Basic properties
| Modulus: | \(8470\) | |
| Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4235}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dk
\(\chi_{8470}(39,\cdot)\) \(\chi_{8470}(79,\cdot)\) \(\chi_{8470}(149,\cdot)\) \(\chi_{8470}(249,\cdot)\) \(\chi_{8470}(359,\cdot)\) \(\chi_{8470}(459,\cdot)\) \(\chi_{8470}(569,\cdot)\) \(\chi_{8470}(739,\cdot)\) \(\chi_{8470}(809,\cdot)\) \(\chi_{8470}(849,\cdot)\) \(\chi_{8470}(919,\cdot)\) \(\chi_{8470}(1019,\cdot)\) \(\chi_{8470}(1229,\cdot)\) \(\chi_{8470}(1339,\cdot)\) \(\chi_{8470}(1509,\cdot)\) \(\chi_{8470}(1579,\cdot)\) \(\chi_{8470}(1619,\cdot)\) \(\chi_{8470}(1689,\cdot)\) \(\chi_{8470}(1789,\cdot)\) \(\chi_{8470}(1899,\cdot)\) \(\chi_{8470}(1999,\cdot)\) \(\chi_{8470}(2109,\cdot)\) \(\chi_{8470}(2279,\cdot)\) \(\chi_{8470}(2349,\cdot)\) \(\chi_{8470}(2389,\cdot)\) \(\chi_{8470}(2459,\cdot)\) \(\chi_{8470}(2559,\cdot)\) \(\chi_{8470}(2669,\cdot)\) \(\chi_{8470}(2769,\cdot)\) \(\chi_{8470}(2879,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{79}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{311}{330}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{329}{330}\right)\) |