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 \(\chi_{4235}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dn
\(\chi_{8470}(59,\cdot)\) \(\chi_{8470}(159,\cdot)\) \(\chi_{8470}(229,\cdot)\) \(\chi_{8470}(339,\cdot)\) \(\chi_{8470}(509,\cdot)\) \(\chi_{8470}(619,\cdot)\) \(\chi_{8470}(719,\cdot)\) \(\chi_{8470}(829,\cdot)\) \(\chi_{8470}(929,\cdot)\) \(\chi_{8470}(999,\cdot)\) \(\chi_{8470}(1039,\cdot)\) \(\chi_{8470}(1109,\cdot)\) \(\chi_{8470}(1279,\cdot)\) \(\chi_{8470}(1389,\cdot)\) \(\chi_{8470}(1489,\cdot)\) \(\chi_{8470}(1599,\cdot)\) \(\chi_{8470}(1699,\cdot)\) \(\chi_{8470}(1769,\cdot)\) \(\chi_{8470}(1809,\cdot)\) \(\chi_{8470}(1879,\cdot)\) \(\chi_{8470}(2049,\cdot)\) \(\chi_{8470}(2159,\cdot)\) \(\chi_{8470}(2369,\cdot)\) \(\chi_{8470}(2469,\cdot)\) \(\chi_{8470}(2539,\cdot)\) \(\chi_{8470}(2579,\cdot)\) \(\chi_{8470}(2649,\cdot)\) \(\chi_{8470}(2819,\cdot)\) \(\chi_{8470}(2929,\cdot)\) \(\chi_{8470}(3029,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{16}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{61}{330}\right)\) | \(e\left(\frac{17}{330}\right)\) |