Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(243,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.ga
\(\chi_{8624}(243,\cdot)\) \(\chi_{8624}(507,\cdot)\) \(\chi_{8624}(859,\cdot)\) \(\chi_{8624}(1123,\cdot)\) \(\chi_{8624}(1475,\cdot)\) \(\chi_{8624}(1739,\cdot)\) \(\chi_{8624}(2091,\cdot)\) \(\chi_{8624}(2355,\cdot)\) \(\chi_{8624}(2707,\cdot)\) \(\chi_{8624}(3323,\cdot)\) \(\chi_{8624}(3587,\cdot)\) \(\chi_{8624}(4203,\cdot)\) \(\chi_{8624}(4555,\cdot)\) \(\chi_{8624}(4819,\cdot)\) \(\chi_{8624}(5171,\cdot)\) \(\chi_{8624}(5435,\cdot)\) \(\chi_{8624}(5787,\cdot)\) \(\chi_{8624}(6051,\cdot)\) \(\chi_{8624}(6403,\cdot)\) \(\chi_{8624}(6667,\cdot)\) \(\chi_{8624}(7019,\cdot)\) \(\chi_{8624}(7635,\cdot)\) \(\chi_{8624}(7899,\cdot)\) \(\chi_{8624}(8515,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,-i,e\left(\frac{5}{42}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(243, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) |