Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.et
\(\chi_{8619}(31,\cdot)\) \(\chi_{8619}(112,\cdot)\) \(\chi_{8619}(148,\cdot)\) \(\chi_{8619}(226,\cdot)\) \(\chi_{8619}(343,\cdot)\) \(\chi_{8619}(346,\cdot)\) \(\chi_{8619}(385,\cdot)\) \(\chi_{8619}(619,\cdot)\) \(\chi_{8619}(694,\cdot)\) \(\chi_{8619}(811,\cdot)\) \(\chi_{8619}(889,\cdot)\) \(\chi_{8619}(1006,\cdot)\) \(\chi_{8619}(1009,\cdot)\) \(\chi_{8619}(1048,\cdot)\) \(\chi_{8619}(1357,\cdot)\) \(\chi_{8619}(1438,\cdot)\) \(\chi_{8619}(1474,\cdot)\) \(\chi_{8619}(1552,\cdot)\) \(\chi_{8619}(1669,\cdot)\) \(\chi_{8619}(1672,\cdot)\) \(\chi_{8619}(1711,\cdot)\) \(\chi_{8619}(1945,\cdot)\) \(\chi_{8619}(2020,\cdot)\) \(\chi_{8619}(2101,\cdot)\) \(\chi_{8619}(2137,\cdot)\) \(\chi_{8619}(2215,\cdot)\) \(\chi_{8619}(2332,\cdot)\) \(\chi_{8619}(2335,\cdot)\) \(\chi_{8619}(2374,\cdot)\) \(\chi_{8619}(2608,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{7}{52}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{208}\right)\) | \(e\left(\frac{123}{208}\right)\) | \(e\left(\frac{3}{104}\right)\) | \(e\left(\frac{7}{208}\right)\) | \(e\left(\frac{167}{208}\right)\) | \(e\left(\frac{125}{208}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{5}{8}\right)\) |