Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4312}(2181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gy
\(\chi_{8624}(9,\cdot)\) \(\chi_{8624}(25,\cdot)\) \(\chi_{8624}(137,\cdot)\) \(\chi_{8624}(345,\cdot)\) \(\chi_{8624}(697,\cdot)\) \(\chi_{8624}(905,\cdot)\) \(\chi_{8624}(1017,\cdot)\) \(\chi_{8624}(1241,\cdot)\) \(\chi_{8624}(1257,\cdot)\) \(\chi_{8624}(1369,\cdot)\) \(\chi_{8624}(1577,\cdot)\) \(\chi_{8624}(1593,\cdot)\) \(\chi_{8624}(2249,\cdot)\) \(\chi_{8624}(2473,\cdot)\) \(\chi_{8624}(2489,\cdot)\) \(\chi_{8624}(2601,\cdot)\) \(\chi_{8624}(2809,\cdot)\) \(\chi_{8624}(2825,\cdot)\) \(\chi_{8624}(3161,\cdot)\) \(\chi_{8624}(3369,\cdot)\) \(\chi_{8624}(3481,\cdot)\) \(\chi_{8624}(3721,\cdot)\) \(\chi_{8624}(3833,\cdot)\) \(\chi_{8624}(4041,\cdot)\) \(\chi_{8624}(4057,\cdot)\) \(\chi_{8624}(4393,\cdot)\) \(\chi_{8624}(4601,\cdot)\) \(\chi_{8624}(4713,\cdot)\) \(\chi_{8624}(4937,\cdot)\) \(\chi_{8624}(4953,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-1,e\left(\frac{8}{21}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{59}{70}\right)\) |