Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(2156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2156}(1571,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gr
\(\chi_{8624}(47,\cdot)\) \(\chi_{8624}(159,\cdot)\) \(\chi_{8624}(367,\cdot)\) \(\chi_{8624}(383,\cdot)\) \(\chi_{8624}(719,\cdot)\) \(\chi_{8624}(927,\cdot)\) \(\chi_{8624}(1039,\cdot)\) \(\chi_{8624}(1263,\cdot)\) \(\chi_{8624}(1279,\cdot)\) \(\chi_{8624}(1615,\cdot)\) \(\chi_{8624}(1951,\cdot)\) \(\chi_{8624}(2159,\cdot)\) \(\chi_{8624}(2271,\cdot)\) \(\chi_{8624}(2495,\cdot)\) \(\chi_{8624}(2511,\cdot)\) \(\chi_{8624}(2623,\cdot)\) \(\chi_{8624}(2831,\cdot)\) \(\chi_{8624}(2847,\cdot)\) \(\chi_{8624}(3183,\cdot)\) \(\chi_{8624}(3391,\cdot)\) \(\chi_{8624}(3503,\cdot)\) \(\chi_{8624}(3727,\cdot)\) \(\chi_{8624}(3855,\cdot)\) \(\chi_{8624}(4063,\cdot)\) \(\chi_{8624}(4079,\cdot)\) \(\chi_{8624}(4415,\cdot)\) \(\chi_{8624}(4623,\cdot)\) \(\chi_{8624}(4959,\cdot)\) \(\chi_{8624}(4975,\cdot)\) \(\chi_{8624}(5087,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,1,e\left(\frac{1}{42}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(3727, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) |