Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(8624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 8624.gb
\(\chi_{8624}(219,\cdot)\) \(\chi_{8624}(571,\cdot)\) \(\chi_{8624}(835,\cdot)\) \(\chi_{8624}(1187,\cdot)\) \(\chi_{8624}(1803,\cdot)\) \(\chi_{8624}(2067,\cdot)\) \(\chi_{8624}(2683,\cdot)\) \(\chi_{8624}(3035,\cdot)\) \(\chi_{8624}(3299,\cdot)\) \(\chi_{8624}(3651,\cdot)\) \(\chi_{8624}(3915,\cdot)\) \(\chi_{8624}(4267,\cdot)\) \(\chi_{8624}(4531,\cdot)\) \(\chi_{8624}(4883,\cdot)\) \(\chi_{8624}(5147,\cdot)\) \(\chi_{8624}(5499,\cdot)\) \(\chi_{8624}(6115,\cdot)\) \(\chi_{8624}(6379,\cdot)\) \(\chi_{8624}(6995,\cdot)\) \(\chi_{8624}(7347,\cdot)\) \(\chi_{8624}(7611,\cdot)\) \(\chi_{8624}(7963,\cdot)\) \(\chi_{8624}(8227,\cdot)\) \(\chi_{8624}(8579,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,-i,e\left(\frac{19}{21}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(4531, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) |