Basic properties
| Modulus: | \(1666\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1666.bf
\(\chi_{1666}(15,\cdot)\) \(\chi_{1666}(43,\cdot)\) \(\chi_{1666}(127,\cdot)\) \(\chi_{1666}(155,\cdot)\) \(\chi_{1666}(253,\cdot)\) \(\chi_{1666}(281,\cdot)\) \(\chi_{1666}(365,\cdot)\) \(\chi_{1666}(519,\cdot)\) \(\chi_{1666}(603,\cdot)\) \(\chi_{1666}(631,\cdot)\) \(\chi_{1666}(729,\cdot)\) \(\chi_{1666}(757,\cdot)\) \(\chi_{1666}(841,\cdot)\) \(\chi_{1666}(869,\cdot)\) \(\chi_{1666}(967,\cdot)\) \(\chi_{1666}(995,\cdot)\) \(\chi_{1666}(1107,\cdot)\) \(\chi_{1666}(1205,\cdot)\) \(\chi_{1666}(1233,\cdot)\) \(\chi_{1666}(1317,\cdot)\) \(\chi_{1666}(1345,\cdot)\) \(\chi_{1666}(1443,\cdot)\) \(\chi_{1666}(1555,\cdot)\) \(\chi_{1666}(1583,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((885,785)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 1666 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(i\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{15}{56}\right)\) |