Basic properties
| Modulus: | \(8470\) | |
| Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4235}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dr
\(\chi_{8470}(17,\cdot)\) \(\chi_{8470}(73,\cdot)\) \(\chi_{8470}(117,\cdot)\) \(\chi_{8470}(173,\cdot)\) \(\chi_{8470}(227,\cdot)\) \(\chi_{8470}(283,\cdot)\) \(\chi_{8470}(327,\cdot)\) \(\chi_{8470}(437,\cdot)\) \(\chi_{8470}(453,\cdot)\) \(\chi_{8470}(523,\cdot)\) \(\chi_{8470}(563,\cdot)\) \(\chi_{8470}(607,\cdot)\) \(\chi_{8470}(633,\cdot)\) \(\chi_{8470}(677,\cdot)\) \(\chi_{8470}(733,\cdot)\) \(\chi_{8470}(787,\cdot)\) \(\chi_{8470}(843,\cdot)\) \(\chi_{8470}(943,\cdot)\) \(\chi_{8470}(997,\cdot)\) \(\chi_{8470}(1053,\cdot)\) \(\chi_{8470}(1097,\cdot)\) \(\chi_{8470}(1223,\cdot)\) \(\chi_{8470}(1293,\cdot)\) \(\chi_{8470}(1333,\cdot)\) \(\chi_{8470}(1377,\cdot)\) \(\chi_{8470}(1403,\cdot)\) \(\chi_{8470}(1447,\cdot)\) \(\chi_{8470}(1487,\cdot)\) \(\chi_{8470}(1503,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,e\left(\frac{1}{6}\right),e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{53}{220}\right)\) | \(e\left(\frac{161}{660}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{193}{660}\right)\) |