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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.hi
\(\chi_{8624}(5,\cdot)\) \(\chi_{8624}(157,\cdot)\) \(\chi_{8624}(213,\cdot)\) \(\chi_{8624}(229,\cdot)\) \(\chi_{8624}(269,\cdot)\) \(\chi_{8624}(493,\cdot)\) \(\chi_{8624}(565,\cdot)\) \(\chi_{8624}(621,\cdot)\) \(\chi_{8624}(773,\cdot)\) \(\chi_{8624}(829,\cdot)\) \(\chi_{8624}(845,\cdot)\) \(\chi_{8624}(885,\cdot)\) \(\chi_{8624}(1125,\cdot)\) \(\chi_{8624}(1181,\cdot)\) \(\chi_{8624}(1237,\cdot)\) \(\chi_{8624}(1389,\cdot)\) \(\chi_{8624}(1445,\cdot)\) \(\chi_{8624}(1461,\cdot)\) \(\chi_{8624}(1725,\cdot)\) \(\chi_{8624}(1741,\cdot)\) \(\chi_{8624}(1797,\cdot)\) \(\chi_{8624}(1853,\cdot)\) \(\chi_{8624}(2005,\cdot)\) \(\chi_{8624}(2061,\cdot)\) \(\chi_{8624}(2117,\cdot)\) \(\chi_{8624}(2341,\cdot)\) \(\chi_{8624}(2357,\cdot)\) \(\chi_{8624}(2413,\cdot)\) \(\chi_{8624}(2621,\cdot)\) \(\chi_{8624}(2693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,i,e\left(\frac{29}{42}\right),e\left(\frac{2}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{420}\right)\) | \(e\left(\frac{367}{420}\right)\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{129}{140}\right)\) |