Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.ha
\(\chi_{8624}(17,\cdot)\) \(\chi_{8624}(145,\cdot)\) \(\chi_{8624}(369,\cdot)\) \(\chi_{8624}(481,\cdot)\) \(\chi_{8624}(689,\cdot)\) \(\chi_{8624}(1025,\cdot)\) \(\chi_{8624}(1041,\cdot)\) \(\chi_{8624}(1249,\cdot)\) \(\chi_{8624}(1361,\cdot)\) \(\chi_{8624}(1377,\cdot)\) \(\chi_{8624}(1601,\cdot)\) \(\chi_{8624}(1713,\cdot)\) \(\chi_{8624}(1921,\cdot)\) \(\chi_{8624}(2257,\cdot)\) \(\chi_{8624}(2593,\cdot)\) \(\chi_{8624}(2609,\cdot)\) \(\chi_{8624}(2833,\cdot)\) \(\chi_{8624}(2945,\cdot)\) \(\chi_{8624}(3153,\cdot)\) \(\chi_{8624}(3489,\cdot)\) \(\chi_{8624}(3505,\cdot)\) \(\chi_{8624}(3713,\cdot)\) \(\chi_{8624}(3825,\cdot)\) \(\chi_{8624}(4065,\cdot)\) \(\chi_{8624}(4177,\cdot)\) \(\chi_{8624}(4385,\cdot)\) \(\chi_{8624}(4721,\cdot)\) \(\chi_{8624}(4737,\cdot)\) \(\chi_{8624}(4945,\cdot)\) \(\chi_{8624}(5057,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,1,e\left(\frac{25}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{27}{70}\right)\) |