Basic properties
| Modulus: | \(1666\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1666.bi
\(\chi_{1666}(27,\cdot)\) \(\chi_{1666}(41,\cdot)\) \(\chi_{1666}(125,\cdot)\) \(\chi_{1666}(139,\cdot)\) \(\chi_{1666}(167,\cdot)\) \(\chi_{1666}(181,\cdot)\) \(\chi_{1666}(209,\cdot)\) \(\chi_{1666}(265,\cdot)\) \(\chi_{1666}(279,\cdot)\) \(\chi_{1666}(335,\cdot)\) \(\chi_{1666}(363,\cdot)\) \(\chi_{1666}(377,\cdot)\) \(\chi_{1666}(405,\cdot)\) \(\chi_{1666}(419,\cdot)\) \(\chi_{1666}(447,\cdot)\) \(\chi_{1666}(503,\cdot)\) \(\chi_{1666}(517,\cdot)\) \(\chi_{1666}(573,\cdot)\) \(\chi_{1666}(601,\cdot)\) \(\chi_{1666}(615,\cdot)\) \(\chi_{1666}(643,\cdot)\) \(\chi_{1666}(657,\cdot)\) \(\chi_{1666}(741,\cdot)\) \(\chi_{1666}(755,\cdot)\) \(\chi_{1666}(811,\cdot)\) \(\chi_{1666}(839,\cdot)\) \(\chi_{1666}(853,\cdot)\) \(\chi_{1666}(895,\cdot)\) \(\chi_{1666}(923,\cdot)\) \(\chi_{1666}(993,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((885,785)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1666 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{112}\right)\) | \(e\left(\frac{1}{112}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{59}{112}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{87}{112}\right)\) |