cdot)\) \(\chi_{8619}(248,\cdot)\) \(\chi_{8619}(326,\cdot)\) \(\chi_{8619}(482,\cdot)\) \(\chi_{8619}(521,\cdot)\) \(\chi_{8619}(755,\cdot)\) \(\chi_{8619}(794,\cdot)\) \(\chi_{8619}(872,\cdot)\) \(\chi_{8619}(911,\cdot)\) \(\chi_{8619}(989,\cdot)\) \(\chi_{8619}(1145,\cdot)\) \(\chi_{8619}(1340,\cdot)\) \(\chi_{8619}(1418,\cdot)\) \(\chi_{8619}(1457,\cdot)\) \(\chi_{8619}(1535,\cdot)\) \(\chi_{8619}(1574,\cdot)\) \(\chi_{8619}(1652,\cdot)\) \(\chi_{8619}(1808,\cdot)\) \(\chi_{8619}(1847,\cdot)\) \(\chi_{8619}(2003,\cdot)\) \(\chi_{8619}(2081,\cdot)\) \(\chi_{8619}(2120,\cdot)\) \(\chi_{8619}(2237,\cdot)\) \(\chi_{8619}(2315,\cdot)\) \(\chi_{8619}(2471,\cdot)\) \(\chi_{8619}(2510,\cdot)\) \(\chi_{8619}(2666,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{9}{13}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{104}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{113}{208}\right)\) | \(e\left(\frac{55}{208}\right)\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{127}{208}\right)\) | \(e\left(\frac{155}{208}\right)\) | \(e\left(\frac{69}{208}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{7}{8}\right)\) |