Basic properties
| Modulus: | \(8470\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(710,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.dj
\(\chi_{8470}(61,\cdot)\) \(\chi_{8470}(101,\cdot)\) \(\chi_{8470}(171,\cdot)\) \(\chi_{8470}(271,\cdot)\) \(\chi_{8470}(381,\cdot)\) \(\chi_{8470}(591,\cdot)\) \(\chi_{8470}(761,\cdot)\) \(\chi_{8470}(831,\cdot)\) \(\chi_{8470}(871,\cdot)\) \(\chi_{8470}(1041,\cdot)\) \(\chi_{8470}(1151,\cdot)\) \(\chi_{8470}(1251,\cdot)\) \(\chi_{8470}(1361,\cdot)\) \(\chi_{8470}(1531,\cdot)\) \(\chi_{8470}(1601,\cdot)\) \(\chi_{8470}(1641,\cdot)\) \(\chi_{8470}(1711,\cdot)\) \(\chi_{8470}(1811,\cdot)\) \(\chi_{8470}(1921,\cdot)\) \(\chi_{8470}(2021,\cdot)\) \(\chi_{8470}(2131,\cdot)\) \(\chi_{8470}(2301,\cdot)\) \(\chi_{8470}(2371,\cdot)\) \(\chi_{8470}(2481,\cdot)\) \(\chi_{8470}(2691,\cdot)\) \(\chi_{8470}(2791,\cdot)\) \(\chi_{8470}(3071,\cdot)\) \(\chi_{8470}(3141,\cdot)\) \(\chi_{8470}(3181,\cdot)\) \(\chi_{8470}(3251,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{59}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(3251, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{97}{330}\right)\) | \(e\left(\frac{142}{165}\right)\) |