Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(8624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | 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.hf
\(\chi_{8624}(3,\cdot)\) \(\chi_{8624}(59,\cdot)\) \(\chi_{8624}(75,\cdot)\) \(\chi_{8624}(115,\cdot)\) \(\chi_{8624}(339,\cdot)\) \(\chi_{8624}(355,\cdot)\) \(\chi_{8624}(467,\cdot)\) \(\chi_{8624}(675,\cdot)\) \(\chi_{8624}(691,\cdot)\) \(\chi_{8624}(731,\cdot)\) \(\chi_{8624}(955,\cdot)\) \(\chi_{8624}(971,\cdot)\) \(\chi_{8624}(1027,\cdot)\) \(\chi_{8624}(1083,\cdot)\) \(\chi_{8624}(1235,\cdot)\) \(\chi_{8624}(1291,\cdot)\) \(\chi_{8624}(1307,\cdot)\) \(\chi_{8624}(1347,\cdot)\) \(\chi_{8624}(1571,\cdot)\) \(\chi_{8624}(1643,\cdot)\) \(\chi_{8624}(1699,\cdot)\) \(\chi_{8624}(1851,\cdot)\) \(\chi_{8624}(1907,\cdot)\) \(\chi_{8624}(1923,\cdot)\) \(\chi_{8624}(1963,\cdot)\) \(\chi_{8624}(2203,\cdot)\) \(\chi_{8624}(2259,\cdot)\) \(\chi_{8624}(2315,\cdot)\) \(\chi_{8624}(2467,\cdot)\) \(\chi_{8624}(2523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,i,e\left(\frac{17}{42}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{420}\right)\) | \(e\left(\frac{163}{420}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{51}{140}\right)\) |