Basic properties
| Modulus: | \(1666\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1666.bl
\(\chi_{1666}(9,\cdot)\) \(\chi_{1666}(25,\cdot)\) \(\chi_{1666}(53,\cdot)\) \(\chi_{1666}(93,\cdot)\) \(\chi_{1666}(121,\cdot)\) \(\chi_{1666}(151,\cdot)\) \(\chi_{1666}(179,\cdot)\) \(\chi_{1666}(219,\cdot)\) \(\chi_{1666}(247,\cdot)\) \(\chi_{1666}(291,\cdot)\) \(\chi_{1666}(331,\cdot)\) \(\chi_{1666}(359,\cdot)\) \(\chi_{1666}(389,\cdot)\) \(\chi_{1666}(417,\cdot)\) \(\chi_{1666}(457,\cdot)\) \(\chi_{1666}(485,\cdot)\) \(\chi_{1666}(501,\cdot)\) \(\chi_{1666}(529,\cdot)\) \(\chi_{1666}(597,\cdot)\) \(\chi_{1666}(627,\cdot)\) \(\chi_{1666}(695,\cdot)\) \(\chi_{1666}(723,\cdot)\) \(\chi_{1666}(739,\cdot)\) \(\chi_{1666}(767,\cdot)\) \(\chi_{1666}(807,\cdot)\) \(\chi_{1666}(835,\cdot)\) \(\chi_{1666}(865,\cdot)\) \(\chi_{1666}(893,\cdot)\) \(\chi_{1666}(933,\cdot)\) \(\chi_{1666}(977,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((885,785)\) → \((e\left(\frac{1}{21}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1666 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{168}\right)\) | \(e\left(\frac{1}{168}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{131}{168}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{56}\right)\) |